Determining the characteristics of the
north-east jet in supernova remnant
Cassiopeia A
Auteur
Ruben Boots
10003736
Begeleider
Dr. Jacco Vink
Tweede beoordelaar
Dr. Phil Uttley
Verslag van Bachelorproject Natuur- en Sterrenkunde, omvang 12 EC
uitgevoerd tussen 01-05-2014 en 25-08-2015
Ingeleverd op 25-08-2015
Universiteit van Amsterdam
Fnwi
Anton Pannekoek Instituut
Samenvattingen
Wetenschappelijke samenvatting
Aims. In 2004 Laming et al. published an article about the polar regions in supernova
remnant Cassiopeia A. In this article they fitted the newly found jet tips in the northeast jet. The ionisation age of about 1013 s cm−3 they found for these tips seems quite
high. These ionisation ages imply an electron density of about 103 cm−3 , which is higher
than in most parts of the remnant. This thesis is a follow up to that research and tried
to reproduce these results by Laming et al. The mass for the jet tips was also calculated.
Methods. The data from the 1 Million Second Chandra View was used in this research,
the same data as used by Laming et al. The obtained spectra have been fitted with NEI
and pshock models, with a hydrogen as well as with an oxygen continuum using xspec.
Results. The values for the ionisation ages for the faint jet tips found in this research
are in the range of 5.8 · 1010 − 6.4 · 1011 s cm−3 . This differs significantly from the values
found by Laming et al. This corresponds to electron densities of about 10 cm−3 . This
is still quite high for an average supernova remnant but similar to densities found in the
other parts of the remnant. The mass of the jet tips is of the order of 10−8 M .
Populaire samenvatting
Als een zware ster (vanaf ongeveer acht keer de massa van de zon) aan het einde van zijn
leven is zal hij ontploffen. Dit noemen we een supernova-explosie. Na zo’n supernova
blijft er een hete gaswolk over die allerlei licht uitzendt, van radiostraling tot harde
röntgenstraling, dit heet een supernovarestant.
Cassiopeia A (Cas A) is zo’n supernovarestant. Hij is nog vrij jong, maar ongeveer
340 jaar. Door zijn lage leeftijd is hij nog heel helder, hij is zelfs de helderste radiobron aan de hemel. Daarnaast is hij speciaal omdat hij als een van de weinige supernovarestanten een duidelijke ‘jet’, een gerichte bundel van uitstromend gas, heeft.
Tijdens dit bachelorproject is er gekeken naar de röntgenstraling die deze jet van Cas
A uitzendt. Door naar het spectrum te kijken en dit te modelleren is er van een aantal
stoffen, zoals ijzer en silicium, bekeken hoeveel er in de gaswolk zit. Ook zijn de temperatuur en de dichtheid bekeken en vergeleken met een eerder onderzoek naar Cas A.
Daarna is met deze gegevens de massa bepaald van de uiterste punten van de jet.
In dit onderzoek is de dichtheid van de uiterste punten van de jet lager uitgekomen
dan in het eerdere onderzoek. De dichtheden die in dit onderzoek zijn gevonden lijken
logischer te zijn dan de hoge dichtheden in het andere onderzoek. Zij vonden namelijk
dichtheden die groter waren de die in de rest van de supernovarestant.
1
Contents
1 Introduction
1.1 Supernovae . . . . .
1.2 Supernova Remnants
1.3 SNR Cassiopeia A .
1.4 Chandra satellite . .
1.5 Motivation . . . . .
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2 Data Analysis
2.1 Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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3 Results
10
3.1 Modelled spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2 Jet tip masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4 Discussion
15
5 Conclusion
16
References
17
A Spectra
19
2
1
1.1
Introduction
Supernovae
Supernovae are highly energetic processes that occur in a late stage of stellar evolution.
This process is so energetic that it is mostly referred to as an explosion. Supernovae
can roughly be divided into two groups, core collapse supernovae and thermonuclear
supernovae. Apart from his classification supernovae can also be split into a few types
based on spectroscopic observations and their light-curves. These types are Ia, Ib, Ic,
IIb, IIP and IIl. Here, all the type II supernovae show hydrogen in their spectrum,
whereas the type I supernovae don’t. The type I subtypes are based on the presence of
Helium and Silicon. The type II subsets are based on the shape of the light-curve, for
IIP it shows a plateau, for type IIL it is a linear light-curve. Type IIb is an intermediate
class of supernovae, at first they behave like a type II, but eventually become a type Ib
supernova.[1]
Of the described types, only the type Ia are thermonuclear supernovae. These supernovae are thought to all have a similar progenitor, namely a C/O white dwarf with a
mass close to the Chandrasekhar limit. These supernovae most likely occur when a white
dwarf in a binary system has accreted enough mass to exceed the Chandrasekhar limit
after which explosive nuclear fusion will take place. Due to the similarity in progenitor,
the light-curves of all type Ia supernovae look alike, but there are small variations in
peak brightness and spectral features. However, the light-curves of these supernovae
show an interesting feature, there is a relation between the peak brightness and the
post-peak decline.[2] This relation can be used to determine the absolute peak brightness. This determination makes them exceptionally useful in cosmology, because they
can now be used as standard candles. Using this it has been shown that the expansion
of the universe is not decelerating but accelerating.[3] Perlmutter, Shchmidt and Riess
were awarded the Nobel prize in physics in 2011 for this discovery.[1]
The core collapse supernovae occur at the end of the lives of stars with a mass
M & 8M .[4] It occurs when all possible fusion reactions have taken place. This is
when the silicon burning phase has ended, since no energy is gained by the fusion of
iron. Because of the absence of fusion, the star will start to collapse due to gravity.
Then, when the core has collapsed to a certain size, depending on the mass of the
original star, it will form a proto-neutron star. This proto-neutron star is rigid and
will stop the collapse, sending a shock wave through the rest of the infalling gas. The
gravitational energy which is liberated during the collapse of the star can be as high
as 1053 erg is what fuels the explosion. The exact mechanics however, are not yet fully
understood. Simulations of supernova explosions show that the shock wave cannot be
the only feature of the explosion. [5] Models which include a form of asymmetry have
been in better agreement with observations, such as non-spherically symmetric standing
accretion shock instability(SASI).[6]. Another means by which the explosion may be
fueled is by magneto-centrifugal jet formation. This could arise when the magnetic field
of the star gets amplified because of differential rotation. This is analogous to the jets
observed in accreting black holes.[7] None of these models however is fully accurate.
3
Supernovae are among the most energetic processes in the universe. They provide most
of the energy of the interstellar medium and are also an important factor in the chemical
evolution of the universe, which makes understanding supernovae a key ingredient of understanding the history of our universe. Because of this and because of their importance
in cosmology, the field of supernovae research is quite big. Supernovae, unfortunately,
are not very common. For a typical spiral galaxy such as our own milky way, one expects
only 2 or 3 supernovae per century.[1]
1.2
Supernova Remnants
Supernova remnants (SNRs) are luminous plasma clouds which remain visible long after
a supernova explosion. These remnants are a useful way to learn about supernova
explosions. Their morphology and element abundances can give us information about the
original star and about the supernova from which it originates. Because the supernova
ejecta collide with the circumstellar material, SNRs can also provide some information
about the latter and can thus reveal some information about their progenitors. SNRs
are also prime candidates for cosmic ray acceleration.[1]
Shocks
Shocks are a key component of SNRs. There are two main shocks in a SNR, the forward
shock and the reverse shock. The forward shock is the region where the ejected mass
from the star collides with the ISM. It moves outward and sweeps up the ISM, which
results in deceleration of the forward shock. Due to this deceleration, the ejected mass
behind the forward shock can catch up with it. The ejecta will then bounce of the
forward shock, creating the reverse shock. This reverse shock heats the ejected mass.
The forward shock gives information about the ISM, while the reverse shock does this
for the SN ejecta.
Because of the low densities in SNRs, the mean free path for particles in the SNRs
is generally larger the the remnant itself. Since these shocks are visible, they have
to be collisionless. All energy transfer occurs through fluctuations in the electric and
magnetic fields. There are quite a few models for collisionless shock, however these all
treat the shock itself as an infinitely narrow region. In reality the shocks are quite broad,
with precursors from swept up mass. So studying SNRs can also be useful for better
understanding shock physics.[1]
The low densities in SNRs also cause the plasma to be underionized, because there are
just not enough ionizing collisions. The term for this state is Non Equilibrium Ionization
(NEI).
Ionisation age
One defining parameter of the SNR plasma is the ionisation age, ne t. It is a measure of
the ionisation equilibrium. As said before, the plasma will most likely be under-ionized.
4
The ionization age can be obtained from the following formula
1 d Fi
= αi−1 (T )Fi−1 − [αi (T ) + Ri−1 (T )]Fi + Ri (T )Fi+1 ,
ne dt
where Fi is the fraction of atoms in a given ionization state, αi (T ) the ionization rate,
i is the ion and Ri the recombination rate. From this formula you can see that the
representation ne t is a simplification, it is not just the product of the electron density
and the time, it is actually the integral over time of the electron density. For a first
crude impression of the electron density you could however just divide the ionization age
by the age of the remnant.[1]
1.3
SNR Cassiopeia A
SNR Cassiopeia A (as pictured in Fig. 1) is a very
interesting object. Not only is it the one of the
youngest galactic SNRs, but it is also the brightest radio source. It is located at a distance of 3.4
kpc[8] and has a radius of 2.55 pc.[9] Through studies of the proper motions of the ejecta, it has been
calculated that the supernova explosion took place
in approximately 1671. This is done assuming no
deceleration of the knots. Introducing a small de- Figure 1: A multi colour image of
celeration would cause the date of the supernova Casssiopeia A: blue is radio emisto shift about ten years to about 1680. This coin- sion, green is Si XIII emission and
cides with the sighting of a probable supernova by red is the ratio of Si XIII over Mg
XI emission. Image taken from reJ. Flamsteed.[10]
Based on spectral observations Cassiopeia A is in- view by Jacco Vink.[1]
ferred to be a type Ib supernova.[9]. However, more
recently it has been shown with the detection of a light echo that Cassiopeia A was actually a type IIb supernova.[11]
An interesting feature about Cassiopeia A are the north-east and south-west jet-like
structures (visible in red in Fig. 1). These structures could indicate a bipolar SN explosion and not as in the simple models a spherically symmetric explosion. Another possible
explanation could be that the explosion itself was indeed spherically symmetric but the
circumstellar medium was inhomogeneous. With low density regions in the circumstellar
medium at the position of the present jets this might have happened. However numerical
simulations indicate that this is highly unlikely.[12] Combined with the high velocities
of the jet ejecta[13] it is concluded that these structures most likely are a direct result
of the explosion. One can therefore classify them as jets.
Motivated by two papers by Laming and Hwang from 2003[14],[15] in 2004 a million
second observation was performed with teh Chandra telescope. In these observations
the faint jet tips were visible for the first time.[16]
5
1.4
Chandra satellite
The data for this research was obtained with the Chandra sattelite. The Chandra x-ray
telescope was launched in 1999. It’s purpose is to image very hot x-ray emitting regions.
It is named after Subrahmanyan Chandrasekhar, who was awarded with a Nobel prize
for his theoretical research on stellar evolution.
The telescope consists of four mirrors which reflect the x-rays onto a combination of the
four scientific instruments. A schematic view of the Chandra telescope can be seen in
Fig. 2.
Figure 2: A schematic view of the Chandra telescope. Image taken from Chandra
website.[17]
ACIS
The Advanced CCD Imaging Spectrograph (ACIS) consists of an array of CCDs. It is
split up in two parts, ACIS-I and ACIS-S. The ACIS-I is a 2x2 array of CCDs used only
for imaging. It does however also record the energy of an incoming photon and not only
its position. Because of this it can also be used as a spectrograph. Hence the name.
The ACIS S is a row of 6 CCDs next to the ACIS I (see Fig. 3). It is used for imaging
as well as spectrography with the transmission gratings. All CCDs are composed of
1024x1024 pixels. These pixels are 23.985 microns, which corresponds to 0.4920 arcsec.
The energy range of both the ACIS-I and ACIS-S is about 0.5–10 keV. Most of the
CCDs are front-illuminated, meaning that the detector pixels are facing towards the
incoming photons. Two CCDs, S1 and S3, which was used for the data in this research,
are however back-illuminated, their pixels are faced away from the incoming photons.
Due to this setup their sensitivity for lower energy photons is higher. They also have a
better average energy resolution.[18]
6
Figure 3: Schematic view of the ACIS instrument (image taken from Chandra Proposers’
Observervatory Guide [18]
HRC
The High Resolution Camera (HRC) is exactly what the name implies, it is an x-ray
camera with a high resolution. It can image details as small as half an arc-second. It only
records only the position where a photon hits the HRC and has no further information
about that photon.
HETGS and LETGS
The High Energy Transmission Grating Spectrometer (HETGS) and the Low Energy
Transmission Grating Spectrometer (LETGS) can both be placed right behind the mirrors of the Chandra satellite. The produced spectrum is then detected with either the
HRC or the ACIS to obtain a high resolution x-ray spectrum. The energy range of the
LETGS is 0.08 to 2 keV, for the HETGS this range is 0.4 to 10 keV.[17]
1.5
Motivation
This research is a follow up to the research done by Laming et al.[12] Laming et al. find
values of about 1013 s cm−3 for the ionisation age in the north-east jet tips. The electron
density of a region can be estimated using the ionization age. The electron density is
roughly the ionization age divided by the age of the remnant. Cassiopeia A was about
320 years old at the time of the observation, which is roughly 1010 seconds. The implied
electron density would then be 103 cm−3 , which is unusually high for a typical SNR. The
ionization age is also higher than in almost any other part of the remnant.[19] Laming
et al. do not give a possible explanation for these high values, although they note that
they are very high. It is therefore interesting to see if the results can be reproduced and
if so look into a possible explanation for these high values.
7
2
2.1
Data Analysis
Dataset
The data used in this thesis is taken from the million second Chandra view of Cas A[16],
which was downloaded from the Chandra Data Archive. Exposure dates and times can
be seen in table 1. All these observations were done with the ACIS-S S3 CCD. First the
individual spectra for each region were extracted from each of the subexposures using
ciao software package version 4.5. They were then combined to get a final spectrum for
each region.
Observation ID
4634
4635
4636
4637
4638
4639
5196
5319
5320
Exposure (ks)
148.62
135.04
143.48
163.5
164.53
79.05
49.52
42.26
54.37
Observation Start
2004-04-28 05:43:26
2004-05-01 00:44:20
2004-04-20 08:41:03
2004-04-22 18:22:53
2004-04-14 19:47:55
2004-04-25 09:37:41
2004-02-08 17:41:35
2004-04-18 21:18:33
2004-05-05 22:59:36
Table 1: Observation data
2.2
Regions
There are three main filaments in the northeast jet. Along each of these filaments four
regions were defined using SAOimage ds9, which leads to a total of twelve regions. See
Fig. 4 for a picture of these regions as well as the background region. The three filaments
were labeled top, mid and bot. The regions of these filaments are given an index from
0 to 4 starting with the outermost region of each filament.
2.3
Models
The spectra were fitted using xspec version 12.7.0. All spectra have been fitted with
both single component NEI and pshock models, each with a hydrogen as well as an
oxygen continuum. A brief explanation of these models is given below.
NEI model
The xspec NEI model models the properties of a shocked, underionized plasma. It is
however a simplification since it assumes an instantly shocked plasma, or an infinitely
narrow temperature step. It also assumes a single temperature and ionization age which
in most cases will not be the actual state of the plasma. Based on the ionization age,
8
Figure 4: The twelve extraction regions in the northeast jet. Also pictured, the large
rectangle, is the background region.
temperature and atomic emission it provides a model spectrum. Due to the simplification
it is not the best model for SNRs, especially for young ones.[20]
pshock model
For young SNRs a better option is the pshock, or plane parallel shock, model. This
model uses the same atomic data, but instead of an infinitely narrow temperature step,
it uses a temperature gradient. Due to the mass swept up by the shock, it will not be an
infinitely narrow shock, but rather have a precursor which broadens the actual shock.
Due to this more realistic approach, the pshock models are generally better than the
NEI models.
In some spectra an argon emission line was present at about 3.13 keV. Both the NEI
and the pshock models did not have this argon emission line included. Where present,
this line was fitted using a Gaussian.
9
3
Results
3.1
Modelled spectra
In table 2 and 3, the results of fitting the spectra are shown. For reference, in table 4
the results for the jet tips from Laming et al.[12] are shown. For most of the spectra the
standard fit-statistic χ2 was used. For the jet tips C-stat was used because of the low
countrates. Errors are calculated with the error command if the fit was good enough,
in the other cases the steppar command was used. All errors correspond to a 90%
confidence interval. In Fig. 5- 7 the spectra and for the jet tips are shown. In Fig. 810 the corresponding kT versus ne t contour plots are shown. For all other spectra see
Appendix A.
Table 2: Model parameters for all spectra
Region
top0
top1
top2
top3
fit-statistic/dof
138.5, 1.07 (c-stat)
393.5, 1.34
740.4, 2.52
2.38
NEI model
NH (1022 )
kT (KeV)
0.96 (0.70–1.07)
0.63 (0.58–0.73)
0.79 (0.75–0.84)
1.58 (1.46–1.72)
0.62 (0.61–0.65)
1.42 (1.37–1.49)
0.65 (0.62–0.69)
1.07 (1.04–1.11)
ne t (s/cm3 )
4.0E11 (>1.5E11)
2.0E11 (1.7E11–2.3E11)
2.1E11 (1.9E11–2.5E11)
3.8E11 (3.2E11–4.7E11)
mid0
mid1
mid2
mid3
488.5, 1.61 (c-stat)
509.7, 1.74
1119.5, 3.81
596.8, 2.03
1.31
0.90
0.71
0.67
(1.19–1.37)
(0.86–0.93)
(0.69–0.72)
(0.64–0.71)
1.18
1.07
1.33
1.36
(1.10–1.36)
(1.04–1.09)
(1.28–1.39)
(1.27–1.42)
8.1E10
2.6E11
1.4E11
2.6E11
bot0
bot1
bot2
bot3
180.9, 1.12 (c-stat)
1358.4, 4.73
959.7, 3.25
14.53
1.39
0.62
0.68
0.56
(1.32–1.47)
(0.60–0.64)
(0.66–0.70)
(0.55–0.58)
0.67
2.15
2.33
2.77
(0.55–0.63)
(2.06–2.24)
(2.23–2.42)
(2.70–2.85)
>6E11
6.8E10 (6.4E10–7.3E10)
7.9E10 (7.4E10–8.5E10)
8.4E11 (8.1E10–8.7E10)
Region
top0
top1
top2
top3
fit-statistic/dof
134.2, 1.04 (c-stat)
361.1, 1.23
585.0, 2.00
478.3, 1.63
pshock model
NH (1022 )
1.13 (1.00–1.25)
0.63
0.96 (0.89–1.06)
1.70
0.89 (0.88–0.96)
1.65
0.70 (0.67–0.73)
1.35
kT
(0.61–0.96)
(1.58–1.87)
(1.60–1.71)
(1.31–1.41)
ne t
6.4E11 (>4.7E11)
4.2E11 (3.0E11–5.3E11)
3.5E11 (3.2E11–3.8E11)
4.4E11 (3.8E11–5.0E11)
mid0
mid1
mid2
mid3
462.1, 1.55 (c-stat)
432.3, 1.48
775.5, 2.65
508.4, 1.74
1.45
1.27
0.97
0.99
(1.42–1.50)
(1.22–1.30)
(0.91–1.09)
(0.89–1.06)
1.28
1.45
1.52
1.59
(1.22–1.49)
(1.22–1.62)
(1.46–1.56)
(1.50–1.67)
1.4E11 (9.2E10–2.2E11)
2.3E11 (1.8E11–3.1E11)
2.0E11 (1.8E11–2.3E11)
3.7E11 (3.2E11–4.6E11
bot0
bot1
bot2
bot3
208.6, 1.27 (c-stat)
1369.3, 4.77
1766.4, 6.15
4228.0, 14.48
1.35
0.69
0.95
0.87
(1.27–1.43)
(0.67–0.71)
(0.94–0.97)
(0.84–0.92)
0.70
2.08
2.00
2.59
(0.64–0.85)
(1.97–2.14)
(1.90–2.09)
(2.53–2.67)
3.5E11
1.5E11
1.5E11
2.2E11
10
(7.6E10–9.0E10)
(2.4E11–2.9E11)
(1.2E11–1.5E11)
(2.2E11–2.9E11)
(1.5E11–1.3E12)
(1.3E11–1.6E11)
(1.4E11–1.7E11)
(2.0E11–2.3E11)
Table 3: Model parameters for all spectra fitted with an oxygen continuum
NEI model with O continuum
NH (1022 )
kT (KeV)
1.20 (1.11–1.27)
0.93 (0.86–1.16)
0.99 (0.97–1.00)
1.31 (1.30–1.36)
0.82 (0.79–0.83)
1.25 (1.20–1.33)
0.89 (0.84–0.92)
1.07 (0.95–0.99)
Region
top0
top1
top2
top3
fit-statistic/dof
137.9, 1.07 (c-stat)
551.3, 1.87
1362.4, 4.63
923.5, 3.13
mid0
mid1
mid2
mid3
488.7, 1.63 (c-stat)
664.5, 2.25
1836.4, 6.25
862.4, 2.93
1.36
0.94
0.97
0.77
(1.30–1.41)
(0.92–0.98)
(0.93–0.98)
(0.74–0.80)
1.27
1.20
1.27
1.36
bot0
bot1
bot2
bot3
187.9, 1.16 (c-stat)
1894.00, 6.60
1191.0, 4.05
6595.2, 22.43
1.37
1.01
1.04
1.10
(1.31–1.43)
(1.00–1.02)
(1.02–1.05)
(1.02–1.18)
0.68 (0.63–0.71)
1.70 (1.66–1.75)
1.67 (1.67–1.68)
2.77
Region
top0
top1
top2
top3
fit-statistic/dof
131.5, 1.01 (c-stat)
557.7, 1.90
829.1, 2.82
639.2, 2.18
mid0
mid1
mid2
mid3
459.9, 1.54 (c-stat)
575.2, 1.94
1260.4, 4.29
723.5, 2.46
1.46
1.44
1.39
1.25
(1.41–1.49)
(1.41–1.47)
(1.36–1.42)
(1.22–1.26)
1.31
1.52
1.69
1.75
bot0
bot1
bot2
bot3
186.4, 1.15 (c-stat)
1724.0, 6.03
1675.6, 5.82
6779.5, 23.14
1.39
1.41
1.40
1.18
(1.28–1.42)
(1.40–1.44)
(1.38–1.41)
(1.06–1.28)
0.73 (0.65–0.82)
1.88 (1.81–1.97)
1.95 (1.89–2.04)
2.60
3.2
(1.16–1.35)
(1.15–1.23)
(1.25–1.28)
(1.28–1.40)
pshock model with O continuum
NH (1022 )
kT
1.24 (1.16–1.29)
1.22 (1.10–1.54)
1.23 (1.21–1.26)
1.35 (1.32–1.41)
1.26 (1.24–1.28)
1.97 (1.93–2.06)
1.11 (1.02–1.12)
1.26 (1.20–1.40)
(1.24–1.40)
(1.45–1.67)
(1.62–1.78)
(1.66–1.92)
ne t (s/cm3 )
7.4E10 (5.9E10–8.3E10)
3.4E11 (3.1E11–3.5E11)
2.9E11 (2.6E11–3.1E11)
6.5E11 (5.9E11–7.0E11)
7.0E10
1.7E11
1.4E11
2.3E11
(6.3E10–7.8E10)
(1.4E11–1.8E11)
(1.3E11–1.5E11)
(2.1E11–2.4E11)
1.1E11 (9.3E10–1.5E11)
9.3E10 (8.7E10–9.4E10)
1.1E11 (1.0E11–1.1E11)
7.0E11
1.1E11
8.2E11
2.1E11
4.7E11
ne t
(8.6E10–1.4E11)
(7.6E11–9.0E11)
(2.0E11–2.3E11)
(4.1E11–5.1E11)
1.5E11
1.8E11
1.4E11
2.5E11
(1.2E11–1.8E11)
(1.7E11–1.9E11)
(1.3E11–1.5E11)
(2.0E11–2.5E11)
2.1E11 (1.7E11–3.0E11)
1.5E11 (1.4E11–1.6E11)
1.5E11 (1.4E11–1.5E11)
2.7E11
Jet tip masses
One of the model parameters is the normalization. It is defined as
Z
10−14
norm =
ne nH dV
4πD2
where D is the distance to the source, ne the electron density, nH the hydrogen density
and V the volume of the region from which the spectrum is taken. If we assume constant
densities throughout the volume, the integral becomes a simple multiplication. We can
write ne = XnH , the formula can then be rewritten as
r
norm 4πD2 14
nH =
10
XV
11
Figure 5: Spectrum for top0 with pshock model and O continuum
Figure 6: Spectrum for mid0 with pshock model and O continuum
Figure 7: Spectrum for bot0 with pshock model and O continuum
12
Figure 8: Contour plot for top0 with pshock model and O continuum
Figure 9: Contour plot for mid0 with pshock model and O continuum
Figure 10: Contour plot for bot0 with NEI model
13
Table 4: NEI Models for Jet Tip Kots with O Continuum
Region
N tip
Counts
3134
Region Size
4.2 × 2.2
χ2 /dof
78.5, 1.11
NH
1.2
M tip
9626
9.5 × 2.7
187.9, 1.36
1.3
S tip
2895
r=1.5
92.2, 1.40
1.38
(1.30-1.46)
kT
0.60
(0.55-0.66)
0.73
(0.70-0.75)
0.60
(0.58-0.62)
ne t
1.6e13
(>1.4e13)
9.6e12
(>4.6e12)
9.4e12
(> 6.5e12)
Si
2200
(1170-4000)
2.3
(1.6-2.6)
3.1
(1.5-672)
Fe
640
(250-1600)
0.44
(0.26-0.59)
4.2
(2.1-673)
Multiplying this by the hydrogen mass and the volume gives us the hydrogen mass of
the region.
r
norm 4πD2 V 14
MH = mH
10
X
For a hydrogen based plasma X = 1.2. For a plasma consisting mainly of other heavy
elements, their contributions to ne have to be taken into account. For the oxygen based
plasma the following expression for ne is used.
ne = [H] + 2[He] + 8[O] + 12[Si]
Here the brackets indicate fitted abundances in terms of solar hydrogen abundance.
Then, once the hydrogen mass is calculated, the abundances and relative masses can be
used to calculate the masses for the other elements. The total mass is then obtained by
summing the masses for the individual elements.
In table 5 for the best fitted models the results of the calculations for the jet tip masses
are shown, along with the parameters used for these calculations. In all cases the distance
used is 3.4 kpc. The abundances of H, He and O are 1, 1 and 10000 respectively. Solar
abundances are taken from Anders & Grevesse.[21]
Region (model)
top0 (NEI O)
top0 (NEI)
mid0 (pshock O)
mid0 (pshock)
bot0 (NEI O)
bot0 (NEI)
Volume (1050 cm3 )
2.74
2.74
39.1
39.1
3.45
3.45
norm
9.24 · 10−9
3.55 · 10−5
5.50 · 10−8
2.16 · 10−6
1.29 · 10−8
4.36 · 10−6
Si
6599
–
7672
–
7187
–
Mass (M )
8.06 · 10−9
3.94 · 10−8
7.47 · 10−8
3.67 · 10−8
1.07 · 10−8
1.55 · 10−8
Table 5: Jet tip masses and the parameters used to calculate them.
14
4
Discussion
Comparing the ionisation ages for the jet tips found by Laming et al.[12] with those
found in this research shows a significant difference. Where Laming et al. find ionisation
ages ranging from 9.4 · 1012 s cm−3 to 1.6 · 1013 s cm−3 , the ionisation ages found in this
research are in the range from 4.0 · 1010 s cm−3 to 3.2 · 1011 s cm−3 . Even with confidence
ranges taken in account these values differ significantly. It is possible that Laming et
al. got stuck in a local fit minimum and the contour plots show that in some cases the
ionization age may be quite free to vary. It must be noted however that Laming et al.
used χ2 so their contour plots might differ.
Comparing the models for the stem of the jets, not much difference is found in the
parameter values. However the fits in this research are quite bad. Looking at the
goodness of the fits it is seen that in most cases the pshock model does indeed fit best.
The bottom filament is an exception, for bot0, bot1 and bot2 the NEI model gave the
best fit. For the latter two regions this might be explained by the large region size and
the fact that the fits are just bad. For the tip region the difference is not that big.
It could be that the low count rate makes the spectrum less sensitive to the difference
between the NEI and pshock models. Another thing that is of interest is the fact that
only top0 and mid0 have better fits with a hydrogen continuum. (in bot3 it’s a tie)
In other researches e.g. Laming et al.[12] and Vink et al.[22] models with an oxygen
continuum consistently gave better fits. A possible reason for this difference is the fact
that both Laming and Vink used multiple component models, whereas this research used
just a single component. This could also explain why the fits get worse as the regions
are further towards the center of the remnant. The regions closer to the center have had
more time to mix and have been passed by the forward shock earlier. Their composition
will therefore be more complicated and are less likely to be fitted well with a single
component model.
In some cases, for example with bot3, the fit is so bad that for some parameters a
confidence range could not be determined. The focus of this research were the jet tips,
therefore less effort has been put in the jet stems. In future research the jet stems might
be also be examined more carefully to get a more complete picture of the jets. Another
possible follow up research might be to model the spectra with another program such as
spex. This could eliminate possible software biases.
The masses calculated for the jet tips are quite small, but taking in account that the
total ejecta has a mass of 4.3 M [22] it does not seem unreasonable if you compare the
size of the jet tips to the size of the remnant. In Vink[22] the masses calculated for the
whole remnant assuming an oxygen continuum were lower than those calculated with a
hydrogen continuum. This is also the case for top0 and bot0 in this research, however
for mid0 the mass turns out higher. It could also be interesting to determine the mass of
the whole jet, but due to the (relatively) bad fits for the stem this has not been done in
this research. One could also consider doing the same for the fainter north-west counter
jet.
15
5
Conclusion
Although the fits are not always good, the ionisation ages found in this research for the
stem of the jets are in global agreement with those found by Laming et al. However
for the jet tips the ionisation ages are significantly lower than Laming et al. found.
Ionization ages of the order of 1010 − 1011 s cm−3 agree better with the rest of the
remnant. The inferred electron densities of about 10 cm3 are in better agreement with
average electron densities in SNRs The calculated mass of the jet tips does not raise
questions, but further research is needed to calculate the mass for the entire jet.
Acknowledgements
Firstly I would like to thank Jacco Vink, my supervisor, for his seemingly endless patience
during this project. I would also like to thank Phil Uttley for being my second examiner
and making sure the thesis was graded as soon as possible. Of course I would like to
thank my girlfriend Tessa for helping me through the rough patches. And lastly I would
like to thank all of inhabitants of the API Master students room for entertaining me and
for not openly judging me if I had one of those days where I would do exactly nothing.
16
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17
[15] J. Martin Laming and Una Hwang. On the determination of ejecta structure and
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[17] NASA. http://chandra.harvard.edu/about/. Subpages ‘Telescope System’ and
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[19] R. Willingale, J.A.M. Bleeker, K.J. van der Heyden, J.S. Kaastra, and J. Vink.
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18
A
Spectra
Figure 11: Spectrum for top1 with pshock model and O continuum
Figure 12: Spectrum for top2 with pshock model and O continuum
19
Figure 13: Spectrum for top3 with pshock model and O continuum
Figure 14: Spectrum for mid1 with pshock model and O continuum
Figure 15: Spectrum for mid2 with pshock model and O continuum
20
Figure 16: Spectrum for mid3 with pshock model and O continuum
Figure 17: Spectrum for bot1 with pshock model and O continuum
Figure 18: Spectrum for bot2 with pshock model and O continuum
21
Figure 19: Spectrum for bot3 with pshock model and O continuum
22