T Tauri stars Optical lucky imaging polarimetry of HL and XZ Tau

T Tauri stars
Optical lucky imaging polarimetry
of HL and XZ Tau
Master of Science Thesis
in Astrophysics
6
5
4
arcseconds
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1
0
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200 AU
-6
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-1
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arcseconds
Magnus
Persson
1
Department of Astronomy
Stockholm University
2010
2
Abstract
Optical lucky imaging polarimetry of HL Tau and XZ Tau in the Taurus-Auriga
molecular cloud was carried out with the instrument PolCor at the Nordic Optical Telescope (NOT). The results show that in both the V- and R-band HL Tau
show centrosymmetric structures of the polarization angle in its northeastern
outflow lobe (degree of polarization∼30%). A C-shaped structure is detected
which is also present at near-IR wavelengths (Murakawa et al., 2008), and higher
resolution optical images (Stapelfeldt et al., 1995). The position angle of the
outflow is 47.5±7.5◦ , which coincides with previous measurements and the core
polarization is observed to decrease with wavelength and a few scenarios are
reviewed. Measuring the outflow witdh versus distance and wavelength shows
that the longer wavelengths scatter deeper within the cavity wall of the outflow.
In XZ Tau the binary is partially resolved, it is indicated by an elongated intensity distribution. The polarization of the parental cloud is detected in XZ
Tau through the dichroic extinction of starlight. Lucky imaging at the NOT
is a great way of increasing the resolution, shifting increases the sharpness by
0.00 1 and selection the sharpest frames can increase the seeing with 0.00 4, perhaps
more during better conditions.
About this thesis
This thesis is the written part towards a Master of Science Degree in Astrophysics at Stockholm University Astronomy Department. The corresponding
work was done under the supervision of Professor Göran Olofsson at Stockholm
University.
The work involves observations with the PolCor instrument, built by Professor Göran Olofsson and Hans-Gustav Florén, mounted on the NOT and the
following reduction, calibration and analysis of the data. The observations were
carried out between 26th and 30th October 2008 and are of two young stellar
objects: XZ Tau and HL Tau in the Taurus-Auriga molecular cloud complex.
The reduction routines are written in the Python programming language. The
result of the reduction is analysed and reviewed. This work has made use of the
SIMBAD database and NASA’s Astrophysics Data System.
This document was typeset by the author in LATEX 2ε .
Acknowledgements
First I would like to thank Göran Olofsson for making all of this possible, if I
never would have sent that e-mail to the wrong Olofsson this would probably
never have happened. You gave me the opportunity to do everything from
start to finish, and I have learned so much, thank you. Hans-Gustav Florén
for answering questions about the reduction software and the company on the
observation run. Matthias Maercker and Sofia Ramstedt for their help and
support during the years. Ramez and Daniel, it would have been really lonely
here without you around. My girlfriend Anca Mihaela Covaci for putting up
with me and my childishness, I hope you can bear with me the rest of your life.
Contents
1 Introduction
1.1
1.2
1.3
Star formation . . . . . . . . . . . . . . . . . . . . .
1.1.1 Background - The Nebular Hypothesis . . . .
1.1.2 ISM - Structures & clouds . . . . . . . . . . .
1.1.3 Early evolution of Low-mass stars . . . . . .
1.1.4 Feedback processes . . . . . . . . . . . . . . .
1.1.5 The Main-Sequence . . . . . . . . . . . . . .
1.1.6 HL Tau and XZ Tau as part of Lynds 1551 in
Polarimetry . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 Background . . . . . . . . . . . . . . . . . . .
1.2.2 Polarization in Astronomy . . . . . . . . . . .
1.2.3 Detecting linearly polarized light . . . . . . .
Diffraction limited imaging from the ground . . . . .
1.3.1 Introduction . . . . . . . . . . . . . . . . . .
1.3.2 Correction methods . . . . . . . . . . . . . .
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Taurus
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2 Observations and Data reduction
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Results . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 XZ Tau . . . . . . . . . . . . . . . . . . .
3.1.2 HL Tau . . . . . . . . . . . . . . . . . . .
3.1.3 Lucky astronomy . . . . . . . . . . . . . .
Summary of results . . . . . . . . . . . . . . . . .
3.2.1 HL Tau . . . . . . . . . . . . . . . . . . .
3.2.2 XZ Tau . . . . . . . . . . . . . . . . . . .
3.2.3 Parameters vs sharpness/psf improvement
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Observations . . . . . . . . . . . . . . . .
2.1.1 The PolCor instrument . . . . . .
2.1.2 Observations . . . . . . . . . . . .
Data reduction . . . . . . . . . . . . . . .
2.2.1 Overview . . . . . . . . . . . . . .
2.2.2 Dark frame and flat fielding . . . .
2.2.3 Determining the centre of reference
2.2.4 Sharpness . . . . . . . . . . . . . .
2.2.5 Shifting and adding . . . . . . . .
Data analysis . . . . . . . . . . . . . . . .
2.3.1 Stokes and additional parameters .
2.3.2 Polarization standards . . . . . . .
3 Results
3.1
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4 Discussion
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Discussion . . .
4.1.1 HL Tau
4.1.2 XZ Tau
4.1.3 Other .
Summary . . .
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List of Figures
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List of Tables
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Bibliography
61
Appendix
A. Data with three valid angles observed .
B. Python code description . . . . . . . .
B.1 Introduction . . . . . . . . . . .
B.2 Help Functions . . . . . . . . . .
B.3 Classes, Attributes and Methods
B.4 Example Usage . . . . . . . . . .
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“Space is the place.”
Sun Ra
1
Introduction
This thesis consists of work in the areas low-mass star formation, lucky imaging
and polarimetry. This chapter gives an introduction to these areas. The first
part is dedicated to the star formation process, the main topic of this thesis.
Second part is an introduction to polarimetry, and lastly an introduction to
lucky astronomy; a technique to obtain diffraction limited images from ground
based telescopes.
Section 1.1 consists of a brief history of the star formation process, a description of interstellar clouds, the early evolution of low-mass1 stars followed
by feedback processes, the main sequence (MS), and lastly a description of the
star forming cloud were the sources in this thesis are located - the Lynds 1551
(L1551) nebula in the Taurus Molecular cloud.
In order to understand how the observations where made an introduction to
polarimetry is given in section 1.2. The section give a background to polarimetry
and a review of polarization in astronomy, were the technique to detect circumstellar dust is described and lastly the theory behind the detection technique is
explained.
The last section (1.3) gives and introduction to various techniques to obtain
(near) diffraction limited images.
1.1 Star formation
Stars form out of the gravitational instability in a turbulent density enhancement, called molecular cloud (MC) in the interstellar medium (ISM), the collapse form a protostar. The protostar starts to accrete matter thus forming an
accretion disk and a bipolar outflow. When it has accreted enough a pre-Main
Sequence (pre-MS) star emerges, the circumstellar envelope starts to dissipate
and by the time the core has ignited its nuclear burning of Hydrogen it has
settled on the Main Sequence (MS) and there is just a small debris disk left.
Somewhere on the journey planets are formed through collisions and coagulation. The protostellar and pre-MS phases are sometimes grouped together and
the object is then be referred to as a Young Stellar Object (YSO), also the phases
of star formation are classified from the Spectral Energy Distribution (SED) of
the unresolved object, i.e. the classification systems origin depended on whether
the object was resolved or not.
1 Low-mass
stars M≤ 2 M , intermediate-mass 2 <M≤ 8 M and high-mass M>8 M .
1
CHAPTER 1. INTRODUCTION
A lot of important and energetic chemistry takes place in forming a star, the
neutral Hydrogen in the MC goes from neutral H2 in the cold MCs to ionized
H+ in the core of stars, complex chemistry on dust grains in the cloud takes
place and creates complex molecules. The enormous density contrast between
typical cloud densities and the hydrogen-burning centres of the final stars is
typically about 24 orders of magnitude.
The following is a description of the current star formation paradigm, which
applies to low- and possibly intermediate-mass stars that form in isolation. Although most stars seem to be formed in clusters (Lada and Lada, 2003); groups
of several stars of different masses, from brown dwarfs to O and B stars. By
having other, possibly more massive, stars forming in the vicinity could effect
the protostar in serious ways. The outflow could trigger other gravitationally
unstable clouds to collapse into stars, but also if the other star has a strong
radiation field it could photoevaporate the circumstellar cloud of the protostar
and limit the growth of the star during its accretion phase.
For a recent review in star formation see McKee and Ostriker (2007) and
for a recent review of the advances in numerical studies of star formation see
Klessen et al. (2009).
1.1.1
Background - The Nebular Hypothesis
The idea that stars are formed out of interstellar clouds have been present for
several centuries. The initial idea, that the Sun and Planets formed out of a
rotating cloud or disk of material was called the Nebular Hypothesis, which was
formulated by Emanuel Swedenborg in 1734. It sprung from the realisation that
the orbital planes of the Planets around the Sun are all, to a good approximation
in the same plane and direction, due to the formation process. Although the
theory was successful in explaining the motion of the Planets, it could not
explain why the Sun has the low, much lower than expected from the theory,
angular momentum. Thus other theories were worked out during the years.
In 1945 Alfred Joy analysed 11 irregular variable stars that shared photometric and spectral properties (Joy, 1945). The characteristics included variability
in the optical lightcurve and emission lines including that from Hydrogen (Hα)
and Calcium (Ca II). The stars, ranging from spectral type F5 to G5 were associated with nebulae. Some of them were located in the constellations of Taurus
and Auriga, after the strongest one he called them T Tauri stars. Being spatially associated with massive O and B stars, i.e. inheritably young they where
suggested to also be young stars but of less mass (Ambartsumian, 1947). Herbig
(1952) saw that the T Tauri stars were found to be systematically brighter than
MS spectral counterparts, suggesting that they were still contracting towards
the MS, confirming Ambartsumians suggestion. Continuing his work Herbig
(1957a) found that their emission line profiles suggested an outflow of material, and wide absorption lines Herbig (1957b) which indicates a higher rate
of stellar rotation than a MS counterpart, both indicating their youth. In the
two decades after this Mendoza V. (1966, 1968); Cohen (1973) both detected
IR excess emission and suggested the excess to be due to thermal emission of
circumstellar dust.
With the fact that this dust was in the form of a circumstellar disk, the
probable site of planet formation, confirms the Nebular Hypothesis as the main
theory of the formation of our solar system.
2
1.1. STAR FORMATION
1.1.2
ISM - Structures & clouds
The average particle density of the ISM in the solar vicinity is 1 cm−3 . Consisting of gas and dust, the main gas components are hydrogen (90 percent) and
helium (10 percent) with traces of of heavy elements while the dust comprise
only 1 percent of the total ISM mass with graphite and silicate as main grain
components.
In the ISM, MCs are formed due to gravitational instabilities, supersonic
turbulence and magnetic fields. The MCs vary in size from small globules with a
few hundred M in mass and giant molecular clouds (GMCs) with over 104 M .
GMCs which are found in the spiral arms (Cohen et al., 1980; Dame et al., 1987)
is where most of the stars in the milky way and other galaxies with star forming
activity form. With typical mass, size and temperature ranging between 104 to
106 M , 10 to 100 pc and ∼15K (Stark and Blitz, 1978; Sanders et al., 1985;
Ostlie and Carroll, 2007; McKee and Ostriker, 2007).
Figure 1.1: A 2×2 degree field centred at l = 60◦ , b ∼ 0◦ in the constellation of the Southern Cross.
The images are taken with both the PACS and SPIRE instruments aboard the Herschel spacecraft.
Blue denotes 70 µm, green 160 µm and red is the combination of all SPIRE bands; 250/350/500 µm.
The wavelengths traces the dust in the molecular cloud and by following the red filaments in the
image, which denotes colder regions, we see where stars are most likely to form. The structure is
clearly filamentary with intricate structures at different scales. Image credits ESA & the SPIRE
and PACS consortia.
3
CHAPTER 1. INTRODUCTION
The low temperatures in MCs makes H2 difficult to detect, direct detection
of cold interstellar H2 is usually only possible through UV absorption observations from space. Luckily the shielding of UV radiation provided by the higher
densities relative to the ISM allows molecules to form, carbon monoxide (CO),
water (H2 O), ammonia (NH3 ), hydroxide (OH) and hydrogen cyanide (HCN)
to name some common examples.
Due to the relatively high abundance of CO to H2 , ∼10−4 × H2 , the by
H2 collisionally excited J=1–0 line of CO is usually used when mapping MCs
(Ostlie and Carroll, 2007; McKee and Ostriker, 2007). Since MCs do not emit
any radiation in the optical they can usually be seen as dark streaks across
the sky, provided they lie in front of bright diffuse emission or stars. Another
possibility to trace the MCs is to observe the cold dust at mid- and far-IR, in
figure 1.1 the space observatory Herschel have observed a star forming region in
our galaxy. Thermally radiating dust grains traces the cold cores.
The smaller MCs form only low- to intermediate-mass stars while the large
GMCs also form high-mass stars. The primary sites of star formation are GMCs,
thats is were star formation in the Milky-Way and other galaxies primarily
occurs.
Density fluctuations create an internal structure of GMCs which exhibit
extremely complex, often filamentary and sheet-like structure (Blitz et al., 2007)
sometimes also described as fractal e.g. Stutzki et al. (1998). Historically clear
substructures have been classified as follows; larger sub-clouds with masses of
a few hundred solar masses and sizes of parsecs are referred to as clumps and
smaller structures with masses of up to tens of solar masses and sizes up to half
a parsec are referred to as cores.
The density fluctuations is attributed to supersonic turbulence and thermal
instabilities, and some of the resulting density fluctuations exceed the critical
mass and density of gravitational stability. This brings us to the next phase —
the collapse of the cloud core.
1.1.3
Early evolution of Low-mass stars
Collapse
The collapse and subsequent star formation of a cloud core is governed by the
complex interplay between gravitational compression and agents such as turbulence, magnetic fields, radiation, rotation, viscosity and thermal pressure that
resists or helps compression. The always quoted attempt at describing this theoretically was the one by Sir James Jeans in 1902, who deduced the minimum
mass required for a gravitationally bound system to collapse, the Jeans mass.
With a sphere of uniform density ρ, and temperature T the Jeans mass is
3/2
5kB T
3
'
MJ =
4πρ
GµmH
3/2 −19
1/2
Tgas
10
g cm−3
.
' 1.1 M
10 K
ρ
The last equation is normalised for typical initial conditions and µ is the
mean molecular weight (Zinnecker and Yorke, 2007). Thus a gravitationally
4
1.1. STAR FORMATION
bound sphere with mass higher than this mass should collapse because gravity
overcomes the internal thermal pressure. This simplified equation does not
account for magnetic field support, turbulence and radiation fields. Although,
it is apparent that it is easier to form stars from a cold and dense core than
a warm and sparse one since it lowers the amount of gas required to undergo
collapse.
Two density cases have been identified, from which end products is quite
different. In the high density core a strong external compression forms a turbulent core that, during the collapse fragments into several star forming cores
creating a cluster of stars. In contrary to this the low density case end products
is just one or a few star forming cores, caused by the lower external pressure.
This is further supported by a connection between the core mass function and
the stellar initial mass function (IMF) (Nutter and Ward-Thompson, 2007).
The collapsing core is cold T ∼ 10 K and optically thin at sub-mm and
mm wavelengths allowing radiation to escape and causing the contraction to be
approximately isothermal and on a free-fall timescale. The free-fall timescale is
defined as the time that a pressureless sphere of gas with initial
pdensity ρ requires
to collapse to infinite density under its own gravity tf f = 3π/(32Gρ), with
typical values of ∼105 years (Galván-Madrid et al., 2007) although simulations
suggest the actual collapse phase lasts about ∼106 years due to turbulence and
magnetic fileds (Ward-Thompson et al., 2007)
With rising density, the Jeans mass decreases and the collapse continues.
At a density of ρ ∼10−12 g cm−3 , the central regions become optically thick,
thus starting the adiabatic part of the collapse with a rise in temeprature as
effect (Masunaga and Inutsuka, 2000; Stamatellos et al., 2007). When the centre of the collapsing core reaches densities of ∼10−9 -10−8 g cm−3 it becomes
thermally supported – a hydrostatic core has formed. The core subsequently
contracts, while material falls on the newly formed central hydrostatic core from
the surrounding medium. This continues until the central temperature reaches
T ∼2000 K and at that point H2 dissociates, thus absorbing thermal energy
causing a break in the hydrostatic balance. The breaking causes a second collapse which continues until all the H2 is exhausted and a subsequent hydrostatic
core is formed — a protostar.
Protostar
The heavily embedded object, a protostar, represents the earliest stages of star
formation, the dense central object accrete matter from its surrounding envelope
and continues to contract on a Kelvin-Helmholtz timescale, radiating away the
thermal energy from the collapse. The early protostars have masses of about
10−2 M (Larson, 2003), thus somewhere between this stage and the final MS
star a large increase in mass takes place. This occurs during the protostellar
phase, derived from the observational properties of YSOs. When the central
object is less massive than the protostellar envelope and the observable SED is
that of a greybody (modified blackbody), i.e. thermal dust emission from the
cold outer region of the molecular core, the object is referred to as having a
Class 0 SED (Andre et al., 1993, 2000).
Due to the conservation of angular momentum the initial rotation of the
prestellar core is greatly increased during the collapse and a flattened circumstellar disk is formed around the protostar (Terebey et al., 1984). This disk acts
5
CHAPTER 1. INTRODUCTION
as a bridge for matter accreting onto the star; gas accretes onto the disk, which
then channels material inwards to the central star. Viscous forces transport
the material inward and allow angular momentum to be transported outwards.
The viscosity in disks around young stars is not completely understood, it has
been suggested that it may be due to magneto-rotational instabilities (Tout and
Pringle, 1992). When matter reaches the innermost parts of the disk, parts of
it accretes onto the protostar and the rest is centrifugally ejected along open
magnetic field lines, carrying away angular momentum. Exactly how it accretes
onto the surface of the protostar is currently unknown, one idea is that the circumstellar material at the innermost parts couples with the protostars magnetic
field, diverts out from the disk plane and falls on to the protostar through accretion columns creating hot continuum when crashing on the surface (Hartmann,
1998).
Infrared
Visible
Herbig-Haro objects
Disk
Jet
Protostar
Bow shock
Figure 1.2: A protostellar outflow with the protostar and its disk, HH111 in the Orion molecular
cloud. The outflow reach far out in the parental cloud. Names of different structures are marked with
lines and text. Perpendicular to the outflow is the flared disk. Image credits NASA/B. Reipurth.
As mentioned, the in-fall of matter is accompanied by outflow of matter
through bipolar jets perpendicular to the plane of the disk, usually along the
rotation axis of the system. The jet removes excess angular momentum from the
system, to understand the importance of this one should bare in mind the share
difference in spatial scales between the parental cloud core and the finished MS
star. The cloud core contract by a factor ∼106 in radius when a star is formed,
thus the angular momentum has to be transported away during the collapse for
the cloud to continue to contract.
With a launching speed of a few hundred kilometres per second the jet transfer energy to the surrounding molecular gas, entrain material and accelerates it
to tens of kilometres per second. Protostellar outflows can have sizes extending
to several parsecs and masses between 10−2 to 200 M . The interaction between
the outflows and the ISM leads to the formation of supersonic shock fronts, the
cooling regions are called Herbig-Haro objects (Herbig, 1951; Haro, 1952). The
infalling material and the outflow are in close relationship, the infall drives the
outflow and while most of the mass is expelled in the outflow some of it is accreted onto the protostar. The outflow–accretion connection was observed by
Hartigan et al. (1995) by looking at the correlation between forbidden line luminosities with accretion luminosities derived from the optical or UV emission
6
1.1. STAR FORMATION
in excess of photospheric radiation.
When the star have accreted enough matter so that the protostar and the
disk start to contribute significantly to mid-IR wavelengths the object is referred
to as having a Class I SED (Lada, 1987; Wilking et al., 1989). The timescale
of the protostellar phase is relatively short, around 105 -106 years.
CoKu Tau/1
DG Tau B
Haro 6-5B
IRAS 04016+2610
IRAS 04248+2612
IRAS 04302+2247
Figure 1.3: Six protostars, they all show the outflow as a glowing cone with sharp edges, perpendicular to the outflow lies the disk and there, heavily enshrouded in gas an dust lies the infant star.
Image credits D. Padgett (IPAC/Caltech), W. Brandner (IPAC), K.Stapelfeldt (JPL) and NASA.
Pre-Main Sequence
With time the outflow disperses the surrounding envelope that have not fallen
onto the accretion disk. The central source can usually be observed in the optical at this time, the accretion and outflow continues although at a greatly
diminished rate, most of the final mass has already been accreted. The protostar is left with a circumstellar disk, a protoplanetary disk. Low-mass stars in
this stage are called T Tauri stars (T Tauri phase), the general type Classical T
Tauri Stars (CTTS), and also the observable spectra is identified as a Class II
SED; essentially a stellar spectrum with thermal dust emission from mid-IR to
sub-mm wavelengths. Except the forementioned variablity, characteristic emission lines and association with nebulosity the CTTS usually exhibit strong Hα
emission and IR-excess stemming from the hot and thermally radiating circumstellar disk. The pre-stellar core continues to contract, releasing gravitational
energy. The relatively “calm” protoplanetary disk is likely to be in vertical hydrostatic equilibrium at all radii, Shakura and Sunyaev (1973) expressed the
7
CHAPTER 1. INTRODUCTION
scaleheight, h of such a disk as
H
= cs
r
r
GM?
1/2
.
1.1 Showing that the scaleheight of the disk increases as a power law H ∝ rβ , i.e.
a flared disk. This was observationally confirmed by Kenyon and Hartmann
(1987), by modelling the SED of a flared disk and comparing it to observations.
Dust grains in the disk grows through collisions and coagulation, which causes
them to decouple from the gas and settle at the mid-plane of the disk (Beckwith
and Sargent, 1991; Miyake and Nakagawa, 1993; D’Alessio et al., 1999, 2001).
The higher density in the mid-plane increases collisions and causes the grains to
grow into pebbles, and later into planetesimals which in turn are the beginning
building blocks for either gaseous planets (the core of), if the gas is still present
or rocky planets.
The pre-MS star is still accreting material from the disk, the strong magnetosphere carve out a hole in the disk, typically a few stellar radi out (Shu et al.,
1994; Kenyon et al., 1996). The magnetic field lines, locked both in the star and
the inner edge of the disk, are twisted due to the differential rotation between
the two mount points. When the field lines reconnect causes X-ray flares e.g.
Preibisch (2007). Matter is channelled away from the disk along the field lines
and crashes on to the surface of the star (Shu et al., 1994). Crashing in to the
hot surface of the pre-MS star causes hot spots with temperatures of 104 K. The
UV excess and blue veiling observed in CTTS attributed to Balmer continuum
and line emission along with Paschen continuum emanate from these hot spots
(Kuhi, 1974; Kuan, 1975; Rydgren et al., 1976).
Pre-MS stars that exhibit a variable mass loss rate between 100-1000 times
greater than CTTS are called FU Orionis stars, explanations to the violent
eruptions are still unknown but some suggests that the additional energy is
produced when large planets are destroyed at the stellar surface or a sudden
and temporary increase in the accretion rate triggered by thermal instabilities
(Hartmann and Kenyon, 1985).
When the dust has settled in the mid-plane of the disk, the gas in the disk
can be removed through photo-ionization over timescales of 105 years. Haisch
et al. (2001) concluded that most protoplanetary disks are likely to be cleared
after 6 million years, and once cleared the star still shows stronger activity than
MS stars.
The accretion–outflow connection mentioned in the previous section also
predicts that when no accretion occurs, the outflow should also be absent, this
is furthered by the sub-group of weak-lined-TTS (WTTS) which lack both detectable forbidden line emission and excess emission. This does not necessary
imply that the WTTS are in a later stage of evolution than the CTTS, the
accretion may be absent owing to the natal environment of the star.
Another sub-group is characterised by an almost dissipated disk and thus
much weaker Hα emission lines, Naked T Tauri Star (NTTS) with a observable
spectrum referred to as Class III SED.
The T Tauri phase lasts a few million years and finally the density and
temperature have increased enough in the central parts for nuclear burning to
start and the star settles on the Main Sequence.
8
1.1. STAR FORMATION
1.1.4
Feedback processes
The formation of stars starts with the fragmentation of an MC into smaller
clumps and cores, but what keeps the star formation going in a cloud? Since
molecular cloud cores are observed to not only house newly ignited mainsequence stars, but also stars in the making there must be something that
triggers star formation over and over again. Several theories have been presented over the years, example triggers include outside forces such as supernovae, and mechanisms inside the cloud; outflows from young stars, the strong
radiation field from high-mass stars. What is believed today is that the injection
of turbulence in a cloud is important for the initiation and continuation of star
formation since the turbulent compression can fragment clumps in the MC with
high enough density for the collapse to start.
In the beginning there is an initial supersonic turbulence in the cloud that
decays quickly (Mac Low et al., 1998; Stone et al., 1998; Padoan and Nordlund,
1999). After this it is unclear what mechanism continues the injection of turbulence, but without turbulence the MC would be in complete free-fall collapse. As
mentioned protostellar outflows is a probable mechanism and numerical MHD
simulations by Li et al. (2006) showed that the initial turbulence helps to form
the first stars and then protostellar, outflow-driven turbulence is the dominating
turbulence for most of the cluster members. Contrary to this Banerjee et al.
(2007) showed that the impact of collimated supersonic jets on MC is rather
small and that protostellar outflows can not be the cause for continued star
formation.
Brunt et al. (2009) investigated on what physical scales the turbulent energy
is injected in. Comparing simulated molecular spectral line observations of
numerical MHD models and corresponding observations of real MCs showed
that only models driven at large scales, with a minimum size corresponding to
size of the cloud, are consistent with observations. Candidates on large scales
are supernova-driven turbulence, magneto-rotational instability and spiral shock
forcing. Small-scale driving mechanisms, such as outflows are also important,
but on limited scales and they can not replicate the observed large-scale velocity
fluctuations in the MCs. One aspect of the results is that the turbulence in the
model was driven by random forcing which will not represent energy injection
by point-like sources very well.
Although the importance of protostellar outflows in injecting turbulence to
the cloud is controversial they do inject large amounts of energy into the parental
cloud and limit the amount of mass a star can accrete from a cloud.
1.1.5
The Main-Sequence
When igniting the nuclear burning core and settling on the MS the accretion
has stopped and the disk has been replaced by a debris disk, dust produced by
collision between comets, asteroids etc and the gas is more or less gone. This
debris disk produces small but detectable IR excess as well, and the first MS
star observed to have this was the standard star Vega (Aumann et al., 1984).
Later on, Vega was shown to have a dust disk, and the most observed debris
disk is the one of β Pictoris, a intermediate mass star. Olofsson et al. (2001);
Brandeker et al. (2004) showed that β Pictoris also have a gas disk in addition
to the debris disk. Even our own star, the Sun show evidence of this subtle
9
CHAPTER 1. INTRODUCTION
disk-remnant in the form of the zodiacal light.
The structured walk-through of the early evolution of a low-mass star entailed
above, including its circumstellar components, is our earnest endeavour at structuring the continuous nature of the star formation process.
1.1.6
HL Tau and XZ Tau as part of Lynds 1551 in Taurus
In the northeastern region of the Taurus-Auriga Molecular Cloud lies XZ Tau
and HL Tau, two YSOs at a rough distance of 140 pc e.g. Elias (1978); Kenyon
et al. (1994); Torres et al. (2009). XZ Tau, a binary system composed of a T
Tauri star and a cool companion (total mass 0.95 M , Hioki et al. (2009)). HL
Tau, just a bit west of XZ Tau (∼2500 ) is a heavily embedded protostar with a
rather massive envelope and powerful jet (∼120 km s−1 both jet and counterjet
Anglada et al. (2007)), the inclination of the jet is ∼60◦ with respect to the
plane of the sky (Anglada et al., 2007). In the figure below a S [II] image taken
with the NOT of the region is shown; dust enshrouded HL/XZ Tau and the edge
on HH 30 YSO with its long northern jet that almost spans the entire field.
XZ Tau
HL Tau
1' (8400 AU)
HH 30
Figure 1.4: The norhtern region of the L1551 cloud, containing HL Tau and XZ Tau along with the
HH 30 YSO. The jet from HL Tau reaches speeds of 120 km s−1 and has an inclination of aout 60◦
with respect to the plane of the sky. From Anglada et al. (2007)
HL Tau
Cohen (1983) proposed that HL Tau is associated with a nearly edge-on circumstellar disk, after this several attempts at imaging this disk were carried
10
1.2. POLARIMETRY
out (Sargent and Beckwith, 1991; Wilner et al., 1996; Looney et al., 2000). It
has been the proposed source for a molecular outflow e.g. Torrelles et al. (1987);
Monin et al. (1996). As being the brightest nearby T Tauri star in the mm and
sub-mm continuum it is estimated to have one of the most massive circumstellar envelopes (Beckwith et al., 1990). A infalling or rotating circumstellar
envelope has been suggested by mm synthesis observations (Sargent and Beckwith, 1991; Hayashi et al., 1993), although Cabrit et al. (1996) showed that the
kinematics are complicated by the orientation of the outflow in respect to the
observer. The envelope has a estimated mass of ∼0.1 M which gives it enough
material to form a planetary system (Sargent, 1989; Beckwith et al., 1990). It
has a well studied collimated optical bipolar jet (Mundt et al., 1990; Rodriguez
et al., 1994; Anglada et al., 2007). It has been observed to harbour a 14 MJ
protoplanet orbiting at a radius of ∼65 AU (Greaves et al., 2008). HL Tau has
been classified as beeing in the boundary inbetween Class I and Class II YSOs,
having a relatively flat spectrum inbetween 2 and 60 µm (Men’shchikov et al.,
1999). Thus it still has its large circumstellar envelope, but the extinction has
dropped enough for the central regions to be observed in the NIR with high
resolution.
XZ Tau
Located ∼2500 to the east of HL Tau is XZ Tau, a binary system; a T Tauri star
accompanied by a cool companion with separation of 0.00 3 (Haas et al., 1990).
Just as HL Tau, XZ Tau is the source of a optical outflow e.g. Mundt et al.
(1990). Krist et al. (1999) used the Hubble Space Telescope (HST) to take an
image sequence of XZ Tau that revealed the expansion of nebular emission,
moving away with a velocity of ∼70 km s−1 . Being very different from the collimated jets usually seen around young stars, further studies by Krist et al. (2008)
showed a succession of bubbles and a fainter counterbubble, and also revealing
that in addition both components of the binary are driving collimated jets.
High angular resolution radio observations of XZ Tau by Carrasco-González
et al. (2009) show signs of a third component, that XZ Tau in fact could be a
triple system. At the wavelength of 7 mm the southern component is resolved
into a binary with 0.00 09 (13 AU) separation.
1.2 Polarimetry
This section describes polarized light in the astronomical context; the history of
polarimetry, the theory that lies behind the technique used in the observations,
and how the linearly polarized light is produced in young stars.
1.2.1
Background
Introduction
2
In the last decade or two polarimetry have matured to become a important
tool in an astronomers arsenal. Other than the most evolved techniques in the
2 Most
of the section taken from T. Gehrels (1974) and Tinbergen (1996)
11
CHAPTER 1. INTRODUCTION
optical, near-infrared and radio regimes, other wavelength regimes are catching up rapidly. The history of polarimetry starts with the discovery of double
refraction in calcite (Iceland spar) by Erasmus Bartholinus in 1669, and an attempt to describe it by Huygens a year later in terms of a spherical and elliptical
wave front. Two years later, 1672 Newton drew parallels of light and the crystal
to poles of a magnet, which leads to the term “polarization”. In 1845 Michael
Faraday discovered the rotation of the plane of linearly polarized light passing
through certain media parallel to the magnetic field, today known as Faraday
rotation. Then, 1852 Stokes studies of polarized light led him to describe the
four Stokes parameters (G.C. Stokes, 1852). The first astronomical use of polarimetry, done by Lyot of the sunlight scattered by Venus in 1923 marks the
start of polarization in astronomy. In 1946 Chandrasekhar predicts linear polarization of Thomson-scattered starlight (Chandrasekhar, 1946), later discovered
in eclipsing binaries. A lot of new discoveries and applications of polarimetry is
presented in the later half of the 2000-century, a few of the important ones are
the observation of interstellar optical polarization, first detection of polarized
astronomical radio emission, polarized X-ray and radio emission (from the Crab
nebula) and the list goes on.
Describing light
y'
y
z
A sinβ
β
x'
φ0
x
Figure 1.5: A polarization ellipse, from this figure the Stokes parameters are defined.
One way of representing (partly) polarized light is by means of the Stokes parameters, as mentioned above introduced by Sir George Gabriel Stokes in 1852.
The four parameters, often denoted I, Q, U, V and components in a four-vector
S, describe an incoherent superposition of polarized light waves, i.e. no information about absolute phase of the waves. The Stokes I is non-negative and
denotes the total intensity of the wave. Q and U relates to the orientation of the
polarized light relative to the x-axis, Q = U = 0, V 6= 0 is completely circular
polarized light. Lastly V describes the circularity, it measures the axial ratio of
the ellipse, it can be positive or negative, and when V = 0 the light is linearly
polarized. All of the parameters denote radiant energy per unit time, unit fre12
1.2. POLARIMETRY
quency interval and unit area. With help of figure 1.5 the Stokes parameters
are defined in terms of properties of the polarization ellipse.
Where A is the amplitude of the wave, β the angle relating the two principal
axes of the ellipse, ϕ0 the polarization angle and z is the direction of propagation.
When β = 0, ± π2 the wave is linearly polarized (V = 0). The mathematical
realtionship between the parameters are
  2
A
I
 Q   A2 cos 2β cos 2ϕ0
 
S=
 U  =  A2 cos 2β sin 2ϕ0
A2 sin 2β
V





1.2 Here the set of parameters are set up in a vector, the Stokes vector. To
understand the relation between Q, U and A2 , 2ϕ0 we can think of Q and U as
Cartesian components of the vector (A2 , 2ϕ0 ). The polarization angle PL then
becomes a simple function of Q, U and I as we shall later discover.
1.2.2
Polarization in Astronomy
Polarimetry can reveal information about objects in astronomy inaccessible to
ordinary observational techniques. Some sources emit polarized radiation, such
as synchrotron radiation from relativistic electrons under influence of a strong
magnetic field. Two other relevant sources of polarization are scattering and
extinction; scattering of light and dichroic extinction by dust. Here the effect is
due to the interaction of unpolarized radiation with dust. The general theory for
scattering of particles is called “Mie scattering”, it account for the size, shape,
refractive index and absorptivity of the scattering particles; a well known special
case of Mie scattering is Rayleigh scattering. When light is scattered off a dust
particle, the scattered light is polarized in all directions except the forward
direction (Bohren and Huffman, 1998). Mie theory, as it also is referred to uses
Mueller 4 × 4 matrices to change the incident Stokes vector, the completeness
of the calculations makes it a prime method for modelling polarized radiation
from protostars.
To visualise and explain the scattering process, figure 1.6 emphasis the
schematics. The unpolarized light is incident from the left, its perpendicular
Ē component sets the electronic oscillators in a dust particle in similar forced
vibrations, thus re-emitting radiation, in all directions. Any light scattered into
a certain direction can only include those identical Ē-vibrations by the oscillators along the y- and z-directions. An observer at A in the figure will only see
polarized light corresponding to vibrations along the z-direction, an oscillator
vibrating in the y-direction can not radiate in the direction of vibration (Rybicki, 2004). At B the light would be partially polarized. Putting it all in one
sentence; the direction of vibration of the electric vector of the scattered radiation is at right angles to the scattering plane, the plane containing the incident
and scattered rays (Tinbergen, 1996). As mentioned, the forward scattered light
shows the same polarization as the incident light.
13
CHAPTER 1. INTRODUCTION
z
y
x
A
B
Figure 1.6: Scattering of light by dust particle, geometry. The scattered radiation attain maximum
polarization at right angles to the incident radiation (inspired from Pedrotti and Pedrotti, 1992, ,
p. 305).
Analysing linear polarization gives possibilities to
• identify the scattering mechanism
• locate an obscured source
• attain information on the properties of the source, i.e. orientation and/or
the scattering medium i.e. size, shape, alignment e.t.c.
Circular polarization is known to occur due to single scattering of linearly
polarized light by a non-spherical grain.
Dichroic extinction
An exception to the statement that light in the forward direction is not polarized is when we account for dichroic extinction; the differential extinction
of orthogonally polarized radiation components. This is simply due to the fact
that the dust particles are non-spherical and/or have crystalline structure which
results in a different scattering cross-section for light linearly polarized parallel
to the geometric or crystalline axis than for light polarized perpendicular to it.
Adding a mechanism that aligns the dust grains an overall systematic polarization is attained. This is common in protostars when viewing the central source
through the very optically thick disk, although multiple scattering can interfere
with the pattern.
Grain alignment
The mechanism that align grains has long been debated since its discovery
in 1949 (Hall, 1949; Hiltner, 1949). Today several ideas exists as to how the
grains are aligned, the most prominent are paramagnetic alignment, mechanical
14
1.2. POLARIMETRY
alignment and radiative torque alignment. They are all thought to be important
within different limits (Lazarian, 2007). As the names suggests, in paramagnetic
alignment the change of grain magnetization due to free electrons in relation
to the external magnetic field causes it to loose rotation energy, this is called
the Davis-Greenstein mechanism after Davis and Greenstein (1951). The grain
align with the longer axes perpendicular to the magnetic field. The second
mechanism referred to as the Gold mechanism after Gold (1952), mechanical
alignment, is caused by bombardment of the non-spherical grains by atoms,
thus transfering momentum and forcing an alignment of the grains. The last
mechanism, radiative torque works by aligning the grains with the radiative
pressure of starlight. On AU scales (100-104 AU), and grain sizes 0.02 to 0.5 µm
radiative torque align the grain with the longer axes perpendicular to the photon
flux (Lazarian, 2007).
Young Stellar Objects in polarization
With their dense circumstellar envelope together with outflows and a emerging
radiation field YSOs exhibit strong polarization due to scattering and extinction,
both linear and circular polarization. This polarization has been shown to be
wavelength dependent, in the core region it seems as the polarization get higher
with shorter wavelength, possibly attributed to the importance of dichroic extinction or the fact that the core region is unresolved (Beckford et al., 2008;
Lucas and Roche, 1998). The maximum polarization in HL Tau have a dependence on wavelength that is opposite that of the core polarization, reflecting the
increasing importance of multiple scattering to rising albedo (Lucas and Roche,
1997; Beckford et al., 2008). Non-spherical dust grains align in the protostellar
environment so that they precesses around the axis of the local magnetic field
with their axis of greatest rotational inertia. These magnetically aligned grains
produce a much broader region of aligned polarization vectors than the classic polarization pattern of centrosymmetric vectors. As discussed the alignment
mechanism may not be a magnetic field, so finding out the alignment mechanism
is important for unlocking the structure of YSOs.
1.2.3
Detecting linearly polarized light
Introduction
To describe the intensity measured by a detector behind a linear polarizer of
some sort (i.e. analyser), one usually defines an angle, ϕ between a line towards
the north celestial pole and the analyser, measured counter-clockwise and also
the degree of linear polarization PL along with the angle of polarization ϕ0 . Let
us also define the transmittance of two identical analysers oriented parallel,
Tk and the transmittance of two perpendicularly oriented analysers, T⊥ . The
intensity then reads (Serkowski, 1974, p.364)
0
I (ϕ) =
Tl + Tr
2
1/2
I+
Tl − Tr
2
1/2
IPL cos 2(ϕ − ϕ0 ).
1.3 To understand the equation we consider light with intensity I falling
p on to a instrument consisting of an analyser and a detector. The first term, I 0.5(Tl + Tr )
tells us how much of the intensity that is transmitted in average over one turn
15
CHAPTER 1. INTRODUCTION
p
of the analyser. The next term, 0.5(Tl − Tr )IPL cos 2(ϕ − ϕ0 ) accounts for
the intensity of linearly polarized light at a specific orientation of the analyser.
For an ideal analyser Tk = 1/2 and T⊥ = 0, i.e. half of incident unpolarized light
comes through, and the light after the analyser is 100% polarized. Replacing
I 1/2 with I0 as a measure of the average intensity that is let through along one
turn of the analyser we have the equation
I 0 (ϕ) = I0 (1 + PL cos 2(ϕ − ϕ0 )) .
1.4 Here we see that if the degree of linear polarization is 100%, i.e. PL = 1, the
minimum intensity will be zero, since all the light is polarized and when the
analyser is perpendicular to the polarization angle, no light will be transmitted.
On the other hand if some light is not linearly polarized, which is usually the
case the minimum intensity will be I0 (1 − PL )
If the analyser is oriented parallel to the polarization angle (ϕ = ϕ0 ) a
maximum occurs, and in addition to the unpolarized part that is let through,
I0 PL is added to the detected intensity. Moreover the intensity with the analyser
oriented perpendicular to the polarization angle (ϕ − ϕ0 = 90◦ ) harbours a
minimum in the detected intensity, since then the polarized component would
not pass. This fact is represented with a factor of two in the argument of
the cosine statement, when the analyser has turned 360◦ it has recorded two
maxima, with a 180◦ interval.
Now, how do we determine these parameters; mean intensity I0 , degree of
linear polarization PL and and polarization angle ϕ0 from observations?
Determining the unkown
Observing the intensity at angles 0◦ , 45◦ , 90◦ and 135◦ the system of equations
becomes over-determined, three unknown and four equations. The intensity at
the formentioned angles put into equation 1.4 then becomes with some simple
trigonometric relations
I 0 (0◦ ) = I0 (1 + PL cos 2ϕ0 )
1.5 π
I 0 (45◦ ) = I0 1 + PL cos
− 2ϕ0
= I0 (1 + PL sin 2ϕ0 )
1.6 2
I 0 (90◦ ) = I0 (1 + PL cos (π − 2ϕ0 )) = I0 (1 − PL cos 2ϕ0 )
1.7 3π
I 0 (135◦ ) = I0 1 + PL cos
− 2ϕ0
= I0 (1 − PL sin 2ϕ0 )
1.8 2
Here we have four equations and three unknown. We then form the differences of
pairs in which the analyser is perpendicularly oriented in respect to one another,
thus surpressing the unpolarized intensity that passes through the analyser with
the same intensity.
1.9 S1 = I 0 (0◦ ) − I 0 (90◦ )
0
◦
0
◦
S2 = I (45 ) − I (135 )
1.10 and also the mean intensity over all angles.
S0 =
16
(I 0 (0◦ ) + I 0 (90◦ ) + I 0 (45◦ ) + I 0 (135◦ ))
4
1.11
1.3. DIFFRACTION LIMITED IMAGING FROM THE GROUND
These gives
S1 = I 0 (0) − I 0 (90) = 2I0 PL cos 2ϕ0
S2 = I 0 (45) − I 0 (135) = 2I0 PL sin 2ϕ0
(I 0 (0) + I 0 (90) + I 0 (45) + I 0 (135))
= I0
4
To solve the system further, we calculate S12 + S22 and S2/S1 .
S0 =
S12 + S22 = 4I02 PL2
r
1 S12 + S22
→ PL =
2
S02
S2
sin 2ϕ0
=
= tan 2ϕ0
S1
cos 2ϕ0
1
S2
→ ϕ0 = arctan
2
S1
1.12 1.13 These relations are what is used in the routines when analysing the reduced
data, since what is observed is the intensity in each position of the analyser.
The Stokes parameters are related to S0, S1 and S2 as
I = 2S0
Q = S1
U = S2
thus concluding the final following relations already mentioned in the definitions
of the Stokes parameters (Serkowski, 1974, p.363).
p
Q2 + U 2
1.14 PL =
I 1
U
ϕ0 = arctan
1.15 2
Q
In the previous discussion the important equations are 1.9, 1.10, 1.11, 1.12
and 1.13 which are all used in the data reduction and analysis.
The degree of polarization consists of the polarized flux divided by the total
flux, so we can also define
p
IL = S12 + S22
1.16
as the polarized flux.
1.3 Diffraction limited imaging from the ground
1.3.1
Introduction
Shortly after Galileo turned his telescope towards the night sky he described
how the objects in the telescope seemed to flicker (Galilei, 1610). He was first
to describe the effects of turbulence on astronomical observations. The turbulent
17
CHAPTER 1. INTRODUCTION
energy is injected at large scales by wind shear. Taking many short exposure
images of a point source shows how the they change in both shape and position
during the observation, see figure below. Thus the usual long integration times
in imaging that seeks to increase the signal-to-noise causes images to be a sum
of all these fluctuations; blurred. The image fluctuations have their origin in
continuous changes of the turbulence structure above the telescope. Essentially
the shape of the point source (point spread function, PSF) is very variable, it
moves around and distorts on small timescales. Short exposure images take the
form of speckle patterns, multiple distorted and overlayed copies of the PSF that
the telescope would have if there were no atmosphere disturbing the image, i.e.
short exposure images retain information about the diffraction limited PSF.
Figure 1.7: An example set of V-band 45◦ analyser angle PolCor raw images from the observation
run at the NOT. The frames are sequential 100 ms exposures (framerate 10 Hz), time increases from
left-to-right and up-to-down. The resolution is 0.00 12/pixel. The image motion and speckle patterns
are clearly seen.
Long exposure images are highly blurred, and the diffraction limited PSF for
a 2.5m telescope is normally 5-15 times sharper than the summed long exposure
atmospherically effected PSF.
The size of a diffraction limited aperture which has the same resolution as an
infinite seeing-limited aperture, r0 is the general characteristic quantity that describes the total atmospheric turbulence strength. Deduced by Tatarski (1961)
from studies by Kolmogorov the atmospheric turbulence is commonly modelled
using a Kolmogorov power spectrum. Although supported by experimental measurments (e.g. Colavita et al., 1987; Buscher et al., 1995) some studies have
found deviations from Kolmogorov statistics (e.g. di Folco et al., 2003).
The effect of the quantity r0 on imaging is that a telescope with an aperture
much smaller than it will be diffraction limited in its imaging. Telescopes much
18
1.3. DIFFRACTION LIMITED IMAGING FROM THE GROUND
larger than r0 will be turbulence limited, Fried (1966) expressed the seeing disk
size at a wavelength λ as
λ
= 0.98 .
r0
At the best sites, r0 <50 cm and the seeing FWHM∼0.00 5 while the theoretical
diffraction limit of a 2.5 m telescope is ∼0.00 05 (not accounting for any obstructing
secondary mirror).
How short does the exposures have to be for lucky imaging to work? Well
there are two timesscales of atmospheric turbulence, first the seeing it self
changes on a wide range of timescales. Secondly the short exposure timescale,
τ0 gives the scale over which high resolution imaging systems must be able to
correct incoming turbulence errors. τ0 has been measured by several researchers,
e.g. Dainty et al. (1981); Roddier et al. (1990); Vernin and Munoz-Tunon (1994)
and result in values on the order of a few milliseconds or tenth of milliseconds.
The fluctuations are very local, observing one patch and correcting for turbulence does not mean that another patch separated with an angle will have
the same distortions. This largest angular distance at which the corrections are
still valid is called isoplanic angle.
1.3.2
Correction methods
There are several correction methods, the most successful ones being lucky imaging, adaptive optics (wavefront correction), tip/tilt correction, speckle interferometry and interferometry.
Lucky imaging relies on the fact that among the rapid turbulent fluctuations
of the atmosphere, moments (tens of milliseconds) of stable air appear. Thus
imaging at a high frame rate that is comparable to τ0 allows the observer follow
these variations and select those images when the seeing is much better than
the average. The flaw is that the observational efficiency is decreasing because
one is only integrating during periods of better seeing.
Adaptive optics (AO) systems senses the distortion of the wavefront imposed
by the turbulent layers above the telescope and actively corrects it in realtime
before it reach the detector. Either the shape of a nearby guide star is tracked, or
an artificial laser guide star (LSG) that relies on downwards Rayleigh scattering
or on the excitation of the high altitude sodium layer of the atmosphere. The
corrections are made by a deformable mirror in the light path and these systems
are common in the near-IR.
Tip/tilt correction corrects for the motion of the centroid over the course of
observation, it uses an simple tip/tilt mirror in the light path to account for the
motion. Usually tip/tilt sensors are integrated in AO systems.
Speckle interferometry was first suggested by Labeyrie (1970) and relies on
that the final image I(x, y) is the convolution of the object function O(x, y)
(objects brightness distribution) with the speckle image of a point object P (x, y)
(the atmospheric PSF).
I(x, y) = O(x, y) ∗ P (x, y)
As mentioned, since the speckle pattern contains information at the diffraction
limit of the telescope. When the speckle patterns are relative simple, as in
imaging binary stars, it can be a very useful technique (e.g. Horch et al., 2002).
19
CHAPTER 1. INTRODUCTION
In interferometry the incoming wavefront is combined from different telescopes producing a set of fringes from which the target objects brightness distribution can be calculated. In the radio regime, interferometric observations
are carried out routinely. In the near-IR both the Keck Interferometer and VLTI
interferometers are available to observers.
The work in this thesis uses data from the PolCor instrument (described
below) that uses the lucky imaging technique to obtain images, but with the
correct settings the data can be analysed as speckle interferometry.
20
“In God we trust, all others must
have data.”
C.R Reynolds, 1981
2
Observations and Data reduction
2.1 Observations
2.1.1
The PolCor instrument
Overview
The PolCor instrument is a combined lucky imager, polarimeter and coronagraph built for the Nordic Optical Telescope (NOT) by Göran Olofsson and
Hans-Gustav Florén at Stockholm University.
The PolCor system is compact and light (∼ 50 kg), during the observations
for this thesis it was mounted in the cassegrain focus of the NOT. The main idea
of the instrument is rotating a polarizer rapidly into five positions, 0◦ , 45◦ , 90◦ ,
135◦ , and “dark”. At each position the fast Andor IXon EMCCD camera takes
many short exposures, typically 30 or more during one second and position.
Doing this repeatedly during one observation averages atmospheric variations.
The data is stored on disk and reduced afterwards. By simply shifting and
adding images one can gain factor of two in sharpness, more so if also applying
a frame selection criteria (lucky imaging). The polarizing element, the analyser,
is a high-quality polarizer which is designed for the 410 − 750 nm region. To
detect circumstellar structures PolCor has a set of coronagraphic masks.
Except for the filter and the cryostat window the optics in the instrument is
all-mirror design, and with good margin diffraction limited. The reflectivity of
the four mirrors in the light path is 99.5% each, resulting in only 2% losses over
the sensitivity range of the detector. With a 1:1 imaging of the relay optics the
pixel scale at the NOT is 0.00 12 per pixel. For speckle interferometry there are
two barlow lenses with two and three times magnification available. To mask the
secondary mirror support blades and minimise the extent of diffraction stripes,
PolCor is equiped with a computer controlled Lyot stop. Also the mask is
slightly undersized to block the diffraction rings caused by the coronagraphic
disks, this blocking suppresses the point spread function wings by 1-2 order of
magnitude.
The standard filters for PolCor are Bessel U, B, V, R and I filters, in addition
narrow-band filters in the 0.3 − 0.5 nm region exists. Two filters are fitted in the
filter holder and the active filter is choosen in the observation software during
operation.
For coronagraphy there is a choice of three sizes of coronagraphic disks with
diameters of 1.00 5, 300 and 600 . Each size with three different optical densities; 5,
21
CHAPTER 2. OBSERVATIONS AND DATA REDUCTION
8.75 and 12.5 magnitudes. Not using totally opaque disks allow for centring of
the star.
Usually the observer is limited by the atmospheric conditions at the site of
observation. By applying the lucky exposure technique, PolCor can overcome
many of the troubles with having an turbulent atmosphere between the observer
and object, even attain near diffraction limited imaging. During a long exposure
the atmosphere effects the light on its way down to the detector; moving around
and getting blurred. Since taking a longer exposure becomes the sum of all the
shifted images the source is not point-like any longer, but a Gaussian. Correcting
for this image motion by taking short exposures and shifting and adding images
typically improves seeing from 0.00 7 to 0.00 4, if using frame selection the resolution
will improve to 0.00 2-0.00 3. The specifics of lucky imaging is covered in section 1.3.
The detector
The Electron Multiplying CCD camera (EMCCD), Andor iXon+ 897 uses a
thinned back-illuminated 512 × 512 CCD array with 15 µm pixels and the chip
is cooled to -90◦ C by a thermo-electric cooler. The camera have two modes of
operation, classic and electron multiplying (EM). Classic mode has a read-out
noise of 6 e− rms and the EM mode has a on-chip gain up to 1000 which is
particularly useful for low light levels. The camera has also a very fast readout
time, fastest full-frame readout rate is 33 Hz, and even higher when defining a
sub-image area on the chip. With a sufficiently high time resolution, speckle
interferometry is possible.
Figure 2.1: The Andor iXon+ 897 QE versus wavelength graph. As seen the QE in the V and R
band region is high. From http://www.andor.com/scientific_cameras/ixon/models/.
The detector utilises a frame transfer CCD structure, in this structure there
are two areas on the chip, one sensor area where the photons are captured and
one storage area. After being captured the image is transfered to the storage
area - usually identical in size to the capture area but covered with an totally
opaque mask. While the sensor area continues the imaging, the image in the
22
2.1. OBSERVATIONS
storage area is transfered to the readout register and onwards to the multiplication register where the data is amplified. To understand how the amplification
occurs one must understand clock-induced charge (CIC) - normally considered
a source of noise in imaging. In the process of moving the charges through the
register there is a very tiny probability that the charges being clocked creates
additional charges by impact ionization. When a charge has enough energy to
induce an electron-hole pair and add a electron to the conduction band one
speaks of impact ionization. This is how the amplification occurs, and as suspected this probability gets higher the more energy the electron has. So by
clocking with a higher charge the amplification gets higher, also the probability
increases with lower temperatures hence cooling the chip increases the amplification. The probability of amplification within any one cell is very low but
taken over the whole register the amplification is very high and gains of up to
thousands can be achieved. This amplification allows for single detections, photons to be amplified over the "noise-floor" and thus photon counting is possible
with the right intrument design. In the table below the main characteristics of
the detector is shown.
Manufacturer
Model
CCD Type
Pixel size
Active pixels
Image area
Pixel well
Max readout rate
Plate scale @ NOT
Read noise
Andor Technologies
EM+ DU-897
Back-illuminated EM-CCD
16 µm
512 × 512
8.2 × 8.2 mm
160 000 e− (max: 220 000 )
10 MHz
0.00 12 per pxl
<1 to 49 e− @ 10 MHz (typical)
Table 2.1: CCD detector characteristics. The field of view is calculated as Ω = 206265µ/1000f where
µ is the pixel size of the CCD and f the focal length of the primary mirror in mm (28160 mm for
NOT).
The software stores the raw-data from the detector in the FITS-format on an
external hard-drive connected to the instrument computer. Also an accumulated
image for each of the analyser positions is stored in a C-binary format.
A walk through PolCor
The instrument layout can be seen in figure 2.2. In the figure the numbers 1
to 9 marks the important parts of the relaying optics, masks, polarizer e.t.c.
From the right (1) the telescope f /11 rays enters the instrument, (2) marks the
placement of the analyser. The analyser, a high quality polarizer optimized for
the operational wavelength, is during polarimetry mode turned rapidly to the
5 positions (0◦ , 45◦ , 90◦ , 135◦ and dark). A classical imaging mode is possible,
just by pulling away the analyser from the light path in the handle above it.
In (3) the focusing mechanics resides and after this, in the image plane the
coronagraphic masks sits on a wheel (4). After being collimated (5), the rays
are parallel and passes the filter wheel (6), where two different filters are loaded.
Directly after the filter wheel sits the computer controlled Lyot stop (7) to mask
23
CHAPTER 2. OBSERVATIONS AND DATA REDUCTION
diffraction stripes from the secondary mirror support blades, it turns with the
same angular speed as the NOT field rotator but in opposite direction. The the
light is focused to an image through (8) and (9) down to the EMCCD camera.
Figure 2.2: The PolCor instrument, it has a very light and compact design. The red lines follow
the light through the instrument. The light enters from the telescope (1) and passes through the
analyser (2), letting through light of the selected polarization angle. The light passes the focusing
mechanics (3) to the mask selection wheel (4), hits the first mirror and the collimator (5) so the
rays are parallel when going through the filter (6) and the spider mask Lyot stop. After this it is
deflected (8 and 9) to the camera below in the image. Image by Hans-Gustav Florén.
2.1.2
Observations
The complete observation run was from the 25th to the 31th October 2008,
due to sever weather only one successful night of observations were carried out,
24
2.1. OBSERVATIONS
between the 27th and 28th. On the dusk and dawn of the observation run
clouds, gusts of wind and rain put and end to the hopes of flat-fields. So the
data is reduced and analysed without accounting for uneven sensitivity of the
CCD.
Atmospheric conditions
Lucky imaging is something that is supposed to improve image quality towards
the diffraction limitation of the telescope. The appalling weather conditions
during the observation run limited the number of observable nights. The seeing
was on average around 1.00 -1.00 5 when observations could be made.
6.0
35
5.5
30
5.0
25 Storm
20
15
Temperature (C)
Wind Speed (m/s)
40
3.5
3.0
10
2.5
5
2.0
1.5
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
18:0 19:0 20:0 21:0 22:0 23:0 00:0 01:0 02:0 03:0 04:0 05:0 06:0 07:0 08:0
0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
18:0 19:0 20:0 21:0 22:0 23:0 00:0 01:0 02:0 03:0 04:0 05:0 06:0 07:0 08:0
100
774.0
773.5
60
40
20
Pressure (mbar)
80
Humidity (\%)
4.5
4.0
773.0
772.5
772.0
771.5
Approx. typical pressure
771.0
0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
18:0 19:0 20:0 21:0 22:0 23:0 00:0 01:0 02:0 03:0 04:0 05:0 06:0 07:0 08:0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
18:0 19:0 20:0 21:0 22:0 23:0 00:0 01:0 02:0 03:0 04:0 05:0 06:0 07:0 08:0
Figure 2.3: Atmospheric conditions during the observation run 27th to 28th October. In comparison
to the other nights of the week, this was the only one with weather good enough to make any
observations at all. The “approximate typical pressure” is for the season, it varies rather greatly
over the year. During the acquisition of the HL/XZ Tau data, at 04:00-05:00 clouds started to
build up around the mountain.
25
26
RA
20:48:56.2909
20:48:56.2909
21:28:57.7610
01:09:12.3410
15:36:21.1642
04:31:39.250
04:31:39.250
DEC
+46:06:50.884
+46:06:50.884
+58:44:23.238
+60:37:40.937
+63:54:00.362
+18:13:57.450
+18:13:57.450
20:28
20:35
04:23
05:01
UT
20:14
Filter
R
V
V
V
V
V
R
0.1
0.1
0.1
0.1
Integration
3
30-10
30-10
30-100
30-77
Mode
Comments
Cal, Corrupt
Cal, Corrupt
Cal, Corrupt, even acc. I(135)
Cal, G:3200
Cal
Sci
Sci
Table 2.2: Observational log, the “Mode” column reads as exposure time – cycles so 30-100 is 30 second exposures and 100 cycles. Catalogues: HD - Henry Draper
catalogue, BD - Bonner Durchmusterung. The V-band HD 204827 I(135) observation was corrupt even in the accumulated image, therefore modified formulas to retrieve
the polarization angle e.t.c had to be used for the algebra see Appendix 1 (A1 on page 69).
Object
HD 198478
HD 198478
HD 204827
HD 236633
BD 64◦ 108
HL+XZ Tau
HL+XZ Tau
with “Cal” in the comments are calibration objects, “Sci” science
objects, “Corrupt” means that the raw data was corrupt in some
In the following table the observation log is show, the columns are way but for calibration data the accumulated image was still useful
object, right ascension, declination, filter band, integration time and “G” followed by a number is the gain settings if other than the
(seconds), exposure mode and additional comments. In the objects standard.
Observation log
CHAPTER 2. OBSERVATIONS AND DATA REDUCTION
2.2. DATA REDUCTION
2.2 Data reduction
The raw data from PolCor comes in 6 different types, the darks, flat-fields and
then the 4 different polarization positions (0◦ , 45◦ , 90◦ and 135◦ ). The existing
routines to reduce and analyse PolCor data was written by Göran Olofsson in
IDL12 . The expensive licsenses, avaliability i.e. running scripts on local server
e.t.c. led to the suggestion to write the routines in Python3 , and also add some
routines to the reduction steps to ascertain what different information can be
extracted from this kind of data.
2.2.1
Overview
In the following list the basic reduction steps will be outlined and later explained
in detail.
1. Calculate the average darkframe of every cycle and and average dark of
all exposures.
2. Calculate the median flat field for each cycle.
3. Determine where the guide star and background field is, by means of
point-and-click.
4. Cut out a square around the guide star and background field from every
frame.
5. Calculate the moments of every guide star frame.
6. Determine where the strongest speckle is in every guide star frame.
7. Calculate the median position of the star, set this as the reference position
of the guide star and calculate the pixel-level deviation of every frame from
this median, calculate for both the moments and strongest speckle centres.
8. Calculate the sharpness in each frame centred around the coordinates of
the moments.
9. Let the user choose an (or several) acceptance sharpness with the aid of
a histogram of the sharpness in all frames.
10. Shift and add the frames with the given pixel-offset.
11. Repeat from 9 with the strongest speckle as method of determining the
star position instead.
12. All steps from step 3 is repeated for all polarization angles.
After this the final reduction steps of the four polarization angles are
1. The guide star’s position is read in and a two dimensional gaussian is
fitted to each frame at the star’s position.
1 Interactive
Data Language by ITT http://www.ittvis.com/ProductServices/IDL.aspx
H-G. Florén and R. Nilsson of the Stockholm University Astronomy department
have their own reduction routines as well
3 http://www.python.org/
2 Actually
27
CHAPTER 2. OBSERVATIONS AND DATA REDUCTION
2. The 0◦ polarization image is used as reference and all the other angles are
shifted with sub-pixel precision to match it.
3. Then S0, S1, S2, polarized flux, polarization degree and polarization angle
are all calculated.
2.2.2
Dark frame and flat fielding
The number of dark frames are the same as the number of frames in a polarization position i.e the number of cycles times the number of exposures. A
typical dark frame is seen in figure 2.4 together with a histogram of the pixel
distribution. The master dark for each cycle is calculated as the mean of all
the exposures in the cycle. Also an average master dark is calculated from all
frames in all cycles. The pixel distribution in figure 2.4 peaks around 92, the
overall shape of the distribution is that of a skew gaussian, with a longer tail
towards higher values.
500
108
400
300
104
5000
100
4000
96
3000
92
200
88
100
00
6000
84
100
200
300
400
500
80
2000
1000
0 85
90
95
100
105
Figure 2.4: Left: V-band typical dark frame, averaged over one cycle (i.e. 30 frames averaged). A
small gradient exists in the left of the image, this could be due to that when read out the pixel rows
last in line can be exposed to dark current longer. It could also be uneven response of the CCD
which could be corrected for by taking flat fields. Right: Pixel ditribution (histogram) over dark
values. Typical gaussian distribution with tail towards high values of the random noise in the dark
current.
Because of the weather conditions during dusk and dawn, flat fields were
never taken. Although the flat is calculated from the median of several exposures
taken at an evenly illuminated surface. Each filter has its own flat field, and
since the flat field measures uneven response of the CCD it is normalised and
applied by dividing the science frame (and dark) with the normalised flat field
so that pixels with lower response will be compensated.
2.2.3
Determining the centre of reference object
Different methods can be used to determine the centre of a point-source. The
two methods used in this thesis are loosely referred to as moment of flux and
maximum speckle. Determining the centre by calculating the moment of flux is
the most widely used, it is also referred to as the centroid of an image. If the
28
2.2. DATA REDUCTION
total flux in the frame is
Ftot =
Ny
Nx X
X
2.1 f (xi , yj )
i=0 j=0
where f (xi , yi ) is the value of the xi , yi pixel, the moment of flux is (Berry,
2005, p.218)
PNx PNy
x̄ =
i=0
j=0
xi f (xi , yj )
Ftot
PNx PNy
and ȳ =
j=0
i=0
yi fi (xi , yj )
Ftot
2.2 for x and y respectively. To save some time and not looping throuht all pixels
one can realise that
PNx PNy
x̄ =
i=0
j=0
xi f (xi , yj )
Ftot
PNx
=
where Fy (xi ) =
xi Fy (xi )
Ftot
i=0
Ny
X
f (xi , yj )
2.3 2.4 j=0
The fact that makes this possible is that the equation weights each pixel along
each axis separetly by the amount of starlight that have hit the pixel. Still,
doing this on 3000 frames takes time, but in Python this can be done rather
elegantly and fast with methods on multi-dimensional array objects, without
having to do loops on the highest level. The result is the centroid of each frame,
(x̄i , ȳi ).
The other method uses the strongest pixel in the frame as the star position,
and it is exactly as simple as it sounds. The maximum speckle in an area close
to the guide star is used as the star position in that frame.
2.2.4
Sharpness
The sharpness of each image is a measure of the quality of the data. With a
high sample rate, the sharpness varies with time and gives a measure of the
atmospheric disturbances. If two boxes are defined in the image around the
object of which the sharpness is to be measured for. One large, referred to as
f1 and one small, referred to as f2 . The sharpness is then simply the fraction
of the two.
s=
f2
f1
2.5 The sharpness is used to discriminate between data with high and low quality, since the source is a point source, the fraction is ideally equal to 1. The
histogram of the sharpness helps to determine the acceptance sharpness that is
applied later to the data when determining which images to be used in the final
image.
29
CHAPTER 2. OBSERVATIONS AND DATA REDUCTION
120
60
2250
50
2000
1750
pixels
40
1500
1250
30
1000
20
750
500
10
0
100
80
60
40
20
250
0
10
20
30
40
pixels
50
00
60
20
40
60
Sharpness (%)
80
100
Figure 2.5: Left:An example of a 64x64 pixel box around the guidestar (XZ Tau) used in the 45◦
polarimetry dataset in the R-band. A 20x20 pixel (f1 ) and 6x6 (f2 ) box are drawn around the
centroid (star sign). The sharpness in this image is 24% which is rather poor, in frames with higher
sharpness the flux in the f2 box (small) is higher and more concentrated. Right: Histogram over
sharpness in all frames in the R-band data (2310 frames), it peaks around 50%.
100
60
2250
50
2000
pixels
40
1500
60
1250
30
1000
20
40
750
500
10
0
80
1750
20
250
0
10
20
30
40
pixels
50
60
00
20
40
60
Sharpness (%)
80
100
Figure 2.6: Left: Same as figure 2.5 but with the centre and boxes around the strongest speckle
Right: Histogram over all R-band images in 45◦ position with the centre at the strongest speckle.
2.2.5
Shifting and adding
After the acceptance sharpness has been determined, the images are ready to
be shifted and added. Each image is now associated with a shift and sharpness,
so when adding the frames the routines check if the shift is not too far, e.g. say
a shift of more than 4 pixels and also if the sharpness meets the requirements.
Before adding the specific image the average dark of the corresponding cycle
is subtracted, and the image devided by the normalised flat-field. Below is an
example of the 0◦ position final image with a sharpness criteria of 40% and a
maximum shift-distance of 4 pixels, but not flat-fielded.
30
2.3. DATA ANALYSIS
Figure 2.7: The 0◦ position final image with a sharpness criteria of 40% and a maximum shiftdistance of 4 pixels. The size of the image is 512×512 pixels and to the left XZ Tau is seen.
2.3 Data analysis
2.3.1
Stokes and additional parameters
With a shifted, dark subtracted, flat fielded and average added final image in
every position of the analyser, what is left to do is to calculate the parameters S0,
S1, S2, ϕ0 , IL and the PL of the field. The specifics are covered in section 1.2.3
on page 16, the important equations are repeated here.
S1 = I 0 (0) − I 0 (90) = Q
S2 = I 0 (45) − I 0 (135) = U
S0 =
2.3.2
(I 0 (0) + I 0 (90) + I 0 (45) + I 0 (135))
1
= I
4
2
1
U
ϕ0 = arctan
2
Q
p
2
IL = Q + U 2
r
1 Q2 + U 2
IL
PL =
=
2
S02
2S0
Polarization standards
The analyser is not aligned with a line towards the north celestial pole, so the
analyser has a certain shift for all observations. To find out how to compensate
for this one performs polarization calibration, and by measuring the polarization
of a polarization standard object one finds out how much the difference is and
the shift applied as
ϕ0,true = ϕ0,obs − ϕ0,calib .
2.6 31
CHAPTER 2. OBSERVATIONS AND DATA REDUCTION
This assumes that the relation between the literature and the observed value is
linear, i.e. that the angle with which the analyser turns between each position
is exactly 45◦ . If this is not the case, it will raise some concerns with the
polarization measurements made. The calibration objects and their coordinates
are listed in the observations log, below is a list of the measured values of
ϕ0 and PL . Although some technical difficulties arose during the acquisition
of calibration data, which resulted in only accumulated images to be used for
calibration.
HD-198478 (R)
HD-198478 (V)
HD-204827 (V)
BD 64◦ 1080 (V)
HD-236633 (V)
PL (% )
2.47
2.63
5.52
3.15
PL,litt (% )
2.8
2.8
5.32
5.69
5.49
ϕ0
103.007◦
103.295◦
160.883◦
21.07◦ (+180◦ )
16.61◦ (+180◦ )
ϕ0,litt
3◦
3◦
58.73◦
96.63◦
93.76◦
ϕ0,litt
Table 2.3: Calibration measurements, the literature values are taken from the NOT homepage on
Polarization standards.
120
100
80
60
40
20
0
2080
y=-96.324+0.963*x
100
120
140
ϕ0,obs
160
180
200
220
Figure 2.8: Polarization calibration, the linear fit has the equation y = −96.324 + 0.963x. The
inclination coefficient is not equal to one, which is not good.
As seen in table 2.2 the I 0 (135) measurment was corrupt, even in the accumulated image. So the formulas derivated in subsection “Analysing linearly
polarized light” had to be modified. The derivation of those formulas is located
in Appendix 1 on page 69.
32
“I don’t believe in astrology; I’m a
Sagittarius and we’re skeptical.”
Arthur C. Clarke
3
Results
3.1 Results
In the following chapter the results are given, and were possible, conclusions
will be drawn and presented. The only visible objects in the images are XZ Tau
and HL Tau, therefore those objects have been “cut-out” and displayed in their
respective sections. The resulting datasets, i.e. S0, S1, S2, IL , PL and ϕ are
shown below; for both filters, V- and R-band and for both objects, HL Tau and
XZ Tau. To visualise structures and the scattering in the sources a combination
of different results are drawn in a vector plot, where the arrows point along the
polarization angle and a contour of the polarized flux is drawn, in HL Tau the
length of the arrows correspond to the degree of polarization (PL )
The data was reduced and analysed for five different scenarios referrd to
as normal, zero, low, medium and high, depending on the chosen acceptance
sharpness.
1. Normal, i.e. no shifting, no frame selection, just adding all frames together.
This is what the image probably would look like after a normal continuous
integration of ∼100 seconds.
2. Zero, only shifting, using all images and calculating a shift through the
centroid positions.
3. Low, using shifting and frame selection and setting the acceptance sharpness to the median sharpness subtracted by 15, using about 80 % of all
the frames.
4. Medium, using shifting and frame selection and setting the acceptance
sharpness to the median sharpness subtracted by 5, resulting in about
60 % of the frames were used.
5. High, using shifting and frame selection and setting the acceptance sharpness to the maximum sharpness subtracted by 7. This resulted in the use
of between 1 and 6 % of the frames.
In “low”, “medium” and “high” the limit for the excursion of the centroid from
the median position is 4 pixels, otherwise there was no limit set. The motivation
for the values chosen is just to get a good spread of the sharpness values and the
frame selection to be able to investigate the effect of frame selection on image
33
CHAPTER 3. RESULTS
sharpness. The resulting acceptance sharpness and the percentage of the total
number of frames used are shown in the table below.
Filter
V
R
Angle
0◦
45◦
90◦
135◦
0◦
45◦
90◦
135◦
Low
36 (77)
34 (79)
36 (75)
35 (75)
31 (80)
30 (82)
30 (79)
30 (79)
Medium
46 (62)
44 (63)
46 (61)
45 (60)
41 (62)
40 (63)
40 (59)
40 (62)
High
68 (1)
63 (4)
63 (6)
67 (1)
59 (3)
61 (1)
59 (3)
64 (1)
Table 3.1: Acceptance sharpness, i.e. percentage of flux that resides in the small box in comparison
to the big box around the centroid, for the different angles and filters. The number in parenthesis
is the percentage of all frames that where used.
Although the two objects are of similar mass and age, they show very different structures. In HL Tau the wide-spread reflection nebulosity is clear, in
S0 the object is faint in comparison to the bright and confined intensity that
XZ Tau show. The polarization is high in both R- and V-band data for HL
Tayu. XZ Tau does not have the kind of gas and dust envelope as HL Tau,
thus the wide-spread reflection nebulosity is not present. Although the observational conditions where not optimal, the elongation of XZ Tau at least hints
the binary nature of the object. Several interesting investigations of HL Tau is
made possible due to the data being polarimetric. The lack of error estimates
here resides in the fact that it is rather cumbersome to calculate and with the
rather high intensities that is shown in the images below it is not needed. The
structures are significant, although in the “high” scenario, only the S0 image is
shown to have enough information to show structures.
3.1.1
XZ Tau
R-band
In the figure below the resulting S0, S1, S2, IL , PL and ϕ0 R-band images of
XZ Tau are shown, the acceptance sharpness is set to medium, east is left and
north is up.
The mean intensity over all angles of the analyser (S0) shows that the object
is slightly elongated in a south-east to north-west direction. Hinting the binary
(multiple) system that it is. If the weather conditions had been more normal
for the site, with around 0.00 7 FWHM mean seeing, the binary system would
probably have been resolved.
The upper right image and the middle left shows the S1 and S2 data. In
S1 the negative intensity is confined to a south-west to north-east stroke while
in S2 it is shifted 90◦ . What is expected from an object that creates polarized
radiation by scattering, in a approximate spherical cloud around the central
object, is that the intensities in S1 and S2 are at an 90◦ angle from one another,
a butterfly shape. Both S1 and S2 shows a tendency towards this.
In the final figures, the IL , PL and ϕ0 it becomes obvious that the degree of
polarization in the system is low, less than 2% . The polarized intensity, the
few percent that is polarized and have high intensity show even stronger the
elongated structure.
34
3.1. RESULTS
S0
S1
3.6
2.8
30
log10(ADU)
2.4
2.0
20
1.6
10
0
10
20
30
40
75
50
30
25
20
0
25
10
1.2
0
100
40
0.8
0
50
0
10
20
S2
10
10
20
30
40
PL
40
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
%
30
20
10
0
10
20
30
40
40
40
log10(ADU)
30
20
10
0
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0
10
20
30
40
ϕ0
160
140
120
100
80
60
40
20
40
30
degree
20
0
80
40
0
40
80
120
160
200
ADU
30
0
30
IL
40
0
ADU
3.2
40
20
10
0
0
10
20
30
40
Figure 3.1: R-band XZ Tau S0, S1, S2, IL , PL and ϕ0 images at medium acceptance sharpness.
Polarization angle ϕ0 is set between 0◦ and 180◦ . The degree of polarization of the central source
seen in IL is low, PL ∼2% and the patterns in S1 and S2 reveal a structure sometimes described as a
“butterfly”. The negative values in S1 are confined in a south-west to nort-east direction while the
“wings” are half-moons in the perpendicular direction. S2 has the same tendency but with a 90◦
shift. The intensity map, S0 and the polarized intensity IL shows signs of the binary system with
an elongated structure. The polarization angle is constant where the polarized intensity is high,
roughly at 45◦ , which is perpendicular to the orientation of the ellipse created by the unresolved
binary system.
35
CHAPTER 3. RESULTS
In the next figure (3.2) a combination of the polarization angle ϕ0 and the
polarized flux IL is shown. The direction of the arrows show the polarization
angle, up is 0◦ with positive direction counter clock wise and the contours are the
polarized flux. The angles were filtered away where values of IL are below the
median added with one standard deviation. In the region where the intensity
is highest, i.e. above 53 in the contours, the angles is constant at an angle
roughly perpendicular to the ellipse of the unresolved binary system. Due to the
low degree of polarization this is probably just the polarization of the parental
cloud/ISM, caused by dichroic extinction of the source starlight.
220
210
200
190
180
100 AU
170120
130
140
150
160
170
Figure 3.2: XZ Tau R-band vector plot, where the direction is the polarization angle ϕ0 and 0◦ is
up (North). The contours are the polarized flux IL with levels (from red to yellow) at 22.75, 44.5,
66.25 and 88. The centre source, where the flux is above 44.5, shows a approximately constant angle
of polarization which is perpendicular to the ellipse created by the unresolved binary system. The
data was filtered with the polarized flux so that sufficiently high levels of flux is shown. The length
of the arrows are constant.
V-band
The V-band images of low acceptance sharpness are shown below. Beginning
with the mean intensity, S0 shows the same elongated ellipse as in the R-band
data. Hinting the binary nature of XZ Tau. The intensity in these images is less
than half that of the R-band. In the V-band images S1 and S2 shows similar
butterfly structures with a 90◦ shift to one another. The red in the S1 image
is inclined, roughly speaking in a east-south-east to west-north-west direction,
while S2 is inclined ∼90◦ to this. Just as with the R-band data the structure is
not as prominent in S2, in IL it looks like the main scattering occurs along the
S1 shape of positive values. Comparing IL with S0 and looking at PL , it has
roughly the same degree of polarization in the brightest parts as in the R-band.
36
3.1. RESULTS
S0
S1
log10(ADU)
30
20
10
0
0
10
20
30
40
40
30
20
10
0
0
10
20
S2
30
40
IL
30
15
ADU
15
30
20
45
10
60
0
10
20
30
40
PL
40
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
%
30
75
20
10
0
10
20
30
40
30
20
10
0
1.50
1.35
1.20
1.05
0.90
0.75
0.60
0.45
log10(ADU)
0
30
0
40
0
10
20
30
40
ϕ0
160
140
120
100
80
60
40
20
40
30
degree
40
0
40
32
24
16
8
0
8
16
24
ADU
40
3.0
2.7
2.4
2.1
1.8
1.5
1.2
0.9
0.6
20
10
0
0
10
20
30
40
Figure 3.3: V-band XZ Tau S0, S1, S2, IL , PL and ϕ0 images. S0 shows the same elongated structure
due to the unresolved binary system, and S1 and S2 shows the butterfly shape, this time with a eastsouth-east to west-north-west direction in S1 and a less prominent but 90◦ shifted similar structure
in S2. The degree of polarization is low, around 2% where the intensity in IL is the greatest. The
polarization angle at that same point in IL is constant, perpendicular to the ellipse direction of the
unresolved binary. The acceptance sharpness is set to low.
37
CHAPTER 3. RESULTS
In the next figure the vector plot of the V-band data around XZ Tau is shown.
As in the longer wavelength, the centre of the object, where the polarization is
the greatest the polarization angle is perpendicular to the elongated structure
that is the unresolved binary.
220
210
200
190
180
100 AU
170120
130
140
150
160
170
Figure 3.4: XZ Tau V-band vector plot. The direction of the arrows is the polarization angle ϕ0
(0◦ is up) and the contours are the polarized flux IL at the levels (from red to yellow) 9.25, 18.5,
27.75 and 38. The polarization vectors in the centre, where the flux is above 18.5 (second level), are
constant. Just as in the R-band data they are perpendicular to the orientation of the major axis
of the ellipse that is the unresolved binary system. The data was filtered with the polarized flux so
that only the significant data is represented and the acceptance sharpness is low.
3.1.2
HL Tau
R-band
In the figure below the resulting S0, S1, S2, IL , PL and ϕ0 R-band images of
HL Tau are shown. The mean intensity S0 is very nebulous with lots of gas
and dust around the YSO, the low intensity wide-spread reflection nebulosity
shows a C-shaped structure. The central source is completely obscured at these
wavelengths, but at longer wavelengths the source can be seen (Close et al.,
1997). Which is what characterise HL Tau, its circumstellar envelope surrounds
the young star, but in the outflow direction the optical depth is higher and thus
letting the photons that scatter against the wall of the outflow to escape.
S1 and S2 does not show much structure. The polarized flux and the degree
of polarization is interesting, the degree of polarization is high, ∼30% the polarized flux is strong and wide-spread, showing no direct signs of the C-shape
that is obvious in the S0; the shape in IL is usually described as cometary.
The polarization angle shows clear a structure, fading from 180◦ red (0◦ ,
blue) in the lower left to roughly 100◦ in the upper right. This shows that the
scattered radiation escapes the envelope after just one or a few scattering events
38
3.1. RESULTS
so that it reaches this high degree of polarization. The plus sign and circle shows
the possible location of the protostar (see the next paragraph for the explanation
of how the possible location was deduced).
S0(high)
S1
6.0
3.0
2.00
3.0
1.5
1.75
1.50
0.0
1.25
-1.5
-3.0
arcseconds
2.25
4.5
-6.0 -4.5 -3.0 -1.5 0.0 1.5
arcseconds
1.5
0.0
1.00
-1.5
0.75
-3.0
140
6.0
1.8
4.5
120
4.5
1.6
3.0
1.4
80
1.5
60
0.0
40
-1.5
20
-1.5
-3.0
0
-3.0
PL
4.5
3.0
%
1.5
0.0
-1.5
-3.0
40
36
32
28
24
20
16
12
8
4
0
-6.0 -4.5 -3.0 -1.5 0.0 1.5
arcseconds
1.0
0.0
0.8
0.6
-6.0 -4.5 -3.0 -1.5 0.0 1.5
arcseconds
0.4
ϕ0
6.0
160
140
120
100
80
60
40
20
4.5
arcseconds
-6.0 -4.5 -3.0 -1.5 0.0 1.5
arcseconds
1.2
1.5
3.0
1.5
degree
3.0
arcseconds
100
log10(ADU)
6.0
6.0
arcseconds
-6.0 -4.5 -3.0 -1.5 0.0 1.5
arcseconds
IL
ADU
arcseconds
S2
15
0
15
30
45
60
75
90
105
ADU
2.50
4.5
log10(ADU)
arcseconds
6.0
0.0
-1.5
-3.0
-6.0 -4.5 -3.0 -1.5 0.0 1.5
arcseconds
Figure 3.5: HL Tau R-band S0, S1, S2, IL , PL and ϕ0 images. S0 shows an approximate C-shape.
The outflow has carved a hole in the envelope and photons scatter against the walls of this outflow
and this scattering causes the observed polarization pattern. The degree of polarization is high
∼30%, and the polarization pattern shows structure around the star that tells us that the outflow
is optically thin for the scattered photons. The images uses the frame selection scenario low, except
S0 which uses high.
39
CHAPTER 3. RESULTS
HL Tau has a thick disk that obscures the central object at these wavelengths,
but the polarization angle is perpendicular to the scattering plane (plane of incident and scattered rays) and by drawing lines perpendicular to the polarization
angle should give the rough position of the central source. In figure 3.6 this is
shown, the possible location of the source is shown by a circle with radius of 0.00 6
(84 AU, 0.2400 /pixel). Also the approximate PA angle of the outflow is drawn
with white lines. The angles of the lines are at 40◦ and 55◦ , giving an estimate of the PA of the outflow equal to 47.5±7.5◦ . The data have been binned
(2 × 2) so that the pixel scale is 0.2400 /pixel, this increases the significance of
the measurements and makes structures more prominent.
6
5
4
arcseconds
3
2
1
0
-1
-2
-3
200 AU
-6
-5
-4
-3 -2 -1
arcseconds
0
1
2
Figure 3.6: HL Tau R-band pinpointing the central object, where the arrows are drawn perpendicular to the polarization angle, and extra long. The “waist” of the hourglass-shaped object hints the
position of the central source. The circle with radius of 0.00 6 (84 AU, 0.2400 /pixel (binned)) shows
the likely position of it. The angles of the lines are at 40◦ and 55◦ , giving an estimate of the PA
of the outflow equal to 47.5±7.5◦ .
The next image shows a vector plot with polarization angle represented by
the direction of the arrows, the degree of polarization by length of the arrows
and the contours represents the polarized intensity with levels at 18.75, 37.5,
56.25 and 75 (red to yellow). The circle shows the previous pinpoint of the
central source with a radius of 0.00 6 (84 AU).
The fact that the counter-jet (and receding outflow lobe) is not visible as in
near-IR observations by e.g. Lucas et al. (2004) shows that the envelope/disk
blocks radiation at shorter wavelengths. The source is obscured by the envelope/disk, but the polarization vectors at the presumed location of the object
are constant. They all point in a south-east direction, the structure is usually
attributed to multiple scattering in the disk and the structure referred to as a
polarization disk (Bastien and Menard, 1988; Whitney and Hartmann, 1993).
The absence of scattered intensity around the outflow shows the thick envelope
40
3.1. RESULTS
that surrounds the object. By averaging the degree of polarization in the circle
that marks the location of the central source, an estimate of the core polarization
can be made. The average core polarization of HL Tau R-band is 12.1%.
6
5
4
arcseconds
3
2
1
0
-1
-2
-3
200 AU
-6
-5
-4
-3 -2 -1
arcseconds
0
1
2
Figure 3.7: HL Tau R-band vector plot. The direction of the arrows represents ϕ0 , length of arrows
- PL , contour IL and the corresponding levels are 18.75, 37.5, 56.25 and 75 (red to yellow). The
data have been binned (2 × 2) and the circle shows the previous pinpoint of the central source
with a radius of 0.00 6 (84 AU, 0.2400 /pixel). The observed structure shows how the photons scatter
against the wall of the outflow and is polarized in the process. The polarization is perpendicular
to the scattering plane. The classical centro-symmetric polarization pattern is clear and stretches
for several hundred AUs. At the pinpointing of the central source there is a line of vectors that are
aligned, this structure is usually appointed to multiple scattering in the disk and is referred to as a
polarization disk.
V-band
The V-band images for HL Tau shows the same structures, but with a lower
intensity. S0 shows the wide-spread nebulosity that characterises Class I/II
YSOs with large envelopes. It also has the C-shape in S0 as the R-band. S1
and S2 also shows the same structure as the longer wavelength images while
IL has the cometary shape but with about one third of the intensity which
causes a higher noise level. The prominent structure of the polarization angles
in the image is also present and also the high degree of polarization. At shorter
wavelengths it is obvious that the object is less luminous and the intensity in
S0 is roughly a bit less than half that of R-band (from ∼360 to ∼160 ADU).
41
CHAPTER 3. RESULTS
S0(high)
0.0
-1.5
-3.0
-6.0 -4.5 -3.0 -1.5 0.0 1.5
arcseconds
3.0
1.5
0.0
-1.5
-3.0
arcseconds
3.0
ADU
1.5
0.0
-1.5
-3.0
-6.0 -4.5 -3.0 -1.5 0.0 1.5
arcseconds
PL
6.0
4.5
arcseconds
3.0
40
36
32
28
24
20
16
12
8
4
0
%
1.5
0.0
-1.5
-3.0
60
50
40
30
20
10
0
10
-6.0 -4.5 -3.0 -1.5 0.0 1.5
arcseconds
6.0
1.50
4.5
1.35
1.20
3.0
1.05
1.5
0.90
0.0
0.75
-1.5
0.60
-3.0
-6.0 -4.5 -3.0 -1.5 0.0 1.5
arcseconds
0.45
ϕ0
6.0
160
140
120
100
80
60
40
20
4.5
arcseconds
4.5
-6.0 -4.5 -3.0 -1.5 0.0 1.5
arcseconds
IL
arcseconds
S2
6.0
8
16
24
32
40
48
56
log10(ADU)
1.5
8
0
4.5
ADU
log10(ADU)
arcseconds
3.0
6.0
3.0
1.5
degree
4.5
2.2
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
arcseconds
6.0
S1
0.0
-1.5
-3.0
-6.0 -4.5 -3.0 -1.5 0.0 1.5
arcseconds
Figure 3.8: HL Tau V-band S0, S1, S2, IL , PL and ϕ0 images. S0 shows a non-circular structure
that can be approximated with a thick C-shape. S1 and S2 shows no special structures, perhaps S1
hints that there is a polarization structure due to its distribution of positive and negative values.
The acceptance sharpness used is low and the degree of linear polarization is high (∼30%) but being
less luminous causes the noise to be higher, which is seen in PL and the ϕ0 . Just as in R-band the
scattering occurs at the walls of the outflow, and creates a centro-symmetric pattern.
42
3.1. RESULTS
In the next figure the pinpointing of the source in the V-band is shown. Just
as with the R-band data it shows a hourglass shape that pinpoints the central
source to the same approximate location. The possible location of the source is
shown by a circle with radius of 0.00 6 (84 AU, 0.2400 /pixel). Also the approximate
PA angle of the outflow is drawn with white lines. The angles of the lines are
at 40◦ and 55◦ , giving an estimate of the PA of the outflow equal to 47.5±7.5◦ .
Noteworthy is that both the R- and V-band images are aligned within 0.1 pixels
before pinpointing the source, this so that the pinpointing would be done in the
same image coordinates.
The average core polarization of HL Tau in the V-band is 14.8%.
6
5
4
arcseconds
3
2
1
0
-1
-2
-3
200 AU
-6
-5
-4
-3 -2 -1
arcseconds
0
1
2
Figure 3.9: HL Tau V-band pinpointing of central source and PA of outflow. The arrows are drawn
perpendicular to the polarization angle, and extra long. Due to the geometry of the scattering and
the outflow an hourglass-shaped structure like this is attained. The “waist” of this figure is where
the central source most likely resides. This is a way of pinpointing the source when viewing at
angles and wavelengths where it is heavily obscured. The circle marking the central source location
has a radius of 0.00 6 (84 AU, 0.2400 /pixel, binned). The angles of the lines are at 40◦ and 55◦ , giving
an estimate of the PA of the outflow equal to 47.5±7.5◦ . The acceptance sharpness was set to low.
The V-band vector plot below shows the same structure as in the R-band,
albeit with a lower confidence level due to the lower intensity. The arrows are
perpendicular to the scattering plane and shows the extent of the outflow region
where the light scatters. Roughly perpendicular to the outflow axis lies the disk.
In this region around the central source the vectors are more or less aligned. As
previously presented, this is commonly referred to as a polarization disk. The
V-band it is significantly weaker, but it still stands out from the random noise.
43
CHAPTER 3. RESULTS
6
5
4
arcseconds
3
2
1
0
-1
-2
-3
200 AU
-6
-5
-4
-3 -2 -1
arcseconds
0
1
2
Figure 3.10: HL Tau V-band vector plot. The direction of the arrows represents ϕ0 , length of
arrows - PL , contour IL and the corresponding levels are 8, 16, 24 and 32 (red to yellow). In this
image it is also easy to see that there is more noise present due to the lower luminosity at the filter
wavelength. The data have been binned (2 × 2) and the circle shows the previous pinpoint of the
central source with a radius of 0.00 6 (84 AU, 0.2400 /pixel). Although the lower significance level, the
classic and clear centrosymmetric polarization pattern can be seen and also the polarization disk at
the position of the source.
Combining R- and V-band
One question that is raised is whether the distance and angle from the source
where the scattering takes place is wavelength dependent. Usually the scattering
occurs deeper within the outflow wall for longer wavelengths, at least comparing near-IR wavelengths (Close et al., 1997). In the next figure a comparison
between R- and V-band relative intensity versus distance is shown. What is
seen is the mean normalised flux in a 5 and 17 pixel column centred around the
outflow axis, starting at the pinpoint circle going outwards along the outflow
axis. For the 5 pixel column, it seems as if the V-band scatters closer to the
source. Looking at the other figure, taking the mean of a wider column, 17
pixels, it looks as the flux is the same over all distances. This shows that light
in the R-band scatters deeper in the outflow walls, the intensity is spread out
wider in the R-band than in the V-band. Turning the argument around; the
light in the V-band scatters closer to the outflow axis.
44
3.1. RESULTS
R-band
V-band
0.8
0.6
0.4
0.2
0.00
5
10
R-band
V-band
1.0
relative flux (17 pixels)
relative flux (5 pixels)
1.0
15
20 25
pixels
30
35
40
0.8
0.6
0.4
0.2
0.00
5
10
15
20 25
pixels
30
35
40
Figure 3.11: The mean normalised polarized flux, IL /max(IL ) in a 4 and 16 pixel column respectively
as a function of distance from the position of the central source, outward along the 48◦ outflow for
both R- and V-band. Each data point is the mean of 5 and 17 pixels along a 2 pixels wide line
perpendicular to the outflow axis. In the V-band 5 pixel column mean the peak polarized flux
comes after 15 pixels while the peak in the R-band resides at 19. On the other hand this is not
present in the 17 pixel column mean. This difference between the two graphs can be interpreted as
a wavelength dependent scattering depth. Longer wavelengths scatter deeper in the outflow walls,
thereby creating an apparently wider outflow.
The average core polarization in the two filters where 12.1% for the R-band
and 14.8% for V-band, i.e. the core polarization is inversely proportional to the
wavelength. That is if the estimate of the location of the central source is good
within the diameter of 10 pixels (1.00 2, 178 AU). The rough inclination of the
polarization disk is ∼135◦ , i.e. ∼90◦ to the outflow axis.
3.1.3
Lucky astronomy
In this section the results of the part that involves lucky astronomy is presented.
The aim is to do a small evaluation of the usefulness of the technique to improve
image sharpness at the NOT. Since the XZ Tau binary is unresolved, it can be
used to analyse seeing and image quality. Most of the values presented are
derived by fitting a rotatable 2D Gaussian function to XZ Tau in each frame.
This way, a time evolution of the different parameters fitted can be analysed.
As previously briefly mentioned, speckle imaging was attempted, and the
routines were implemented in the code (see Appendix B), but the time and
spatial resolution were to low for it to work. The method of choosing the
strongest speckle as the most significant position of the star is a good method
when the time and spatial resolution is high enough, otherwise choosing the
centroid is more robust.
Image motion
Below is a figure of the image motion during the V-band observation. The
positions of the values represents the x and y positions of the fitted 2D Gaussian
in each frame. The circle shows the excursion limit of 4 pixels for the low,
medium and high scenarios, where images that have moved further away than
this limit is not used in the final shift and add routine, regardless of their
sharpness. As seen the image movement is highly random but is mostly confined
to within the circles border.
45
CHAPTER 3. RESULTS
10
5
0
5
10
1515
10
5
0
5
10
Figure 3.12: Image movement in the V band data, positions (x,y) of the fitted Gaussians. The
dashed circle shows the excursion limit, i.e. points outside of the circle are not included in the final
shifted and added images. The positions are mostly confined within the circle but moves very far
out, at times as far as ∼16 pixels (∼200 , pixelscale 0.00 12/pixel). A mechanical tip-tilt system will
manage to counteract this image movement.
Elongation
In the next figure, the elongation (σx /σy ) is shown, it has a empty stripe at
σx /σy ∼1. This could be due to the fact that the object used as reference is not
completely circular, but elliptical. Since XZ Tau is a binary and evidently a bit
elongated as shown in the previous sections this shows it is not optimum for
determining the image sharpness. Never the less, the mean of these values seem
to be roughly unity.
46
3.1. RESULTS
2.5
FWHP, arcsec
2.0
0◦
45 ◦
90 ◦
135 ◦
1.5
1.0
0.5
0
2000
4000
6000
8000
10000
Frames used (%)
12000
14000
Figure 3.13: The figure shows the elongation (σx /σy ) of the reference object, XZ Tau in all the
V-band frames as a function of time. Between the positions, no difference seems to be evident. The
curious aspect of the figure is that the values seems to avoid unity, that is the object never seems
to be a circle but allways an ellipse. This could be due to the unresolved (partially) binary causing
an elliptical shape, as shown in the S0 images of section 3.1.1 on page 34.
Sharpness improvement
To see how the image sharpness is improved with the different reduction scenarios described in the beginning of the chapter, a figure of the Full Width at
Half Power (FWHP) versus the percentage
of frames used is shown below. The
√
FWHP is calculated as FWHP = = 2 2 ln 2 σ̄ where σ̄ = (σx + σy )/2.
The first conclusion is that by just accounting for image motion, the sharpness improves around 0.00 1. By setting a frame selection criteria based on sharpness and centroid excursion the gain is ∼0.00 4 (the “high” scenario). These conclusions apply to the conditions during the night of observation and the site,
i.e. an acceptable seeing and the Observatorio del Roque de los Muchachos. A
normal seeing for the site is around 0.00 7, in which case the improvement of lucky
imaging could have been enough to resolve the XZ Tau binary (0.00 3). Depending on what information that is to be extracted from the final data, different
acceptance sharpness should be set. If broad structures and overall geometry is
to be studied a low acceptance sharpness should be used so that the low surface
brightness regions reach above the noise. Contrary to this, if attempting to resolve, say a binary or small but bright structures, a high acceptance sharpness
should be chosen. Comparing the different filters, the sharpness in the V-band
is approximately 0.00 1 systematically sharper for almost all scenarios.
47
FWHP, arcsec
CHAPTER 3. RESULTS
1.10
1.05
1.00
0.95
0.90
0.85
0.80
0.75
0.70
0.65
0.60
0.55
0◦
45 ◦
90 ◦
135 ◦
0
10
20
30
40 50 60
Frames used (%)
70
80
90
100
Figure 3.14: FWHP in arcseconds versus the percentage of frames used. The circles are the V-band
and the stars the R-band, while the marker colour is the same as in the legend for all filters. See
table 3.1 for details about the acceptance sharpness for the different scenarios. Only shifting and
adding increases the sharpness with 0.00 1 while applying a frame selection criteria it can improve as
much as 0.00 4. From right to left; uppermost values are the Normal, below them lies Zero, to the left
Low, then Medium and lastly High scenario.
The next image shows histograms of the sharpness in both of the filters. The
scale on the x- and y-axis is the same for both figures. Around 10% have values
higher then 1.00 5 in both filters. The sharpness for the V-band is significantly
better, as also shown in previous figure.
R-band
0
1
2
3
FWHP, arcsec
V-band
4
5
5000
4500
4000
3500
3000
2500
2000
1500
1000
500
0
0
1
2
3
FWHP, arcsec
4
5
Figure 3.15: Histograms showing the sharpness/seeing, full width at half power (in arcseconds)
for all exposures in R- and V-band. The V-band histogram shows more sharper images, which
dominates the seeing as seen in previous figure, but it also has a few more with worse sharpness.
The tail towards low sharpness shows that alot of the images in the data have low sharpness.
48
3.2. SUMMARY OF RESULTS
3.2 Summary of results
3.2.1
HL Tau
HL Tau is a embedded source where the radiation detected at these wavelengths
is scattered light from the envelope mainly in the outflow where the optical depth
is lower. The mean intensity (S0) shows this nebulosity, and also a C-shaped
structure. The degree of polarization in the outflow is high, around 30%. The
polarization angle vector plot shows clear structures with vectors forming an
arc around the central source where the outflow is, the pattern is said to be
centrosymmetric.
Since the central source is completely obscured at these wavelengths, there
was an attempt at pinpointing the central source. This is realised through the
fact that the polarization angle is perpendicular to the scattering plane, and
by drawing lines long the scattering plane the central source was pinpointed
within a 0.00 6 radius. This endeavour also produced an estimate of the PA of
the outflow to about 47.5±7.5◦ . The absent counter-jet and receding lobe,
observed by others at Near-IR filter bands, indicates that the envelope/disk
blocks radiation at these wavelengths.
What also is seen is a polarization disk, that extends roughly perpendicular
to the outflow axis (∼135◦ ) and through the pinpointed source.
The core polarization increases from 12.1% in the R-band to 14.8% in the
V-band. The intensity is approximately half in the V-band in comparison to
the R-band. An investigation of the flux versus width of the outflow concluded
that the radiation in the R-band scatters deeper within the outflow walls, and
the intensity is spread out wider in the images than in the V-band.
3.2.2
XZ Tau
The mean intensity, S0 shows a (partially) unresolved binary system with its
elliptic shape. The polarized intensity (IL ) also shows this elliptical shape. It
also shows scattering in a spherical manner a bit away from the central source,
although it is hard to interpret due to the low degree of polarization. The
polarization pattern in the most central regions show aligned vectors with low
(<2%) degree of polarization. The intensity in the V-band is less than half of
that in the R-band, this is the most significant difference between the filters.
3.2.3
Parameters vs sharpness/psf improvement
Most frames does not shift above the excursion limit. The elongation of the
image is attributed to that the measurements were done on a binary system,
although not resolved it has an elongated structure that would tend to increase
the uncertainty in measuring the sharpness (FWHP) of the image. With this
in mind the sharpness improvement is significant, by just shifting images 0.00 1 in
sharpness can be gained. Going further and selecting images with high sharpness
one can gain as much as 0.00 4; by selecting the ∼1% of all the frames that are
the sharpest. The low number of frames used for images with high sharpness
affects the sensitivity of the image. Hence, depending on what information
that is to be extracted different selection criteria should be applied. Broad
nebulous structures and overall shapes suggests a low sharpness criteria, causing
49
CHAPTER 3. RESULTS
much of the images to be used, causing the low surface brightness regions to
reach above the noise limit. On the contrary, resolving a binary only a high
sharpness criteria can give the resolution necessary. Around 10% of the images
have a sharpness (FWHP) greater than 1.00 5, which is very bad. With better
site/weather conditions, a higher overall sharpness would have been achieved.
Comparing the filters, we see that the V-band sharpness is about 0.00 1 higher.
50
4
“All truths are easy to understand
once they are discovered; the point
is to discover them.”
Galileo Galilei
Discussion
4.1 Discussion
4.1.1
HL Tau
The mean intensity image, S0 shows the nebulous region around HL Tau, the
intensity extends far out (∼3.00 6, 500 AU) and is wide (∼2.00 4, 340 AU) from the
central source. Stellar light escapes the dense and dusty flared disk/envelope
along the upper cavity cleared by the jet, light is then scattered in the cavity
walls, toward the observer. In figure 4.2 below an illustration of the scenario is
shown. This reflection nebula is what is seen in the S0 image and it is responsible
for the observed large degree of polarization (∼30%).
Interestingly, both R- and V-band shows a C-shaped structure with an ∼1.00 1
(∼154 AU) extension. Close et al. (1997) and Murakawa et al. (2008) both show
that this structure is prominent at J and H band, but at longer wavelengths the
central object is more visible and the feature is harder to distinct. In the optical
HST images of HL Tau by Stapelfeldt et al. (1995) show the C-shaped structure
with high resolution. A figure from that article is shown below together with
this thesis S0 contours. As seen the pinpointing is OK, the VLA source marked
with a plus sign in the data from Stapelfeldt et al. (1995) is at the norteastern
edge of the pinpointed circle.
4
arcseconds
2
0
-2
-4
-2
arcseconds
0
Figure 4.1: HST FW555 figure from Stapelfeldt et al. (1995) and S0 contours from the results of
this thesis. The C-shape is seen in both figures and the location of the central source is not at the
same position. Although the positioning in this thesis is OK.
51
CHAPTER 4. DISCUSSION
The origin of this C-shape in the outflow is unknown, the polarized intensity
seems to be higher in the part of the C that is further away from the source (in
the northeast). Stapelfeldt et al. (1995) argue that the shape could be produced
by either the distribution of absorbing material, causing lower intensity in the
centre of the C-shape, or the distribution of reflecting material causing light
hitting the ridge of the C-shape to be reflected stronger. The absorbing material
could be a foreground clump in the circumstellar envelope that would superpose
a dark blot on the otherwise classical cometary nebula. The high-resolution
data from Murakawa et al. (2008) show this C-shape in their intensity maps
with higher intensity approximately along the C-shaped ridge. The cause of
the C-shape is probably complex, owing to the orientation of the system and
the scattering geometry in combination with higher density cloud components
in the envelope. Further multi-wavelength high-resolution investigations could
shed some light on the dark spot creating the C-shape in this outflow.
A bipolar nebula seen approximately edge-on show a centrosymmetric polarization vector pattern in the lobes and a polarization disk in the equatorial plane
where the disk resides, as shown by both observations (e.g. Lucas and Roche,
1997; Perrin et al., 2004; Beckford et al., 2008) and computational modelling
(e.g. Bastien and Menard, 1988; Whitney B. A. and Wolff M. J., 2002). The
resulting model consists of a flared disk and an infalling envelope accompanied
with a jet/outflow (e.g. Fischer et al., 1994).
With this in mind we turn our focus on to the results in this thesis. The
centrosymmetric polarization pattern shows that at least one of the lobes of
the outflow is visible. The pattern is roughly perpendicular to the observed
optical jet reported by several authors (Mundt et al., 1990; Rodriguez et al.,
1994; Anglada et al., 2007). The absence of a bipolar structure in the images
suggests that the opacity in the south-western lobe is high enough for the light
to be completely extinct, the extinction in the cloud is AV ≈ 24−30 mag (Monin
et al., 1989; Beckwith and Birk, 1995; Close et al., 1997). This can be explained
by a system where the north-eastern outflow axis is tilted towards the observer
(Hayashi et al., 1993; Mundy et al., 1996).
At the possible location of the central source extending roughly perpendicular to the outflow axis a polarization disk is seen in both R- and V-band
polarization vector fields. The alignment of polarization vectors along the disk
location can be produced by multiple scattering and the illusory disk arising
from limited spatial resolution (Lucas and Roche, 1998).
The figure showing the normalised polarized intensity versus distance from
source and filter, figure 3.11 on page 45 show that the R-band scatters deeper
in to the disk wall than the V-band. R-band is steadily rising about 0.1 points
above V-band in both figures and since the outflow is inclined towards us, it is
natural that the intensity will be higher closer to the source in the image plane
in the R-band. Also the sum of the small stripe (5 pixels) causes the V-band
to reach its maximum value earlier than the R-band for the same width, but in
the wide stripe, they reach the maximum at the same, this also points to the
fact that the R-band polarized intensity is wider along the outflow axis than
the V-band which is confirmed in the J, H and K band by Close et al. (1997).
The high extinction together with the youth of the star causes the R-band
flux to be roughly twice that of the V-band.
Knowing where the star is in relation to all the detected structures, that
have their origin in the central source, is obviously important. Since the central
52
4.1. DISCUSSION
Figure 4.2: An illustration of the structure of the protostar HL Tau. The inclination of the outflow
is 60◦ towards the observer. The envelope is thick, with a centrally peaked density distribution
and evacuated bipolar cavities. Light emanating from the protostar scatter of the cavity walls and
escape the envelope through the optically thin regions as shown by the solid lines. The stellar light
is extinct in the envelope, and only longer wavelength photons (near-IR) can penetrate through the
envelope and reach the observer. The figure was inspired by a similar in Whitney et al. (1997).
star starts to become visible in the H, perhaps K band it is not seen in any
of the data. Since the data lacks accurate coordinates and enough objects to
register the images there is no way of knowing. A simple approach was made
to position the central source. By drawing extra long polarization vectors with
a 90◦ shift a position was deduced, other more sophisticated methods exists,
e.g. Murakawa et al. (2005), but the lack of bipolar structure in the data causes
the pinpointing carried out here to be the best way. The lack of error analysis
causes the results to be a bit doubtful, just by adopting an polarization angle
error of about 5∼10◦ causes a rather large error. Assuming the pinpointing here
is roughly correct, we see that the extinction is indeed very high, there is no
sign of the source in the data. The dense disk/envelope covers the young star
so that the only signpost for it is the scattering of its light in the outflow.
In positioning a rough location of the source, the PA of the outflow was
derived (∼47.5±7.5◦ ). In comparison to other measurements of this; e.g. the
jet - Mundt et al. (1990) 48.5◦ and Anglada et al. (2007) ∼45◦ it stands rather
good. Thus the jet coincides with the outflow as expected.
The core polarization decreases with wavelength, from ∼14.8% in the V-band
to ∼12.1% in the R-band. The dependence on wavelength can give information
about the scattering and absorption mechanisms. Beckford et al. (2008) investigated the wavelength dependence in the near-IR of 10 class I, 7 class II and
1 class II sources and came to the same conclusion of wavelength dependence.
If dichroism is the mechanism responsible for the polarization this is expected.
53
CHAPTER 4. DISCUSSION
Although there are a couple of possible scenarios where scattering can produce
the same dependence, one is if the unresolved underlying scattering polarization
averages to the observed polarization (Whitney et al., 1997). The polarization
could be attributed to multiple scattering, and this would produce the observed
pattern (Lucas and Roche, 1998). At shorter wavelengths the Rayleigh limit
(wavelengthgrain size) is reached and scattering becomes more efficient.
4.1.2
XZ Tau
The binary in XZ Tau was not resolved, but the parts of highest intensity in
the S0 image show an elongated structure in a southeast to nortwest direction.
Which is the direction that the two stars line up at (Haas et al., 1990; Hioki
et al., 2009). The polarized intensity shows the same structure and it shows
that even though the binary is not resolved, with further observations using one
of the barlow lenses and perhaps a higher temporal resolution the binary can
be resolved.
In S1 and S2 the faint butterfly structure could indicate a spherical region
where scattering of starlight occurs. This is probably just scattering in the
foreground cloud that is detected, just as with the polarization in the core
region, where IL is strongest. As shown by Krist et al. (1999) there are bubbles
of gas/dust to the northeast and southwest of the system, which then could
scatter light into the observer’s direction. The degree of polarization in the core
region is low, <2% which is close to the cloud polarization of 1.6% reported by
Vrba et al. (1976). Thus, what is seen is aligned grains in the surrounding cloud
that causes dichroic extinction, which explains the low degree of polarization.
4.1.3
Other
The lack of error analysis is a flaw when looking at structures that only are a
few standard deviations above the noise. For examples of how the error analysis
could have been done see Sparks and Axon (1999); Murakawa et al. (2004, 2005).
The axial ratio of the guide star/reference star is not unity, instead it is
fluctuating without really equalling one. This can be interpreted as that the
object is elliptical to the shape, or perhaps it is observed as that because of
aberrations in the light path. Being a unresolved binary it is natural that the
object should be elongated, but since this is the case here it is not optimal to
measure sharpness variations on a object like that.
The gain in lucky astronomy is clearly evident, tip/tilt corrections in this
data increases sharpness with 0.00 1 and using frame selection up to 0.00 4.
The systematically 0.00 1 sharper V-band images in the different scenarios is
opposite to normal seeing conditions. Usually the longer wavelength filters have
higher sharpness. The fact that the R-band dataset is smaller than the Vband (77 cycles R, 100 in V) and the fluctuating weather conditions could cause
the discrepancy between the measured values and the expected. The weather
conditions indeed seems to worsen during the R-band run when looking at the
weather graphs on page 25.
54
4.2. SUMMARY
4.2 Summary
Optical polarimetry of HL Tau show a centrosymmetric pattern, indicating scattering of light by dust around a protostar. The dust grains resides in the outflow,
the evacuated out less denser part of the circumstellar cloud. Because the opacity is lower in the cleared cavity of the outflow the scattered photons escape
the envelope and reach the observer with relatively high degree of polarization,
∼30% for both R- and V-band.
The outflow of HL Tau show a structure in the intensity that can be described by a “C”, the origin of this shape is unknown but several theories exists.
The outflow has a approximate PA of 48.5±7.5◦ coinciding with the previously
detected jet. A polarization disk is observed which is probably produced by
multiple scattering and the illusory disk arising from limited spatial resolution.
The core polarization has a wavelength dependence, decreasing with wavelength, but the exact mechanism producing this is unknown.
The apparent width of the outflow in HL Tau changes with wavelength,
longer wavelengths scatters deeper into the cavity walls thus creating a wider
intensity map.
Although the XZ Tau binary is not resolved, an elliptical shape extending
in the same direction as the known binary is seen. The polarization that is
detected is the polarization of the surrounding cloud (<2%).
The gain in sharpness is 0.00 1 for tip/tilt corrections and up to 0.00 4 when also
using frame selection. The gain is applicable to the same observation site and
conditions. Lucky astronomy is a powerful tool, combining it with polarimetry
shows promising results.
55
List of Figures
1.1
PACS and SPIRE image of a star forming region . . . . . . . . .
3
1.2
Protostellar outflow - HH111 - the structure of a protostar . . . .
6
1.3
Six protostars showing the structure of a protostellar disk . . . .
7
1.4
L1551 of the Taurus-Auriga star forming cloud in S II . . . . . .
10
1.5
Polarization ellipse showing the Stokes parameters . . . . . . . .
12
1.6
Scattering of light by dust particle, geometry . . . . . . . . . . .
14
1.7
Sequential raw images from observation run illustrating speckle
patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
2.1
Andor iXon+ 897, quantum efficiency (QE) versus wavelength
.
22
2.2
The PolCor instrument layout and light path . . . . . . . . . . .
24
2.3
Atmospheric conditions 27th-28th October 2008 . . . . . . . . . .
25
2.4
Typical V-band dark frame and pixel distribution . . . . . . . . .
28
2.5
Sharpness boxes for moment of flux and histogram of sharpness .
30
2.6
Sharpness boxes for strongest speckle centre and histogram of
sharpness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
◦
30
2.7
0 final image. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
2.8
Polarization calibration . . . . . . . . . . . . . . . . . . . . . . .
32
3.1
XZ Tau R-band S0, S1, S2, IL , PL and ϕ0 . . . . . . . . . . . . .
35
3.2
XZ Tau - R-band vector plot . . . . . . . . . . . . . . . . . . . .
36
3.3
XZ Tau V-band S0, S1, S2, IL , PL and ϕ0 . . . . . . . . . . . . .
37
3.4
XZ Tau - V-band vector plot . . . . . . . . . . . . . . . . . . . .
38
3.5
HL Tau R-band S0, S1, S2, IL , PL and ϕ0 images . . . . . . . . .
39
3.6
HL Tau - R-band pinpointing the central object . . . . . . . . . .
40
3.7
HL Tau - R-band vector plot . . . . . . . . . . . . . . . . . . . .
41
3.8
HL Tau V-band S0, S1, S2, IL , PL and ϕ0 images . . . . . . . . .
42
3.9
HL Tau - V-band pinpointing the central object . . . . . . . . . .
43
3.10 HL Tau - V-band vector plot . . . . . . . . . . . . . . . . . . . .
44
3.11 Polarized flux versus distance from source . . . . . . . . . . . . .
45
3.12 Image movement in the V band data . . . . . . . . . . . . . . . .
46
3.13 Elongation of the reference object (XZ Tau) in all V-band frames
versus time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
47
3.14 FWHP versus percentage of frames used . . . . . . . . . . . . . .
48
3.15 Histogram of the FWHP, i.e. the sharpness/seeing R- and V-band 48
57
LIST OF FIGURES
4.1
4.2
58
Comparison of shapes and intensity of HL Tau between this thesis and Stapelfeldt et al. (1995) . . . . . . . . . . . . . . . . . . .
51
Illustration of HL Tau structure . . . . . . . . . . . . . . . . . . .
53
List of Tables
2.1
CCD detector characteristics . . . . . . . . . . . . . . . . . . . .
23
2.2
Observational log . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
2.3
Polarimetry calibration . . . . . . . . . . . . . . . . . . . . . . . .
32
3.1
The acceptance sharpness values . . . . . . . . . . . . . . . . . .
34
59
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68
Appendix
A. Data with three valid angles observed
Removing one of the detected intensities for an angle of the analyser (equations
1.5 to 1.8) we end up with
I 0 (0◦ ) = I0 (1 + PL cos 2ϕ0 )
A1.1 I 0 (45◦ ) = I0 (1 + PL sin 2ϕ0 )
A1.2
I 0 (90◦ ) = I0 (1 − PL cos 2ϕ0 ) .
A1.3
Now we have a system of three unknown and three equations. To solve this we
first take equation A1.1 and add A1.3
I0 =
I 0 (0◦ ) + I 0 (90◦ )
.
2
A1.4 This is the mean intensity, then we take equation A1.1 and solve for PL
PL =
I 0 (0)/I0 − 1
cos 2ϕ0
A1.5 For the polarization angle we take equation A1.1 and add A1.2
I 0 (0) + I 0 (45)
= 2 + PL cos 2ϕ0 + PL sin 2ϕ0
I0
Now inserting equation A1.5 we get
0
0
I (0)
I (0)
I 0 (0) + I 0 (45)
=2+
−1 +
− 1 tan 2ϕ0
I0
I0
I0
0
I (45)
/I0 − 1
tan 2ϕ0 = I 0 (0)
/I0 − 1
0
I (45) − I0
1
ϕ0 = arctan
2
I 0 (0) − I0
A1.6 Which is the last equation we need.
69
B. PYTHON CODE DESCRIPTION
B. Python code description
B.1 Introduction
Here is a description of the Python code that was written for the reduction
of PolCor data. Python was also used to analyse the final data and produce
all the graphs in the thesis. First there is a description of the help functions,
functions that were used in conjunction to the main class with its methods. A
short description of both the help functions and the main class with its methods
is covered in the coming to sections. Lastly a short example of how the PolCor
python module can be used. The code produced is not finished, for example
it does not have a method for handling flat field data since there was not such
data, which would be very simple to implement if needed in the future.
B.2 Help Functions
lsFiles(arg0, arg1)
Takes as input a file extension to search for and returns all the files in the
specified path containing this file extension. arg0 is the path and arg1 is
the file extension.
display(f, fsize, image, **kwargs)
Function that displays image into figure number f, with figure size fsize as
a tuple. Additional keyword arguments are; csor=0/1 - if the cursor should
be marked with a cross, title=’string’ - title of plot, xlabel=’string’
- x label and ylabel=’string’ - y label.
getCursor(*args)
Gets the cursor position at click for an arbitrary number of characteristic
strings as input, e.g. getCursor(’star’,’sky’) will first ask user to click
on star then on sky and subsequently return two positions.
saveatbl(filename, dataList, names)
Saves a list of data arrays (dataList) in to a table with the column names
(names) as an ASCII file with name filename (can include path as well).
loadatbl(filename)
Loads a list of data arrays in filename, returns a array of the data (loads arrays saved with the savetable command). An example, a = loadtable(filename)
and then a[:,0] for first column, a[:,1] for second and so on.
infoatbl(filename)
Returns the lines with comments (i.e. the column names) from an *.atbl
file.
phot(frame, boxside,R=0,R1=0,R2=0)
Asks for cursor input from user and calculates aperture photometry on a
centroid at the cursor position, with the radius R, R1 and R2 representing
the inner annulus (star) outer radius, outer annulus (sky) inner radius and
outer annulus outer radius. It calculates the flux as
F = Caperture − naperture
Cannulus
nannulus
where C denotes the sum of pixel values within the corresponding annulus
70
APPENDIX
and n the number of pixels within it, from Berry (2005, p.277)1 .
imstat(cube, skycube)
Returns simple image statistics on a two cubes of images, on with a star
in it and the other a sky-area. The statistics that are determined are median, average, standard deviation, simple photometry (only on star frame;
removes median sky and sums all pixels in frame).
gaussphot(cube, skycube)
Subtracts the median of the corresponding skyframe from the skycube and
fits a rotatable, elliptical gaussian to each of the frames in the cube. Returns
height, amplitude, x, y, widthx , widthy and rotation angle of every frame
as lists.
sig2fwhp(sig1=0, sig2=0, scale=0.12)
Calculates the FWHP, supply the sigma(s) (gaussian width(s) in pixels) and
the plate scale (arcsec/pixel), it returns the FWHP (arcsec)for
the given
√
plate scale in arcsec/pxls. Calculated as FWHP = = 2 2 ln 2 σ̄ where the
σ̄ is the mean sigma when two is supplied.
load_CBinary(file, shape=0)
Loads a binary file saved in C, in some cases the shape has to be supplied
for it to load correctly.
B.3 Classes, Attributes and Methods
The main class is named Data it has several attributes and methods that does a
particular thing with the data, and in the end the final shift and added images
are saved and returned.
class Data
A class that defines data from the PolCor instrument, when initiated the main
path to the data have to be supplied; the directory where all data from the
different polarization angles are stored, i.e. one path per object. In addition to
this the names of the folders where the different polarization angles are stored
and if the shift is to be on a sub-pixel level have to be supplied. An example
would be
PATH=’/path/to/data’
FOLDERS = (’Dark’,’pos0’, ’pos45’,’pos90’,’pos135’)
obsNov08 = Data(PATH, FOLDERS, sbpxl=False)
The methods that are avaliable are (except the initiator and _str_ method):
calcDark, readIn, getBoxes, getCenterOfFlux, getStrongestSpeckle, getSharpness and shiftAndAdd. Before any of the methods can be used the data has to
be initiated as the example above.
calcDark(darkframename, avgdarkname)
Reads in all the dark frames and calculates the average dark for each cycle
and over all cycles, then saves the files as darkframename and avgdarkname.
Example: obsNov08.calcDark(’mdark.fits’, ’avgdark.fits’).
readIn(polangle, n)
Read in images from n cycles and return the average image of them, polangle
refer to from what data the images should be read in from, 0=0◦ , 1=45◦ ,
2=90◦ , 3=135◦ . Example: data_to_display = obsNov08.readIn(0, 3).
1 The
equation given in Berry (2005) has a typo, instead of Cannulus it says Caperture .
71
B. PYTHON CODE DESCRIPTION
getBoxes(starpos, skypos, boxside, skyboxside, polangle)
Cuts out boxes from the data at the guidestar position and a sky patch position given. Retrieves boxes of size boxsize x boxsize, and the same for
skyboxside around the given positions starpos=[x,y] and skypos=[x,y]
for the given polangle (defined as above). This way the memory imprint
is low, ∼240 MiB each (3000*50*50*32/1e6) for a boxside of around 50
pixels and 32-bit floating point precision. Example: starcube, skycube
= obsNov08.getBoxes([194,177], [200,300], 50, 90, 0).
getMaxSpeckle(starcube)
Returns the position of the speckle with the maximum intensity in all the
frames of the cube. Example: centers = obsNov08.getMaxSpeckle(starcube).
getMoments(starcube)
Calculates moments of flux (centroid) for each frame in input starcube.
Example: centers = obsNov08.getMoments(starcube).
getSharpness(starcube, big, small, centers)
Returns the fraction of flux in a box with side small divided by the
flux in a box of side big, both centred around the given center. This
is done for each frame in the cube that is supplied. Example: sharpness
= obsNov08.getSharpness(starcube, 20, 6, centers).
shiftAdd(darkfile, flatfile, sharpness, accept_sharp, excursion, deltacent,
polangle, starpos, method)
Applies the dark frame, the flat field frame, shifts and adds images with acceptance sharpness higher than accept_sharp and within sqrt(excursion)
pixels. sharpness is the array with the calculated sharpness of all frames,
darkfile is a path to the dark frame (.fits), flatfile the flat field frame.
deltacent is the excursion from the median position that each frame have,
method describes the method of determining the center (‘speckle’ or ‘moments’) and the rest is defined as before. Returns the final frame for that
polarization angle, number of files used, total number of frames available
and exactly which frames that were used.
Example: final_data,nfiles,ntot,frameindices = obsNov08.shiftAdd(darkfile,
sharpness, 30, 16, deltacent, 0, [194,177], ’moments’).
B.4 Example Usage
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
# importing module
from polcordata import *
# initiating data
FOLDERS = (’Dark’,’pos0’, ’pos45’,’pos90’,’pos135’)
obsNov08 = Data(PATH, FOLDERS, subpixelshift)
# calculating dark frame
DARKFILE = ’mdark.fits’; AVGDARKFILE = ’avgmdark.fits’
mdark, avgmdark = obsNov08.calcDark(DARKFILE, AVGDARKFILE)
# getting guide star and sky positions
preview = obsNov08.readIn(polangle,3)
display(0,(6,6),preview,csor=1)
xystar, xysky = getCursor(’GUIDESTAR’,’SKY’)
# rounding off to integers
xstar = []; ystar = []
xstar, ystar = (array(xystar[0])-0.49).round().astype(’int’)
xsky, ysky = (array(xysky[0])-0.49).round().astype(’int’)
# reading in the data, cutting out boxes
starcube_noskysub, skycube = obsNov08.getBoxes([xstar, ystar], [xsky, ysky], cubesize, skyboxsize
, polangle)
# subtracting sky
for i in xrange(starcube_noskysub.shape[0]):
starcube[i] = starcube_noskysub[i] - median(skycube[i])
72
APPENDIX
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
# calculating and saving statistics
stats, stats30 = imstat(starcube_noskysub, skycube)
filename = str(FOLDERS[polangle+1]) +’_stats.atbl’
saveatbl(PATH+filename, stats, [’sum’, ’std’, ’mean’, ’med’, ’max’, ’skymed’])
filename = str(FOLDERS[polangle+1]) +’_stats30.atbl’
saveatbl(PATH+filename, stats30, [’sum’, ’std’, ’mean’, ’med’, ’skymed’])
# fitting a gaussian to all frames and saving the statistics
statsgauss = gaussphot(starcube_noskysub, skycube)
filename = str(FOLDERS[polangle+1]) +’_statsgauss.atbl’
saveatbl(PATH+filename, statsgauss, [’height’, ’amplitude’, ’X’, ’Y’, ’dX’, ’dY’, ’ROT’])
# calculating the centroid (moment of flux) for each frame
moments_centers = []; moments_deltacent = []; moments_median_center = []
moments_centers, moments_deltacent, moments_median_center = obsNov08.getMoments(starcube)
# correcting the star coordinates to the new ‘best’ position
xstar, ystar = [xstar, ystar] + median_center - cubesize/2
# calculating the sharpness of every frame, and saving the values
bigbox = 20; smallbox= 6; sharpness = []
sharpness = obsNov08.getSharpness(starcube, bigbox, smallbox, centers)
sharpness = (sharpness*100).round()
filename = str(FOLDERS[polangle+1]) +’_’+method+’_sharpness.atbl’
saveatbl(PATH+filename, [sharpness], [’sharpness’])
# shifting and adding. accept_sharp, excursion and method not defined here
final, used, ntot, f_index = obsNov08.shiftAdd(DARKFILE, sharpness, accept_sharp_values[i], excursion[i], deltacent, polangle, starpos, method)
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