Determining the characteristics of the north-east jet in supernova remnant Cassiopeia A

(1)

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

(2)

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 north-east 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 r¨ontgenstraling, 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 radio-bron aan de hemel. Daarnaast is hij speciaal omdat hij als een van de weinige su-pernovarestanten een duidelijke ‘jet’, een gerichte bundel van uitstromend gas, heeft. Tijdens dit bachelorproject is er gekeken naar de r¨ontgenstraling 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 tem-peratuur 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.

(3)

1 Introduction

1.1 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 su-pernovae 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 bright-ness. 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

(5)

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 un-derstanding 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, net. It is a measure of

(6)

The ionization age can be obtained from the following formula 1

ne

d Fi

dt = αi−1(T )Fi−1− [αi(T ) + Ri−1(T )]Fi+ Ri(T )Fi+1,

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 net 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

Figure 1: A multi colour image of Casssiopeia A: blue is radio emis-sion, green is Si XIII emission and red is the ratio of Si XIII over Mg XI emission. Image taken from re-view by Jacco Vink.[1]

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 bright-est radio source. It is located at a distance of 3.4 kpc[8] and has a radius of 2.55 pc.[9] Through stud-ies 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-celeration would cause the date of the supernova to shift about ten years to about 1680. This coin-cides with the sighting of a probable supernova by J. Flamsteed.[10]

Based on spectral observations Cassiopeia A is in-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 ac-tually 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 explo-sion and not as in the simple models a spherically symmetric exploexplo-sion. 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]

(7)

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]

(8)

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 mir-rors 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 1013s 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.

(9)

2 Data Analysis

2.1 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 Exposure (ks) Observation Start 4634 148.62 2004-04-28 05:43:26 4635 135.04 2004-05-01 00:44:20 4636 143.48 2004-04-20 08:41:03 4637 163.5 2004-04-22 18:22:53 4638 164.53 2004-04-14 19:47:55 4639 79.05 2004-04-25 09:37:41 5196 49.52 2004-02-08 17:41:35 5319 42.26 2004-04-18 21:18:33 5320 54.37 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,

(10)

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.

(11)

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. 8-10 the corresponding kT versus net contour plots are shown. For all other spectra see

Appendix A.

Table 2: Model parameters for all spectra

NEI model

Region fit-statistic/dof NH(1022) kT (KeV) net (s/cm3)

top0 138.5, 1.07 (c-stat) 0.96 (0.70–1.07) 0.63 (0.58–0.73) 4.0E11 (>1.5E11) top1 393.5, 1.34 0.79 (0.75–0.84) 1.58 (1.46–1.72) 2.0E11 (1.7E11–2.3E11) top2 740.4, 2.52 0.62 (0.61–0.65) 1.42 (1.37–1.49) 2.1E11 (1.9E11–2.5E11) top3 2.38 0.65 (0.62–0.69) 1.07 (1.04–1.11) 3.8E11 (3.2E11–4.7E11) mid0 488.5, 1.61 (c-stat) 1.31 (1.19–1.37) 1.18 (1.10–1.36) 8.1E10 (7.6E10–9.0E10) mid1 509.7, 1.74 0.90 (0.86–0.93) 1.07 (1.04–1.09) 2.6E11 (2.4E11–2.9E11) mid2 1119.5, 3.81 0.71 (0.69–0.72) 1.33 (1.28–1.39) 1.4E11 (1.2E11–1.5E11) mid3 596.8, 2.03 0.67 (0.64–0.71) 1.36 (1.27–1.42) 2.6E11 (2.2E11–2.9E11)

bot0 180.9, 1.12 (c-stat) 1.39 (1.32–1.47) 0.67 (0.55–0.63) >6E11

bot1 1358.4, 4.73 0.62 (0.60–0.64) 2.15 (2.06–2.24) 6.8E10 (6.4E10–7.3E10) bot2 959.7, 3.25 0.68 (0.66–0.70) 2.33 (2.23–2.42) 7.9E10 (7.4E10–8.5E10) bot3 14.53 0.56 (0.55–0.58) 2.77 (2.70–2.85) 8.4E11 (8.1E10–8.7E10)

pshock model

Region fit-statistic/dof NH(1022) kT net

top0 134.2, 1.04 (c-stat) 1.13 (1.00–1.25) 0.63 (0.61–0.96) 6.4E11 (>4.7E11) top1 361.1, 1.23 0.96 (0.89–1.06) 1.70 (1.58–1.87) 4.2E11 (3.0E11–5.3E11) top2 585.0, 2.00 0.89 (0.88–0.96) 1.65 (1.60–1.71) 3.5E11 (3.2E11–3.8E11) top3 478.3, 1.63 0.70 (0.67–0.73) 1.35 (1.31–1.41) 4.4E11 (3.8E11–5.0E11) mid0 462.1, 1.55 (c-stat) 1.45 (1.42–1.50) 1.28 (1.22–1.49) 1.4E11 (9.2E10–2.2E11) mid1 432.3, 1.48 1.27 (1.22–1.30) 1.45 (1.22–1.62) 2.3E11 (1.8E11–3.1E11) mid2 775.5, 2.65 0.97 (0.91–1.09) 1.52 (1.46–1.56) 2.0E11 (1.8E11–2.3E11) mid3 508.4, 1.74 0.99 (0.89–1.06) 1.59 (1.50–1.67) 3.7E11 (3.2E11–4.6E11 bot0 208.6, 1.27 (c-stat) 1.35 (1.27–1.43) 0.70 (0.64–0.85) 3.5E11 (1.5E11–1.3E12) bot1 1369.3, 4.77 0.69 (0.67–0.71) 2.08 (1.97–2.14) 1.5E11 (1.3E11–1.6E11) bot2 1766.4, 6.15 0.95 (0.94–0.97) 2.00 (1.90–2.09) 1.5E11 (1.4E11–1.7E11) bot3 4228.0, 14.48 0.87 (0.84–0.92) 2.59 (2.53–2.67) 2.2E11 (2.0E11–2.3E11)

(12)

Table 3: Model parameters for all spectra fitted with an oxygen continuum

NEI model with O continuum

Region fit-statistic/dof NH(1022) kT (KeV) net (s/cm3)

top0 137.9, 1.07 (c-stat) 1.20 (1.11–1.27) 0.93 (0.86–1.16) 7.4E10 (5.9E10–8.3E10) top1 551.3, 1.87 0.99 (0.97–1.00) 1.31 (1.30–1.36) 3.4E11 (3.1E11–3.5E11) top2 1362.4, 4.63 0.82 (0.79–0.83) 1.25 (1.20–1.33) 2.9E11 (2.6E11–3.1E11) top3 923.5, 3.13 0.89 (0.84–0.92) 1.07 (0.95–0.99) 6.5E11 (5.9E11–7.0E11) mid0 488.7, 1.63 (c-stat) 1.36 (1.30–1.41) 1.27 (1.16–1.35) 7.0E10 (6.3E10–7.8E10) mid1 664.5, 2.25 0.94 (0.92–0.98) 1.20 (1.15–1.23) 1.7E11 (1.4E11–1.8E11) mid2 1836.4, 6.25 0.97 (0.93–0.98) 1.27 (1.25–1.28) 1.4E11 (1.3E11–1.5E11) mid3 862.4, 2.93 0.77 (0.74–0.80) 1.36 (1.28–1.40) 2.3E11 (2.1E11–2.4E11) bot0 187.9, 1.16 (c-stat) 1.37 (1.31–1.43) 0.68 (0.63–0.71) 1.1E11 (9.3E10–1.5E11) bot1 1894.00, 6.60 1.01 (1.00–1.02) 1.70 (1.66–1.75) 9.3E10 (8.7E10–9.4E10) bot2 1191.0, 4.05 1.04 (1.02–1.05) 1.67 (1.67–1.68) 1.1E11 (1.0E11–1.1E11) bot3 6595.2, 22.43 1.10 (1.02–1.18) 2.77 7.0E11

pshock model with O continuum

Region fit-statistic/dof NH(1022) kT net

top0 131.5, 1.01 (c-stat) 1.24 (1.16–1.29) 1.22 (1.10–1.54) 1.1E11 (8.6E10–1.4E11) top1 557.7, 1.90 1.23 (1.21–1.26) 1.35 (1.32–1.41) 8.2E11 (7.6E11–9.0E11) top2 829.1, 2.82 1.26 (1.24–1.28) 1.97 (1.93–2.06) 2.1E11 (2.0E11–2.3E11) top3 639.2, 2.18 1.11 (1.02–1.12) 1.26 (1.20–1.40) 4.7E11 (4.1E11–5.1E11) mid0 459.9, 1.54 (c-stat) 1.46 (1.41–1.49) 1.31 (1.24–1.40) 1.5E11 (1.2E11–1.8E11) mid1 575.2, 1.94 1.44 (1.41–1.47) 1.52 (1.45–1.67) 1.8E11 (1.7E11–1.9E11) mid2 1260.4, 4.29 1.39 (1.36–1.42) 1.69 (1.62–1.78) 1.4E11 (1.3E11–1.5E11) mid3 723.5, 2.46 1.25 (1.22–1.26) 1.75 (1.66–1.92) 2.5E11 (2.0E11–2.5E11) bot0 186.4, 1.15 (c-stat) 1.39 (1.28–1.42) 0.73 (0.65–0.82) 2.1E11 (1.7E11–3.0E11) bot1 1724.0, 6.03 1.41 (1.40–1.44) 1.88 (1.81–1.97) 1.5E11 (1.4E11–1.6E11) bot2 1675.6, 5.82 1.40 (1.38–1.41) 1.95 (1.89–2.04) 1.5E11 (1.4E11–1.5E11) bot3 6779.5, 23.14 1.18 (1.06–1.28) 2.60 2.7E11

3.2 Jet tip masses

One of the model parameters is the normalization. It is defined as norm = 10

−14

4πD2

Z

nenHdV

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

nH =

r

norm 4πD2

XV 10

(13)

Figure 5: Spectrum for top0 with pshock model and O continuum

Figure 6: Spectrum for mid0 with pshock model and O continuum

(14)

Figure 8: Contour plot for top0 with pshock model and O continuum

(15)

Table 4: NEI Models for Jet Tip Kots with O Continuum

Region Counts Region Size χ2_/dof _N

H kT net Si Fe N tip 3134 4.2 × 2.2 78.5, 1.11 1.2 0.60 1.6e13 2200 640 (0.55-0.66) (>1.4e13) (1170-4000) (250-1600) M tip 9626 9.5 × 2.7 187.9, 1.36 1.3 0.73 9.6e12 2.3 0.44 (0.70-0.75) (>4.6e12) (1.6-2.6) (0.26-0.59) S tip 2895 r=1.5 92.2, 1.40 1.38 0.60 9.4e12 3.1 4.2 (1.30-1.46) (0.58-0.62) (> 6.5e12) (1.5-672) (2.1-673)

Multiplying this by the hydrogen mass and the volume gives us the hydrogen mass of the region. MH = mH r norm 4πD2_V X 10 14

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) Volume (1050 cm3) norm Si _{Mass (M)} top0 (NEI O) 2.74 9.24 · 10−9 6599 8.06 · 10−9 top0 (NEI) 2.74 3.55 · 10−5 – 3.94 · 10−8 mid0 (pshock O) 39.1 5.50 · 10−8 7672 7.47 · 10−8 mid0 (pshock) 39.1 2.16 · 10−6 – 3.67 · 10−8 bot0 (NEI O) 3.45 1.29 · 10−8 7187 1.07 · 10−8 bot0 (NEI) 3.45 4.36 · 10−6 – 1.55 · 10−8 Table 5: Jet tip masses and the parameters used to calculate them.

(16)

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 · 1012s cm−3 to 1.6 · 1013s cm−3, the ionisation ages found in this research are in the range from 4.0 · 1010s cm−3to 3.2 · 1011s 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.

(17)

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.

(18)

References

[1] Jacco Vink. Supernova remnants: the X-ray perspective. Astronomy and Astro-physics reviews, 20, 2012.

[2] Mark M Phillips et al. SN 1991T - further evidence of the heterogeneous nature of type IA supernovae. The Astronomical Journal, 103:1632–1637, 1992.

[3] S. Perlmutter et al. Discovery of a supernova explosion at half the age of the universe. Nature, 391:51, 1998.

[4] Stan Woosley and Thomas Janka. The physics of core-collapse supernovae. Nature Physics, 1:147–154, 2005.

[5] H.-Th. Janka, K. Laganke, A. Marek, G.Martinez-Pinedo, and B. Mueller. Theory of Core-Collapse Supernovae. Physics Reports, 442:38–74, 2007.

[6] John M. Blondin, Anthony Mezzacappa, and Christine DeMarino. Stability of standing accretion shocks, with an eye toward core collapse supernovae. The As-trophysical Journal, 584:971–980, 2003.

[7] J. Craig Wheeler, David L. Meier, and James R. Wilson. Asymmetric supernovae from magneto-centrifugal jets. The Astrophysical Journal, 568:807–819, 2002. [8] Jeri E. Reed, J. Jeff Hester, A.C. Fabian, and P.F. Winkler. The three-dimensional

structure of the Cassiopeia A supernova remnant I. the spherical shell. The Astro-physical Journal, 440:706, 1995.

[9] Jacco Vink. X- and γ-ray studies of Cas A: exposing core collapse to the core. New Astronomy Reviews, pages 61–67, 2003.

[10] John R. Thorstensen, Robert A. Fesen, and Sidney van den Berg. The expansion center and dynamical age of the galactic supernova remnant Cassiopeia A. The Astronomical Journal, 122:297–307, 2001.

[11] Oliver Krause et al. The Cassiopeia A supernova was of type IIb. Science, 320:1195– 1197, 2008.

[12] J. Martin Laming, Una Hwang, Balint Radics, Gergely Lekli, and Endre Tak´acs. The polar regions of Cassiopeia A: The aftermath of a gamma-ray burst? The Astrophysical Journal, 644:260–273, 2006.

[13] R. A. Fesen et al. The expansion asymmetry and age of the Cassiopeia A supernova remnant. The Astrophysical Journal, 645:283–292, 2006.

[14] Una Hwang and J. Martin Laming. Where was the iron synthesized in Cassiopeia A. The Astrophysical Journal, 597:362–373, 2003.

(19)

[15] J. Martin Laming and Una Hwang. On the determination of ejecta structure and explosion asymmetry from the x-ray knots of Cassiopeia A. The Astrophysical Journal, 597:347–361, 2003.

[16] Una Hwang, J. Martin Laming, et al. A million second Chandra view of Cassiopeia A. The Astrophysical Journal, 615:L117–L120, 2004.

[17] NASA. http://chandra.harvard.edu/about/. Subpages ‘Telescope System’ and ‘Science Instruments’ visited June 17 2015, Chandra image obtained from underly-ing page.

[18] Chandra. http://cxc.cfa.harvard.edu/proposer/POG/html/index.html. [19] R. Willingale, J.A.M. Bleeker, K.J. van der Heyden, J.S. Kaastra, and J. Vink.

X-ray spectral imaging and Doppler mapping of Cassiopeia A. Astronomy and Astrophysics, 381:1039–1048, 2001.

[20] Kazimierz J. Borkowski, Willial J. Lyerly, and Stephen P. Reynolds. Supernova Remnants in the Sedov expansion phase: thermal x-ray emission. The Astrophysical Journal, 548:820–835, 2001.

[21] Edward Anders and Nicolas Grevesse. Abundances of the elements: Meteoritic and solar. Geochimica et Cosmochimica Acta, 53:197–214, 1989.

[22] J. Vink, J.S. Kaastra, and J.A.M. Bleeker. A new mass estimate and puzzling abundances of SNR Cassiopeia A. Astronomy and Astrophysics, 1996.

(20)

A

Spectra

(21)

(22)

(23)

Determining the characteristics of the north-east jet in supernova remnant Cassiopeia A