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Investigating the Time Evolution of X-Ray Absorption in Gamma-Ray Bursts

Author:

Hannah Deprez (980102-7062) deprez@kth.se

Department of Physics

Royal Institute of Technology (KTH)

Supervisor: Josefin Larsson

June 29, 2020

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Typeset in L A TEX

TRITA-SCI-GRU 2020:96 ©Hannah Deprez, 2020

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Abstract

Understanding the absorption in gamma-ray burst spectra can teach us about the prop- erties of the host galaxy and the intergalactic medium. A possible decrease in X-ray absorption with time is expected to be related to time-dependent ionisation and dust destruction of the surrounding medium, caused by the gamma-ray burst. These interac- tions are expected to occur in the medium close to the burst. No change in absorption may point to most of the absorbing material being further away from the host, in the intergalactic medium. In this thesis, the evolution of the X-ray absorption is investi- gated for a sample of five gamma-ray bursts. A comparison is made between the column density from the early Swift X-ray observations, starting around 100 s after the trigger, and XMM-Newton observations, starting about a day later. Time-integrated and time- resolved X-ray spectroscopy is performed for the XMM-Newton observations. It is found that only one of the bursts in the sample, GRB 060729, shows a significant decrease in column density. The four other bursts show similar values during the two measurements.

From this it is concluded that a dominant contribution from the intergalactic medium

cannot be ruled out.

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Contents

1 Introduction 3

1.1 Introduction . . . . 3

1.2 Outline of the Thesis . . . . 3

1.3 Author’s Contribution . . . . 4

2 Gamma-Ray Bursts 5 2.1 Classification and progenitor models of GRBs . . . . 6

2.2 Prompt . . . . 7

2.2.1 Lightcurves & spectra . . . . 7

2.3 Afterglow . . . . 8

2.3.1 Lightcurve . . . . 8

2.3.2 Spectrum . . . . 9

3 X-Ray Absorption 11 3.1 Basic concepts . . . . 11

3.2 Galactic X-ray absorption . . . . 12

3.3 Excess absorption in the X-ray afterglow . . . . 13

3.3.1 Time evolution of absorption . . . . 15

4 Telescopes and Instruments 17 4.1 XMM-Newton . . . . 17

4.2 Swift . . . . 20

5 Observations and Data Reduction 21 5.1 Data reduction . . . . 22

6 Lightcurves 25 6.1 Hardness ratio . . . . 26

6.2 Bayesian Blocks . . . . 28

7 Spectra 30 8 Evolution of the Absorption 37 9 Discussion 40 9.1 Uncertainties and limitations . . . . 40

9.2 Interpretation of the results . . . . 41

9.3 Future prospects . . . . 42

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10 Conclusions 43

11 Acknowledgments 44

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Chapter 1 Introduction

1.1 Introduction

Gamma-ray bursts (GRBs) are the brightest explosions in the universe and the most distant observable objects. Because of their high energies and multiwavelength afterglow they are good candidates to probe distant galaxies and the intergalactic medium (IGM) along the line of sight. One way to study these regions is to determine the absorption from X-ray spectral analysis. Individual absorption features can not be detected because of limitations of the current X-ray instruments, that have too low spectral resolution and sensitivity. Therefore, only the total amount of absorbing material is measured, which is quantified as the equivalent hydrogen column density (N H ). The location of the absorp- tion along the ling of sight is a major outstanding question. There are likely contributions from the IGM and the GRB host galaxy, including the immediate environment of the GRB. A better understanding of the absorption in GRBs can improve our understanding about properties of the IGM, the host galaxies, as well as the GRB progenitors.

Here, a spectral analysis is performed to determine the X-ray absorption in the XMM- Newton spectra for a sample of five GRBs. The aim of this thesis is to determine whether a decrease in column density can be measured with statistical significance for these GRBs.

Such a decrease would indicate that significant absorption occurs close to the GRB and that this absorbing material is being ionised by the GRB. It is assumed that the column density does not vary during the XMM observation. Instead, the inferred column density is compared with the column density retrieved from a Swift X-ray Telescopes (XRT) analysis (Valan et al., 2018). The Swift XRT has a much faster reaction time than XMM-Newton, allowing it to detect the burst at an earlier time. The Swift observation starts about 100 s after the trigger, the XMM-Newton observation about a day later.

1.2 Outline of the Thesis

The thesis is organised as follows. Some theoretical background is presented in chapters 2 and 3. Chapter 2 introduces the topic of GRBs, focusing on the observational properties.

In chapter 3 the concept of X-ray absorption is introduced in the context of GRBs. An

overview of the relevant instruments and characteristics of the XMM-Newton and Swift

satellites is given in chapter 4. In chapter 5, general information about the observations

and the data reduction is outlined. Chapters 6, 7 and 8 contain the main results of the

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analysis. Lightcurves and spectra are presented in 6 and 7 respectively, and the column density evolution in 8. In chapter 9 the results are discussed and conclusions are drawn in chapter 10.

Throughout the thesis a standard flat cosmological ΛCDM model with H 0 = 70 kms −1 Mpc −1 and Ω Λ = 0.73 is adopted. Errors are given at a 90% confidence level unless otherwise stated and cgs units are used.

1.3 Author’s Contribution

The XMM-Newton data analysis has been performed by me. Results regarding the N H

from Swift were mainly provided by Vlasta Valan. Teodor Jonsson and Oscar Wistemar

provided the results regarding the time-evolution of N H durin the Swift observations for

GRB 060729. All figures and tables were made by me, unless otherwise stated in the

caption, and I wrote the manuscript.

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Chapter 2

Gamma-Ray Bursts

In this chapter an introduction to GRBs is presented and some relevant properties are discussed. For a more comprehensive overview the reader is referred to review papers such as M´ esz´ aros (2006), Kumar and Zhang (2015) and Schady (2017).

GRBs are extremely bright, short-lived gamma radiation events that occur at cosmo- logical distances. They are the brightest events in the observable universe with luminosi- ties between 10 51 and 10 53 ergs s −1 . In a matter of seconds the bursts produce as much energy as the sun will produce during its complete lifetime.

After the first discovery in the 1960s (Klebesadel et al., 1973) little was known about the origin of the GRBs. Only short observations in the gamma-ray regime were available at this time, and they showed diverse properties. The lack of strong limitations from the data encouraged theorists to think up a wide range of potential models to explain the origin of the GRBs. The increasing number of GRB discoveries, after the launch of the Compton Gamma-ray Observatory (CGRO) (Gehrels et al., 1994), brought some interesting trends to light. The spatial distribution of GRBs was found to be isotropic.

Additionally, the number versus intensity distribution did not follow the expected trend for a distribution of sources in the Galaxy (Meegan et al., 1992). These observations implied a cosmological origin of GRBs. A potential cosmological origin had been pre- viously discussed by Paczynski (1986) and Goodman (1986) because they noticed two coincidences. Firstly, the GRB energy would be similar to the supernova energy (about 10 51 ergs) if it occurred at cosmological distances. Secondly, the effective temperature of a 10 km spherical surface that radiates this energy in 1 s is ∼ 3 × 10 10 K, peaking around 8 MeV, corresponding to gamma-ray radiation.

Since the original discovery some huge strides have been made in the understanding of GRBs. This is mainly thanks to the observations made by satellites such as BeppoSax, KONUS/Wind, HETE-2, Swift, Integral, AGILE, and Fermi as well as the observational follow-up on earth. The observational data from the telescopes is often presented in two ways: temporal and spectral. The temporal variability of the radiation is plotted in the light curve. The light curve presents the flux of incoming photons as a function of time for a specific energy range. The spectrum presents the flux as a function of energy, frequency or wavelength for a specific time interval.

We now know that after an initial “prompt”phase, with high energy gamma-rays, the

GRB also emits in radio, optical and X-ray during the so-called “afterglow” phase. A

more detailed description of the two phases is given below in 2.2 and 2.3.

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2.1 Classification and progenitor models of GRBs

The most popular, and most significant classification of GRBs is based on the duration of the prompt emission. The duration of the prompt is defined as “T90”, the time interval in which 90% of the total flux is observed, starting at 5% and ending at 95% of the total fluence registered by the detector. Some limitations of the T90 measure include: detector dependency, not accounting for multiple emission peaks and that the emission within the T90 time may come from different sites. Kouveliotou et al. (1993) observed that the T90 distribution has two distinct peaks, as can be seen in figure 2.1. The GRBs in the first peak, centered at about 0.2 − 0.3 s, are called short GRBs. At ∼ 2 s there is a minimum after which there is a second peak, around 20 − 30 s, with the long duration GRBs. The two populations also show different spectral hardness. A harder spectrum has a larger fraction of high energy photons. The short GRBs on average have harder spectra than the long GRBs.

Figure 2.1: The duration of the 4B Catalog GRBs recorded with the Burst And Transient source Experiment (BATSE) on board NASA’s CGRO, taken from Paciesas et al. (1999).

These differences inspired separate progenitor theories for short and long GRBs re- spectively.

Most long GRBs are thought to originate from the death of massive stars. Woosley (1993) first proposed the collapse of a single Wolf-Rayet star 1 as a promising candidate for long duration GRBs. Since then this connection has been further established, not in the least because of the discovery of the GRB-supernova (GRB-SN) connection (Woosley and Bloom, 2006). The GRB-SNe correlation had been proposed very early on by Colgate (1974). When SN 1998bw was discovered in the error box of GRB 980425 (Galama et al., 1998), it was found to be a special Type Ic with a broad lined spectrum. All supernova associated with GRBs so far discovered have also been classified as Type Ic- BL. Type Ic SNe are core collapse supernova that come from massive stars that have lost their hydrogen and most of their helium envelopes. The outer envelopes of the star are thought to be lost either due to high stellar winds, as in Wolf-Rayet stars, or because of interaction in a binary (shedding the layers to a close companion). The broad lines in the spectrum are due to the high kinetic energy of the ejected material.

1 Wolf-Rayet stars are hot, massive stars with a high rate of mass loss. They have prominent broad

emission lines due to the strong stellar winds that blow material from the star.

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The short GRBs, on the other hand, are thought to originate from the binary merger of two neutron stars (NS) (Paczynski, 1986; Eichler et al., 1989) or a neutron star and a black hole (BH) (Paczynski, 1991; Narayan et al., 1992). These mergers are also accompanied by bursts of gravitational waves. The Advanced Laser Interferometer Gravitational- Wave Observatory (LIGO) and Advanced Virgo gravitational-wave detectors detected the first NS-NS merger signal on August 17th, 2017. The gravitational wave detection GW170817 was accompanied by the short GRB 170817A, confirming that some short GRBs are associated with binary NS mergers (Abbott et al., 2017).

This classification into long and short GRBs with different properties and origins is in reality not always so easily applicable. There are many exceptions to the previously outlined framework, and there is no one theory that can explain the wide variety of GRB observations.

No matter the progenitor model, it is thought that GRBs are emitted in the form of a relativistic jet (Sari et al., 1999; Kumar and Zhang, 2015). A collimated 2 outflow travels outwards producing the prompt phase, when the jet interacts with the surrounding medium and slows down the afterglow is produced. In the afterglow it can also be possible to detect a jet break, see below in 2.3.1. The jet model has two interesting consequences.

Firstly, the total energy needed to produce the GRB is greatly reduced. The energy requirements pose a big challenge for the uniform outflow model, when assuming jet emission more realistic total energies are found. Secondly, the rate of GRBs has to be much higher. If the GRB emission occurs in a narrow jet they are only detected when the jet is pointed towards us. It would be natural to assume that a large fraction of GRBs goes undetected because they are pointed in another direction.

2.2 Prompt

The short, high energy radiation that announces the GRB is called the prompt emission.

Initially it was the only part of the GRB that could be observed, and recently the prompt phase has gained more attention again. The mechanism behind the prompt emission is not well understood and the large amount of variability in the observations complicates the interpretation. General properties such as the duration of the prompt and the location of the energy peak help constrain the suggested models.

2.2.1 Lightcurves & spectra

As mentioned, the prompt observations are all unique, it is hard to find common features in the light curves and spectra. Nonetheless, researchers have made significant progress and some promising observational evidence supporting current theories has been found (Pe’er, 2015).

The light curve of the prompt phase does not only look different for each GRB but also varies with energy band. Fermi, a high energy satellite launched in 2008, provides data from 10 keV up to more than 300 GeV. This allowed the comparison between very high energy (GeV) and lower energy (< MeV) emission. In most cases the high energy radiation is detected a few seconds later and lasts longer. The pulse width also varies with energy band, showing narrower pulses in harder (more energetic) bands.

2 A collimated beam has parallel rays, and therefore spreads out minimally as it propagates.

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The peak energy for most GRBs is in the sub-MeV to MeV range, but softer bursts with peaks in the X-ray regime have been found to be a natural extension of GRBs to the softer, less luminous regime (Heise et al., 2001). The interpretation of GRB prompt spectra is a rather complicated field, with different models being able to fit the data equally well. The prompt spectrum can often be fit with a smoothly broken power law (Band et al., 1993). Preferred explanations include photospheric emission or synchrotron radiation.

2.3 Afterglow

The emission after the prompt phase is called the afterglow. The afterglow radiation can include radio, optical and/or X-ray wavelengths. Most GRBs have an X-ray afterglow, and only about half are observed in optical. If there is no optical afterglow the burst is a so-called “dark” GRB. In this thesis, only X-ray data is used therefore the focus of the following discussion is on the X-ray afterglow.

Paczynski and Rhoads (1993) and Meszaros and Rees (1993) predicted that the ini- tial burst of gamma-rays should be followed by multi-wavelength emission due to the interaction with the surrounding medium. On February 28th, 1997 X-ray and optical radiation was detected about a day after GRB 970228 (Costa et al., 1997; van Paradijs et al., 1997). The discovery of the afterglow greatly advanced GRB research, the door had been opened to the collection of a vast amount of new data.

2.3.1 Lightcurve

Pre Swift era the afterglow observations started several hours after the trigger, this time was needed to reposition the telescopes. The Swift satellite is a NASA space observatory dedicated to studying GRBs, it can reposition its X-ray telescope in a matter of minutes (see chapter 4.2). Even so, these “late” afterglow observations provided a lot of new data that helped substantiate the theoretical models. One particularly interesting trend is a steepening in the lightcurve (Sari et al., 1999). Rhoads (1999) predicted an increase in decay rate when assuming that the GRB emits in a strongly beamed jet. The light curve steepens when the beaming angle equals or exceeds the physical jet opening angle (θ=1/Γ, with Γ the Lorentz factor 3 ) and the jet decelerates in the surrounding medium.

The break has been observed at X-ray, optical and radio wavelengths. In the GRBs detected by Swift the jet break has proven harder to detect (Cenko et al., 2010).

Swift ’s fast reaction time, revealed a complex behaviour of the afterglow in the first few hours after the trigger (Zhang et al., 2006). Common components of the early afterglow lightcurve are: an early steep decay phase, a shallow decay phase or plateau phase, a normal decay phase and a late steep decay phase. Additionally, X-ray flares can be present in the lightcurve. The early steep decay phase is the tail of the prompt emission. The plateau phase is caused by a prolonged continuous energy injection, this could be e.g. from a spinning magnetar or a black hole created after the collapse of a massive star. The normal decay phase is the expected decay when the GRB interacts with the surrounding medium and the steepening could, as mentioned above, be caused

3 The Lorentz factor is the factor by which time, length and mass change for an object moving at

relativistic speeds. Γ = 1/p1 − v 2 /c 2

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by a jet break. The X-ray flares are most likely caused by late central engine activity, they are similar to the prompt emission but somewhat less energetic (Lazzati and Perna, 2007). Figure 2.2 shows what a typical lightcurve with all five components could look like, not every GRB shows all of these features.

Figure 2.2: Canonical X-ray afterglow, with five components: I. the early steep decay phase, II. the shallow decay phase (or plateau), III. the normal decay phase , IV. the late steepening phase and V. the X-ray flares. The numbers next to the slopes represent the typical decay index for the segment. Figure taken from Zhang et al. (2006).

2.3.2 Spectrum

The afterglow spectrum can in many cases be described relatively well by synchrotron

emission. Synchrotron radiation is a non-thermal radiation mechanism, meaning it does

not depend on the temperature of the emitter. It occurs when charged relativistic par-

ticles are accelerated by a magnetic field. It is generally assumed that the afterglow is

produced when the relativistic jet interacts with the surrounding medium in external

shocks. The synchrotron radiation for an expanding relativistic shock consists of several

power-law segments (Sari et al., 1998). Figure 7.1 shows example spectra derived for

these theoretical predictions. Afterglow spectra in a specific energy range can often be

well fitted with a single or broken powerlaw function. In a very small number of spectra

an additional thermal component can be identified in the early Swift data (Valan et al.,

2018).

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Figure 2.3: Synchrotron spectrum, figure taken from Sari et al. (1998).

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Chapter 3

X-Ray Absorption

An important feature when fitting the GRB spectra is the absorption component. For X-rays below 10 keV the main absorption process is photoelectric absorption, or photo- ionisation (Wilms et al., 2000). The incoming photon interacts with an atom and ionises or excites it. Only specific photon energies can be absorbed by the atoms since they have discrete energy levels. These absorption lines can currently only be resolved by at very low signal-to-noise ratio, so instead the total absorption effect is considered.

In this chapter, a brief review of the terms used when discussing absorption is given and the absorption observed in GRB spectra is discussed.

3.1 Basic concepts

In physics a cross-section σ is a measure for the probability, expressed as an area, that a specific process will take place when two or more particles interact. The absorption cross-section represents the probability of absorption as the area that is blocked to in- coming photons. For X-ray radiation all not fully ionised elements will contribute to the absorption cross-section. The cross-section has a strong dependence on the atomic number Z. Therefore, heavier elements, even though less abundant, can contribute more to the total cross-section than the more abundant hydrogen (Longair, 2011).

Optical depth τ is a measure for the amount of light blocked when the rays pass through the medium. It is defined by:

I obs (E) = e −τ I source (E) (3.1) With I obs the observed flux of X-rays after passing through the absorbing medium, and I source the initially emitted flux at the source. The optical depth can also be expressed as the total absorption cross-section σ tot divided by the total area. Assume that n is the number density of absorbers, each with a cross-section σ, in the volume V , while L is the distance traveled by the rays through the medium. The total absorption cross-section can then be written as σnV , or σnAL if the radiation passes through a surface with area A. Giving the optical depth:

τ = σnL (3.2)

Often the distribution of absorbers along the line of sight is not known. It is, therefore,

common to use the number of absorbers per unit surface area instead of per volume. This

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measure is called the column density. In the above scenario the column density is N = nL, so that:

τ = σN (3.3)

Even though X-ray absorption is dominated by metals, it is convention to report the total absorption with the equivalent hydrogen column density N H . The cross-section is normalised to the hydrogen number density, the effective cross-section σ e is a sum over the different elements weighted by their cosmic abundances (Longair, 2011):

σ e = 1 n H

X

i

n i σ i (3.4)

σ i are the cross-sections for the different absorbing materials, the fraction n i /n H represents the cosmic abundance of absorber i compared to the amount of hydrogen. After the normalisation the observed X-ray spectrum should relate to the source spectrum as:

I obs (E) = e −σ

e

(E)N

H

I source (E) (3.5) In GRBs, the N H value is inferred from fitting an absorbed model to the X-ray spec- trum (Lazzati and Perna, 2002). A single powerlaw or broken powerlaw model has been shown to agree rather well with observations and is based on the assumption that the afterglow arises from synchrotron emission (see section 2.3.2). The effect of absorption on the spectrum is a lowering of the flux at low energies. Low energy photons are more eas- ily absorbed than the energetic photons. i.e. the more energetic photons have a smaller absorption cross-section.

It is important to be aware of the degeneracy between N H and the slope of the spectrum and/or the spectrum break, as it may affect the inferred N H value (Lazzati and Perna, 2002). If there is more absorption the spectrum is lowered at low energies, but this can also be caused by a flatter spectrum (possibly with a spectral break).

3.2 Galactic X-ray absorption

Absorption in GRB spectra can occur in the local GRB environment, in the IGM and in the observer environment, i.e. our own galaxy.

In order to interpret the X-ray absorption by extragalactic sources it is important to properly account for the Milky Way absorption. That is, to have a good estimate of the Galactic hydrogen column density (Wilms et al., 2000). In this thesis it is calculated using a tool developed by UKSSDC (UK Swift Science Data Centre). Given a GRB position, the method described in Willingale et al. (2013) is applied to calculate N H,gal for the line of sight towards the GRB. The total hydrogen column density consists of an atomic and a molecular component, the atomic absorption accounts for the majority (about 80%) of the absorption. The atomic component is determined from surveys of the 21 cm radio emission lines 1 (Kalberla et al., 2005). The molecular component is estimated from an empirical study using X-ray afterglows of GRBs (Willingale et al., 2013). This estimate relies on measurements of the dust extinction and the atomic H.

1 The hydrogen line, or 21 cm line, is a spectral line created by the change in energy state of a neutral

hydrogen atom due to the spin-flip transition.

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For spectral analysis the XSPEC software is used, it allows easy implementation of common GRB models. The Galactic absorption model from Willingale et al. (2013) can be implemented in XSPEC with the tbabs model. The abundance table in XSPEC is set to wilm to use the element abundances from Wilms et al. (2000).

3.3 Excess absorption in the X-ray afterglow

Once the Galactic absorption component is accounted for, a significant amount of ab- sorption is still present in the spectra (Campana et al., 2006). This “excess absorption”

can occur in the GRB host galaxy and/or in the IGM along the line of sight. Tradi- tionally, high redshift observations are performed with quasars 2 . For blazars negligible absorption within the host galaxy can be assumed, making them well suited to study the IGM, see for example Arcodia et al. (2018). GRB observations can complement these quasar studies (Campana et al., 2007).

Due to the lack of sufficient spectral resolution and low signal to noise ratio (S/N) the redshift of the absorption component cannot be inferred from the X-ray data (Campana et al., 2014; Sako et al., 2005). It is common to assume that all excess absorption takes place at the redshift of the source when fitting the spectrum. The redshifted absorption component, i.e. the host galaxy of the GRB, is often assumed to have the same solar abundances as the Galactic absorption. Since most GRB host regions actually have a sub-solar metallicity 3 the solar abundance assumption gives a lower limit for N H . A higher metal abundance gives a higher absorption cross-section, and thus requires a lower column density to give the same resulting spectrum. In a recent paper, Dalton and Morris (2020) use improved metal abundances for the host galaxies of a large sample of GRBs to try and isolate the IGM contributions.

The ztbabs model component in XSPEC models the absorption at a redshifted source.

The equivalent hydrogen column density in the GRB environment is the variable of interest in the fit. The redshift of the absorption component is set to the GRB redshift.

Spectroscopic confirmed redshifts are obtained from UV/optical afterglow spectra, via the detection of Lyman-α absorption 4 features and absorption lines from heavier elements.

The neutral intrinsic hydrogen column density N HI for optical absorption can also be estimated from the Lyman-alpha measurements.

After many years of observing GRB absorption some trends stand out, see figures 3.1, 3.2 and 3.3:

• An increase of N H with redshift (Campana et al., 2010; Behar et al., 2011; Watson et al., 2013; Starling et al., 2013), recently confirmed with an up-to-date sample by Rahin and Behar (2019).

• No significant correlation has been found between N HI and redshift (Watson et al., 2007), where N HI is the neutral hydrogen column density derived from optical observations.

• The X-ray column density N H is often found to be around an order of magnitude

2 A quasar is an extremely luminous active galactic nucleus.

3 Abundance of elements heavier than hydrogen or helium.

4 The Lyman-α lines are absorption lines from neutral hydrogen electron-transitions.

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larger than the optical column density N HI (Galama and Wijers, 2001; Watson et al., 2007; Campana et al., 2010).

Figure 3.1: Column density from Swift XRT spectra as a function of redshift. The red triangles denote upper limits. Figure taken from Rahin and Behar (2019).

Figure 3.2: Column densities from damped Ly α lines for a sub sample of 129 GRB afterglows with z > 1.6, taken from Rahin and Behar (2019).

Figure 3.3: X-ray column densities compared to their Ly α counterparts for a sub sample of 129 GRB afterglows with z > 1.6. Red triangles are upper limits, the solid line indicates equal column densities. Taken from Rahin and Behar (2019).

The observed increase of X-ray absorption with redshift has been suggested to be

a consequence of dust-extinction bias (Watson and Jakobsson, 2012). They find that

when adding highly extinguished bursts to the sample the increase with redshift becomes

less significant. However, Campana et al. (2012) and Starling et al. (2013) show that

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selection effects and bias are unlikely to fully explain the trend. Since the X-ray equivalent hydrogen column density traces the total metal content, it should in fact be compared to absorption from all metals instead of only considering the neutral hydrogen (Schady et al., 2011). It seems that this discrepancy can not account for all of the excess, the X-ray absorption is still significantly larger than the optical absorption for many GRBs.

Arcodia et al. (2016) inspect the effect of an improved model for Galactic hydrogen (Willingale et al., 2013). The model considerably affects column density values but does not drastically change the distribution with redshift.

Since the location of the absorbers can, as of now, not be confirmed, trends in the observations can help determine possible models. When fitting the spectrum it is common to assume that all absorption occurs at the location of the GRB host. A few propositions for the GRB environment include:

• A large molecular cloud (Galama and Wijers, 2001; Krongold and Prochaska, 2013);

• A dense metal-rich environment (Campana et al., 2010, 2012);

• Dense H II regions with low metallicity containing He, where the He is responsible for the X-ray absorption (Watson et al., 2013).

To recreate the trends in absorption, with the host galaxy as the dominant source of the X-ray absorption, the host galaxy has to have some special characteristics. Buchner et al. (2017) argued that most of the absorption should take place in the host galaxy, not because of the increase with redshift but, because the column density depends on the host galaxy mass.

However, arguments for an intergalactic absorption source have also been made. In Tanga et al. (2016), a model for a collisionally ionised and turbulent interstellar medium (ISM) is explored. They conclude that hot gas in the host ISM is likely not the main contributor to the X-ray absorption.

The increasing trend of X-ray, and not optical, absorption with redshift is often attributed to an increasing amount of intergalactic absorbers along the line of sight. A cold, neutral, metal-enriched, diffuse IGM is modeled by Behar et al. (2011), and could explain the increase in absorption for redshift z ≥ 2. A more realistic, warm-hot IGM (WHIM) with T ∼ 10 5 − 10 6 K and Z ∼ Z /5 is modeled by Starling et al. (2013). They propose that the WHIM contribution becomes significant for z ≥ 3 and is the dominant absorption site at z ∼ 6. Cosmological simulations of this warm-hot IGM are performed by Campana et al. (2015).

With the current information, or lack thereof, it is hard to say for certain what the origin of the high X-ray absorption in GRBs is. It seems likely that at high redshifts the X-ray absorption is dominated by the IGM (Rahin and Behar, 2019), for more nearby GRBs the host galaxy may play a more significant role.

3.3.1 Time evolution of absorption

The emphasis of this thesis is studying the time evolution of absorption, more specifically

the possible detection of a variable column density with time. The GRB afterglow alters

the equilibrium of the surrounding medium on an observable time scale (Perna and Loeb,

1998; Watson et al., 2007). The GRB photons can ionise the surrounding medium and

vaporise dust grains. The dust destruction may be caused by thermal sublimation, ion

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field emission or Coulomb explosion (Perna and Lazzati, 2002). It has been proposed that a change in absorption due to ionisation could be observed during the timescales of the GRB (Lazzati and Perna, 2002). Ionisation of the surrounding medium alters the amount of absorption because once an atom is fully ionised it can no longer absorb energy from the photon. If a decrease in absorption is robustly observed, it would point to a host galaxy origin of the absorption. A measurable absorption evolution on these time scales would imply that the absorbers are being modified by the burst. A more compact absorbing region corresponds to faster ionisation (Perna and Loeb, 1998).

An evolving column density during the GRB afterglow has been claimed by Campana et al. (2007); Rol et al. (2007); Starling et al. (2005) and Grupe et al. (2007) amongst others. These claims were questioned by Butler and Kocevski (2007), because other effects could produce the same change in spectrum as a decreasing N H . More specifically, they favor the curvature effect 5 for the cause of the spectral evolution. In this thesis, the evolution of N H is investigated, while allowing for other types of spectral evolution.

5 The curvature effect describes the effects of a curved emission front, see for example Ryde and

Petrosian (2002).

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Chapter 4

Telescopes and Instruments

All data analysed in this thesis have been collected by the XMM-Newton EPIC-pn cam- era. Results from Swift data analysis are also considered. In this chapter a short overview of the XMM-Newton properties is presented, and compared with Swift characteristics.

4.1 XMM-Newton

The X-ray Multi Mirror Mission, XMM-Newton, is ESA’s X-ray space observatory and a cornerstone mission of their 2000 space science plan (Jansen et al., 2001). It was launched by an Ariane 5 rocket on December 10th, 1999 from the ELA-3 launch site in Kourou, French Guiana. XMM-Newton follows a 48 h elliptical orbit, with a perigee of ∼ 7000 km and an apogee of about 114000 km. The spacecraft consists of four main elements: the Service Module (SVM), the Focal Plane Assembly (FPA), the telescope tube, and the Mirror Support Platform (MSP). See figure 4.1 for a transparent view of the spacecraft.

The SVM contains the spacecraft subsystems that control the orbit, provide resources to the instruments, handle the data, etc. The telescope tube is a long carbon fibre tube that connects the FPA with the MSP and SVM. On the mirror platform there are three mirror modules, each containing 58 Wolter Type I wafer-thin concentric mirrors.

The mirrors have a diameter between 0.3 and 0.7 m and focal length of 7.5 m and are

nested in a coaxial and cofocal configuration. Each telescope has a total effective area of

1550 cm 2 at 1.5 keV, making a total of 4650 cm 2 . The platform also has two star-trackers

and an Optical Monitor (OM). The OM can detect photons with a wavelength between

180 − 600 nm, and has a Field Of View (FOV) of 17 arcmin. The FPA holds the X-ray

instruments: two Reflection Grating Spectrometers (RGS) (den Herder et al., 2001), the

European Photon Imaging Camera (EPIC) pn detector (Str¨ uder et al., 2001), and the

two EPIC Metal Oxide Semiconductor (MOS) detectors (Turner et al., 2001).

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Figure 4.1: Open view of the spacecraft showing the XMM-Newton payload. Figure adapted from Jansen et al. (2001)

Two of the X-ray telescopes are fitted with grating assemblies, directing 44% of the light to one of the EPIC MOS cameras and ∼ 40% to the RGS. The third X-ray telescope sends an unobstructed beam to the EPIC pn camera. Therefore, the effective area of the pn camera is about twice as large as the effective area for one MOS camera. Table 4.1 and 4.2 list some of the most important characteristics of the instruments and is largely based on the “XMM-Newton Users Handbook” 1 . They also includes values for the X-ray telescope of the Swift satellite, see section 4.2. Note that the analysed energy intervals are somewhat narrower due to calibration uncertainties and low effective area at the edges.

Instrument Energy range FOV Effective area (at 1.5 keV)

[keV] [arcmin] [cm 2 ]

XMM : EPIC pn 0.15-12 30 1200

XMM : EPIC MOS 0.15-12 30 400

XMM : RGS 0.35-2.5 5 150

Swift : XRT 0.2-10 23 110

Table 4.1: Characteristics of X-ray instruments. Note that the values are approximate and can vary depending on the mode or the filter of the camera, and the energy of the incoming photons. The effective area listed is for one of the EPIC MOS cameras. Based on values from the XMM-Newton Users Handbook.

1 https://xmm-tools.cosmos.esa.int/external/xmm_user_support/documentation/uhb/

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Instrument

Angular resolution Time resolution Spectral resolution

PSF (FWHM/HEW) (at 1 keV)

[arcsec] [ms] [eV]

XMM : EPIC pn 6”/15” 0.03 80

XMM : EPIC MOS 5”/14” 1.75 70

XMM : RGS N/A 600 3.2/2.0

Swift : XRT 8.8”/18” 2.2 70

Table 4.2: Best possible resolutions for the X-ray instruments. Note that the minimum possible resolution is given, the values can be significantly different depending on the mode or the filter of the camera, and the energy of the incoming photons. Based on values given in the XMM-Newton Users Handbook.

The RGS consists of an array of reflection gratings that diffract the X-rays to an array of 9 MOS Charged Coupled Devices (CCDs). The RGS cameras are mostly used to perform high resolution spectroscopy in the low X-ray regime.

The EPIC pn camera has 12 CCDs on a single wafer, and the EPIC MOS cameras have an array of 7 CCDs. The cameras are shown in figure ??. There are small gaps between the CCDs that form the EPIC MOS array. In order to fill these gaps the cameras are rotated 90 degrees in the focal plane, with respect to one another.

The EPIC cameras have a lower energy resolution than the RGS but have a larger FOV, a broader energy range and a finer time resolution. Among the EPIC cameras, the pn camera has a finer time resolution and a higher effective area. The MOS cameras have a slightly higher angular resolution. Angular resolution is described by the Point Spread Function (PSF), which expresses how much a point source is spread out by an imaging system. It is quantified as the Full Width at Half Maximum (FWHM) or the Half Energy Width (HEW) of the PSF.

(a) EPIC MOS camera with an array of 7 CCDs.

(b) EPIC pn CCD array, twelve 3 × 1 cm pn-CCDs on a single waver. The four indi- vidual quadrants each have three pn-CCD subunits.

Photographs of EPIC camera components. Source: https://www.cosmos.esa.int/web/xmm- newton/technical-details-epic

The detectors operate in photon counting mode, creating an event list with one entry

line per event. For each event the arrival time, location and energy of the detection are

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registered. The events are read out at a fixed, mode-dependent frequency. The XMM- Newton data is accessible from the XMM Science Archive in the form of Observational Data Files (ODFs).

4.2 Swift

Swift is a telescope launched by NASA on November 20th, 2004 as part of their medium explorer (MIDEX) program. The main objective of the Swift mission is the study of GRBs. Its fast detection and follow-up of GRBs in multiple wavelengths caused a giant leap in GRB data. The instruments on the spacecraft are: the Burst Alert Telescope (BAT), the Ultra Violet and Optical Telescope (UVOT), and the X-Ray Telescope (XRT).

For a more complete description see Gehrels et al. (2004).

BAT is triggered by the prompt emission of gamma-rays and determines a 3 arcmin position estimate within 20 s. In order to detect GRBs across a large part of the sky, BAT has a FOV of 2 steradians. The detector is sensitive to gamma-ray energies: 15−150 keV.

The UVOT design is based on the optical monitor aboard the XMM-Newton, and has very similar characteristics. The XRT (Burrows et al., 2005) operates similarly to the EPIC MOS cameras. Due to the differences in the X-ray telescope, XRT only has an effective area of ∼ 110 cm 2 at 1.5 keV.

Compared to XMM-Newton, Swift has a much faster reaction time. After the trigger in BAT, XRT and UVOT slew to the source location and start observations after ∼ 100 s.

It can observe the prompt phase and the early afterglow, whereas XMM only observes the afterglow. Thanks to XMM s high sensitivity it is well suited to detect the decreased X-ray flux in the afterglow phase.

Figure 4.3: Model of the Swift satellite showing the different instruments. Based on Gehrels

et al. (2004), taken from UKSSDC.

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Chapter 5

Observations and Data Reduction

An analysis of data from the EPIC pn camera on XMM-Newton is performed for a sample of five GRBs: GRB 050730, GRB 060729, GRB 090618, GRB 111209A and GRB 151027A. The sample is selected from the GRBs analysed in Valan et al. (2018) and Valan (2020, in prep). The GRBs are also chosen to have a high number of photon counts during the XMM-Newton observation. EPIC MOS data is also available for the bursts but, because of the better quality and higher count rate of the pn detector (see Chapter 4), only EPIC pn data is used. See Holland et al. (2005); Grupe et al. (2006);

Schady et al. (2009); Hoversten et al. (2011) and Maselli et al. (2015) for the Gamma- ray Coordinates Network (GCN) announcements of the first detection. All bursts are discovered by the Burst Alert Telescope (BAT) on Swift, and within a matter of minutes the Swift X-ray Telescope (XRT) and Ultra Violet and Optical Telescope (UVOT) are positioned to observe the GRB location.

Some general information about the GRB observations is presented in table 5.1 (see Pandey et al., 2006; Grupe et al., 2007; Campana et al., 2011; Gendre et al., 2013 and Nappo et al., 2017 for detailed reports on the respective GRBs). The redshift is estimated from absorption lines identified in the spectra. Four of the GRBs have a reported redshift smaller than 1, for GRB050730 a larger redshift of z = 3.967 is obtained by Chen et al.

(2005) and later confirmed by Rol et al. (2005) and Prochaska et al. (2005). A measure often used in GRB classification is the T90 time, defined as the time needed for the prompt phase to emit 90% of the total flux (see Chapter 2). Most long duration GRBs have a T90 time around 30 seconds (Zhang and Choi, 2008), as is the case for four of the GRBs in our sample. GRB 1111209A, however, has been classified as an ultra-long GRB with an estimated T90 larger than six hours (Gendre et al., 2013).

A few hours after the trigger (t XM M in table 5.1), XMM-Newton is repositioned to

observe the bursts for a duration of ∼10 hours (∆t obs in table 5.1). For all bursts the

pn camera is operated in Prime Full Window Mode with either the Thin1 filter or the

Medium filter. Only part of the XMM observation is used in the analysis, because time

intervals with a high background are discarded (see section 5.1). The total exposure time

of the analysed data is referred to as the clean time (∆t clean ), and can be significantly

shorter than the observation time. All the XMM-Newton spectra have enough counts to

enable the use of χ 2 -statistics.

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z T90 t XM M ∆t obs ∆t clean Count Rate pn Filter [s] [ks] [ks] [ks] [counts/s]

050730 3.967 155 25.30 33.91 14.63 1.307 Thin1 060729 0.54 115 44.91 61.51 34.77 3.632 Medium 090618 0.54 113.2 19.18 22.92 10.38 5.349 Thin1 111209A 0.677 25000 56.66 53.82 45.61 0.6904 Medium

151027A 0.81 130 76.87 51.5 37.2 0.5794 Thin1

Table 5.1: General information about GRB observations; t XM M is the start time of the XMM detection with respect to the BAT trigger, ∆t obs is the duration of the XMM-Newton observation, ∆t clean is the duration after filtering.

5.1 Data reduction

All raw data is available from the XMM-Newton Science Archive in Observational Data File (ODF) format. In order to process the raw data, the Science Analysis Software v.18.0.0 (SAS) 1 for XMM-Newton is used (Gabriel et al., 2004). The Current Calibration File (CCF) contains additional data sets that are necessary to reduce and analyse XMM- Newton data. They are available online and continuously updated. Using cifbuild the Calibration Acces Layer (CAL) is pointed to the relevant CCF constituents by creating a CCF index file (CIF). Running the odfingest command extends the ODF summary file (SF) with data extracted from the instrument housekeeping data files and the calibration database and creates a new summary file, the SAS ODF summary file (SOSF). epchain reprocesses the ODF files to generate a calibrated and concatenated EPIC-PN event list in Flexible Image Transport System (FITS) format. The event list contains information such as position, energy and arrival time, for each detection event.

The event list is filtered for flaring, i.e. high background activity. To determine high background time intervals, a lightcurve for single high energy events is extracted since this regime is most likely to be dominated by the background. To select single events, set PATTERN = 0. For XMM-Newton, high energy events can be defined as events with an energy from 10-12 keV. The low background time intervals are then selected by setting a threshold on the count rate, this is about 0.4 counts/s for the EPIC pn camera. 2 A Good-Time-Interval (GTI) file is created with tabgtigen, and the eventlist is filtered to only contain events at “good” times with evselect. The clean time after filtering can be found in table 5.1, and the flaring intervals are shaded in light blue on the lightcurves in chapter 6.

Another possible effect to consider is detector pile-up. Pile-up occurs when there is more than one incoming photon in one event, and the photons cannot be distinguished.

The event is registered as a single photon with an energy equal to the sum of the photon energies. This has a double effect: a hardening of the source spectrum and a lower observed photon flux per unit time over the whole energy band. If the sum of the photon energies is higher than the threshold for rejection, the pile-up events will be lost. Pile- up is likely to occur if the X-ray source is too bright for the selected observing mode.

1 The users guide for SAS can be found at https://xmm-tools.cosmos.esa.int/external/xmm_

user_support/documentation/sas_usg/USG.pdf

2 https://www.cosmos.esa.int/web/xmm-newton/sas-thread-epic-filterbackground

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To detect if pile-up occurred the event pattern statistics are considered; if the single and double pattern fractions are equal to one, within one standard deviation, no pile-up effects are present. The pattern fractions are generated using epatplot, this command also plots the pattern distributions and fractions (including single and double fraction model curves) as a function of PI channel. In the analysed sample there is no indication of significant pile-up in any of the burst.

Now that a clean, filtered event file is created, the spectra and lightcurves of the GRB can be extracted from the data using evselect. To exclude bad/hot pixels and pixels on the edge of the detector set FLAG to 0. To select only single and double events PATTERN≤4 is set, single events correspond to pattern 0 and double events to patterns 1-4. The software also allows for a camera specific filter. In the case of the EPIC-pn camera the selection expression is #XMMEA EP. The source and background regions are selected by defining a circular region, such as shown in figure 5.1. These regions are defined manually using DS9 to visualise the event rate on the detector surface. The reported burst position can be used to determine the source corresponding to the GRB, the source can often be easily identified as the brightest and largest point source on the detector. The source region is chosen such that it contains as much of the source as possible without including other sources or chip edges. The background region is chosen on the same chip and should not include any sources or chip edges either. The extracted regions have a radius of about 30-40 arcsec.

Figure 5.1: Selection of source and background region for GRB 050730.

To calculate the area of the source region and write it into the header of the spec-

trum files the backscale command is used. To allow the spectra to be fit in Xspec, it

is necessary to create a Redistribution Matrix File (RMF) and an Ancillary Response

File (ARF) for the spectra. The RMF is generated with rmfgen, this file describes the

response of the instrument as a function of energy and PI channel. The ARF, created

with arfgen, contains a table listing area values for different energy ranges. These files

are connected to the spectrum with specgroup. This command is also used to bin the

spectrum. The spectra are rebinned with in each bin at least 25 counts and an intrinsic

energy resolution that is not oversampled by more than a factor of 3. Meaning that there

should be no energy bins smaller than one third of the energy resolution FWHM at a

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given energy. Time resolved spectra are also created in a similar way, with an additional

selection expression to specify the chosen time interval for each spectrum.

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Chapter 6 Lightcurves

In this chapter the time variability of the GRB is discussed in three areas. First of all, the lightcurves of the sample are presented and analysed. The hardness ratio, a measure for spectral change, is discussed in 6.1. In 6.2 time binning, and more specifically the Bayesian block algorithm, is introduced.

When creating lightcurves there are two important parameters to consider: the time- bin size and the energy range. When choosing the timebin size a trade off between the amount of noise and the amount of information in the plot has to be made. A size of 300 s or 1000 s is found to be a reasonable trade off, the results for the two sizes are compared to asses the impact of this choice. The nominal energy range for the pn cam- era is 0.5 − 10 keV. To distinguish the lightcurves at hard and soft energies, a range of 0.5 − 2 keV and 2 − 10 keV is chosen for soft and hard X-rays respectively. Lightcurves are created for the source and background regions, then the source lightcurve is back- ground subtracted and corrected with epiclccorr. The lightcurves of the five GRBs in the sample are plotted together in figure 6.1.

10

5

2 × 10

4

3 × 10

4

4 × 10

4

6 × 10

4

t−t 0 [s]

10

0

10

1

R at e [c ou nt s s − 1 ]

050730 060729 090618 111209A 151027A

Figure 6.1: Background subtracted XMM-Newton lightcurves with timebins of 300 s. t-t 0 is the time since the Swift trigger.

Using the terminology for the X-ray lightcurve phases from section 2.3.1, the XMM

observations of the GRBs are associated with different phases. The phases are identified

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by looking at the full Swift XRT lightcurves and finding where the XMM observation is found during this time. The XRT lightcurves and a preliminary classification and fit is available in the Swift XRT GRB catalogue (Evans et al., 2009) of the UKSSDC 1 . For GRB 090618 and GRB 151027A, the normal decay phase is observed, this is the typical afterglow decay. GRB 050730 shows a steepening of the lightcurve which might correspond to the end of the normal decay phase and the transition to the late steepening phase. However, in the Swift lightcurve a possible jet break and steepening was found at an earlier time (8.6 ks after the trigger) and no significant change in slope is observed during the XMM observation (Pandey et al., 2006). For GRB 060729 Swift observed a very long plateau phase up to approximately 56 ks (Grupe et al., 2007). XMM therefore observes the end of the plateau phase and the beginning of the normal decay phase.

Perhaps the most peculiar is the lightcurve of GRB 111209A, the curve flattens during the observation. As can be seen from table 5.1, GRB 111209A has a much longer prompt phase than the other bursts. The XMM observation covers the end of the prompt phase, i.e. the early steep decay phase, the plateau phase and the start of the normal decay phase (Gendre et al., 2013).

6.1 Hardness ratio

When performing a spectral analysis it is important to consider the possibility that the shape of the spectrum changes over time. One simple measure for the spectral shape is the hardness of the spectrum, a harder spectrum has a higher flux at high energy.

To determine if and when the hardness varies, the hardness ratio of the spectrum is considered. The hardness ratio is defined as HR = H−S H+S , with H and S the count rates from the hard and soft spectra respectively. In order to determine whether the hardness ratio changes significantly with time, the function is fit to a constant. The hardness ratios with the corresponding constant fit are plotted in figure 6.2. A least-square fit is performed and χ 2 is calculated as:

χ 2 =

n

X

i=1

 y i − µ i σ i

 2

(6.1)

This is a sum of squares over the data points, with y i the value of the data point, µ i the expected value of this point from the fitted function, and σ i the error associated with the data point. In the case of a constant fit, µ will of course be the same value for all data points. The p-value is the probability of observing a χ 2 value at least as extreme as the observed value for the number of degrees of freedom (DOF). If the p-value is smaller than the confidence level, conventionally set at 0.05, then the null hypothesis can be rejected with statistical significance. So if a p-value smaller than 0.05 is found, the hardness ratio can certainly not be fit with a constant. The statistics for our sample are given in table 6.1.

1 https://www.swift.ac.uk/xrt_live_cat/

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χ 2 (DOF) p-value 050730 73.39(55) 0.05 060729 146.15(131) 0.17 090618 44.25(40) 0.297 111209A 249.94(173) 0.00012 151027A 151.76(139) 0.22

Table 6.1: Statistics for fitting the hardness ratio as a function of time with a constant, when using 300 s timebins. All GRBs except GRB 111209A are consistent with the constant fit.

For all but one the p-value is strictly higher than the confidence level, so here the

constant fit hypothesis is not rejected. The same conclusion is found when using 1000 s

timebins instead of 300 s. For GRB 111209A a p-value of 0.00012 is found, the constant

fit is rejected with high significance. The hardness ratio for GRB 111209A is observed

to become more negative with time (see figure 6.2), meaning that the spectrum becomes

softer.

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0 1 2 3

t−t

XMM

[10

4

s]

−0.8

−0.7

−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

Hardness ratio

(a) GRB050730

0 1 2 3 4 5

t−t

XMM

[10

4

s]

−0.65

−0.60

−0.55

−0.50

−0.45

Hardness ratio

(b) GRB060729

0 1 2

t−t

XMM

[10

4

s]

−0.5

−0.4

−0.3

−0.2

−0.1

Hardness ratio

(c) GRB090618

0 1 2 3 4 5

t−t

XMM

[10

4

s]

−1.0

−0.9

−0.8

−0.7

−0.6

−0.5

−0.4

Hardness ratio

(d) GRB111209A

0 1 2 3 4

t−t

XMM

[10

4

s]

−0.8

−0.7

−0.6

−0.5

−0.4

−0.3

Hardness ratio

(e) GRB151027A

Figure 6.2: Hardness ratio as a function of time. The horizontal line is the best fit to a constant value. GRB 111209A is the only burst that is not consistent with the constant fit, within the chosen confidence level.

6.2 Bayesian Blocks

Even though no strong evolution was observed in the majority of the hardness ratios,

the possibility of spectral changes is further investigated. To allow for variability in the

spectrum during the observation time, the spectrum is split into time bins. This time

binning can be done in multiple ways. The simplest method would be to make bins of a

constant size. It is often more meaningful to choose the bins in such a way that each bin

shows little variability in the light curve. The time intervals are then determined based

on the amount the count rate changes in the lightcurve. In this thesis the Bayesian block

algorithm is used to accomplish this type of binning. The Bayesian block algorithm is

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used to detect and characterise local variability in time series. It is implemented with the Bayesian block function of the astropy package in Python, based on Scargle et al.

(2013).

The event files have been filtered for flaring. Therefore, there are gaps in the data at which there are seemingly no events detected. Since these data gaps will affect the algorithm, they are ignored when applying the Bayesian block algorithm. The data is compressed to eliminate the time intervals where flaring occurs, the analysis is performed on the compressed data, and then the original times are restored.

The result of this algorithm is a spectrum split in time intervals, where in each interval the lightcurve is approximately constant. See for example figure 6.3, showing how the lightcurve for GRB 111209A was split. For each of the time intervals, or “blocks”, a spectrum is created as described in 5.1. These spectra can then be fit simultaneously in XSPEC.

0 1 2 3 4 5

t−t

XMM

[10

4

s]

0.4 0.6 0.8 1.0

R at e [c ou nt s s

−1

]

Figure 6.3: Bayesian blocks for the lightcurve of GRB 111209A. Lightblue areas are time

intervals that are filtered out due to background flaring. The dashed vertical lines show the

edges of the Bayesian blocks as found by the algorithm.

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Chapter 7 Spectra

In this chapter the spectra of the GRBs are analysed. The spectral fitting model is described and the best fit parameters are presented. The total flux and luminosity for the spectra are also given.

Background subtracted spectra are created for the complete good time interval of the observation and for the time intervals determined by the Bayesian block algorithm. The spectra are then fit using XSPEC. The fit is performed by folding the absorbed power-law model spectrum through the response matrix of the EPIC pn detector, and comparing with the observed spectrum using χ 2 statistics. The X-ray spectrum from the GRB is conventionally fit to either a power-law or a broken power-law (see section 2.3.2). For a single power-law the photon spectrum N(E) relates to energy as:

N (E) ∝ E −Γ (7.1)

The photon index Γ is the exponent of the contribution of energy in the photon spectrum.

N(E) has units of photons s −1 area −1 energy −1 . The energy spectrum S(E) is equal to the photon spectrum × energy, therefore the spectral index β = Γ + 1.

S(E) = E × N (E) ∝ E −Γ+1 = E −β (7.2)

The absorption components are fit with the tbabs and ztbabs models as described in chapter 3. The Galactic absorption component N H,gal and the redshift z of the bursts are considered fixed variables, set to values available in the online documentation 1 . The spectra and corresponding best fit models for the five bursts are plotted in figure 7.1.

1 See: http://www.mpe.mpg.de/~jcg/grbgen.html for redshifts and https://www.swift.ac.uk/

analysis/nhtot/index.php for the Galactic column density.

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10

0

10

1

Energy [keV]

10

−3

10

−2

10

−1

10

0

C ou nt s s − 1 k eV − 1

050730 060729 090618 111209A 151027A

Figure 7.1: Spectra and best fit models of the GRBs in the sample. An absorbed single power-law model is used for all bursts except GRB 111209A which is fit with an absorbed broken power-law.

The unfolded spectrum and the residuals for the GRBs are presented in figures 7.2−7.6). To plot the energy squared, unfolded spectrum E 2 f(E) the eeufspec plot command can be used. In the unfolded plot the spectral model is more clearly visible as it has not yet been folded through the detector response matrix. When interpreting the unfolded spectrum be aware that the plot is model-dependent. The data points that are plotted are calculated by multiplying the observed data with (unfolded model)/(folded model). The (unfolded model) is the absorption and (broken) power-law model inte- grated over the plot bin, the (folded model) is the model multiplied by the response as it is seen in figure 7.1. The square root of χ 2 plots show the difference between the folded model and the data points scaled with the error. Trends in this plot may point to the need for an additional model component.

For the spectra of GRB 050730, 060729 and 090618 a power-law spectrum is found to

provide a sufficiently accurate fit of the observations (see figures 7.2, 7.3 and 7.4), with

a reduced χ 22 /DOF) close to one (see table 7.1). A broken power-law spectrum was

also tested but does not provide a significant improvement. A thermal component has

been found in a minority of GRB X-ray afterglows (Valan et al., 2018). Adding a thermal

emission component, in the form of a black body, does not show a notable improvement

to the fits. At the time of the XMM observation, a power-law component, in accordance

with synchrotron emission, dominates the spectrum.

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10

0

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1

Energy [keV]

10

−3

3×10

−4

4×10

−4

6×10

−4

ph oto ns cm

−2

s

−1

ke V

(a) GRB050730: Unfolded spectrum

100 101

Energy [keV]

−3

−2

−1 0 1 2 3

(data

-m od el) /er ror

(b) Square root of χ 2 for the folded spec- trum

Figure 7.2: Unfolded spectrum and model deviations plot for the best fit model of GRB 050730, the spectrum is fit with an absorbed power-law model.

10

0

10

1

Energy [keV]

10

−3

2×10

−3

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ph oto ns cm

−2

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ke V

(a) GRB060729: Unfolded spectrum

100 101

Energy [keV]

−4

−2 0 2 4

(data

-m od el) /er ror

(b) Square root of χ 2 for the folded spec- trum

Figure 7.3: Unfolded spectrum and model deviations plot for the best fit model of GRB 060729, the spectrum is fit with an absorbed power-law model.

10

0

10

1

Energy [keV]

10

−3

ph oto ns cm

−2

s

−1

ke V

(a) GRB090618: Unfolded spectrum

100 101

Energy [keV]

−4

−2 0 2 4

(data

-m od el) /er ror

(b) Square root of χ 2 for the folded spec- trum

Figure 7.4: Unfolded spectrum and model deviations plot for the best fit model of GRB 090618, the spectrum is fit with an absorbed power-law model.

For GRB 111209A a broken power-law model is preferred, see figure 7.5. A systematic excess at the hard end of the spectrum was observed in the residuals of the power-law fit.

The broken power-law model also has significantly improved χ 2 statistics (χ 2 improves

with 36 for only two DOF). An F-test probability of the order of 10 −7 is found. The

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F-test probability is a p-value that represents the probability of obtaining the observed or more extreme statistics due to spurious effects.

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(a) GRB111209A power-law: Unfolded spectrum

100 101

Energy [keV]

−4

−3

−2

−1 0 1 2 3

(data

-m od el) /er ror

(b) Square root of χ 2 for the folded spec- trum

10

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−1

ke V

(c) Broken power-law: Unfolded spec- trum

100 101

Energy [keV]

−4

−3

−2

−1 0 1 2 3

(data

-m od el) /er ror

(d) Square root of χ 2 for the folded spec- trum

Figure 7.5: Unfolded spectrum and model deviations plot for GRB 111209A. Figures a and b are for the power-law fit, the lower two figures c and d are the result of a broken power-law fit.

GRB 151027A is fit with an absorbed power-law model, see figure 7.6. Nappo et al.

(2017) suggest that a statistically significant thermal component should be added to the spectrum, namely a black body with a temperature of ∼0.11 keV. In our fit adding a thermal component does not significantly improve the statistics (∆χ 2 = 5 for 2 DOF).

These contrasting results may be due to minor differences in the data analysis. A different low energy limit is used for the spectra, Nappo et al. (2017) use 0.3 keV instead of 0.5 keV.

10

0

10

1

Energy [keV]

2×10

−4

3×10

−4

4×10

−4

6×10

−4

ph oto ns cm

−2

s

−1

ke V

(a) GRB151027A: Unfolded spectrum

100 101

Energy [keV]

−4

−3

−2

−1 0 1 2 3 4

(data

-m od el) /er ror

(b) Square root of χ 2 for the folded spec- trum

Figure 7.6: Unfolded spectrum and model deviations plot for the best fit model of GRB

151027A, the spectrum is fit with an absorbed power-law model.

(37)

The parameters and statistics of the best fit models are presented in table 7.1. N H is the equivalent hydrogen column density for the excess X-ray absorption, Γ is the photon index of the spectrum.

For GRB 111209A, two additional parameters are given. E break is the energy at which the photon index of the spectrum changes and Γ 2 is the photon index after the spectral break. Γ represents the photon index for only the low energy part of the spectrum for this burst.

z f rozen N H,gal f rozen N H Γ E break χ 2 (DOF)

[10 21 cm −2 ] [10 21 cm −2 ] [keV]

050730 3.967 0.349 2.2 ± 7.1 1.85 ± 0.036 0.027 108.96(117)

060729 0.54 0.54 0.8 ± 0.13 2.05 ± 0.015 168.56(154)

090618 0.54 0.76 2.2 ± 0.21 1.92 ± 0.02 150.69(145)

111209A 0.677 0.154 2.1 ± 0.4 Γ 1 = 2.42 ± 0.09 0.06

3.12 ± 0.64 0.89 102.14(113) Γ 2 = 1.88 ± 0.1 0.2

151027A 0.81 0.375 2.4 ± 0.5 2.08 ± 0.036 111.75(114)

Table 7.1: Best fit parameters. Redshift z, and Galactic column density N H,gal are taken from the online documentation. N H represents the excess absorption as the equivalent Hydrogen column density with all the absorption at the redshift of the host. Γ is the photon index for the power law spectra. For 111209A, Γ 1 is the low energy photon index before E break , and Γ 2

is the high energy photon index after the spectral break. In the last column the χ 2 and the degrees of freedom (DOF) for these best fits are given.

Time-averaged Time-resolved

N H [10 21 cm −2 ] χ 2 (DOF) N H [10 21 cm −2 ] χ 2 (DOF) 050730 2.2 ± 7.1 108.96(117) 2.5 ± 6.6 265.22(281) 060729 0.80 ± 0.13 168.56(154) 0.87 ± 0.13 795.5(761) 090618 2.2 ± 0.2 150.69(145) 2.1 ± 0.2 540.94(560) 111209A 2.1 ± 0.4 102.14(113) 2.1 ± 0.5 278.03(294) 151027A 2.4 ± 0.5 111.75(114) 2.5 ± 0.5 323.22(320)

Table 7.2: N H values and statistics obtained from the time-integrated and time-resolved fit of the XMM-Newton X-ray spectrum. A single power-law model is used for all but GRB 111209A which is fit with a broken power-law.

As mentioned in 3.1 there is a degeneracy between N H and the slope of the spectrum.

This slope can be represented with the photon index. A fit-statistics contour plot for

N H and Γ is presented in figure 7.7. If the parameters were perfectly independent the

confidence levels would be circles, this is clearly not the case here.

References

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