Download The evolution of Supernova 1987A probed by Hubble Space

The evolution of Supernova 1987A probed by Hubble
Space Telescope observations in the narrow F502N
filter
Author:
Camilla Kihlström (920207-0323)
[email protected]
Department of Physics
KTH Royal Institute of Technology
Supervisor: Josefin Larsson
February 26, 2016
Typeset in LATEX
ISRN KTH/FYS/– – 16:08 – – SE
ISSN 0280-316X
TRITA-FYS 2016:08 ©Camilla Kihlström, 2016
Abstract
Supernova 1987A is the closest supernova in the era of modern telescopes, which makes it
possible to study its evolution in great detail. In this thesis several different aspects of SN
1987A were studied using Hubble Space Telescope observations in the F502N filter, which
is produced by an [O III] line for the equatorial ring around SN 1987A and by Fe I lines
for the ejecta at the center of this ring. To ensure accurate results from the measurements
a thorough data reduction was performed. Flux measurements were performed for the
ring, regions outside the ring, as well as the ejecta. The morphology of all three parts
were examined as well.
The measurements show that the ring flux for the [O III] line has its peak earlier
than for the R and B bands due to recombination of the shocked gas. They also show
that ground based observations tend to underestimate the ring flux more with time and
that there are no measurable traces of faint light outside the ring. The ejecta is visible
due to broad iron peaks overlapping the narrow wavelength interval of the F502N filter.
Though the ring provides an elevated background, through scattered light, the increase
in the flux from the ejecta is a real effect, caused by X-rays from the collision between
the shock wave from the supernova explosion and the ring.
Contents
Introduction
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Author’s Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1 Supernovae
1.1 What is a SN? . . . . . . . . . .
1.2 Formation of core collapse SNe
1.3 Radioactive elements in SNe . .
1.4 SN remnants . . . . . . . . . .
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2 Supernova SN 1987A
2.1 Rings around SN 1987A . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 The ejecta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Emission in the F502N filter . . . . . . . . . . . . . . . . . . . . . . . . .
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3 Telescopes
3.1 Hubble Space Telescope, HST . . . . . . . . . . . .
3.1.1 Wide Field Planetary Camera 2, WFPC2 . .
3.1.2 Advanced Camera for Surveys, ACS . . . . .
3.1.3 Wide Field Camera 3, WFC3 . . . . . . . .
3.2 Very Large Telescope, VLT . . . . . . . . . . . . . .
3.2.1 Ultraviolet and Visual Echelle Spectrograph,
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UVES
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4 Observations
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5 Data reduction
5.1 The drizzling process . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Resulting images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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6 Light curve of the ring
6.1 Background measurements . . . . . . . . . . .
6.2 Light curve from elliptical aperture . . . . . .
6.3 Light curve from UVES slit . . . . . . . . . .
6.4 Corrections for the use of different cameras . .
6.5 Loss of CTE in the 2009 WFPC2 observation
6.6 Error analysis . . . . . . . . . . . . . . . . . .
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6.7
Comparison to other measurements
6.7.1 The R and B bands . . . . .
6.7.2 The [O III] line from UVES
6.7.3 Effects of seeing . . . . . . .
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7 Morphology of the ring and search for emission outside
7.1 Photometry of the outer regions . . . . . . . . . . . . . . . . . . . . . . .
7.2 Model of the ring around SN 1987A . . . . . . . . . . . . . . . . . . . . .
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8 Photometry of the ejecta
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9 Discussion
9.1 Morphology and light curve of the ring . . . . . . . . . . . . . . . . . . .
9.2 Regions outside the ring . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.3 Light curve of the ejecta . . . . . . . . . . . . . . . . . . . . . . . . . . .
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10 Conclusions
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11 Acknowledgments
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List of figures
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List of tables
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Bibliography
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Introduction
Introduction
Mankind has always been fascinated by objects in the night sky; the moon, stars, and
temporary bright objects that appear out of nowhere and vanish without a trace have
been the source of many myths and stories throughout history. As early as 185 AD
Chinese astronomers made notes of a ”guest star” that was visible for eight months.
This is the first known observation of a supernova.
Historical descriptions of supernovae are rare, and before the beginning of the 20th
century only a few different supernova events have been recorded. Even though supernova
explosions are among the most energetic events in the universe the vast distances means
few are visible to the naked eye on Earth. The invention and development of telescopes
have been crucial for our understanding of these events and most models and theories
regarding supernovae have been introduced during the past decades.
One particularly interesting supernova is SN 1987A. This is the closest one in the era
of modern telescopes, which makes it possible to study it in great detail. Since its first
appearance in early 1987 it has baffled astronomers all over the world and lead to many
new insights about supernovae, but it still holds secrets that remain to be uncovered.
In this thesis the evolution of SN 1987A has been studied using observations performed by the Hubble Space Telescope (HST) in the narrow F502N filter, which has not
previously been done. This probes the [O III] emission from the surrounding ring of gas
and Fe I emission from the ejecta. The main objective was to confirm the evolution of
the ring as observed at other wavelengths, and use the light curve of the ring as a way to
calibrate some ground-based measurements. In addition studies of emission outside the
ring and the ejecta were also carried out. By studying light outside the ring the idea was
to find out more about the progenitor star, and studying the ejecta is an important way
to learn more about the energy source of the emitted light.
Outline of the Thesis
This thesis first gives a theoretical background to the subject by describing supernovae
in general, and SN 1987A in particular, as well as providing information about the telescopes used for the observations. After a brief summary of the observations an extensive
description of the data reduction follows. The next chapters describe the performed measurements and present the obtained results. Finally there is a discussion of the results
and their importance, which leads to the conclusions in the end.
3
Author’s Contribution
The first part of my work consisted of performing the data reductions, such as improving
the image quality and aligning all the observations, needed to facilitate the measurements
I was going to make. After that I measured the light from the ring around SN 1987A
(in two different apertures), light from regions outside the ring, and light from the ejecta
inside the ring. All these measurements were compared with measurements at different
wavelength intervals or measurements from a different telescope. For some of these
measurements and comparisons additional effects had to be accounted for, so I also
reduced the spatial resolution as well as made a model of the ring to study how the
bright light from it affected the outer regions and the ejecta.
I did all the data reduction and analysis myself. For the measurements in the F502N
filter I was provided with python scripts, which I had to modify to make them better
suited for my data. For the Very Large Telescope (VLT) measurements I was provided
spectra for all epochs, but I had to make the measurements myself. All the results of
the R and B band measurements were given to me so I could make comparisons with my
measurements in the F502N filter.
4
Chapter 1
Supernovae
1.1
What is a SN?
A supernova, SN, is very bright stellar explosion that ejects a star’s material at high
velocities. Since these explosions are so energetic they are able to create heavier elements
than can be obtained from the fusion inside stars.
Supernovae are divided into groups based on the absorption lines in their spectra,
where the two main groups, Type I and Type II, are separated by the existence of
hydrogen lines (absent for Type I, present for type II). The subgroups of Type I are
classified as follows; Ia shows a strong silicon line, Ib shows helium lines, and Ic does
not show helium lines. The subgroups of Type II are divided based on the shape of the
light curve or the spectrum, where the IIP light curve has a plateau, the IIL light curve
has a linear decline, and IIn has narrow lines in the spectra. There are also some SNe
that cannot be assigned either of these types, such SNe are then labeled as ”peculiar”.
Figure 1.1 shows some examples of spectra and the typical shape of the light curves for
the different types of SNe.
(b) Light curves
(a) Spectra
Figure 1.1: Examples of the spectra [1] and light curve [2] of different types of SNe.
5
All types of SNe, except Ia, are core-collapse events that occur when the progenitor
star has used up all of its fuel and acquired an iron core. Since iron cannot be fused
to produce energy the outward radiation pressure will no longer balance the inward
gravitational pull, and as a result the core will collapse. Type Ia on the other hand are
thermonuclear SNe caused by an exploding white dwarf that has reached the upper mass
limit for stability.
All SNe are named after the year they were observed together with a capital letter, or
two lower case letters. The first 26 that were discovered during the year are labeled with
capital A-Z, discovery number 27 and up are labeled with two lower case letters, starting
with aa. Until the late 1980’s the single capital letter was enough, but during the 21st
century hundreds of SNe are found each year, making the double letters a necessity.
1.2
Formation of core collapse SNe
All stars begin their life in a hydrogen burning phase, but what comes after that is
determined by the mass of the star (see e.g. [3]). If the mass is above ∼ 8M the star
will go through all the possible burning stages (H, He, C, O and Si) leading up to an iron
core. Between each stage the core contracts when the nuclear burning has stopped, since
the outward radiation pressure decreases. This contraction stops when the temperature
in the core is high enough to start the next stage of burning. The burning of heavier
elements releases less and less energy per mass unit, which means that the burning stages
after hydrogen burning progress increasingly fast. Hence the star will soon entirely run
out of fuel and enter the final phase.
During this final phase the core once again contracts, but this time there is no new
burning stage that can begin since iron is the most stable element and any processes
that converts iron to other elements require energy. The contraction continues until the
electrons in the core form a degenerate gas. When this degenerate core becomes larger
than 1.4M the electrons are forced into the nuclei and combine with the protons to
form neutrons (see e.g. [4]). By doing this the outward pressure caused by the Coulomb
force disappears and, collapsing under the gravity, the core contracts even more rapidly
until it is the neutrons that form a degenerate gas. Finally there is once again a force to
balance out gravity so the core stops contracting. The outer layers of the star ”bounce”
on the core, which results in a shock wave being driven outwards. The details of how
this subsequently leads to an explosion are not fully understood.
The contraction released a large amount of gravitational potential energy. Around
99% of the total energy is released as neutrinos (see e.g. [4]). Though neutrinos very rarely
interact with matter the large amount combined with the exceptionally high densities
makes a fraction of the neutrinos deposit their energy in the outer layers of the star. This
is likely of key importance in triggering the explosion. Though only ∼ 1% of the total
energy is emitted as photons a SN can be bright enough to outshine an entire galaxy
during its first days or weeks.
1.3
Radioactive elements in SNe
The vast number of neutrons involved in the SN explosion makes it possible for neutron
capture to take place. In the explosion the capture rate is so high that the created
6
elements do not have time to β-decay, which means that heavy elements far from the
stable isotopes can be formed. But as soon as the neutron flux and temperatures go
down this neutron capture process will stop. The elements then start to approach stable
isotopes through a series of β-decays.
After the explosion the radioactive elements created during it provide an energy source
for the SN so that it remains visible for a longer time. The energy initially comes from
56
Ni decaying to 56 Co, with a half-life of 6 days [5], which will in turn decay to the
stable isotope 56 Fe, with a half-life of 77 days [5]. The subsequent radioactive decays also
provide the SN with enough energy for light to be emitted, but at this point it is too
faint to be seen for distant SNe.
The electrons and positrons emitted when these elements decay ionize and excite
the gas surrounding the SN, by losing their energy to the gas. Each ionization will in
turn produce a new high-energy electron, causing a chain reaction of ionizations and
excitations. The excitations will instead produce photons when atoms in the gas return
to their ground states.
1.4
SN remnants
When the shock wave from the explosion hits areas with higher density of interstellar
medium a reverse shock is created that moves inward towards the ejecta. In this process
radiation is created since the material hit by the shock becomes heated. This radiation
will result in a new increase in the light from where the SN took place. What is seen now
is the remnant of the SN, which is the cloud of matter that was ejected in the explosion.
The remnant continues to expand and can stay visible long after the SN has faded
away if it is close enough, like the Crab Nebula and Cassiopeia A seen in Figure 1.2. At
the center of the remnant the remainder of the core can be found, usually in the shape
of a neutron star or a pulsar. If the collapsed core is massive enough, over ∼ 3M (see
e.g. [4]), it is possible for a black hole to form instead.
A neutron star is what becomes of the core when it has turned into small dense
sphere of neutrons, as described in Section 1.2. If the progenitor star was rotating even
slightly before it collapsed the period of this rotation can be reduced drastically due to
the conservation of angular momentum (see e.g. [4]). The core collapse also amplifies the
magnetic field of the star which accelerates any surrounding charged particles enough for
them to emit synchrotron radiation in a beam along the magnetic poles. This beam will
then rotate with the neutron star, like the light from a lighthouse, and become visible at
regular intervals when the beam is directed towards Earth, if it ever is, which is known
as a pulsar. A black hole, on the other hand, is formed if the outward pressure caused
by the neutron degeneracy is not enough to counteract gravity.
7
(b) Cassiopeia A
(a) The Crab Nebula
Figure 1.2: Example images of SN remnants, taken from NASA’s website; (a) from [6] and
(b) from [7].
8
Chapter 2
Supernova SN 1987A
The supernova SN 1987A exploded 23 February 1987. It is a Type II SN located in
the outskirts of the Tarantula Nebula in the Large Magellanic Cloud, 168,000 ly from
Earth, and was the first SN visible to the naked eye since the invention of telescopes.
Due to its proximity to Earth a high spatial resolution can be obtained when studying it
through telescopes, something that is not possible for other SNe. Before the light from
the explosion could be seen an unusually large number of neutrinos were detected on
Earth, 11 in Japan [8] and 8 in USA [9], which was the first and only time neutrinos from
a SN explosion could be directly observed.
Another remarkable thing about SN 1987A is its progenitor star, which could be
identified as the blue supergiant Sanduleak -69° 202, with a mass of ∼ 20 M [10]. It is
not known exactly how this star was formed, but one popular theory states that it could
have been a merger of two smaller stars, of masses ∼ 15 M and ∼ 5 M , in a close
binary system [11]. Previous to this event blue supergiants were considered unable to
turn into SNe.
2.1
Rings around SN 1987A
There are three glowing rings visible around SN 1987A, which are thought to have been
ejected from the progenitor star about 20 000 years before the explosion, possibly as a
result of the binary merger [12]. The bright equatorial ring expands at 10 km s−1 , while
the two fainter rings (placed axi-symmetrically on either side of the first one) are moving
three times faster. Though the rings are circular they appear elliptical in the sky, as seen
in Figure 2.1, due to the line of sight being at a 43° angle [13] with the northern parts of
the rings tilted towards us.
9
Figure 2.1: An image showing the three rings around SN 1987A, taken by WFPC2 in September 1996 using the F658N filter. The field of view is 9.4” × 5.9”. North is up and east is to the
left in this image, as well as all following images of SN 1987A.
In this report only the equatorial ring was studied. It emits light in wavelengths
ranging from radio to X-ray, but this work focuses on the optical light from the ring.
The optical light curve of the ”R” and ”B” bands (described in more detail in Section
6.7.1) can be seen in Figure 2.2a.
The emission from the ring is first powered by the flash-ionization, followed by recombination, caused by the SN explosion, and later by the shock wave from when the outer
parts of the ejecta collides with the material in the ring. Since this material is clumped
up in many small regions with higher density than the surroundings there are several
hotspots visible in the ring, which give the ring its distinctive appearance. When these
hotspots are dissolved by the shock the light starts to fade away. A full optical spectrum
of the emitted light from the ring is seen in Figure 2.2b, where an arrow marks the [O
III] line that was studied in this thesis. The spectrum was obtained by the Ultraviolet
and Visual Echelle Spectrograph (UVES) at VLT in Chile.
10
1e−12
2.0
R band
B band x2
10-13
Flux [ergs/s/cm2 /Å]
Flux [ergs/s/cm2 ]
1.5
1.0
10-14
10-15
0.5
10-16
0.0
2000
3000
4000
5000 6000 7000 8000
Days since explosion
9000 10000 11000
4000
5000
(a) Light curve for ”R” and ”B” bands
6000
7000
8000
Wavelength [Ångstrom]
9000
10000
(b) Optical spectrum
Figure 2.2: An example of the optical light curve in two different wavelength intervals [14] and
the optical spectrum taken by the UVES camera in 2009. The arrow in the spectrum marks
the [O III] line.
2.2
The ejecta
The inner part of the ejecta is dense enough to be observed in the optical region by HST.
It has been seen to first slowly fade until ∼ 5500 days after the explosion [15], after which
it starts to become brighter again. The initial decline is powered by the radioactive decay
of 56 Ni, 57 Ni and 44 Ti, while the following increased flux has been found to be caused
by X-rays from the interaction between the very faint outer part of the ejecta and the
equatorial ring [15].
As the ejecta expands it changes shape, from being a uniform ellipse to having a more
irregular shape with a hole in the middle. This change in the shape coincides with the
re-brightening of the ejecta, and the change of power source is likely to be the cause
of the changed shape [16]. It is also possible that the evolution of the observed ejecta
is affected by dust that absorbs light that otherwise would have reached the detectors
used to study the ejecta [16]. The irregular shape of the ejecta further shows that the
explosions was asymmetric.
2.3
Emission in the F502N filter
The narrow F502N filter covers a wavelength interval of about 50 Å and is centered
around 5020 Å, though the exact interval and central wavelength varies slightly between
different HST detectors (see Chapter 3 for a description of the detectors). In Figure
2.3a the filter profile of F502N in WFPC2 is shown superposed on the UVES spectrum
from Figure 2.2b. For the equatorial ring this filter shows emission almost exclusively
from the [O III] λ5007 line, but there is also a much smaller He I λ5016 peak [17]. The
[O III] line comes from a forbidden transition in doubly ionized oxygen. Even though
this transition breaks the usual rules for allowed transitions the high temperature and
low density of the material in the ring makes interactions between particles rare enough
that even forbidden, or more correctly highly unlikely, transitions take place. Figure
11
2.3a also shows that there are two components of the emission line. These have width of
∼ 10 km/s and ∼ 300 km/s, and are thought to arise from un-shocked and shocked gas,
respectively [18].
For the ejecta the F502N filter covers a part of a broad peak originating from several
Fe I peaks around 5000 Å [19], which can be seen in Figure 2.3b. Since the material
has been heated the atoms are in excited states and emit light when they return to the
ground states. In Figure 2.3b you can also distinguish a narrow peak corresponding to
the [O III] line, but this is simply light scattered from the equatorial ring and does not
come from the ejecta itself.
1.0 1e−14
1.0 1e−15
Ring spectrum
WFPC2
0.8
Flux [ergs/s/cm2 /Å]
Flux [ergs/s/cm2 /Å]
0.8
0.6
0.4
0.2
0.0
4900
Ejecta spectrum
WFPC2
0.6
0.4
0.2
4950
5000
Wavelength [Ångstrom]
5050
0.0
4000
5100
(a) Ring spectrum
4500
5000
Wavelength [Ångstrom]
5500
6000
(b) Ejecta spectrum
Figure 2.3: An example of a throughput profile, from F502N in WFPC2, superposed in (a)
on the spectrum of the ring, taken by UVES in 2009, and in (b) on the spectrum of the ejecta,
taken by the Faint Object Spectrograph on HST in 1997.
In this thesis light in this filter will be studied for the equatorial ring, regions outside
this ring, and the ejecta. By studying the ring the hope is to confirm its destruction
and using the measurements to improve the calibration of UVES. While the outstanding
spectral resolution of UVES makes it possible to separate the shocked and un-shocked
components, the absolute flux calibration is uncertain. Since the flux calibration of HST
is excellent, it can be used to calibrate the UVES observations.
Regions outside the ring might give valuable information about the progenitor star
and its life shortly before the explosion. Specifically, mass loss of the progenitor star
prior to the explosion may emit in [O III] if it is ionized by the X-rays from the ring.
The ejecta will then be studied to obtain more information about its energy source, and
confirm the previously observed changes of the ejecta shape.
12
Chapter 3
Telescopes
This chapter contains a brief description of the telescopes and instruments that are
relevant for this thesis. Observations from HST were used for the measurements, while
VLT was only used for comparison.
3.1
Hubble Space Telescope, HST
HST is a 2.4-meter reflecting telescope that was launched in April 1990 to orbit 600 km
above Earth [20], seen in Figure 3.1. Every three years a service mission has been launched
to take care of the needed maintenance and reparations, as well as install new equipment.
These service missions have been crucial to keep HST in orbit, and in a functional state,
for the past 25 years, which is a whole decade longer than the designed life-time of the
telescope. The service mission in May 2009 was the last one to be performed [21], so now
the many instruments on board will be used until they eventually break. A description
of the three CCDs used in this thesis follows in the sections below.
Figure 3.1: An image of HST from NASA’s website [22].
13
3.1.1
Wide Field Planetary Camera 2, WFPC2
The Wide Field Planetary Camera 2 (WFPC2) has made the majority of all the HST
observations due to its long time in service. It was installed at the end of 1993 and not
removed until the middle of 2009, after over 15 years of operation. WFPC2 cover the
wavelength range 1150-11,000 Å, and consists of four cameras; three wide field (WF)
cameras and one so called planetary camera (PC). These four cameras have slightly overlapping fields of view so their images are combined to one large image. All observations
used in this thesis were from the part of that image corresponding to the PC.
The PC received its name because it has a field of view that makes it possible to
obtain full disk images of all planets in the solar system, except Jupiter. It has a pixel
size of 0.0455”, which is half as big as the wide field cameras, and with 800 x 800 pixels
in total this results in a field of view of 36” x 36” [23].
Over the years WFPC2 has suffered an increased loss of Charge Transfer Efficiency
(CTE) due to radiation damage on the detectors. Even from the start a loss of the
detected signal was present, but thanks to a lowered operating temperature it could be
limited to 3-4% for point sources in 1994 [23]. Over time radiation damage increased the
CTE loss and by the time WFPC2 was taken out of service it could be as high as 50%
or more for faint targets [23].
This CTE loss is due to radiation creating electrical traps in the silicon lattice of the
CCD detectors. During observations these traps prevent photoelectrons from moving
towards the output node and thus reducing the registered flux. Besides the time in orbit
for WFPC2 the CTE loss also depends on the signal from the source, the background
illumination and the location of the source image on the CCD. Bright sources and high
background illuminations help reduce the CTE loss, while a position far from the output
node, especially in the y-direction, increases the loss of CTE.
3.1.2
Advanced Camera for Surveys, ACS
In the beginning of 2002 the Advanced Camera for Surveys (ACS) was installed. It
covers wavelengths between 1700 Å and 11,000 Å and has three different parts, or subinstruments, called channels. All channels operated without problems for 5 years until
a failure of the CCD electronics occurred early in 2007, which affected the Wide Field
Channel (WFC) and the High Resolution Channel (HRC) but not the solar blind channel. WFC could be restored in the middle of 2009, but unfortunately not HRC. All
ACS observations used in this thesis were taken with HRC, which has a pixel size of
approximately 0.028” x 0.025” and a field of view of 29” x 25” for the 1024 x 1024
pixels [24].
3.1.3
Wide Field Camera 3, WFC3
The Wide Field Camera 3 (WFC3) replaced WFPC2 in 2009 and is intended to last the
remaining years of the HST observational life time. It covers wavelengths in the range
2000-17,000 Å with its two channels, for ultraviolet-visible light (UVIS) and infrared light
respectively. In this study images from UVIS were used, which has two CCDs of 4096 x
2051 pixels, with 0.040” per pixel resulting in a field of view of 162” x 162” [25].
14
3.2
Very Large Telescope, VLT
VLT is a ground-based telescope located in the Atacama desert in Chile. It consists of an
array of four telescopes with 8.2-meter mirrors, seen in Figure 3.2, and four smaller and
movable auxiliary telescopes with 1.8-meter mirrors. It is hard to give an exact value for
the resolution of these telescopes since it depends on the atmospheric conditions at the
time of the observation, and the used instrument, among other things.
Like HST there are different instruments in VLT and below follows a description of
the one used for the comparisons in this thesis.
Figure 3.2: An image of VLT from European Southern Observatory’s website [26], showing
the four main telescopes.
3.2.1
Ultraviolet and Visual Echelle Spectrograph, UVES
Since the atmosphere limits all instruments on VLT it determines many properties of
the UVES. One such phenomenon that affects the observations is seeing. This makes all
light sources more obscure, and hence light can appear to come from a slightly different
area than it should.
UVES is divided into two parts, or arms, where one covers the wavelengths from
ultraviolet to blue and the other covers all visible light as well as the infrared, hence called
the blue and red arms. The HST observation in this report are compared to observations
made by the red arm of UVES, which consists of two CCDs with 2000 x 4000 pixels,
a pixel scale of 0.16” per pixel, and a spectral resolution1 limited to 110,000 [27]. The
wavelength range for both arms combined is limited to 3000-11,000 Å.
1
A ratio between the observable wavelength and the smallest distinguishable wavelength separation.
15
Chapter 4
Observations
This report is based on measurements from 14 observations of SN 1987A made by three
different HST cameras (WFPC2, ACS and WFC3) and they constitute all the available
observations in the narrow filter F502N. This filter covers wavelengths in close proximity
to 5010 Å and hence it almost exclusively contains light from the [O III] λ5007 line. The
details of all observations can be found in Table 4.1. As can be seen the exposure times
were longer for the observations during the 1990’s and early 2000’s. This is, partly, in
order to compensate for the low flux expected from the ring around SN 1987A at these
epochs. Naturally it takes longer to get many data counts in total if the flux is low, and
a high number of counts is necessary to obtain scientifically useful images.
The data files for all observations were downloaded from the Space Telescope Science
Institute’s archive [28], and the observation dates were converted to number of days after
the explosion on February 23rd 1987.
Date
Days since explosion
03-02-1994
2537
06-02-1996
3270
12-07-1997
3792
16-06-2000
4862
14-11-2000
5013
07-12-2001
5401
05-01-2003
5795
28-11-2003
6122
15-12-2004
6505
18-11-2005
6843
08-12-2006
7228
29-04-2009
8101
12-12-2009
8328
20-06-2014
9979
a
Camera
WFPC2
WFPC2
WFPC2
WFPC2
WFPC2
WFPC2
ACS
ACS
ACS
ACS
ACS
WFPC2
WFC3
WFC3
Dither patterna
None
None
None
None
Box
Box
Box
Box
Box
Box
Box
Custom
Box
Box
Exposure time [s]
2 * 1600
6 * 1500
6 * 1300
2 * 1400
8 * 700
8 * 600
5 * 500
4 * 1000
4 * 900
3 * 1060
4 * 650
6 * 1150+
4 * 775+
8 * 735+
Dither patter is explained in Section 5.1.
Table 4.1: Information about the HST observations used in the measurements. The exposure
time is listed as number of images multiplied by the exposure time for each image. Those
marked with + consist of two equally large sets of images with slightly different exposure times.
In these cases the exposure times have been averaged and the number of images is that of both
sets combined.
16
Chapter 5
Data reduction
Before any measurements could be performed on the images from the observations a
number of preparatory steps had to be made to improve the image quality and simplify
the measurements. The first step, described in Section 5.1, was to remove contaminations
in the images and improve the resolution. After that had been done the 14 images needed
to be aligned so that the pixel coordinates for the ring were the same for all epochs, see
Section 5.2.
5.1
The drizzling process
The raw data from HST is contaminated with cosmic rays, may contain distortions and
has a resolution that is limited by the pixel size of the camera used to capture the image.
To improve the resolution, and at the same time eliminate all the unwanted cosmic rays
and distortions, a method called drizzling is used. This method combines several images
of the same object by mapping each pixel from the original images onto a new finer pixel
grid, which can be seen in Figure 5.1. Drizzling is most useful for images with slight
spatial offsets, which is why the observations seen in Table 4.1 are split into multiple
exposures.
The original pixels of an image are first reduced to a fraction between 0 and 1 of the
initial size. A pixel fraction of 1 means that the pixel is added to the output image as it
is, resulting in an image that will be a convolution of all the input images. If the pixel
fraction is set to zero it corresponds to adapting point functions at the center of the pixel
before they are added to the output image, also know as interlacing.
17
Figure 5.1: An illustration of how the shrunken pixels are mapped from the original pixel
grid to the finer output grid. Image is taken from the HST Dither Handbook [29].
The rescaled pixels (blue in Figure 5.1) are added to the new pixel grid (green in
Figure 5.1) by weighing the flux value of the pixel with the proportional area of the
overlap between the blue and green pixels. This can be thought of as drops of water
falling on the ground, like a light rain or a drizzle, which is how the algorithm received
its name. During this process of adding pixels to the new grid all cosmic rays in the
original image can be compensated for by comparing the different images in the dither
pattern with each other. Since cosmic rays rarely appear in the same place in consecutive
exposures, pixels with unusually high flux values can be removed to improve the image.
The best results of drizzling (see Figure 7.4 for an example) are obtained with a
pixel fraction set to a value between the two extremes 0 and 1, and for sets of images
where there are small shifts (typically less than one pixel) in both the x- and y-directions
between the images. Systematic shifts like these are called dither patterns. For all the
HST cameras there are sets of predefined dither patterns, but it is also possible to create
custom patterns by defining the shifts between the different exposures. The default dither
patterns used have changed over the years; at first the camera was only shifted along a
line but since 2000 the shifts are in the shape of a parallelogram. The patterns used for
the observations in this thesis are listed in Table 4.1.
The use of a dither pattern means that the true image (the image you would see with
infinitely small pixels) is sampled slightly differently in the different images, which makes
it possible to get better approximations of the point spread functions in the image. As
can be seen in Table 4.1, the very first observations do not have any dither pattern, and
hence it is not possible to increase the resolution. However the drizzling algorithm can
still be used, but then the main benefit is the removal of cosmic rays and distortions.
18
(a) Raw data
(b) Optimal drizzle
Figure 5.2: Images from ACS in November 2003. In (a) one of the raw data images is shown,
and (b) is the result of an optimal drizzle. The field of view is 6” × 3.75” for both images.
To drizzle the images the function astrodrizzle in IRAF [30] was used, where the
pixel fraction of the original images and the pixel scale of the new pixel grid were given
as input parameters. To limit uncertainties and to simplify the measurements all images
were drizzled to the same pixel size. An optimal pixel scale is usually 50-60% of the
original width and height of the pixel [31], which means that WFPC2 sets the lower limit
of the pixel size to 0.0225” per pixel. This is only slightly smaller than the original size
of the ACS pixels, and therefore this value, 0.025” per pixel, was chosen instead.
In order to evaluate the quality of the final result astrodrizzle provides a weight
image as output, together with the drizzled image. The weight image contains information about the weights used for each pixel. The general color of the weight image will go
from white (signifying high weights) to dark gray or black (signifying low weights) when
the pixel fraction is reduced, since an increasing part of the image will not be covered by
any pixel drops at all. For well chosen values of the pixel scale and the pixel fraction the
weight image will show all cosmic rays and bad pixels as darker areas (see Figure 5.3),
since they are given lower weights, in an otherwise bright image, but besides that there
will be no visible traces of anything that can be seen in the original images. However
if there is something wrong with one (or more) of the images in the dither you can see
traces of larger objects, such as the ring around SN 1987A. One cause of these traces
could be that one of the images in the dither pattern was misaligned with the others to
begin with, so that the world coordinates of stars in that image do not correspond to
those of the remaining images.
19
Figure 5.3: The weight image of the ACS data from November 2003. Darker areas have lower
weights, indicating pixels that were removed to increase the image quality.
A method to determine whether the drizzled image is suitable for scientific measurements is to analyze a smaller area of the weight images, around the size of a few hundred
to a few thousand pixels in total. For the best increase in resolution, without increasing
the noise too much, the standard deviation of the weight can be compared to the median
value in that small region. If the standard deviation is less than 20-30% it might be
possible to decrease the pixel fraction some more, but if the standard deviation is higher
than 30% [31] the pixel fraction is too small and needs to be increased, in order to reduce
the noise.
The pixel fractions that could be used varied for the three different cameras, and
finding the optimal one was a systematic process of trial and error. Due to the poor
quality of all WFPC2 images, and also the lack of dither pattern for the ones taken in
January 2000 or earlier, a pixel fraction of 1 had to be used since the standard deviation
in the weight image was higher than the recommended 30% if the pixel fraction was decreased. For the ACS images I could choose arbitrarily small fractions without obtaining
a standard deviation that was too high. Instead the lower limit was set by the visual
appearance of the weight image. At a fraction of 0.05 the standard deviation was 19%,
which is considered to be acceptable though it is on the high side, however at fractions
lower than 0.5 a regular pattern started to become visible, which indicates that the pixel
fraction is too low. Therefore a pixel fraction of 0.6 was chosen for all the ACS images
and an example of a resulting image can be seen in Figure 7.4b. In a similar way it could
be seen that the quality of the two WFC3 images was reduced for pixel fractions below
0.6, so this value was chosen for these images as well. All values for the optimal pixel
scale and pixel fraction are listed in Table 5.1.
Camera
WFPC2
ACS
WFC3
Initial pixel size
0.045”/pixel
0.025”/pixel
0.040”/pixel
Pixel scale Pixel fraction
0.025”/pixel
1.0
0.025”/pixel
0.6
0.025”/pixel
0.6
Table 5.1: The pixel scale and the optimal pixel fractions used in the drizzling for the three
HST cameras.
20
5.2
Alignment
After the images from all epochs were drizzled they needed to be aligned and cropped
so that all objects had the same pixel coordinates in all images. This was done by using
the IRAF function imalign. To use imalign a set of stars is needed as a reference for
the alignment. These stars are used to find the right area in all images, and if there are
not enough stars included imalign might give a false match for another region where
stars have the same relative positions. Ideally each star should be in an otherwise empty
region located at a safe distance from the edge in all images that are to be aligned.
The first WFPC2 image (from 1994) has many bad pixels even after the drizzle was
performed, which limited the number of possible reference stars. Eventually nine stars
around SN 1987A were chosen, with slightly fewer stars below the SN than there were in
any other direction.
The input arguments for imalign are a list of images to align, a list of the star
coordinates, and an initial guess of the shifts. In the list of input images the reference
image, which was chosen as the smallest one, was listed first so that it could be used to
determine the size of the aligned and cropped images. The guess of shifts had to be given
for all images in comparison to this reference image. These values can be obtained by
comparing the pixel coordinates in the images for one of the reference stars. Since the
guess is provided to ensure that the alignment will pair up the correct stars, instead of
making a false match with other stars, the guess does not have to be very accurate.
To determine the accuracy of the resulting alignment the position of three different
stars were compared between the aligned images. The deviation was calculated as the
difference between the highest and lowest value of both the x- and y-coordinates. The
largest deviation was 0.016” (0.64 pixels) in the x-direction and 0.019” (0.76 pixels) in
the y-direction, which was for the bright star northwest of SN 1987A. Compared to the
width, 2.0”, and height, 1.5”, of the ring around SN 1987A (measured between the outer
edges of the ring) those values correspond to 0.8% and 1.3%. Hence the uncertainties in
the alignment will have a negligible impact on the measurements.
5.3
Resulting images
The resulting images from the drizzling are shown in Figure 5.4 and Figure 5.5, using
different scales. The scale in Figure 5.4 is set to show the evolution of the ring as well as
the ejecta, while the scale in Figure 5.5 is optimized to show the hotspots in the ring.
21
Figure 5.4: An overview of how the ring and ejecta change over time, between February 1994
and June 2014 (days 2537-9979). The color scale is in units of 10−19 erg cm−2 Å−1 s−1 . The
field of view is 3” × 3” for each image. Note that the evolution is very similar to that seen in
the R and B bands [14].
In Figure 5.4 it is easy to follow the changes in the ring that occurs over time. It
is clear that the ring almost ”breaks” on the right side around the time when most of
the hotspots start to appear in 2000-2001, and how that same side then becomes the
brightest in 2009. The evolution of the ejecta can also be seen. It fades away and almost
disappears completely in the beginning of 2000 and then slowly becomes brighter and
larger until the end of 2009. In 2014 the ejecta is significantly fainter again, and at this
time it is so large that the lower part can no longer be separated from the surrounding
ring. The changes in the shape, described in Section 2.2, are also clearly visible.
It also shows that the image from April 2009 has a lower quality than the other images
around the same time. In part this is due to he fact that it was taken by WFPC2, which
has a lower resolution, but a lower resolution cannot explain the cluttered region inside
the ring where the ejecta should be distinguishable.
22
Figure 5.5: An overview of how the hotspots appear and change over time, between February
1994 and June 2014 (days 2537-9979). The color scale is in units of 10−18 erg cm−2 Å−1 s−1 .
The field of view is 2.5” × 2.5” for each image. The bright spot to the lower right, seen in the
images from 1997 and 2000, is a star.
When the scale of the images is altered to show higher fluxes, like in Figure 5.5,
it becomes possible to see where and when hotspots appear and disappear over time.
Between 1997 and 2001 the first hotspots start to show at three locations in the ring,
then during the following 2-3 years they appear almost around the entire ring, with only
small gaps at the bottom and on the right side. On the southeast side the hotspots start
to fade away first, between 2006 and 2009, until there are only some remaining on that
side by 2014.
23
Chapter 6
Light curve of the ring
6.1
Background measurements
The background light had to be measured so it could be subtracted from the flux of
the ring. This was done by finding small regions of 0.5” × 0.5” that were dark for all
14 epochs, see Figure 6.1, and measuring the flux from these regions using the fitsky
function from IRAF. This function is specifically designed to calculate the background,
or sky, values of images. To make sure that the results were not affected by systematic
variations of the background across the image, five regions at different locations around
the SN were selected.
Figure 6.1: The regions used to measure the background, displayed in an image from November 2003 taken by ACS. The field of view is 20.5” × 12.8”.
When the flux had been measured for the five selected regions any regions that deviated by more than three times the median value were excluded before the mean back24
ground flux was calculated. Such exclusions were only necessary for three epochs; 1994,
2004 and April 2009.
These mean background fluxes had varying values for the images but they were generally around 5% of the ring flux for the WFPC2 images and up to 0.7% for the ACS
and WFC3 images. For the WFPC2 image from 2001 the background was as high as
13% of the ring flux which is high enough to affect the measurement results. Due to this
the background was subtracted from all measurements.
6.2
Light curve from elliptical aperture
To measure the light from the ring two ellipses were defined so that one was placed right
along the outer edge of the ring and one inside the inner edge of all the hotspots, as seen
in Figure 6.2. This way the light from the inner ellipse can be subtracted from the light
of the larger outer ellipse to yield the light flux from the ring alone. Both ellipses were
centered in the middle of the ring with semi-major axis of 1.0” and 0.6” respectively,
ellipticity of 0.25 and 0.375 as well as a 10° clockwise rotation.
Figure 6.2: The elliptical regions used to measure the flux, displayed in an image from
November 2003 taken by ACS. The field of view is 4” × 2.5”.
To perform these measurements the IRAF function ellipse was used in a photometryonly mode. This means that it does not carry out the fitting of elliptical regions with
constant flux, instead the elliptical regions provided by the user are used in the measurements. The fluxes from ellipse are given in counts per second. To obtain the results
seen in Figure 6.3 all count rates had to be converted to flux densities, as well as have the
background subtracted. This conversion to flux densities is done by using a conversion
factor that is well determined for each detector. The uneven shape of the light curve
25
is caused by differences between the filters in the three cameras, corrections for this are
made in Section 6.4.
2.2 1e−15
2.0
Flux [ergs/s/cm2 /Å]
1.8
1.6
1.4
1.2
1.0
0.8
0.6
2000
3000
4000
5000 6000 7000
Days since explosion
8000
9000
10000
Figure 6.3: The light curve of the ring from an elliptical aperture without any corrections
applied.
6.3
Light curve from UVES slit
The flux measurements of SN 1987A obtained with UVES were performed in a 0.8”
slit across the center of the ring, at an angle of 30° [14]. To enable a comparison with
the UVES data, measurements with the HST observations were also performed using
an aperture that corresponds to this slit. To make sure there was no light from other
sources the slit had a length of 2.5”, see Figure 6.4 for the slit’s position relative to the
ring. Using the coordinates of the four corners of the slit the IRAF function polyphot
was then used to measure the flux, which sums up the total counts from this region in all
14 images. The results of this measurement are seen, compared to those of the elliptical
aperture, in Figure 6.6.
26
Figure 6.4: The slit used for the UVES measurements, displayed in an image from November
2003 taken by ACS. The field of view is 4.8” × 3”.
6.4
Corrections for the use of different cameras
As mentioned earlier, the uneven shape of the light curve in Figure 6.3 is caused by
different throughput profiles for the F502N filter, which can be seen in Figure 6.5. These
differences were accounted for by using the calcphot and bandpar functions in the IRAF
package synphot. These functions take information about the filter, camera, and the
detector in that camera, that was used to make the observations and return the expected
flux densities and information about the filter profile. To get the best results possible
from calcphot it was also necessary to give a custom table of wavelengths since the
default one is too sparse for narrow filters.
27
1.0 1e−14
Ring spectrum
WFPC2
ACS
WFC3
Flux [ergs/s/cm2 /Å]
0.8
0.6
0.4
0.2
0.0
4960
4980
5000
5020
5040
Wavelength [Ångstrom]
5060
5080
Figure 6.5: The throughput profiles for the F502N filter in the different cameras superposed
on the spectrum of the ring, taken by UVES in 2009.
Since fluxes are more informative than flux densities when dealing with narrow emission lines, the obtained information was used to calculate an effective width, weff, corresponding to the width of a perfectly rectangular filter profile, for each camera. Calcphot
gave values of the flux density, f lam, one could expect to measure in units of erg s−1
cm−2 Å−1 , and bandpar gave the equivalent rectangular filter width, rectw (in Å), the
maximum throughput, tpeak (in percent), and the throughput at a reference wavelength,
tref (also in percent), which can all be found in Table 6.1.
To get the effective width the values obtained from bandpar were combined as displayed in Equation 6.1. This value was multiplied by the expected flux densities, and the
product was then normalized by the value for WFC3 so that all measured fluxes would
correspond to measurements made by WFC3. The resulting correction factors are also
included in Table 6.1.
wef f = rectw ∗
Camera
WFPC2
ACS
WFC3
f lam
4.58 ∗ 10−16
3.40 ∗ 10−16
3.05 ∗ 10−16
rectw [Å]
35.8
56.6
65.3
tpeak
tref
tpeak [%]
58.0
19.4
25.7
(6.1)
tref [%]
57.2
18.3
23.1
wef f [Å]
54.5
66.9
72.7
corr
0.75
0.92
1.0
Table 6.1: Values of all parameters used for calculating the corrections as well as the resulting
effective width and normalization factor used to adjust the light curve.
After the corrections were applied to the measurements from both the elliptical aperture and the slit, these two could be compared to make sure that they were almost
identical, except for a factor 2 since the UVES slit only covers half of the ring. This
28
comparison is seen in Figure 6.6 and any larger differences in the fluxes are caused by
hotspots appearing (or disappearing) outside the slit.
1.2 1e−13
Ellipse
Slit x2
Flux [ergs/s/cm2 ]
1.0
0.8
0.6
0.4
0.2
2000
3000
4000
5000 6000 7000 8000
Days since explosion
9000 10000
Figure 6.6: The light curves from both the elliptical aperture (blue), seen in Figure 6.2, and
the slit (red), seen in Figure 6.4, with applied corrections.
6.5
Loss of CTE in the 2009 WFPC2 observation
In Firgure 6.6 it can be seen that even after the proper corrections have been applied
the data point at 8100 days lies below the expected light curve. This is expected since
that observation was made by WFPC2, which suffers from a CTE loss, as mentioned in
Section 3.1.1.
To attempt to quantify the degree of CTE loss the flux of nine different stars around
the SN were measured in all images taken by WFPC2 and the result is plotted in Figure
6.7. Unfortunately there is no clear indication of the CTE loss since all the stars vary
too much in flux. This is likely due to the low signal in the narrow filter. Because of
this the CTE loss cannot be determined by examining stars surrounding SN 1987A, and
all existing correction formulas are for point sources, so they are not applicable either.
To get an approximation of the CTE loss it can be assumed that the fluxes from 8100
days should be slightly higher than those at 8300 days, which gives that a correction of
∼ 20% is needed. However it is not possible to quantify the correction needed so this
observation will be excluded from all plots and measurements from now on.
29
1.1
Normalized flux, fraction of max
1.0
0.9
0.8
0.7
0.6
0.5
2000
3000
4000
5000
6000
7000
Days since explosion
8000
9000
Figure 6.7: The flux from nine stars around SN 1987A in all WFPC2 observations. Each
symbol and color represent a different star. No clear trend can be seen for the star fluxes.
6.6
Error analysis
The formula used to calculate the statistical errors can be seen in Equation 6.2 [32], where
f lux is the total number of counts from the ring with the counts from the background
subtracted, gain is the number of electrons per data number for the camera used for the
observation (values are found in Table 6.2), area is the total area of the measured region,
stdev is the standard deviation of the estimated background flux, and nsky is the area
of the region used to approximate the background flux (or sky value).
Camera
Gain
WFPC2
7
ACS
2
WFC3
1.54
Table 6.2: Values of the gain for the HST cameras.
All values, except for the gain, were obtained from the polyphot function used to
make the measurements in Section 6.3. To get the errors for the elliptical aperture, the
two regions first had to be adapted to polygons in order to use polyphot. The obtained
values were then used to calculate corresponding values for the region covering only the
ring (e.g. the areas were subtracted while an average of the standard deviations were
taken), before Equation 6.2 was used.
s
f lux
area2 ∗ stdev 2
error =
+ area ∗ stdev 2 +
(6.2)
gain
nsky
The values obtained from Equation 6.2 are displayed in Figure 6.8. The error bars
for each data point here, and in all coming figures, correspond to one sigma. The figure
shows that the errors are too small to have a significant impact on the light curve, and
30
many are even too small to be seen. As expected, the largest errors of 3 − 4% are for
some of the WFPC2 observations, which clearly have a poorer image quality than the
two other cameras.
5.5 1e−14
5.0
Flux [ergs/s/cm2 ]
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
2000
3000
4000
5000 6000 7000
Days since explosion
8000
9000
10000
Figure 6.8: The light curve from the slit with statistical errors included.
An uncertainty regarding the errors is that it is unclear where polyphot makes the
background measurements, which might be the reason why the last two terms in Equation
6.2 usually contribute with 80 − 90% of the total error. If these measurements are
performed in a region containing a star the values obtained will not be an accurate
representation of the background, and the resulting errors would be overestimated. To
investigate this further a more careful investigation would be needed.
6.7
6.7.1
Comparison to other measurements
The R and B bands
Figure 6.9 shows a comparison of [O III] results with the R and B band light curves of the
ring [14]. All measurements were normalized by the maximum flux for each light curve.
This was necessary since the total fluxes for the three different light curves differed by
too much, and scaling two of them up or down by a constant factor did not prove useful.
The R band consists of the two filters F675W and F625W, spanning wavelengths
in the range 5500-7100 Å, and the B band consists of the filters F439W, F435W and
F438W, with wavelengths in the range 4000-4600 Å1 . For the R band most of the flux
comes from Hα, [N II] λλ6548, 6583, and [O I] λλ6300, 6364, while Hγ, Hδ, and [S II]
λ4069 dominate the B-band [14].
Figure 6.9 shows that the [O III] line has its peak more than 1000 days earlier than
the R and B bands. It also varies slightly less between its highest and lowest point, but
1
The different filters are for different cameras covering mainly the same wavelengths. The wavelength
given here is given by the lowest and highest wavelengths in any one filter.
31
Normalized flux (percentage of maximum flux)
all three light curves have the same shape.
1.0
[OIII] λ5007
R band
B band
0.8
0.6
0.4
0.2
2000
3000
4000
5000 6000 7000 8000
Days since explosion
9000 10000 11000
Figure 6.9: The light curve for [O III] λ5007 from the measurements in this thesis compared
to the light curve from the R and B band [14], normalized by the maximum of the respective
curves.
6.7.2
The [O III] line from UVES
To make a comparison of the [O III] line measured by HST and UVES the spectra from
the UVES measurements were convolved with the WFC3 filter throughput profile. This
filter was chosen since this is the camera that was used to normalize the correction factors
in Section 6.4, but any of the other filters could have been used as well. As can be seen
in Figure 6.10 the resulting UVES light curve is for the most part lower than the one
for HST, and not as smooth. This reflects the uncertainty in the flux calibration for the
UVES data. It also seems like the UVES data is more accurate for the earlier times, and
loses precision over time.
32
6 1e−14
HST
UVES
Flux [ergs/s/cm2 ]
5
4
3
2
1
2000
3000
4000
5000 6000 7000
Days since explosion
8000
9000
10000
Figure 6.10: The light curve for [O III] λ5007 from the HST measurements compared to the
light curve from the UVES data [14] convolved with the WFC3 filter profile. The aperture is
shown in Figure 6.4
To quantify the difference between the two curves a linear interpolation was performed
to approximate the HST fluxes at the times of the UVES observations. After that
the ratio between the UVES fluxes and the HST fluxes were calculated. The obtained
interpolated flux values can be seen in Table 6.3, together with the calculated ratios. To
get a better overview the ratios are plotted in Figure 6.11. This clearly shows that the
UVES measurements tend to differ more from the HST ones as time passes. The values
go from differing by only a few percent around 5000 days after the explosion, to being
20 − 30% lower after 9000 days.
Date [days]
5039
5704
6621
6814
7160
7547
7943
8638
8990
9734
UVES flux
1.73*10−14
2.81*10−14
4.38*10−14
5.44*10−14
5.61*10−14
4.61*10−14
3.99*10−14
3.83*10−14
2.90*10−14
2.83*10−14
Interpolated HST flux
1.71*10−14
2.93*10−14
4.98*10−14
5.18*10−14
5.23*10−14
5.07*10−14
4.86*10−14
4.38*10−14
4.07*10−14
3.42*10−14
Ratio
1.01
0.96
0.87
1.05
1.07
0.91
0.82
0.87
0.71
0.83
Table 6.3: The ratios between the UVES and HST flux measurements at the time of the
UVES observations, which is plotted in Figure 6.11. The fluxes are measured in ergs s−1 cm−2 .
33
1.0
Percentage of HST flux
0.8
0.6
0.4
0.2
0.0
5000
6000
7000
8000
Days since explosion
9000
10000
Figure 6.11: The ratio of the UVES data and interpolated HST data for the [O III] λ5007
line measured in the slit.
6.7.3
Effects of seeing
Because of the Earth’s atmosphere an image of the ring around SN 1987A, if it could
be imaged by UVES, would be so blurry that it would appear as a solid ellipse instead
of the ring seen by HST. This effect is called seeing and can be simulated for the HST
images by convolving them with a two-dimensional elliptical Gaussian function. In IRAF
this can be done by using the function gauss, which takes the image and the standard
deviation σ, in pixels, as input. The seeing at VLT, defined by the image size measured
at full width half maximum (FWHM), is 0.8”, which is equivalent to a σ of 13.6 pixels
in the HST images. An example of the resulting image can be seen in Figure 6.12.
Figure 6.12: An image from November 2003, captured by ACS, convolved with the elliptical
Gaussian function. The bright circles are the large nearby stars, and the dimmer ellipse in
between is SN 1987A.
34
Since the UVES slit only covers half of the ring seeing can cause light close to the
edges of the slit to be spread across the edge, either making light from the slit end up
outside it or making light from the outside enter the slit. To examine whether these two
effects cancel each other out the original HST light curve is compared to the one obtained
when the HST observations are convolved with Gaussian. A comparison between these
two light curves can be seen in Figure 6.12 below.
As Figure 6.13 shows, seeing has a very small impact on the light curve and even with
seeing accounted for most fluxes are almost exactly the same as without it. It is only for
the observations 5000-6000 days that seeing clearly lowers the measured fluxes, but the
impact is much smaller than the differences observed in Section 6.7.2.
5.5 1e−14
5.0
Seeing
No seeing
Flux [ergs/s/cm2 ]
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
2000
3000
4000
5000 6000 7000
Days since explosion
8000
9000
10000
Figure 6.13: The light curve for the UVES slit in [O III] λ5007 with and without seeing effects
accounted for.
35
Chapter 7
Morphology of the ring and search
for emission outside
To learn more about what happened with the progenitor star of SN 1987A the material
outside the equatorial ring needs to be studied. This is hard to do when no light is
being emitted from the area, but as the visible part of the ring keeps moving outwards
it increases the chances of observing new regions. For this reason it is interesting to
try to find any faint glowing material outside the ring. In this chapter two different
methods have been used to find such regions, first by subtracting images of consecutive
observations to make differences more apparent and then by direct measurements in some
selected regions where diffuse light was thought to exist.
7.1
Photometry of the outer regions
In some of the images from the years after the hotspots start to appear there seems to be
a fainter glowing region on the right side of the ring, seen most clearly in the images from
2003 in Figure 5.4. To see if any similar faint light can be seen in more recent images a
set of difference images was created by using the function imarith in IRAF to subtract
one image from an other. This was done between all pairs of consecutive observations.
In Figure 7.1 the resulting images are shown, and the scale portrays increased flux densities in yellow and decreased flux densities in black. Purple represents unchanged flux
densities.
36
Figure 7.1: Difference images of all pairs of adjacent points in time. Numbers XXXX - YYYY
shows the time in days for the two images that have been subtracted, with the time difference
in days given underneath. The field of view is 3.1” × 3.1” for each image.
In the first images in Figure 7.1 it is clearly seen how the ring fades before the hotspots
start to appear when the shock wave hits the material in the ring, as described in Section
1.4. For the difference images around 5000 days (image four and five) the time elapsed
between the two images that have been subtracted is a bit too short so almost no changes
have occurred. The last six images in Figure 7.1 show that the ring is expanding and
slowly shifting to becoming brighter on the right side, and fainter on the left. The changes
of the ring and its hotspots show up most clearly in the middle where the time difference
is 300-400 days. First it shows where all new hotspots form, and later it shows that both
the hotspots and the light surrounding them is slowly expanding. In the very last image
there is even a visible trace of the expanding ejecta.
However the traces of faint light outside the ring, that could be seen in Figure 5.4,
have vanished. And contrary to observations in other filters there are no traces of new
hotspots [14] outside the ring. To examine the presence of faint light more closely five
regions outside the ring, shown in Figure 7.2, were chosen and the flux from these five
regions were measured in the same way as in Section 6.3.
37
Figure 7.2: The regions used to measure the flux outside the ring, displayed in an image from
November 2003 taken by ACS. The field of view is 7.3” × 4.8”.
The result of the flux measurements in these five regions is shown in Figure 7.3, where
it is clearly seen that the three regions above and below the ring do not vary significantly
over time. In fact the errors are so large, several times the measured flux, that they are
left out in the figure. Though this is most likely caused by an overestimation of the errors
these regions cannot be used to draw any conclusions. However, for the two regions on
the right side the flux does change, but since they are closer to the ring they should be
subject to higher background fluxes caused by scattered light from the ring. In order to
determine if the flux changes depend solely on the ring, or if they depend on emitting
gas located within the regions, it is necessary to estimate the scattered light from the
ring. This can be done by creating a synthetic model of the ring by approximating it as
a collection of point sources with different amplitudes.
38
6 1e−15
Bottom
Top right
Top left
Right top
Right bottom
5
Flux [ergs/s/cm2 ]
4
3
2
1
0
2000
3000
4000
5000 6000 7000 8000
Days since explosion
9000
10000
Figure 7.3: The measured flux in the regions outside the ring. The colors correspond to those
of the regions seen in Figure 7.2. Error bars are only shown for the yellow and blue lines.
7.2
Model of the ring around SN 1987A
As mentioned above a model of the ring is needed to be able to get an approximation
of how much the ring affects the closest surroundings, such as the yellow and light blue
regions shown in Figure 7.2. To create that model a software called TinyTim, specifically
designed to simulate HST point spread functions (PSFs), was used [33]. This software
is used in three steps to create one image per point source that will be in the model.
The first step (tiny1) is to provide information about the observation which the model
will represent, the second step (tiny2) creates the point sources that will make up the
model, and the third step (tiny3) distorts these point sources.
To begin with some basic information about the observation is provided by the user.
This includes the camera (eg. WFC3) and the instrument in that camera (eg. UVIS), as
well as the filter used and the date of the observation. It is also necessary to have a list
of the coordinates where the synthetic PSFs should be centered. This list is later used
to make the correct distortions, and since these depend on the position on the chip it is
important that the coordinates are given as pixel coordinates in the original image. When
the initial information has been provided tiny1 will suggest values for some settings for
the PSFs (eg. their size), but it is possible to choose other values as well.
When all these things have been provided to tiny1 it will create a parameter file
with all the information needed for the two following steps. Running tiny2 with this
parameter file creates all the individual PSFs, with the total flux normalized to one,
without any further input from the user. Finally the same parameter file is sent as input
to tiny3, but this time accompanied by the index for each individual position.
After all three steps are completed the model needs to be assembled by combining all
39
images of individual PSFs. To create the ring around SN 1987A each PSF image had to
be renormalized so that their fluxes corresponded to the observation. The images also
had to be rescaled to the same pixel size as was used in the drizzling, see Section 5.1,
and shifted to the correct position to end up in the same place as in the image of the
observation. Both of these steps can be done by using the IRAF function geotran, and
when it is finished all point source images can be combined to one single image by using
imcombine, also in IRAF.
(a) Observation
(b) Model
Figure 7.4: In (a) the image taken by WFC3 in 2014 is shown, and in (b) is the corresponding
model of the ring. The field of view is 3.6” × 2.3” for both images.
In the attempt to make the models look as much like the observations as possible
point sources were added even where there were no hotspots. For the brighter parts of
the ring the model appears very similar, while for the fainter parts it differs more. This
is a natural consequence of making a model from a collection of point sources, since that
structure makes it harder to simulate the diffuse light. Despite the regional differences in
the ring, between the observation and the model, the total flux measured in the elliptical
aperture from Section 6.2 is the same for both due to the re-normalization described
above.
In Figure 7.5 the fluxes in all five outer regions have been corrected for the background
from the ring at two points in time, December 2006 (7228 days) and June 2014 (9979
days). As can be seen this correction greatly reduced the flux for the light blue and
yellow regions, so much that the entire increase in flux seems to be due to the high flux
from the ring. These results indicate that there is no significant signal from diffuse gas
outside the ring, which was expected after examining the difference images, Figure 7.1.
However, a more careful analysis is needed to establish any precise limits. Given these
results the faint light seen in 2003, see Figure 5.4, is likely to be in the same location as
the ring at later times, but whether it is a part of the ring or in a different plane cannot
be determined without other measurements.
40
6 1e−15
Bottom
Top right
Top left
Right top
Right bottom
5
Flux [ergs/s/cm2 ]
4
3
2
1
0
2000
3000
4000
5000 6000 7000 8000
Days since explosion
9000
10000
Figure 7.5: The measured flux in the regions outside the ring. The colors correspond to
those of the regions seen in Figure 7.2. The empty symbols correspond to flux obtained by
subtracting the background caused by the ring.
41
Chapter 8
Photometry of the ejecta
To measure the light from the ejecta an elliptical aperture was used, and since the ejecta
becomes larger over time that elliptical region had to increase as well. Based on the
constant expansion of the ejecta, where the radius is given by r = v ∗ t, a linear relation
was used to gradually increase the size of the ellipse. The basic ellipse used in the
calculations represents the size in September 1994. It has a Semi-Major Axis of 0.11”,
an ellipticity of 0.27 and it is rotated 73° clockwise, just like in [15]. An example of the
region is shown in Figure 8.1. It shows that a part of the ejecta is outside the marked
region, this is to avoid measuring light from the ring during the last observations when
the ejecta gets very close to the ring.
Figure 8.1: The variable elliptical region used to measure the flux of the ejecta, displayed in
an image from November 2003 with the size used for that time. The field of view is 4.5” × 2.8”.
Just like the regions outside the ring, the ejecta also experiences a much higher
background due to the ring. This was estimated in the same way as in Section 7.2, by
42
using the two models to measure the flux in the ejecta regions for 2006 and 2014. This
was done in [15] as well, but for four points in time, and the comparison between the [O
III] line and the R and B band is shown in Figure 8.2.
8 1e−14
7
Flux [ergs/s/cm2 ]
6
5
F502N x15
Corrected F502N x15
R band
Corrected R band
B band
Corrected B band
4
3
2
1
2000
3000
4000
5000 6000 7000 8000
Days since explosion
9000
10000
Figure 8.2: The light curve of the ejecta measured for the [O III] λ5007 line, compared to
the light curves measured for the R and B bands. The dashed lines have been corrected for the
high background flux caused by the ring, see Section 7.2.
Here it appears as though the light curve of the [O III] line is smoother than those of
the R and B bands, but since the R and B bands are more well-sampled, especially at
7000-10,000 days, this is not necessarily the case. Figure 8.2 also shows that the flux for
the [O III] line has a smaller decrease than the R and B bands before the increase starts.
The increasing size of the errors seen for the ACS data between 6000 and 7000 days,
as well as 8000 − 10, 000 days for the WFC3 data, is likely caused by the uncertainties in
the background measurements mentioned in Section 6.6. Since the standard deviation of
the background is multiplied with an increasing area of the region used to measure the
ejecta flux the total errors will mainly be proportional to this area.
43
Chapter 9
Discussion
9.1
Morphology and light curve of the ring
When studying the evolution of the ring in Section 5.3 it was seen that the right side
of the ring almost appears to ”break” in the early 2000s. A similar overview of the ring
is shown for the R and B bands in [14], but there this part of the ring only becomes
fainter during that time. Except for this the [O III] line shows the same evolution of
the ring and its hotspots as the R and B bands do. The 1000 days delay for the R and
B bands is hard to see by comparing the early images, as shown in Figure 5.5, but for
the images when the [O III] line has reached its peak and starts to decrease the R and
B band images appear to keep increasing for a while. As an example the image of the
[O III] line from December 2009 (8328 days) is more similar to the R and B band image
from June 2014 (9979 days) than the corresponding image from December 2009. In the
[O III] image from June 2014 (see Figure 5.4) it can be seen that the ring is once again
starting to ”break”, but this time on the lower left side.
As mentioned in Section 6.7.1 the light curve of the [O III] line has its peak about 1000
days earlier than the R and B bands, in fact the entire light curve is shifted about 1000
days. It would be tempting to think that it is due to different distances from the center
for the material emitting in the respective intervals. However, there is no indication of
this in the images, hence it is more likely that the delay is a result of the recombination
of the shocked gas. The lines dominating the R and B bands are due to lower ionization
states and their relative contribution will therefore increase with time.
In Figure 6.11 it is seen that the current UVES calibration is more likely to underestimate the flux from the [O III] line for later times. To correct for this a linear adaptation
of the data in Figure 6.11 could be made. To get the best possible calibration the approximations of the HST fluxes would benefit from using a well-fitted curve adapted to
the HST data, instead of using straight lines between two neighboring data points as was
done in Section 6.7.2. Having a good calibration of the total flux is important in order
to get correct fluxes when the shocked and un-shocked components are separated.
9.2
Regions outside the ring
As seen in Figure 7.3 the green, purple and red regions (above and below the ring) are too
far from the ring to be affected by the light from the ring itself, and evidently they do not
44
contain any material that emits faint light, at least not yet. The blue and yellow regions
on the other hand are close to the region where some faint light could be seen in the
image from 2003, in Figure 5.4, but since they are so close to the ring they have a highly
increased background caused by light scattered from the ring. At a first glance it seems
as though there are traces of material emitting light on its own, but to make sure the
changes in the flux are in fact a sign of this the light from the ring needed to be accounted
for. When this was done, by the model described in Section 7.2, it became clear that the
entire increase in the flux between 6000 and 10,000 days is most likely explained by the
ring. Though no model was made for the earliest observations, 2500-3000 days, it is very
likely that the high flux at those times is caused by the ring as well.
The faint light seen outside the ring in 2003 can therefore not be measured or studied
by itself. If it is in the same plane as the ring it subsequently becomes a part of the ring
in later observations. If it is above or below this plane it may be possible to determine
where the material resides by using spectra.
It is interesting to note that the regions just outside the ring evolves slightly differently
between the [O III] line and other wavelength intervals. In [14] there are traces of both
diffuse light and new hotspots outside the ring on the lower left side, but in [O III] there
are never any similar signs. Possibly any potential diffuse light in these areas are too
faint to be seen in the F502N filter.
9.3
Light curve of the ejecta
The source of energy powering the ejecta changes with time, which shows in the shape
of the light curve from the ejecta. The initially declining flux is powered by radioactive
decay, which gets depleted as time passes. The subsequent increase in flux is caused
by X-rays, see Section 2.2, that heats up the material in the ejecta when they interact.
As the X-ray flux increases so will the flux of visual light from the ejecta since the two
are directly proportional to each other. It also appears as though this change of energy
source affects the shape of the ejecta, which goes from being elliptical to having a more
irregular shape with a center region that is no longer visible.
For all three wavelength intervals the fraction of the background light for the ejecta
(i.e. light scattered from the ring) compared to the total flux is about the same. It is
interesting to note that while the fraction appears to increase with time for the R and B
bands, it instead decreases for the F502N filter. This can be explained by comparing the
scattered light to the total flux from the ring for the points in time where models of this
scattered light have been made. For the F502N filter the ring flux decreases dramatically
between 7000 and 10,000 days, while for the R and B bands the flux increases steadily
between 5000 and 7000 days, and the flux at 10,000 days is comparable to that at 7000
days. Since the background light for the ejecta is dependent on the total flux from the
ring a high ring flux will lead to a high background.
The light curve in the F502N filter thus offers a cleaner signal than the other bands,
which will be useful for future theoretical modeling of the conditions in the ejecta.
45
Chapter 10
Conclusions
The conclusions from the measurements in this report are here summarized in three lists;
one for the equatorial ring, one for the regions outside this ring, and one for the ejecta.
Morphology and light curve of the ring
• The light curves of the [O III] line and the R and B bands have very similar shapes,
but the [O III] line peaks 1000 days earlier. The displacement of the light curves
is thought to be caused by the recombination of the shocked gas.
• After the initial dimming, and ”break”, of the ring it becomes brighter again 5000−
6000 days after the explosion, and then starts to fade away again after 7000 − 8000
days.
• The UVES calibration holds well for the earlier times, but becomes worse with
time. To compensate for that a time dependent linear scaling factor could be used.
Regions outside the ring
• There were no traces of diffuse light outside the ring in the difference images or the
measured regions.
• All changes in the flux from the measured regions can be attributed to light scattered from the ring.
Light curve of the ejecta
• It was confirmed that the power source for the ejecta shifted from radioactive decay
at early times, to X-rays from the shock wave collision with the ring at later times.
• This change in energy source also seems to cause the elliptical shape to become
more irregular, and for the center to stop being visible.
• The ejecta measurements are somewhat affected by scattered light from the ring,
but not so much that it completely cancels the increase in flux. In fact, the background from the ring in the F502N filter is smaller than in the other HST filters.
46
Chapter 11
Acknowledgments
First of all I would like to thank my supervisor Josefin Larsson for all the help and
guidance she has given me. Her advice has been very valuable throughout the whole
process. I also want to thank Claes Fransson and Katia Migotto for their useful input
and comments on my results.
Finally I want to thank everyone at the Particle- and Astroparticle physics group for
the warm welcome and for all the interesting lunch discussions during my thesis work.
47
List of Figures
1.1
1.2
2.1
2.2
2.3
3.1
3.2
5.1
5.2
5.3
5.4
5.5
Examples of the spectra [1] and light curve [2] of different types of SNe. .
Example images of SN remnants, taken from NASA’s website; (a) from [6]
and (b) from [7]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
An image showing the three rings around SN 1987A, taken by WFPC2 in
September 1996 using the F658N filter. The field of view is 9.4” × 5.9”.
North is up and east is to the left in this image, as well as all following
images of SN 1987A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
An example of the optical light curve in two different wavelength intervals
[14] and the optical spectrum taken by the UVES camera in 2009. The
arrow in the spectrum marks the [O III] line. . . . . . . . . . . . . . . . .
An example of a throughput profile, from F502N in WFPC2, superposed
in (a) on the spectrum of the ring, taken by UVES in 2009, and in (b)
on the spectrum of the ejecta, taken by the Faint Object Spectrograph on
HST in 1997. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
An image of HST from NASA’s website [22]. . . . . . . . . . . . . . . . .
An image of VLT from European Southern Observatory’s website [26],
showing the four main telescopes. . . . . . . . . . . . . . . . . . . . . . .
An illustration of how the shrunken pixels are mapped from the original
pixel grid to the finer output grid. Image is taken from the HST Dither
Handbook [29]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Images from ACS in November 2003. In (a) one of the raw data images is
shown, and (b) is the result of an optimal drizzle. The field of view is 6”
× 3.75” for both images. . . . . . . . . . . . . . . . . . . . . . . . . . . .
The weight image of the ACS data from November 2003. Darker areas
have lower weights, indicating pixels that were removed to increase the
image quality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
An overview of how the ring and ejecta change over time, between February
1994 and June 2014 (days 2537-9979). The color scale is in units of 10−19
erg cm−2 Å−1 s−1 . The field of view is 3” × 3” for each image. Note that
the evolution is very similar to that seen in the R and B bands [14]. . . .
An overview of how the hotspots appear and change over time, between
February 1994 and June 2014 (days 2537-9979). The color scale is in units
of 10−18 erg cm−2 Å−1 s−1 . The field of view is 2.5” × 2.5” for each image.
The bright spot to the lower right, seen in the images from 1997 and 2000,
is a star. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
5
8
10
11
12
13
15
18
19
20
22
23
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
6.10
6.11
6.12
6.13
7.1
7.2
7.3
7.4
7.5
The regions used to measure the background, displayed in an image from
November 2003 taken by ACS. The field of view is 20.5” × 12.8”. . . . .
The elliptical regions used to measure the flux, displayed in an image from
November 2003 taken by ACS. The field of view is 4” × 2.5”. . . . . . .
The light curve of the ring from an elliptical aperture without any corrections applied. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The slit used for the UVES measurements, displayed in an image from
November 2003 taken by ACS. The field of view is 4.8” × 3”. . . . . . .
The throughput profiles for the F502N filter in the different cameras superposed on the spectrum of the ring, taken by UVES in 2009. . . . . . .
The light curves from both the elliptical aperture (blue), seen in Figure
6.2, and the slit (red), seen in Figure 6.4, with applied corrections. . . . .
The flux from nine stars around SN 1987A in all WFPC2 observations.
Each symbol and color represent a different star. No clear trend can be
seen for the star fluxes. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The light curve from the slit with statistical errors included. . . . . . . .
The light curve for [O III] λ5007 from the measurements in this thesis
compared to the light curve from the R and B band [14], normalized by
the maximum of the respective curves. . . . . . . . . . . . . . . . . . . .
The light curve for [O III] λ5007 from the HST measurements compared to
the light curve from the UVES data [14] convolved with the WFC3 filter
profile. The aperture is shown in Figure 6.4 . . . . . . . . . . . . . . . .
The ratio of the UVES data and interpolated HST data for the [O III]
λ5007 line measured in the slit. . . . . . . . . . . . . . . . . . . . . . . .
An image from November 2003, captured by ACS, convolved with the
elliptical Gaussian function. The bright circles are the large nearby stars,
and the dimmer ellipse in between is SN 1987A. . . . . . . . . . . . . . .
The light curve for the UVES slit in [O III] λ5007 with and without seeing
effects accounted for. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Difference images of all pairs of adjacent points in time. Numbers XXXX
- YYYY shows the time in days for the two images that have been subtracted, with the time difference in days given underneath. The field of
view is 3.1” × 3.1” for each image. . . . . . . . . . . . . . . . . . . . . .
The regions used to measure the flux outside the ring, displayed in an
image from November 2003 taken by ACS. The field of view is 7.3” × 4.8”.
The measured flux in the regions outside the ring. The colors correspond
to those of the regions seen in Figure 7.2. Error bars are only shown for
the yellow and blue lines. . . . . . . . . . . . . . . . . . . . . . . . . . . .
In (a) the image taken by WFC3 in 2014 is shown, and in (b) is the
corresponding model of the ring. The field of view is 3.6” × 2.3” for both
images. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The measured flux in the regions outside the ring. The colors correspond
to those of the regions seen in Figure 7.2. The empty symbols correspond
to flux obtained by subtracting the background caused by the ring. . . .
49
24
25
26
27
28
29
30
31
32
33
34
34
35
37
38
39
40
41
8.1
8.2
The variable elliptical region used to measure the flux of the ejecta, displayed in an image from November 2003 with the size used for that time.
The field of view is 4.5” × 2.8”. . . . . . . . . . . . . . . . . . . . . . . .
The light curve of the ejecta measured for the [O III] λ5007 line, compared
to the light curves measured for the R and B bands. The dashed lines have
been corrected for the high background flux caused by the ring, see Section
7.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
50
42
43
List of Tables
4.1
5.1
6.1
6.2
6.3
Information about the HST observations used in the measurements. The
exposure time is listed as number of images multiplied by the exposure
time for each image. Those marked with + consist of two equally large
sets of images with slightly different exposure times. In these cases the
exposure times have been averaged and the number of images is that of
both sets combined. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
The pixel scale and the optimal pixel fractions used in the drizzling for
the three HST cameras. . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
Values of all parameters used for calculating the corrections as well as the
resulting effective width and normalization factor used to adjust the light
curve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Values of the gain for the HST cameras. . . . . . . . . . . . . . . . . . .
The ratios between the UVES and HST flux measurements at the time of
the UVES observations, which is plotted in Figure 6.11. The fluxes are
measured in ergs s−1 cm−2 . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
28
30
33
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