Observations of Magnetars: from Outburst to Quiescence

Observations of Magnetars: From Outburst to Quiescence

Paul Andrew Scholz Department of Physics McGill University Montréal, Québec Canada

November 2016

A Thesis submitted to McGill University in partial fulfillment of the requirements for the degree of Doctor of Philosophy

Dedicated to my parents, who made all this possible.

Abstract

Magnetars are pulsars, rotating neutron stars, that display extreme activity and typically have X- ray luminosities that are in excess of their rotational energy loss. The cause of both the activity and excess luminosity is thought to be the large energy reservoir provided by their high magnetic fields. We present studies of three different magnetars, 1E 1547−5408, Swift J1822.3−1606, and 1RXS J170849.0−400910. Using detailed spectral and timing observations of these three magnetars from the Swift, Rossi X-ray Timing Explorer, Chandra, and XMM-Newton X-ray telescopes, we test several different aspects of the magnetar model. Specifically, we study the correlation between the hardness and flux of the X-ray emission following magnetar outbursts, the relation between timing and radiative activity, and whether a magnetic field in excess of ∼ 1014 G is required to power magnetar activity. We first present Swift observations of 1E 1547−5408 following its 2009 January outburst. We show the X-ray radiative evolution following the outburst as well as a statistical study of the short

X-ray bursts emitted during the event. We find that the X-ray flux increased by a factor of ∼>500 and hardened significantly. We present the hardness-flux evolution of the persistent emission of the 2008 and 2009 outbursts of 1E 1547−5408 and compare it to those from other magnetars and find that although an overall trend does exist, the degree of hardening for a given increase in flux is not uniform from source to source. We then present two studies of the newly discovered low-magnetic-field magnetar (i.e lower than ∼ 1014 G) Swift J1822.3−1606. First, we present a timing analysis of the first ∼ 400 days following the 2011 July outburst that resulted in the magnetar’s discovery. We show that the timing measurements are affected by the choice of number of frequency derivatives and that there is ambiguity in its timing properties and thus spin-down measured magnetic field. Us- ing an additional ∼ 500 days of Swift observations, we then resolve the timing ambiguity in Swift J1822.3−1606 by finding that it was due to an unmodelled exponential recovery following a glitch at the onset of the 2011 July outburst. After accounting for the glitch recovery, we measure a long-term spin-down rate which implies a dipolar magnetic field of 1.35 × 1013 G, lower than all previous estimates for this source, and the second lowest measured for any magnetar showing conclusively that Swift J1822.3−1606 is a low-magnetic field magnetar. Lastly, we present a X-ray flux and spectral analysis of the magnetar 1RXS J170849.0−400910 over a baseline of 10 years and show that the X-ray flux did not vary significantly and there is only evidence for low-level spectral variability. This is in contrast with previous studies in which significant flux variability associated with rotational glitches was claimed. This shows

v that magnetar timing activity can occur without any radiative changes. We then conclude by comparing the radiative properties of the three magnetars and show how their differences and similarities fit into the overall magnetar population. We hypothesize that transient magnetars like 1E 1547−5408 evolve into the slower-rotating persistent magnetars such as 1RXS J170849.0−400910 and then undergo significant magnetic field decay and cooling to evolve into the low-magnetic-field magnetars similar to Swift J1822.3−1606. We discuss how these observations relate to magnetothermal models of magnetar evolution as well as how they fit within the wider pulsar population. Résumé

Les magnétoiles sont des pulsars radios (un type d’étoile à neutrons en rotation) sujettes à des évènements extrêmement énergétiques, et ont typiquement des luminosités dans les rayons X plus grandes que la quantité d’énergie libérée via rotation. Les champs magnétiques très puis- sants des magnétoiles pourraient agir en tant que réservoirs d’énergie et pourraient possiblement expliquer ces évènements énergétiques ainsi que leurs grandes luminosités. Une étude de trois différentes magnétoiles, soit 1E 1547−5408, Swift J1822.3−1606, et 1RXS J170849.0−400910, est présentée dans cette thèse. En utilisant des observations spectrales et chronométriques très dé- taillées de ces trois sources prisent par les télescopes rayon X Swift, Rossi X-ray Timing Explorer, Chandra et XMM-Newton, nous testons plusieurs aspects des différents modèles de magnétoiles. Plus précisément, nous étudions la corrélation entre l’énergie moyenne des photons et le flux des émissions dans les rayons X suivant les évènements radiatifs des magnétoiles, la relation entre les changements dans les paramètres chronométriques et les activités radiatives, et nous tentons de déterminer s’il est nécessaire d’avoir un champ magnétique en excès d’environ 1014 G pour alimenter les activités des magnétoiles. Premièrement, les observations de 1E 1547−5408 prisent avec le télescope rayon X Swift suivant l’évènement radiatif qui s’est produit en janvier 2009 sont présentées, incluant l’évolution radiative dans les rayons X ainsi qu’une étude statistique du court sursaut énergétique émit durant l’évènement radiatif. Le flux dans les rayons X a augmenter par un facteur de plus 500 et les photons sont devenus plus énergétiques. L’évolution du flux et de l’énergie moyenne des photons associée à l’émission persistante des évènements radiatifs de 2008 et de 2009 de la magnétoile 1E 1547−5408 est présentée et comparée à celles produites par d’autres magnétoiles. On peut y conclure que même si, en général, une tendance existe, l’augmentation de l’énergie moyenne des photons pour une certaine augmentation dans le flux n’est pas uniforme d’une source à l’autre. Ensuite, deux études portant sur la magnétoile récemment découverte ayant un faible champ magnétique, Swift J1822.3−1606, sont apportées dans ce travail. D’abord, une analyse chrono- métrique des données collectées durant les premiers 400 jours suivant l’évènement radiatif de juillet 2011 (ayant mené à la découverte de cette magnétoile) est présentée. Nous démontrons que les mesures chronométriques sont affectées par le choix du nombre de dérivées des fréquences et qu’il y a une ambiguïté dans les propriétés chronométriques, donc dans la détermination du champ magnétique via le ralentissement de la rotation de l’étoile. En utilisant environ 500 jours d’observations supplémentaires avec le télescope Swift, nous résolvons cette ambiguïté et nous trouvons que celle-ci s’expliquait par un rétablissement exponentiel qui n’était pas modélisé,

vii suivant un changement soudain dans sa vitesse de rotation lors de l’évènement radiatif de juillet 2011, un phénomène que l’on appelle ‘glitch’. Après avoir considéré le rétablissement suivant le ‘glitch’, nous déterminons un ralentissement à long terme de la vitesse de rotation, ce qui im- plique un champ magnétique dipolaire d’environ 1.35 × 1013 G. Cette mesure de la force du champ magnétique est plus faible que tous les autres estimés faits pour cette source, et la deux- ième plus faible de toutes les magnétoiles connues, ce qui catégorise Swift J1822.3−1606 comme étant une magnétoile à faible champ magnétique. Dernièrement, une analyse du flux et du spectre dans les rayons X de la magnétoile 1RXS J170849.0−400910 basée sur 10 ans de données est présentée dans cette thèse. Ces don- nées suggèrent que le flux de rayons X n’a pas varié de façon significative et qu’il y a une minime variabilité dans le spectre. Ce résultat est en contraste avec de précédentes études, lesquelles sou- tiennent que des variations de flux sont associées aux changements dans la vitesse de rotation. Ceci suggère que les moments où il y changements dans les paramètres chronométriques peuvent se produire sans qu’il y ait de changement dans les propriétés radiatives. Pour conclure, une comparaison entre les propriétés radiatives des trois magnétoiles à l’étude est faite et nous démontrons comment leurs différences et leurs similarités cadrent dans la population globale des magnétoiles. Hypothétiquement, les magnétoiles transitoires comme 1E 1547−5408 pourraient évoluer en magnétoiles avec des rotations lentes, comme 1RXS J170849.0−400910, pour ensuite refroidir et subir une diminution dans la force de leurs champs magnétiques et puis éventuellement devenir des magnétoiles avec un faible champ mag- nétique, comme Swift J1822.3−1606. Une discussion regardant la manière dont cette observation est reliée aux modèles magnétothermiques de l’évolution des magnétoiles ainsi que comment cela s’insère dans la plus large population de pulsars radios est finalement soulevée dans cette thèse. Contents

Abstract v

Résumé vii

Acknowledgments xv

Preface xvi

1 Introduction 1 1.1 Neutron Stars and Pulsars ...... 1 1.1.1 History ...... 1 1.1.2 Description ...... 2 1.1.3 Pulsar Power Sources ...... 3 1.1.4 Pulsar Spin Down ...... 5 1.2 Magnetars ...... 8 1.2.1 Discovery ...... 8 1.2.2 Phenomenology: The Many Faces of Magnetars ...... 10 1.2.3 Theory: The Magnetar Model ...... 14 1.2.4 The Emerging Magnetar Population ...... 16

2 Telescopes and Techniques 19 2.1 X-ray Observatories ...... 19 2.1.1 X-ray Detectors ...... 19 2.1.2 X-ray Optics ...... 21 2.1.3 The Swift Gamma Ray Burst Mission ...... 21 2.1.4 The Chandra X-ray Observatory ...... 23 2.1.5 The XMM-Newton Telescope ...... 24 2.1.6 The Rossi X-ray Timing Explorer ...... 25 2.2 X-ray Spectroscopy ...... 26 2.3 Pulsar Timing Techniques ...... 29 2.3.1 The Pulse Profile ...... 29 2.3.2 The Pulse Time of Arrival ...... 29 2.3.3 Phase-coherent Pulsar Timing ...... 33

ix x Contents

3 The 2009 Outburst of Magnetar 1E 1547−5408 35 3.1 Introduction ...... 35 3.2 Observations ...... 36 3.3 Analysis and Results ...... 37 3.3.1 Persistent Flux Evolution ...... 37 3.3.2 X-Ray Bursts ...... 42 3.4 Discussion ...... 52 3.4.1 Persistent Flux ...... 52 3.4.2 Bursts ...... 56 3.5 Conclusions ...... 59

4 Post-outburst X-ray Timing Evolution of Swift J1822.3−1606 61 4.1 Introduction ...... 61 4.2 Observations ...... 62 4.2.1 Swift Observations ...... 62 4.2.2 RXTE Observations ...... 65 4.2.3 Chandra Observations ...... 66 4.2.4 ROSAT Observation ...... 66 4.3 Analysis & Results ...... 66 4.3.1 Imaging and Archival Spectral Analysis ...... 66 4.3.2 Timing Analysis ...... 68 4.3.3 X-ray Bursts ...... 76 4.4 Discussion ...... 77 4.4.1 Timing Behaviour ...... 78 4.4.2 Distance Estimate and Possible Association ...... 79 4.5 Conclusions ...... 79

5 The Long-term Post-outburst Behaviour of Magnetar Swift J1822.3−1606 81 5.1 Introduction ...... 81 5.2 Observations ...... 83 5.2.1 Swift Observations ...... 83 5.2.2 RXTE and Chandra Observations ...... 84 5.3 Analysis & Results ...... 84 5.3.1 Timing ...... 84 5.3.2 Flux and Spectral Evolution ...... 88 5.4 Discussion ...... 91 5.4.1 Post-outburst Spin-down Behaviour ...... 91 5.4.2 Flux and spectral evolution ...... 94 Contents xi

5.4.3 Models of Flux Relaxation ...... 97 5.5 Conclusions ...... 102

6 On the X-ray Variability of Magnetar 1RXS J170849.0−400910 105 6.1 Introduction ...... 105 6.2 Observations ...... 106 6.2.1 Swift Observations ...... 106 6.2.2 Chandra and XMM-Newton Observations ...... 107 6.3 Analysis & Results ...... 110 6.3.1 Flux and Spectra ...... 110 6.3.2 Timing ...... 113 6.4 Discussion ...... 114 6.4.1 Flux Variability of RXS J1708 ...... 115 6.4.2 Radiative Activity and Glitches in Magnetars ...... 116 6.5 Conclusions ...... 119

7 Summary and Conclusions 121 7.1 Emerging Trends in the Magnetar Population ...... 122 7.2 Relation to Other Classes of Neutron Stars ...... 129 7.3 Concluding Remarks ...... 130

References 132 List of Figures

1.1 Diagram of a pulsar and its magnetosphere...... 4 1.2 The period-period derivative diagram ...... 7 1.3 Giant flare of SGR 0526−66...... 9 1.4 Examples of short X-ray bursts from a magnetar...... 11 1.5 An example of pulse shape evolution during magnetar outbrusts...... 13

2.1 Diagram of a Wolter I telescope...... 20 2.2 Diagram of a Wolter I telescope...... 21 2.3 Nested mirror segments of the XMM-Newton telescope...... 22 2.4 The Swift satellite...... 23 2.5 Schematic of Chandra ACIS...... 24 2.6 The Rossi X-ray Timing Explorer ...... 26 2.7 An example of a pulse profile ...... 30

3.1 Properties of the persistent emission of the 2009 outburst of 1E 1547−5408 ... 40 3.2 2-10 keV RMS pulsed flux evolution of 1E 1547−5408 ...... 41 3.3 1-10 keV RMS pulsed fraction as a function of 1-10 keV unabsorbed flux. .... 42 3.4 Examples of bursts from 1E 1547−5408...... 44 3.5 Temporal properties of X-ray bursts from 1E 1547−5408...... 45 3.6 Flux properties of X-ray bursts from 1E 1547−5408...... 47 3.7 Bursts folded at pulsar ephemeris ...... 49 3.8 Power-law index as a function of average absorbed flux for 1E 1547−5408 bursts. 51 3.9 Fluxes and hardnesses for magnetar outbursts...... 54

4.1 ROSAT and Chandra images of the field of Swift J1822.3−1606...... 67 4.2 Timing residuals of Swift J1822.3−1606...... 69 4.3 Pulse profiles of the Chandra observations of Swift J1822.3−1606...... 73 4.4 Pulse profiles for Swift J1822.3−1606 as a function of energy...... 75

5.1 Timing residuals of Swift J1822.3−1606...... 85 5.2 Spectral evolution of Swift J1822.3−1606...... 90 5.3 Spectral hardness as a function of unabsorbed flux for Swift J1822.3−1606. ... 95 5.4 1–10 keV absorbed flux as a function of the blackbody emitting area for Swift J1822.3−1606.101

xii List of Figures xiii

6.1 Absorbed 1–10 keV flux and photon indices of 1RXS J170849.0−400910. ... 111 6.2 Timing Residuals of 1RXS J170849.0−400910...... 113

7.1 P –P˙ diagram of magnetars ...... 124 7.2 Magnetothermal model of magnetar evolution ...... 128 List of Tables

1.1 Properties of Known Magnetars...... 17

3.1 Summary of Swift XRT observations of the 2009 outburst of 1E 1547−5408 ... 38 3.2 Burst statistics of magnetars ...... 46

4.1 Summary of observations of Swift J1822.3−1606...... 63 4.0 Spin Parameters for Swift J1822.3−1606...... 70 4.1 RXTE-detected X-ray Bursts from Swift J1822.3−1606...... 77

5.1 Timing Parameters for Swift J1822.3−1606...... 87 5.2 Empirical Models of the Flux Evolution of Swift J1822.3−1606...... 91

6.1 Summary of Swift observations of RXS J1708 ...... 108 6.1 Timing Parameters for RXS J1708...... 114

xiv Acknowledgments

First, I would like to thank my supervisor, Vicky Kaspi, for taking me on as a grad student and introducing me to the exciting field of pulsars. She somehow manages to provide substantial support for all of her students despite being amazingly busy all of the time. I would like to thank her for being accessible and supportive and always making time for meetings both with the pulsar group and one-on-one to help with our research projects and keep us all on track. I have no idea how she does it. I would also like to thank the members of the McGill Pulsar Group for being great colleagues and collaborators as well as friends. Especially helpful to the research that went into this thesis were those who taught me the basics of pulsar and X-ray astronomy in the first couple years of my PhD: particularly Maggie Livingstone, Patrick Lazarus, Anne Archibald, Ryan Lynch, and Stephen Ng. Thanks also go out to my collaborators on my magnetar-related projects (i.e. those included in this thesis), especially Robert Archibald with whom I’ve had many discussions about magnetars and many other things. I would also like to thank collaborators on my other projects that are not contained in this thesis, notably members of the PALFA Survey. Working on varied projects within pulsar astronomy in the past six years is what has kept me motivated to continue to pursue a career in astronomy. I would also like to acknowledge the support of the National Science and Engineering Re- search Council of Canada which supported my PhD research through an Alexander Graham Bell Canada Graduate Scholarship and the McGill Department of Physics who awarded me a Schulich Graduate Fellowship. My greatest thanks go to my parents, Rudi and Marian Scholz, to whom this thesis is dedicated, for their constant support. Their boundless encouragement to pursue my interests is what made all this work possible. Finally, I would like to thank Anna Delahaye for making the past eight years the best in my life (at least so far).

xv Preface

Statement of Originality and Contribution of Authors

This thesis is a collection of papers published in the Astrophysical Journal (Chapters 3–6). Each paper reports new and original results regarding the X-ray behaviour of magnetars both following outbursts and in quiescence. Here we summarize the main results of each paper and detail the contributions of the authors.

• Chapter 3 – The 2009 Outburst of Magnetar 1E 1547−5408

The contents of this chapter originally appeared in the article:

Scholz, P.; Kaspi, V. M. The 2009 Outburst of Magnetar 1E 1547−5408: Persistent Ra- diative and Burst Properties. The Astrophysical Journal, 739:94 (2011)

We present an analysis of the persistent radiative evolution and a statistical study of the burst properties during and following the 2009 January outburst of the magnetar 1E 1547- 5408 using observations from the Swift X-Ray Telescope. We find that the 1-10 keV flux increased by a factor of ∼ 500 and hardened significantly, peaking ∼ 6 hr after the onset of the outburst. The observed pulsed fraction exhibited an anti-correlation with phase- averaged flux. Properties of the several hundred X-ray bursts during the 2009 outburst were determined and compared to those from other magnetar outburst events. We find that the peaks of the bursts occur randomly in phase but that the folded counts that compose the bursts exhibit a pulse which is misaligned with the persistent pulse phase. We compare the hardness-flux evolution of the persistent emission of the 2009 outburst to those from this and other magnetars and find that although an overall trend does exist, the degree of hardening for a given increase in flux is not uniform from source to source. These results are discussed in the context of previous results and within the magnetar model.

I performed all of the analysis in the work and authored the manuscript. Dr. Victoria Kaspi conceived of the project and contributed significantly to the planning of the analysis as well as to the text and interpretation of the results.

• Chapter 4 – Post-outburst X-ray Timing Evolution of Swift J1822.3−1606

All of the contents of Chapter 4 originally appeared in the article:

xvi Preface xvii

Scholz, P.; Ng, C.-Y.; Livingstone, M. A.; Kaspi, V. M.; Cumming, A.; Archibald, R. F. Post-outburst X-Ray Flux and Timing Evolution of Swift J1822.3−1606. The Astrophysi- cal Journal, 761:66 (2012) However, some of the analysis and results in that work are presented in Chapter 5 (see below). In this Chapter, we present analyses of the phase-connected timing properties using Rossi X-ray Timing Explorer, Swift, and Chandra observations of the first 400 days following the 2011 July outburst of Swift J1822.3−1606. We measure a spin frequency of 0.1185154343(8) s−1 and a frequency derivative of −4.3 0.3 × 10−15 at MJD 55761.0, in a timing analysis that includes significant non-zero second and third frequency derivatives that we attribute to timing noise. This corresponds to an estimated spin-down inferred dipole magnetic field of B ∼ 5 × 1013 G, consistent with previous estimates though still possibly affected by unmodeled noise. We also present the flux and spectral properties of an archival ROSAT observation when the source is in quiescence. Based on proximity and similarity in absorption column density, we suggest that Swift J1822.3−1606 may have a distance comparable to that of the H II region M17, 1.6 0.3 kpc, making it one of the closest magnetars yet known. We compare the properties of Swift J1822.3−1606 with those of other magnetars and their outbursts. The contributions of the co-authors are as follows. The project was conceived by Dr. Vic- toria Kaspi and me. The Chandra observations were proposed for by Dr. Kaspi. The Swift observations were proposed for by me with assistance from Mr. Robert Archbald, Dr. Margaret Livingstone and Dr. Kaspi. Dr. C.-Y. Ng performed analysis of the archival ROSAT observation and contributed significantly to the text in sections related to that observation. Dr. Livingstone aided with the extraction of pulse time of arrivals from Rossi X-ray Timing Explorer observations. Mr. Archibald and I wrote timing analysis software used for Swift observations. Dr. Kaspi provided a significant contribution to the interpretation of the results as well as suggestions on improvements to both the analysis and text of the manuscript. I performed all other analyses and authoring of the text.

• Chapter 5 – The Long-term Post-outburst Behaviour of Magnetar Swift J1822.3−1606 The majority of the analysis and results presented in this chapter originally appeared as: Scholz, P.; Kaspi, V. M.; Cumming, A. The Long-term Post-outburst Spin Down and Flux Relaxation of Magnetar Swift J1822.3−1606. The Astrophysical Journal, 786:62 (2014) Since that work presents a similar analysis as in Scholz et al. (2012) but with a longer dataset, the flux and spectral evolution results from Scholz et al. (2012) that overlap with Scholz et al. (2014b) are presented in Chapter 5 rather than Chapter 4. xviii Preface

In this chapter, we present the timing behaviour and flux relaxation from over two years of Swift Rossi X-ray Timing Explorer, and Chandra observations following the 2011 July outburst of Swift J1822.3−1606. Previous X-ray studies of the post-outburst rotational evolution of Swift J1822.3−1606 yielded inconsistent measurements of the spin-inferred magnetic field (e.g. Chapter 4). We find that the ambiguity in previous timing solutions was due to enhanced spin down that resembles an exponential recovery following a glitch at the outburst onset. After fitting out the effects of the recovery, we measure a long-term spin-down rate of ν˙ = (−3.0 0.3) × 10−16 s−2 which implies a dipolar magnetic field of 1.35 × 1013 G, lower than all previous estimates for this source. We also consider the post-outburst flux evolution, and fit it with both empirical and crustal cooling models. We discuss the flux relaxation in the context of both crustal cooling and magnetospheric relaxation models.

I conceived of the project and proposed for the Swift data. The Chandra data were proposed for by Dr. Victoria Kaspi. All of the data analysis of Swift Rossi X-ray Timing Explorer, and Chandra data were performed by me. Dr. Andrew Cumming performed the crustal cooling modelling that was fit to the data. He also authored the section in the text pertaining to that analysis. The discussion of the magnetospheric relaxation model was authored primarily by Dr. Cumming with significant contributions from Dr. Kaspi and me. I authored the remainder of the manuscript. Dr. Kaspi provided substantial contributions to the text and to the interpretation of the results.

• Chapter 6 – On the X-ray Variability of Magnetar 1RXS J170849.0−400910

The contents of this chapter originally appeared in the article:

Scholz, P.; Archibald, R. F.; Kaspi, V. M.; Ng, C.-Y.; Beardmore, A. P.; Gehrels, N.; Kennea, J. A. On the X-Ray Variability of Magnetar 1RXS J170849.0−400910. The As- trophysical Journal, 783:99 (2014)

In this Chapter, we present a long-term X-ray flux and spectral analysis for 1RXS J170849.0−400910 using data from the Swift X-Ray Telescope from 2005 to 2013. We also analyze two observations from the Chandra and XMM-Newton X-ray observatories in the period from 2003 to 2004. In this period, between 2003 and 2013, 1RXS J170849.0−400910 under- went several rotational glitches. Previous studies claimed variations in the X-ray emission associated with some of these glitches. From our analysis we find no evidence for significant X-ray flux variations and evidence for only low-level spectral variations. We also present an updated timing solution for 1RXS J170849.0-400910, from Rossi X-ray Tim- ing Explorer and Swift observations, which includes a previously unreported glitch. We discuss the frequency and implications of radiatively quiet glitches in magnetars. Preface xix

The project was conceived by Dr. Victoria Kaspi. I performed all of the flux and spectral analysis of the Swift, Chandra, and XMM-Newton data. Dr. C.-Y. Ng extracted the Chan- dra and XMM-Newton spectra from the raw data. Mr. Robert Archibald performed the timing analysis using the RXTE and Swift observations and contributed to the text regarding that analysis. I authored all other sections of the work. Dr. Kaspi provided a substantial contribution to the text as well and the interpretation of the result. Drs. Andrew Beard- more, Neil Gehrels, and Jamie Kennea made helpful suggestions pertaining to the analysis and discussions of the results.

1 Introduction

1.1 Neutron Stars and Pulsars

1.1.1 History

The concept of a neutron star, a star composed primarily of neutrons, was first proposed by Baade & Zwicky (1934) as the result of the collapse of the core of a massive star as it explodes in a supernova. Observational evidence for neutron stars arose in July 1967 when then graduate student Jocelyn Bell discovered repeating short radio pulses using the Interplanetary Scintillation Array, an array of dipole antennae sensitive to 81.5 MHz radio waves at the Mullard Radio Astronomy Observatory near Cambridge, UK. The pulses all originated from a fixed declination and right ascension, i.e. the same location on the sky, and therefore could not have had a terrestrial origin. The ∼0.3-second-long pulses arrived 1.337 seconds apart with shocking regularity; the period was found to be constant to at least one part in 107 (Hewish et al., 1968). The short duration of the pulses as well as their periodic nature argued for a small emitting region and a massive com- pact object. Thomas Gold was the first to recognize that this implied that the origin of the pulses was the rotation of a neutron star (Gold, 1968). The 1974 Nobel prize in physics was awarded to Anthony Hewish, Bell’s PhD supervisor, and Martin Ryle, who designed the aperture synthesis technique used by the telescope array, for the discovery of pulsars. In the nearly 50 years since the discovery of pulsars, over 2500 pulsars have been discovered (Manchester et al., 2005)1. Within this population, multiple source classes have emerged as well as a rich phenomenology.

1see the Australia Telescope National Facility Pulsar Catalogue at http://www.atnf.csiro.au/people/ pulsar/psrcat/

1 2 1 Introduction

1.1.2 Description

As Baade & Zwicky (1934) first correctly proposed, neutron stars are an endpoint of stellar evolution. They are, however, not the only endpoint of stellar evolution. When a star has exhausted all of the fuel available for nuclear burning, its core collapses. What happens to this core depends

on the mass of the star. Star with masses below ∼8 solar masses (M⊙) become white dwarfs when nuclear burning ceases and the core becomes supported by electron-degeneracy pressure. The outer layers of the star are expelled and what is left is the degenerate core of the star, or a white dwarf.

For stars with masses in excess of ∼8 M⊙, the electron-degenerate core inside the star grows to the point that it exceeds the so-called Chandrasekhar mass, the maximum mass that can be supported by electron degeneracy pressure, 1.35 M⊙ (Chandrasekhar, 1931). At this point, the core collapses in a violent explosion called a supernova. The remnant of a core-collapse supernova depends, again, on the mass of the progenitor star. If the supernova progenitor has mass, M, in

the range 8 M⊙∼

by degeneracy pressure between neutrons. At stellar masses above ∼25 M⊙, the stellar core can overcome the neutron-degeneracy pressure during the supernova and collapse into a black hole. Note that the above progenitor mass limits are approximate and depend on other parameters such as the metallicity of the star.

Neutron stars have masses in the range ∼1–2 M⊙. The minimum mass is set by the Chan- drasekhar limit. Although it was determined to be 1.35 M⊙ by Chandrasekhar (1931), the precise limiting mass depends on several details and assumptions (e.g. Kiziltan et al., 2013). The lowest

precisely measured neutron star masses are around 1.2 M⊙ (Kramer et al., 2006; Rawls et al., 2011). The maximum neutron star mass is more uncertain and depends on the details of the neutron star equation of state. The best constraint that we have on the maximum mass of a neutron star is from the pulsar PSR 0348+0432, which has a mass determined through pulsar timing of

2.01 0.04M⊙ (Antoniadis et al., 2013). The mass of a neutron star is related to its radius through the equation of state. The form of the equation of state for the hot, dense matter that compose neutron stars is currently unknown, but is a active area of research (for a recent review, see Lattimer & Prakash, 2016). Constraints from theory and observations show that neutron star 1.1 Neutron Stars and Pulsars 3 radii should fall in the range 10–20 km. Pulsars are neutron stars that emit radiation in narrow beams that we detect with telescopes as pulses of light. They are highly magnetized and rapidly rotating (spin periods of 1 ms–10 s) and are surrounded by co-rotating magnetosphere that is full of plasma (Goldreich & Julian, 1969). A schematic of the pulsar emission mechanism is shown in Figure 1.1. The magnetosphere ac- celerates particles along magnetic field lines. This accelerated plasma is densest at the magnetic poles and so the polar region gets heated and emits radiation. Since the rotation axis of the pulsar can be misaligned with the magnetic axis, the radiation beam from the polar cap rotates with the star, creating a lighthouse-like effect.

1.1.3 Pulsar Power Sources

The pulsed emission from neutron stars can be powered in one of three ways: rotation, accretion, and from the magnetic field. Rotation-powered pulsars (RPPs) are powered by the energy lost due to their rotation in an effect known as “magnetic braking”. Since a time varying magnetic field (often assumed to be a pure magnetic dipole) loses energy, the star slows down with time. RPPs are by far the most numerous of known pulsars and are primarily observed as radio pulsars (for a review see Lyne & Graham-Smith, 2006). The emission of accretion-powered pulsars is caused by the accretion of material onto the magnetic poles of the pulsar. This matter is heated due to the loss of graviational potential energy as it falls towards the neutron star surface. This heated, infalling material causes pulsations in the X-ray light-curve at the rotation period of the pulsar. Depending on the relative spin rates of the accreting material and the neutron star, an accreting pulsar can either spin down or spin up (in contrast with RPPs, which exclusively spin down) as it either loses or gains angular momentum from the accreted material (for a review see Frank et al., 1992).

14 Pulsars with high magnetic fields, B ∼> 10 G, are either called magnetars or high-magnetic field pulsars depending on the activity they display. Magnetars are generally defined as pulsars that have X-ray luminosities, LX , that exceed the energy available from their rotational spin down, E˙ . They also display activity such as short X-ray bursts and week to month long outbursts that are thought to be fueled by their high magnetic fields. High-magnetic field pulsars, on the other > 14 ˙ hand, have magnetic fields in excess of B ∼ 10 G, but do not have LX > E and do not display 4 1 Introduction

Figure 1.1: Diagram of a pulsar and its magnetosphere. Adapted from https://ase.tufts. edu/cosmos/print_images.asp?id=52. 1.1 Neutron Stars and Pulsars 5

activity (i.e. changes in their radiative state). However, the division between magnetars and high ˙ magnetic field pulsars is a blurry one. Many magnetars only have LX > E in their outburst states (e.g. Gotthelf et al., 2004; Scholz et al., 2012) and at least two sources that were designated as a high-magnetic field pulsars have shown magnetar-like activity (Gavriil et al., 2008; Archibald et al., 2016).

1.1.4 Pulsar Spin Down

The spin properties of pulsars are commonly modelled by a Taylor expansion of the spin phase,

1 1 ϕ(t) = νt + νt˙ 2 + νt¨ 3 + ... , (1.1) 2 6 where ϕ is the phase of a fiducial point on the neutron star surface, ν is the spin frequency, ν˙ is the first time-derivative of the spin frequency, and ν¨ is the second spin-frequency time derivative. The spin-down behaviour of many isolated pulsars can be described by only the first two terms in the expansion, ν and ν˙. Only for the best-timed or, as we shall see, the most erratically behaving, pulsars are higher-order derivatives needed. Additionally, pulsars in binary systems also need timing model parameters for their orbital behaviour, but such systems will not be considered in this thesis. The spin parameters ν and ν˙ are also commonly represented by the spin period and first time derivative of the period, i.e.

1 ν˙ P = , P˙ = − . (1.2) ν ν2 From the period and period derivative (or equivalently, frequency and frequency derivative) sev-

eral physical properties of the pulsar can be inferred. The rotational kinetic energy is Erot = (1/2)Iω2 where I is the moment of inertia of the neutron star, and ω = 2π/P is the rotational angular frequency. If we assume a canonical neutron star as a sphere of uniform density with

45 2 M = 1.4 M⊙ and R = 10 km, I ∼ 10 g cm . The rotational energy output of a rotating neutron star is thus

dE − E˙ = − rot = −Iωω˙ = 4π2IPP˙ 3. (1.3) dt 6 1 Introduction

This quantity is often called the pulsar’s “spin-down luminosity” and it represents the total power lost by the neutron star. For rotation-powered pulsars, only a small fraction of this energy is used by the pulsations that we observe; the majority is taken away by the pulsar’s relativistic particle wind and other losses. If we assume that the neutron star magnetosphere can be approximated as a dipole spinning in a vacuum, we can estimate the surface magnetic field from its rotational spin-down. The radiated power of a magnetic dipole with magnetic moment µ spinning at an angular frequency ω is (Jackson, 1962)

2 E˙ = µ2ω4 sin2 α, (1.4) dipole 3c3 where α is the angle between the magnetic moment and the spin axis. If we recall that E˙ = −Iωω˙ (Equation 1.3) and use that the magnetic moment is related to the magnetic field by B = µ/r3 for a dipole, we arrive at √ √ 3Ic3 ˙ ≃ × 19 ˙ Bsurface = B(r = RNS) = 2 6 2 P P 3.2 10 G P P. (1.5) 8π RNS sin α We can estimate the age of a pulsar by integrating the following equation (which follows from Equations 1.3 and 1.4) and making several simplifying assumptions:

2µ2 sin2 α ω˙ = − ω3. (1.6) 3Ic3 Note that this equation applies for a dipole spinning in a vacuum and so this equation is often generalized to ω˙ = −Kωn where n is called the “braking index”. If we then integrate, we arrive at

( ) ν νn−1 t = − 1 − , (1.7) − n−1 (n 1)ν ˙ νi where νi is the birth spin-frequency of the pulsar. If we assume that n = 3 and that νi ≫ ν, i.e that the pulsar is born spinning much faster than at present, then we get

1 ν τ = − . (1.8) c 2 ν˙ /s g er 33 1.1 Neutron Stars and Pulsars 7 10

-8 10 /s g er 36 -9 Pulsars 0 10 1 -10 Binaries 10 1 15 Magnetars 0 G -11 10 -12 10 1 14 0 G -13 10

) -14

s 10 1 13 / 0 G s

( -15

˙ 10 P /s g er -16 39 0 10 1 1 12 0 G -17 10 -18 10 1 11 0 G -19 10 -20 /s 10 g 10 10 er G 30 1 9 0 G -21 10 10 -3 -2 -1 0 1 10 10 10 10 10 P (s)

Figure 1.2: The period-period derivative, or “P –P˙ ”, diagram. Small black dots denote pulsars. Points encircled in red denote pulsars with binary companions and points surrounded with blue squares indicate magnetars. Lines of constant magnetic field (B; see Equation 1.5) are shown as dashed lines. Lines of constant E˙ (see Equation 1.3) are shown as dotted lines.

This quantity is known as the “characteristic age” and is often used to estimate the age of a pulsar. However, it must be noted that this equation assumes that the pulsar is born spinning rapidly and that n = 3 (i.e. it spins down solely by magnetic dipole radiation) for its entire lifetime. The characteristic age can therefore differ from the true age of the pulsar signficantly.

The pulsar population is commonly summarized on a diagram of the measured periods plotted against period derivatives, called a “P –P˙ diagram”. An example is shown as Figure 1.2. Broadly, the pulsar population is grouped into three separate classes on this diagram. The majority of the pulsar population have spin periods between 0.1 and 2 seconds, have magnetic fields in the range ∼ 1011 − 1013 G, and characteristic ages between 10 kyr and 1 Gyr. At fast periods, there is an island of pulsars with large characteristic age and low magnetic fields. These are the “millisecond 8 1 Introduction pulsars”, whose spin periods have been increased by accretion from a companion star in a process known as “recycling”. As such, most millisecond pulsars are found in binary systems. Finally, in the top-right corner of the P –P˙ diagram are the magnetars, the subject of this thesis. Magnetars are pulsars with high magnetic fields, long periods and young characteristic ages.

1.2 Magnetars

In this section I will first outline the discovery of magnetars as a source class. I will then describe the unique phenomenology that defines magnetars and makes them distinct from other high-magnetic field pulsars. I will then outline the theoretical framework of the magnetar model that seeks to explain their behaviour. Finally, a summary of the last 10 years of the magnetar field, which has experienced a large increase in the number of sources, will be presented.

This structure, with separate summaries of the field from the initial decades followed by the last ten years, reflects a transition of the magnetar field from discovery of unique objects to char- acterization of a population.

1.2.1 Discovery

Magnetars were first classified as two separate source classes: soft gamma repeaters (SGRs) and anomalous X-ray pulsars (AXPs). SGRs were first discovered in 1979 January when a short (less than a second) burst of gamma rays was detected from SGR 1806−20. It, and several other short, soft gamma ray bursts detected by the Venera satellites, were originally classified as a subset of the gamma-ray burst (GRB) population (Mazets & Golenetskii, 1981). The repeating nature of SGR 1806−20 was made apparent in 1983 when a cluster of bursts occurred (Laros et al., 1987).

Shortly after the 7 January 1979 burst of SGR 1806−20, a much more energetic event was detected from the supernova remnant (SNR) N49 in the Large Magellanic Cloud (LMC) on 5 March 1979. This event, called a giant flare, began with a rapid onset and a bright (1 × 10−3 erg s cm−2) ∼ 0.2 s peak followed by a rapid quasi-exponential flux decay. The entire event released > 5 × 1044 erg in ∼ 3 min (Figure 1.3; Mazets et al., 1979b). During the decay of the giant flare, extremely energetic pulsations were detected with a period of 8.00 0.05 s (Terrell et al., 1980). The source of this giant flare is now designated as a SGR and is SGR 0526−66, a magnetar 1.2 Magnetars 9

Figure 1.3: 50–150 keV light-curve of the 1979 giant flare of SGR 0526−66 from the Venera 11 probe (Mazets et al., 1979b).

located in the LMC, possibly associated with SNR N49.

The 5 March 1979 giant flare remained a unique event until 27 August 1998 when SGR 1900+14, which was previously detected as a soft gamma-ray burst source (Mazets et al., 1979a), displayed a giant flare similar in many ways to the 1979 event of SGR 0526−66: it had a sharp rise followed by a ∼ 5 min decay and displayed pulsations with a period of 5.16 s (Hurley et al., 1999). A third giant flare occurred from SGR 1806−20 on 17 December 2004 (Hurley et al., 2005) and short, soft, gamma-ray bursts have since been seen in several more sources (e.g. Woods et al., 1999; Israel et al., 2010; Rea et al., 2009). The energy source for the extreme activity of SGRs is thought to come from the high magnetic field (see Section 1.2.3; Thompson & Duncan, 1995).

In parallel with the discovery of SGRs as a source class, a new type of X-ray pulsar was being identified. X-ray pulsations were found in the X-ray source at the center of SNR CTB 109 (Fahlman & Gregory, 1981) that were much too bright to be powered by the rotational energy of the pulsar (Koyama et al., 1987). Several other similar sources were discovered in the following decades and grouped together with accretion-powered low-mass X-ray binaries (Helfand, 1994; Mereghetti & Stella, 1995). However, these pulsars, 1E 2259+586, 1E 1048−5937, and 4U 0412+61, had soft X-ray spectra (in comparison to the majority of X-ray binaries), no optical counterparts, no evidence for orbital motion, and are located in young environments, i.e. SNRs and in the plane of the Galaxy (van Paradijs et al., 1995). This is unlike pulsars in low-mass X-ray 10 1 Introduction binaries which are in orbit around their donor stars and must have aged enough to have evolved companions. These sources were eventually called “anomalous X-ray pulsars”, or AXPs, due to the unknown power source for their high X-ray luminosities that far exceeded the energy available from their rotational spin-down. Thompson & Duncan (1996) suggested that the source of the anomalous emission is the decay of their high (1014−16 G) magnetic fields. In the years following the introduction of the magnetar model for both SGRs and AXPs, several more AXPs have been discovered (e.g. Vasisht & Gotthelf, 1997; Sugizaki et al., 1997). It has also become evident that not only are SGRs and AXPs both explained by the magnetar model, but that SGR and AXP properties can be displayed by the same source. Short X-ray (or soft gamma ray) bursts have been detected from several AXP sources (Gavriil et al., 2002; Kaspi et al., 2003; Woods et al., 2005), showing they can display behaviour typical of SGRs. Further, AXP-like pulsations have since been seen in the persistent X-ray sources that power SGR activity (Kouveliotou et al., 1998; Kouveliotou et al., 1999). SGRs and AXPs are therefore not two separate sub-classes but rather two observational manifestations of a single source class.

1.2.2 Phenomenology: The Many Faces of Magnetars

Magnetars display a variety of variability in both their radiative and pulsar timing properties. Here we describe the unique phenomenology that has been observed since the discovery of magnetars as a source class.

Radiative Behaviour

Magnetars display radiative changes in a range of timescales. They show bursts that last millisec- onds to seconds, giant flares that last for several minutes, and periods of outburst that take up to many years to fade. Magnetars display short bursts at hard X-ray to soft gamma-ray energies, i.e. the namesake activity of SGRs. Their durations are typically in the range 10 ms to 10 s and their luminosities can reach up to 1041 erg s−1, well in excess of the Eddington limit (some examples of bursts are shown in Figure 1.4). The energy distributions for magnetar bursts seem to follow a power- law distribution, dN/dE ∝ Eα, and a log-normal waiting time distribution (Cheng et al., 1996; 1.2 Magnetars 11

40 20

30 15

20 10 Counts Counts

10 5

0 0

30 30

20 20 Counts Counts

10 10

0 0

1.5 1.5 1.5 1.5

1.0 0.5 0.0 0.5 1.0 1.0 0.5 0.0 0.5 1.0

Time relative to peak (s) Time relative to peak (s)

Figure 1.4: Examples of short X-ray bursts from magnetar 1E 1547–5408 during its 2009 outburst observed with the Swift/XRT. Time series are binned on a 1/16 s timescale in the 0.5–10 keV energy range. They display a wide range of morphologies (see Chapter 3).

Göğüş et al., 1999, 2000; Gavriil et al., 2004) similar to the Gutenberg-Richter law for earthquakes and energy distributions for solar flares (Crosby et al., 1993; Lu et al., 1993).

The most extreme radiative behaviour displayed by magnetars are giant flares. They are also the rarest events: only three have occurred in the past ∼ 35 years (Mazets et al., 1979b; Hurley et al., 1999; Hurley et al., 2005). A giant flare begins with a bright ∼ 1 s spectrally hard burst followed by an approximately exponential decay with a timescale of minutes. In the decay tail of giant flares bright pulsations at the rotation period of the magnetar are evident (e.g. Terrell et al., 1980).

The next longest timescale radiative change displayed by magnetars are outbursts. An outburst usually begins with a short X-ray burst or a giant flare, and is an increase in the persistent flux 12 1 Introduction

(i.e. not including burst or flare emission) that persists over a long timescale. The persistent flux increase usually fades rapidly on a timescale of days, followed by a slower decay lasting months to years (for an overview see Rea & Esposito, 2011). Outbursts are often accompanied by an increase in the rate of short X-ray bursts. The spectrum of the persistent emission generally hardens (i.e. is composed of higher energy photons) at the onset of the outburst and then softens as the X-ray flux of the magnetar decays (Scholz & Kaspi, 2011, and Section 3.4.1). In quiescence, i.e. outside of any burst, flare, or outburst activity, magnetars have 2–10 keV X-ray luminosities in the range ∼ 1030−35 erg s−1 and their spectra are often well described by a soft blackbody component and a hard power-law component. Their quiescent blackbody temperatures, typically in the range 0.4–0.5 keV are significantly higher than high-magnetic field RPPs, indicating an additional source of heating, likely related to their radiative activity (Olausen et al., 2013).

Timing Behaviour

The timing behaviour of magnetars is extremely variable; much more variable than RPPs. Mag- netars display a large number of rotational glitches, order-of-magnitude changes in their rotational torque, and a large amount of pulse profile variations. In quiescence magnetar pulse profiles can often be described by a sinusoidal profile (e.g. profile “P” in Figure 1.5), although some have more complicated structure (e.g. 1E 2259+586; Kaspi et al., 2003). In outburst, their profiles often display additional components and variability (e.g. profiles “A” to “O” in Figure 1.5; Dib et al., 2012). Using the technique of phase-coherent timing (see Section 2.3), variability in the rotational properties of magnetars has been observed. Magnetars show a high amount of variation in the derivative of their spin period (P˙ ). These variations are often called “timing noise” or “torque variations”. Many RPPs display unexplained “wandering” in their spin evolution (Hobbs et al., 2010) which has been called timing noise. The magnitude of these variations in magnetars is much higher than those displayed by RPPs (e.g. Gavriil & Kaspi, 2002; Woods et al., 2002), and it is unclear if the physical origin of these variations is the same as for RPPs. Since the torque on the neutron star is directly proportional to P˙ , these variations can be called torque variations. These torque variations range from changes in P˙ of a few percent to an order of magnitude and 1.2 Magnetars 13

Figure 1.5: An example of pulse shape evolution during magnetar outbursts. Normalized 2– 6.5 keV pulse profiles of 1E 1547.0−5408 from 2008 October to 2010 December from RXTE observations presented in Dib et al. (2012). The letters shown in the top-left corner of each plot refer to the time segments marked by arrows in the bottom plot, where the 2–10 keV RMS pulsed flux is shown. The first and third dotted lines in the bottom plot correspond to the onsets of the two outbursts of 1E 1547.0−5408 in 2008 October and 2009 January. 14 1 Introduction

occur on timescales of ∼ 100 − 1000 days (Dib & Kaspi, 2014). Glitches, nearly instantaneous increases of the rotational frequency of the pulsar, are almost always displayed by magnetars during outburst (Dib & Kaspi, 2014) and can also occur during quiescence (e.g Dib et al., 2008). In RPPs, glitches are thought to be caused by the transfer of angular momentum from the superfluid inner crust to the slower-spinning solid outer crust of the neutron star (Anderson & Itoh, 1975). It is unclear whether or not magnetar glitches are caused by the same or a different mechanism. Magnetar glitches display larger fractional increases in frequency compared to RPPs and magnetars are among the most active glitchers (Dib et al., 2008). Out of the 29 known magnetars and magnetar candidates1 (Olausen & Kaspi, 2014) only five are monitored sufficiently frequently to detect unambiguously the occurrence of glitches (Dib & Kaspi, 2014). Of those five, one, 1E 1841−045, has never displayed any radiative activity associated with its glitches (Zhu & Kaspi, 2010) whereas 1E 1048.1−5937, 1E 2259+586, and 4U 0142+61 have had radiative events (e.g. outbursts or giant flares) during some or all of their glitches (Dib et al., 2009; Kaspi et al., 2003; Gavriil et al., 2011; Dib & Kaspi, 2014). There has been some debate whether or not the fifth well-timed magnetar, 1RXS J170849.0−400910, has had radiatively loud glitches (see Chapter 6). An anti-glitch, a prompt decrease in the rotational frequency of the pulsar rather than the usual increase, has also been observed in at least one magnetar (Archibald et al., 2013).

1.2.3 Theory: The Magnetar Model

The key feature of the magnetar model is that the decay of the huge magnetic fields provides the energy reservoir for their extreme activity and anomalously bright X-ray emission from the neutron star. For magnetic fields above ∼ 1014 G, the magnetic field decay becomes a significant contributor to the energetics of the pulsar. Due to the high density of the neutron star crust and the immobility of particles within it, the magnetospheric field lines of a magnetar are pinned to the crust and unable to move without crustal motion. The crust of neutron stars is extremely resistant to vertical motion as it is held by the balance between an inward force of gravity and an outward pressure force provided from the degeneracy pressure between particles (Reisenegger & Goldreich, 1992). The main effect of

1See the magnetar catalog at http://www.physics.mcgill.ca/~pulsar/magnetar/main.html 1.2 Magnetars 15

strains due to the evolving magnetic field in the interior of the neutron star is therefore to provide lateral forces, i.e. a shear strain on the crust. These strains can influence the magnetosphere of the star in two ways: if the crust is resistant to these strains and a large amount of force is allowed to build up, a large scale breaking1 of the crust can occur. This leads to a large energy release due to the mechanical forces on the crust as well as a large scale rearrangement of the magnetospheric field lines (Thompson & Duncan, 1995). If the crust is elastic, the shear strains can move parts of the crust in a more secular manner and slowly build up twists in the magnetosphere (Thompson & Duncan, 1996).

When the exterior magnetic field lines of a magnetar move, currents are driven in the magnetosphere. Therefore, any twists, whether built up promptly in a “star quake” or slowly over time, will accelerate particles in the magnetosphere. These particles can impart energy on outgoing thermal photons from the surface of the neutron star scattering them to higher energies (a process called resonant cyclotron scattering, or RCS; Thompson et al., 2002). This leads the thermal spectrum of the neutron star surface to be modified by a power-law tail, which is observed in many magnetars, especially during outburst when the amount of accelerated particles increases (Mereghetti, 2008). The accelerated magnetospheric plasma also impacts the surface of the neutron star where the footpoints of the magnetic field are anchored in the crust. This causes hotspots to form on the surface if the magnetospheric twists are confined to a bundle of field lines. Such hot-spots are thought to be the cause of magnetar X-ray pulsations.

Both the short X-ray bursts and long-term outbursts displayed by magnetars are thought to be due to a direct injection of energy into the magnetosphere from a prompt event that causes a rearrangement of the magnetic field and dissipation of localized currents. The prompt event could be due to the above mentioned crustal quake (Thompson & Duncan, 1995) or magnetic reconnection events (Lyutikov, 2003), similar to solar flares.

The currents in the magnetosphere caused by twists also cause an additional torque on the neutron star (Thompson et al., 2002). The variable nature of these magnetospheric twists thus also cause a variable rotational torque observed as P˙ . Torque variations can also arise from a change

1Note: Due to the intense pressures involved on a neutron star surface, voids cannot form between portions of the crust. Therefore the “cracks” that form involve only shear motion. 16 1 Introduction

in the fraction of open field lines which may change during magnetospheric rearrangements.

1.2.4 The Emerging Magnetar Population

The above summary of magnetar history, phenomenology, and theory, although supplemented with some more recent results, more or less paints a picture of the state of the field around the launch of the Swift X-ray mission in 2004. However, since the launch of Swift, as well as the Fermi mission in 2009, many more magnetars have been discovered, due to the large field-of- view monitors for hard X-ray (Swift’s Burst Alert Telescope) and soft gamma-ray bursts (Fermi’s Gamma-ray Burst Monitor) provided by those satellites. In 2004 there were nine known magnetars, while at the time of writing in 2016 there are 23 known magnetars and several promising candidates1. In the past decade a population of magnetars has emerged and we can group them according to their observed phenomenology and quiescent properties. The five “classical” anomalous X- ray pulsars, i.e. the sources that resemble the three sources first grouped by Mereghetti & Stella (1995), persistently display X-ray pulsations significantly more energetic than the pulsar’s rota- ˙ tional spin-down luminosity (i.e. LX ≫ E). These persistent magnetars have been outnumbered in the past decade by transient magnetars. The first such magnetar discovered was 1E 1810−197, found due to its 2003 outburst when it increased its persistent flux by a factor of over 100 (Ibrahim ˙ et al., 2004). These magnetars only have LX ≫ E during their outbursts, in which they can in- < ˙ crease their X-ray fluxes several orders of magnitude, and have LX ∼ E in quiescence (see Table 1.1). It should be noted that the division between these classes is not a clean one, as there are ˙ several sources with LX ∼ E and in reality the magnetar population likely forms a continuum of activity and quiescent properties. A third type of magnetar, the low-magnetic field magnetar, emerged in 2009 when SGR 0418+5729 was discovered by the Fermi Gamma-ray Burst Monitor through its outburst activity (van der Horst et al., 2010). Phase-coherent timing of the new magnetar revealed that its spin-down magnetic field was < 7.5 × 1012 G(Rea et al., 2010), much lower than the ∼ 1014 G thought to be necessary for magnetar-like behaviour. It was not until 2013 that a period derivative became

1See the McGill Magnetar Catalog (Olausen & Kaspi, 2014) at http://www.physics.mcgill.ca/~pulsar/ magnetar/main.html 1.2 Magnetars 17

Table 1.1: Properties of Known Magnetars.

Name Period P˙ B E˙ LX (s) (10−11 s s−1)(1014 G) (1033 erg s−1)(1033 erg s−1)

CXOU J010043.1−721134 8.02 1.88 3.93 1.44 65 4U 0142+61 8.68 0.20 1.34 0.12 110 SGR 0418+5729 9.07 0.0004 0.061 0.00021 0.00096 SGR 0501+4516 5.76 0.59 1.87 1.23 0.81 SGR 0526−66 8.05 3.8 5.60 2.87 190 1E 1048.1−5937 6.45 2.25 3.86 3.30 49 1E 1547.0−5408 2.07 4.77 3.18 211 1.3 PSR J1622−4950 4.32 1.7 2.74 8.29 0.44 SGR 1627−41 2.59 1.9 2.25 42.9 3.6 CXOU J164710.2−455216 10.61 < 0.04 < 0.65 < 0.013 0.45 1RXS J170849.0−400910 11.00 1.94 4.68 0.57 42 CXOU J171405.7−381031 3.82 6.40 5.01 45.1 56 SGR J1745−2900 3.76 1.38 2.31 10.3 < 0.11 SGR 1806−20 7.54 49.5 19.6 45.5 160 XTE J1810−197 5.54 0.77 2.10 1.80 0.043 Swift J1822.3−1606 8.43 0.0021 0.13 0.0014 < 0.00040 SGR 1833−0832 7.56 0.35 1.65 0.32 Swift J1834.9−0846 2.48 0.79 1.42 20.5 < 0.0084 1E 1841−045 11.78 4.09 7.03 0.98 180 PSR J1846−0258a 0.326 0.71 0.49 8060 19 3XMM J185246.6+003317 11.55 < 0.014 < 0.41 < 0.0036 < 0.0060 SGR 1900+14 5.19 9.2 7.00 25.8 90 SGR 1935+2154 3.24 1.43 2.18 16.5 1E 2259+586 6.97 0.048 0.58 0.056 17 Candidates SGR 0755−2933 SGR 1801−23 SGR 1808−20 AX J1818.8−1559 AX J1845.0−0258 6.97 2.9 SGR 2013+34 aRotation-powered X-ray pulsar that displayed a magnetar-like outburst (Gavriil et al., 2008) All data from the McGill Magnetar Catalog (Olausen & Kaspi, 2014) at http://www.physics.mcgill.ca/~pulsar/magnetar/main.html 18 1 Introduction

detectable for SGR 0418+5729 and it was found to correspond to a surface dipolar magnetic field of 6 × 1012 G(Rea et al., 2013). Since 2009, two more low-magnetic field magnetars have been discovered (Livingstone et al., 2011; Rea et al., 2014). This work will present the properties of three different magnetars both in quiescence and during outburst: one persistent magnetar, 1RXS J170849.0−400910, one transient magnetar, 1E 1547.0−5408, and one low-magnetic field magnetar, Swift J1822.3−1606. I will then conclude with a discussion of how the results from the studies of these three objects affect our understanding of the magnetar population. 2 Telescopes and Techniques

2.1 X-ray Observatories

The majority of the data analysed in this work was obtained using X-ray telescopes. Since X-rays are unable to penetrate the Earth’s atmosphere (a fortunate arrangement for those of us that enjoy having life on Earth) telescopes sensitive to X-rays must be located in space.

2.1.1 X-ray Detectors

The X-ray detectors used in telescopes in this work detect incident X-ray photons from their interaction with atoms in the detector. When an X-ray interacts with an atom, it liberates electrons in a process called photoelectric absorption.

One type of detector is the proportional counter. A proportional counter is a container, typically many centimeters across, of neutral gas. Noble gases such as argon or xenon, are desirable as they are inert and so are unlikely to react chemically with other components of the instrument. When an X-ray photon liberates an electron in the gas, that electron can ionize nearby atoms and liberate electrons from further atoms. This causes a cascade of negative charges (free electrons) in the detector. The number of free electrons in the cascade, typically hundreds to thousands, is proportional to the energy of the incident X-ray photon, thus the name “proportional counter”. The free electrons are attracted to a positively charged anode that runs through the proportional counter. The electron cascade causes a pulse in the anode that can be detected by a circuit. The positively charged ions recombine with electrons at a negatively charged cathode, but do not participate in the cascade.

This same principle can be used in solids, where electrons are liberated and detected in electronic circuits that run through the detector medium. A major advance in astronomy is the charge- coupled device (CCD) where rows of potential wells are set up in a silicon medium to trap the

19 20 2 Telescopes and Techniques

X-ray Photon

- - - e e e

Anode Circuit

Inert Gas

Figure 2.1: Diagram of a Proportional Counter. An X-ray photon liberates electrons from the atoms in the gas which causes an electron casacade. The cascade causes a pulse in the anode which is registered by an electronic circuit.

liberated electrons in distinct pixels in the detector. The potential wells are moved to one side of the detector where readout electronics record the number of detected electrons per potential well. This allows the focal plane of focussing X-ray telescopes to be sampled at high spatial resolution. For example, the ACIS CCD of the Chandra X-ray Observatory (see below) is composed of 1024 × 1024 pixels with a scale of 0.492′′ per pixel. In contrast to the relatively large centimeter-scale proportional counters, each pixel of a CCD is several microns across. In X-ray astronomy, for both proportional counters and CCDs, the assumption is that an electron cascade is caused by a single X-ray photon. However, if the count rate of X-ray photons on a detector element (i.e. an anode for a proportional counter or a pixel for a CCD) is comparable to or higher than a single photon per readout time for the element (i.e. the time resolution of the detector) the detector will register multiple photons as a single event. This single event will have a higher energy than that of a single X-ray photon since it results from the sum of the electron cascades from each photon. This effect is called pile-up and causes the detector to register fewer X-ray photons than are actually arriving in the detector, but with higher energies than the true photon energies. In practice, pile-up is avoided by using detector readout modes (outlined in the 2.1 X-ray Observatories 21

Figure 2.2: Diagram of a Wolter I telescope. (Credit: NASA’s Imagine the Universe) sections below for the detectors used in this work) with sufficiently high time resolution so that the effect is negligible.

2.1.2 X-ray Optics

Focussing X-ray photons is difficult because X-rays tend to either pass through or be absorbed by materials. However, at grazing incidence (i.e. shallow angles), the chance of reflection of X- rays is much higher. Using this, Wolter (1952) outlined three different optical designs involving two grazing-incidence reflections that bring X-rays to a focal point. The majority of modern focussing X-ray telescopes use the Type I Wolter design where the incident X-rays reflect first off a paraboloid-shaped surface followed by a reflection on a hyperboloid shape (see Figure 2.2). The low angle of incidence leads to a very small effective area that is sensitive to incident X- rays. Therefore to increase the number of X-rays accumulated at the focal point, sets of mirrors are nested in a coaxial configuration (for example see Figure 2.3).

2.1.3 The Swift Gamma Ray Burst Mission

The majority of the work in this thesis utilises data from the Swift Gamma Ray Burst Mission (Gehrels et al., 2004). The Swift mission was launched November 20, 2004 and, as its name implies, it was designed to observe gamma-ray bursts (GRBs). Swift has three different telescopes: the Burst Alert Telescope (BAT), the X-ray Telescope (XRT), and the Ultraviolet/Optical Tele- scope (UVOT). The BAT is a wide field-of-view instrument that is sensitive to hard X-ray bursts and detects the onset of GRBs. After detecting a burst using the BAT (not just GRBs, but also, importantly for this work, the short X-ray bursts emitted by magnetars) the Swift satellite slews 22 2 Telescopes and Techniques

Figure 2.3: Nested mirror segments of the XMM-Newton telescope. The diameter of the outermost mirror shell is 70 cm. See Section 2.1.5 for more information. Photo courtesy of D. de Chambure, XMM-Newton Project, ESA/ESTEC.

to the location of the event and begins observing with the XRT and UVOT in order to detect persistent X-ray and UV/optical counterparts. A diagram of Swift and its instruments is shown in Figure 2.4.

The Swift data used in this thesis are primarily from the XRT (Burrows et al., 2005), so it is explained in more detail here. The XRT consists of a Wolter I telescope with an effective area of 110 cm2 at 1.5 keV and a 3.5-m focal length and an XMM-Newton/EPIC MOS CCD detector (see Section 2.1.5) which provides sensitivity to X-rays in the 0.3–10 keV range. The XRT has a field of view of 23.6′ × 23.6′ and an angular resolution of ∼ 5′′.

The XRT can operate in four separate modes: image (IM), photodiode (PD), windowed timing (WT), and photon counting (PC). Image mode provides full spatial information but sacrifices all spectral information to provide fast localizations of GRBs. Photodiode mode provided the best time resolution, 0.14 ms, by integrating over the entire CCD during readout and therefore forgoing any spatial information. Unfortunately, PD mode can no longer be used due to micrometeorite damage that occurred on 2005 May 27. Windowed timing mode collapses the central 200 rows of the CCD into a single spatial dimension during readout in order to achieve a time resolution 2.1 X-ray Observatories 23

Figure 2.4: Left: Computer-generated image of the Swift satellite. Credit: NASA E/PO Right: Diagram of instruments on the Swift satellite. Credit: NASA/GSFC. The Swift spacecraft is 5.5 m in length.

of 1.76 ms. Photon counting mode provides a full two-dimensional image, but gives the coarsest time resolution at 2.5 s. In this work we use data from the XRT in WT and PC modes.

2.1.4 The Chandra X-ray Observatory

The Chandra X-ray Observatory was launched on July 23, 1999 and provides the best angular resolution for any existing X-ray telescope (Weisskopf et al., 2002). Chandra uses a Type I Wolter mirror assembly and two different types of camera: the Advanced CCD Imaging Spectrometer (ACIS) and the High Resolution Camera (HRC). The ACIS CCDs can collect imaging and spectral information with a spatial resolution of 0.5′′ (limited by its pixel scale) and a time resolution of 3.2 s in the energy range 0.2-10 keV. The HRC provides superior spatial resolution (0.4′′) and a time resolution (16 µs) but has poorer energy resolution compared to the ACIS cameras. Spectral gratings (LETG and HETG) can be used with either ACIS or HRC to acquire high resolution spectra from bright sources, but this sacrifices spatial resolution and sensitivity.

This work primarily uses the ACIS cameras, and so we will describe them in more detail. ACIS is composed of two arrays of CCDs: ACIS-I, an array of 4 CCDs positioned in a 2 × 2 grid and ACIS-S, an array of 6 CCDs positioned in a row below the ACIS-I CCDs. Up to six CCDs can be used simultaneously, though it is encouraged to turn off unused CCDs (i.e. those that will not 24 2 Telescopes and Techniques

Figure 2.5: A schematic of the ACIS focal plane. The ACIS-I array consists of chips I0-I3 ar- ranged in two rows. The ACIS-S array consists of chips S0-S5 in a single row. The default aimpoints for ACIS-I (on chip I3) and ACIS-S (on chip S3) are marked. Figure adapted from the Chandra Proposers’ Observatory Guide1.

have science targets in their fields of view) in order to avoid overheating the telescope1. Each ACIS CCD has 1024 × 1024 pixels with a pixel size of 0.492′′ leading to a 8.4′ × 8.4′ field of view.

ACIS can operate in two modes: Timed Exposure (TE) and Continuous Clocking (CC) modes. TE mode has a nominal time resolution of 3.2 s and provides full two-dimensional spatial information and CC mode forgoes a dimension of spatial information (similar to Swift’s WT mode) to provide a time resolution of 2.85 ms. The time resolution of TE mode can be improved slightly by reading out a fraction of the CCD; for example, reading out a 1/8 subarray can provide a time resolution of 0.4 s with ACIS-S1.

2.1.5 The XMM-Newton Telescope

The XMM-Newton observatory (Jansen et al., 2001) was launched on December 10, 1999 by the European Space Agency. In comparison to NASA’s Chandra observatory, launched earlier in 1999, XMM-Newton provides superior sensitivity but worse angular resolution. The telescope is composed of three mirror modules each with 58 nested gold-coated Wolter I mirrors which

1See http://cxc.harvard.edu/proposer/POG/html/ 2.1 X-ray Observatories 25

provide an effective area of ∼ 1500 cm2 at 1.5 keV and a angular resolution of ∼ 6′′. The three mirror assemblies feed three separate CCD arrays called the European Photon Imaging Cameras (EPIC). Two of the EPIC cameras contain arrays of seven 600 × 600 pixel MOS CCDs which image a 10.9′ × 10.9′ field of view. The third camera consists of twelve 200 × 64 pixel ‘pn’ CCDs each with a 13.6′ × 4.4′ field of view. About half of the X-rays from the mirror modules that feed the MOS cameras are redirected to the Reflection Grating Spectrometer (RGS) which provides high-resolution spectroscopy on bright sources. This redirection reduces the effective area of the MOS cameras by ∼ 44%. The time resolutions of the pn and MOS cameras when reading out the full CCD arrays are 73.4 ms and 2.6 s respectively. However, the cameras can be operated in readout modes where only a portion of each CCD are read out to achieve better time resolution. For example, the pn in “small window” mode reads out a 63 × 64 pixel area of the CCD and provides a 5.7 ms time resolution.

2.1.6 The Rossi X-ray Timing Explorer

The Rossi X-ray Timing Explorer, or RXTE, unlike the above three telescopes does not focus X-rays and therefore does not provide much angular resolution. However, it has excellent time resolution and a much larger collecting area than the aforementioned telescopes. RXTE was shut down in 2012 January after over a decade and a half of operation. RXTE had three instruments: the All Sky Monitor (ASM), the Proportional Counter Array (PCA) and the High Energy X-ray Timing Experiment (HEXTE). The ASM was able to survey 80% of the sky during each 96-min orbit of RXTE and provided a coarse spatial resolution of 3′ ×15′ in the 1.5–12 keV energy range. HEXTE was sensitive to hard X-rays in the range 15–250 keV using eight ‘phoswich’ scintillation counters organized in two clusters which provided a total collecting area of ∼ 1600 cm2 (Rothschild et al., 1998). The PCA probed the energy range 2–60 keV using five proportional counter units which provided a total effective area, when all five units were active, of 6500 cm2 (Jahoda et al., 1996). PCA and HEXTE were co-aligned to observe the same ∼ 1◦ field of view. In this thesis, only RXTE data from the PCA is used. The PCA consisted of five proportional counter units (PCUs) that were filled with xenon gas. The entire instrument was shielded from X-rays except in the viewing direction of the telescope. To arrive in a PCU, the X-ray photons 26 2 Telescopes and Techniques

Figure 2.6: Left: Technicians working on RXTE in 1995. Credit: NASA/Goddard Right: Diagram of RXTE. Credit: Bradt et al. (1993) . passed through a collimator with beryllium-copper walls that only allowed the passage of photons from a 1◦ field of view. The PCA had no imaging resolution; the entire field of view was read as a single ‘pixel’. However, it provided a much larger collecting area (1300 cm2 per active PCU) compared to focussing X-ray telescopes such as XMM-Newton and Chandra. It also provided an excellent time resolution of 1 µs.

2.2 X-ray Spectroscopy

An X-ray spectrum is constructed from the individual photon events detected by X-ray detectors. For each photon that hits the detector, an energy is measured based on the size of the electron cascade triggered by the incident photon. These discrete events are binned into energy channels which results in a spectrum, i.e. the number of photon counts from the source, Ni, for each energy channel, i. If a spectrum of the background, Bi, is also available, we can subtract that spectrum from the source spectrum with:

Ni Bi tS Si = − (2.1) AS AB tB where AS and AB are the area on the sky of the regions from which the source and background 2.2 X-ray Spectroscopy 27

photons were extracted and tS and tB are the source and background exposure times. Before fitting a spectrum to the data, the instrumental response to the incident photons must be taken into account. In practice, this is done using two files: the redistribution matrix file (RMF) and the ancillary response file (ARF). The RMF relates the observed size of the electron cascade (quantified as the pulse height amplitude or PHA), to the energy of the incident photon. The ARF contains the sensitivity (effective area and quantum efficiency of the combined telescope/detector system) as a function of position on the CCD and time.

The relation between the observed channelized spectrum, Si, and the true source spectrum,

fT (E), is: ∫

Si = fT (E)R(i, E)dE (2.2)

where R(i, E) is the instrumental response as encoded by the RMF and ARF. In order to get

fT (E), this equation must be inverted. This is a difficult task as it involves deconvolving the instrumental response. We therefore fit the observed spectrum with a trial model that is convolved with the instrument response and then iterate with new parameters to find the best-fit model. To test a model, the χ2 statistic is most often used:

∑N (S − M )2 χ2 = i i (2.3) σ2 i=1 i

where σi is the uncertainty on Si and Mi is the number of predicted spectral counts from the

model being tested (i.e. the predicted model, fP (E), convolved with the instrumental response as in Equation 2.2). For a low number of counts it is often advisable to use the C-statistic as the χ2 statistic assumes that the data are Gaussian distributed whereas for low count rates the data will be Poisson distributed. Cash (1979) generated the C-statistic based on the likelihood ratio for Poisson distributed source counts:

∑N C = 2 (Mi) − Si ln(Mi) + ln Si! (2.4) i=1 In this thesis, both the χ2 and C-statistics are used to fit spectra. The software xspec (Arnaud, 1996) is used to perform the X-ray spectral fitting as outlined above. 28 2 Telescopes and Techniques

The spectral models used in this thesis are composed of two components: a blackbody, parameterized by its temperature, kT , and/or a power law, parameterized by an index, Γ1 In xspec, the blackbody and power-law models are of the form2, respectively,

8.0525KE2dE f (E) = , (2.5) BB (kT )4 [exp(E/kT ) − 1]

and

−Γ fPL(E) = KE , (2.6)

where, in both cases, K is a normalization parameter.

These underlying spectrum components are modified by photoelectric absorption caused by the material between us and the source, which is parameterized by the column density of neutral

hydrogen, NH. The underlying spectrum is multiplied by

fNH(E) = exp[−NHσ(E)], (2.7)

where σ(E) is the photoelectric cross-section which depends on the assumed abundances of X-ray absorbing elements along the line of sight as well as models of the cross-section of these elements

to photoelectric absorption. Note that although the absorption is parameterized by NH, it is not hydrogen that dominates the absorption, but heavier elements instead so accurate assumptions on the abundances and cross-sections for these elements are important. By default, xspec uses abundances from Anders & Grevesse (1989) and photoelectric cross sections from Balucinska- Church & McCammon (1992).

So, for example, a predicted spectrum for a photoelectrically absorbed power law plus blackbody model would have the form:

fP (E) = fNH(E)[fPL(E) + fBB(E)]. (2.8)

1Note that here Γ is a photon index and not a spectral index as f(E) corresponds to the numbers of photons at an energy rather than a spectral flux. 2From the xspec manual: https://heasarc.gsfc.nasa.gov/xanadu/xspec/manual/manual.html 2.3 Pulsar Timing Techniques 29

2.3 Pulsar Timing Techniques

The spin parameters of pulsars can be precisely determined using the technique of phase-coherent timing. Measurements of these spin parameters are used in many scientific applications from inferring properties of the neutron star to testing theories of general relativity. In phase-coherent timing, each rotation of the pulsar is accounted for so that the phase of the pulsar is known at any point in time that the phase-coherent timing solution is valid. Briefly, in order to obtain a phase-coherent timing solution, a pulse profile for each observation is constructed and the observed profile is compared to a standard template. The offset between the template and the observed profile allows a precise determination of the average time-of-arrival of a pulse during the observation. This time-of-arrival can be compared to a prediction in order to refine a model of the spin-down properties of the pulsar. Below, this process is described in detail.

2.3.1 The Pulse Profile

Pulsars each have a unique emission profile as a function of rotational phase. Most pulsars are too faint to allow the detection of a single pulse from a single rotation, so many rotations of the neutron star (typically hundreds to thousands) are summed to achieve a high signal-to-noise average profile. Often, this is done by summing the rotations from a single observation. In order to construct such a summed profile, the time series is divided up into subsets of length equal to the period of the pulsar and these subsets are then summed. This process is called folding. If an accurate pulsar ephemeris is known from a phase-connected time solution, this can be used to assign phases to each time series bin or photon arrival time, and the bins or events can be grouped into phase bins. A pulse profile that has been folded in this way can be seen in Figure 2.7 for the magnetar Swift J1822.3−1606.

2.3.2 The Pulse Time of Arrival

In order to perform phase-coherent timing, each observed profile must be translated into a pulse time of arrival or TOA. A TOA is the time that a fiducial point in the profile arrives at the telescope (or, as we’ll see, in the case of barycentric TOAs, the solar-system barycentre). If pulse profiles were noiseless, the ephemeris used to fold the profile were a perfect description of the pulsar’s 30 2 Telescopes and Techniques

5000

4500

4000

3500

3000 Counts

2500

2000

1500

1000 0.0 0.5 1.0 1.5 2.0 Phase

Figure 2.7: The 0.5–6.0 keV X-ray pulse profile of Swift J1822.3−1606 from a 15-ks Chandra ACIS-S observation on 2011 July 27. Swift J1822.3−1606 has a period of 8.4 s 2.3 Pulsar Timing Techniques 31 rotation, and there were no variation in the emitted profile from the pulsar, a TOA could simply just be the peak of the profile. However, statistical noise and pulse-to-pulse variability occur, so a more robust method is needed. Pulse profiles that result from a large number (hundreds or more) of pulse periods are typically stable on time scales of years. So, a profile from a given observation, p(t), can be compared to a high signal-to-noise template s(t) in order to measure an offset which can be used to measure a TOA. A profile from an individual observation is assumed to be a noisy version of the template:

p(t) = As(t − τ) + N(t) (2.9) where A is a scaling factor, N(t) is the background noise, and τ is an offset between the two profiles. The name of the game in TOA measurement is determining this offset, τ, and its uncertainty. Since observations are taken from a moving observatory due to both the rotational and orbital motion of the Earth as well as the orbital motion of the satellite in the case of space observatories, TOAs must be corrected to a consistent frame. Typically we correct the times to the solar-system barycentre. For observations that are performed using ground facilities, e.g. from radio telescopes, the TOAs are corrected while fitting the pulse timing model (Section 2.3.3). However, for space telescopes, which orbit the Earth, the arrival times of the photon events are corrected before TOA extraction using software and spacecraft orbital ephemerides provided by the observatory.

TOAs from a binned profile

If the data are folded into a binned profile, i.e an array of phase bins with the number of events per phase bin, the optimal offset can be measured using the cross-correlation:

∫ ∞ ∗ (s ⋆ p)(δϕ) = s (ϕ)p(ϕ − δϕ)dϕ. (2.10) −∞ The value of the phase offset, δϕ, that maximizes the cross-correlation, s ⋆ p, is the optimal phase offset. The phase offset is related to the time offset, τ, by τ = δϕ P (t0) where P (t0) is the period of the pulsar at a reference epoch for the observation, t0. 32 2 Telescopes and Techniques

The cross-correlation can also be performed in the frequency domain using the convolution theorem:

F (s ⋆ p) = F(s)F(p), (2.11)

where F is the Fourier transform. Performing the cross-correlation in the frequency domain has two advantages. First, the fast version of the Fourier transform (FFT) is a faster operation than a sum or integral in the time domain. Secondly, in the frequency domain higher order harmonics of the profile can be filtered out. This can be quite useful for X-ray pulsars which tend to have broad, sinusoidal profiles which therefore have low harmonic content. This can avoid noise erroneously being identified as narrow profile features in the cross correlation.

TOAs from photon arrival times

If the observations used in phase-coherent timing come from instruments that can detect each photon arrival time individually, as in X-ray astronomy, instead of a binned time series, these photon arrival times can by used to measure a TOA. Using discrete events instead of a binned time series avoids the information loss that arises from binning.

The method used in this thesis is a simple maximum likelihood analysis (Livingstone et al., 2009). If a continuous model of the pulse profile, m(ϕ), is known, either from fitting a high signal-to-noise template (s(ϕ)), or assuming a simple model, the optimal offset can be found using the likelihood, L:

∏N L = m(ϕi − δϕ) (2.12) i where ϕi is the phase corresponding to the ith photon arrival time. The optimal phase offset is the δϕ that maximizes the likelihood. Since the number of photon arrival times in a given observation can be quite large (thousands to millions), the multiplication of the probabilities in the likelihood can quickly result in numbers to large or small for computers to handle. So, the logarithm of the likelihood is often calculated so that the multiplicative product in the likelihood calculation becomes an additive sum: 2.3 Pulsar Timing Techniques 33

∑N log L = log m(ϕi − δϕ). (2.13) i The distribution of the likelihood as a function of offset, δϕ, can then be normalized by dividing by its integral. The optimal offset is the peak of the probability distribution and the width is the error. The width can be measured either by integrating to 68% of the area centred on the peak or by fitting a Gaussian.

2.3.3 Phase-coherent Pulsar Timing

Typically, in pulsar timing, the TOAs are fitted by a Taylor expansion of the pulse phase, ϕ:

1 1 1 ... ϕ(t) = ϕ(t ) + ν (t − t ) + ν˙ (t − t )2 + ν¨ (t − t )3 + ν (t − t )4 + ... (2.14) 0 0 0 2 0 0 6 0 0 24 0 0

where t0 is the epoch at which the Taylor coefficient values (i.e. time derivatives of the phase) are referenced (Manchester & Taylor, 1977). This fitting procedure is performed, in this thesis, using the software packages TEMPO1 and TEMPO22 (Hobbs et al., 2006). These software packages take in a description of the input spin parameters (i.e. the frequency,

3 2 ν0 and its time derivatives ), reference epoch, and sky position and perform a χ minimization between the spin-down model and the TOAs. Phase-coherent timing is inherently an iterative process. The inputs to phase-coherent timing are a pulsar ephemeris and a set of TOAs. Pulsar ephemerides are measured using phase-coherent timing. Above, we saw that TOAs are measured from pulse profiles, or photon phases if using photon arrival times, which also require an ephemeris to create. To time a pulsar we must therefore start with an informed “guess” of the pulsar ephemeris to extract TOAs and use as a starting timing model. The output best-fit model from TEMPO or TEMPO2 is then used as input in the next iteration of fitting where model parameters or additional data (TOAs) are added as warranted. The refined ephemeris can also be used to re-extract more accurate TOAs as needed.

1http://www.atnf.csiro.au/research/pulsar/tempo/ 2http://www.atnf.csiro.au/research/pulsar/tempo2/ 3As well as any orbital parameters if the pulsar is in a binary system; however, no such systems are considered in this thesis. 34 2 Telescopes and Techniques 3 The 2009 Outburst of Magnetar 1E 1547−5408

The work presented in this chapter has previously been published in the article: Scholz & Kaspi, 2011, The 2009 Outburst of Magnetar 1E 1547-5408: Persistent Radiative and Burst Properties, Astrophysical Journal, 739, 94. The text of this chapter has been adapted from that work.

3.1 Introduction

1E 1547−5408 was first discovered as an X-ray source by the Einstein satellite (Lamb & Markert, 1981). It was identified as a magnetar by Gelfand & Gaensler (2007) based on its X-ray spectrum and infrared flux, as well as its possible association with the supernova remnant G327.24−0.13. Pulsed radio emission was detected by Camilo et al. (2007) at a period of ∼2 s, the shortest period of all known magnetars (Olausen & Kaspi, 2014)1. An XMM-Newton observation in 2007 showed a significant flux enhancement from what was previously measured (Halpern et al., 2008), thus revealing that an X-ray outburst event had occurred between 2006 and 2007. Another outburst event occurred on 2008 October 3 and was detected by the Swift (Israel et al., 2010) and Fermi (Kaneko et al., 2010) satellites. 1E 1547−5408 entered yet another active phase on 2009 Jan- uary 22 when hundreds of bursts were detected by Swift, INTEGRAL, and Fermi. Tiengo et al. (2010) report the appearance of dust scattering rings around 1E 1547−5408 after the 2009 burst in follow-up observations with XMM-Newton and Swift. The energy released by the event causing the rings was estimated to be 1044 − 1045 ergs. From these rings, a distance to the source was determined to be 3.9 kpc. Ng et al. (2011) report on Chandra observations beginning ∼ 2 days following the outburst. They note a lack of spectral variation during the flux decay as well as an anti-correlation between pulsed fraction and phase-averaged flux. The origin and flux evolution of magnetar outbursts are not presently well understood (but see Perna & Pons, 2011), and the sample of observed outbursts is still relatively small (for a review,

1see the McGill SGR/AXP Online Catalog, http://www.physics.mcgill.ca/∼pulsar/magnetar/main.html

35 36 3 The 2009 Outburst of Magnetar 1E 1547−5408

see Rea & Esposito, 2011). Hence, it is important for each magnetar outburst to be promptly observed and studied. The magnetar model suggests that outbursts are a result of magnetospheric twists of the magnetic field structure following some form of internal energy or stress release (Thompson et al., 2002; Beloborodov, 2009, and see Section 1.2.3), which predicts a correlation between hardness and X-ray flux in magnetar outbursts. Indeed a universal relationship between flux increase and spectral hardening might be expected, if not from source to source, at least for individual sources. Also, the origin and physics of X-ray bursts from magnetars are poorly understood. Bursts have been proposed to be magnetospheric in origin (Lyutikov, 2003) as well as originating from stresses in the crust of the neutron star (Thompson & Duncan, 1995). Detailed statistical studies of magnetar bursts can help determine their properties for comparison with model predictions, yet have only been done for three sources prior to this work (Göğüş et al., 2001; Gavriil et al., 2004).

This chapter presents the results of an analysis of the persistent emission from the 2009 event as well as a statistical study of the bursts using observations from Swift. The burst study will focus primarily on bursts from the 2009 outburst since the number (∼ 400) is much higher than in the 2008 event, in which 8 bursts were detected by Swift (Israel et al., 2010). A summary of the observations is presented in Section 3.2. The analysis performed on the data as well as the results for the persistent emission are reported in Section 3.3.1. The analysis and results for the burst study are presented in Section 3.3.2. The results and their possible physical interpretations are discussed in Section 3.4. Finally, our findings are summarized in Section 3.5.

3.2 Observations

The data presented in this paper were obtained using the X-Ray Telescope (XRT) on the Swift satellite (see Section 2.1.3). During the 2008 outburst of 1E 1547−5408, the Swift BAT triggered at 09:28:08 UT on 2008 October 3 and Swift promptly slewed to the source position. The XRT began taking observations 99 s after the trigger. On 2009 January 22, the BAT triggered at 01:32:41 UT and the first XRT observation began ∼50 min later. Table 3.1 shows a summary of the observations following the 2009 outburst event as well as two observations preceding the outburst. The observations following the 2008 outburst were previously presented by Israel et al. 3.3 Analysis and Results 37

(2010); here we focus on the 2009 event. Cleaned data products in both windowed-timing (WT) and photon-counting (PC) modes were obtained from the HEASARC Swift Archive. Data were corrected to the solar-system barycentre using the position of 1E 1547−5408, 15h50m54s.11, −54◦18′23′′.7 (Camilo et al., 2007). For WT mode, a source region consisting of a 40-pixel-long strip centered on the pulsar position was extracted. A background region of the same size was extracted on a source-free position away from 1E 1547−5408. For the PC mode data, an annulus with outer radius 20 pixels and 4 pixel inner radius was extracted for the source, and an annular region of 20 pixel inner radius and 50 pixel outer radius was used for the background. The 4 pixel inner region was excluded to avoid pileup.

3.3 Analysis and Results

3.3.1 Persistent Flux Evolution

In order to investigate the behaviour of the persistent flux of 1E 1547−5408 during the 2009 outburst, the observations were fitted with spectral models. Spectra were extracted from the event lists using xselect. Spectral fitting was performed using the XSPEC1 package version 12.6. The spectra were grouped with a minimum of 20 counts per energy bin. Ancillary response files were created using the FTOOL xrtmkarf and the standard spectral redistribution matrices from the Swift CALDB were used. Bursts were then removed from the observations using the method described in Section 3.3.2. The first two observations following the BAT trigger were split into shorter intervals ∼2 ks in length, since the spectral properties were evolving rapidly during that time. These split observations occurred during the first day of the outburst when the dust scattering rings (Tiengo et al., 2010) were not fully resolved by the Swift XRT. For these observations, the radiative properties of the source cannot be simply disentangled from the delayed emission from the dust scattering rings (A. Tiengo & P. Esposito, private communication). Appropriate modelling of this is currently under investigation (A. Tiengo, private communication) but beyond the scope of our work. Following the first day after the outburst, the dust scattering rings were outside of the extraction

1http://xspec.gfsc.nasa.gov 38 3 The 2009 Outburst of Magnetar 1E 1547−5408

Table 3.1: Summary of Swift XRT observations of the 2009 outburst of 1E 1547−5408

Sequence Mode Observation date MJD Exposure time Time since trigger (TDB) (ks) (days)

00090007024 WT 2009-01-04 54835.0 3.3 −18.033 00090007025 WT 2009-01-12 54844.0 4.2 −9.066 00340573000 WT 2009-01-22 54853.1 6.1 0.035 00340573001 WT 2009-01-22 54853.4 9.2 0.321 00340923000 PC 2009-01-23 54854.6 1.7 1.575 00090007026 WT 2009-01-23 54854.7 8.2 1.657 00340986000 PC 2009-01-24 54855.2 2.9 2.110 00030956031 PC 2009-01-24 54855.3 2.5 2.195 00090007027 WT 2009-01-25 54856.1 3.3 2.990 00341055000 PC 2009-01-25 54856.1 4.0 3.065 00341114000 PC 2009-01-25 54856.9 4.6 3.851 00090007028 WT 2009-01-26 54857.1 3.5 3.987 00030956032 PC 2009-01-27 54858.1 6.2 4.996 00090007029 WT 2009-01-27 54858.4 1.8 5.330 00030956033 PC 2009-01-28 54859.2 5.1 6.143 00090007030 WT 2009-01-28 54859.9 1.9 6.811 00030956034 PC 2009-01-29 54860.0 5.9 6.941 00090007031 WT 2009-01-29 54860.7 2.2 7.614 00090007032 WT 2009-01-30 54861.5 2.9 8.476 00030956035 WT 2009-01-30 54861.7 3.0 8.677 00030956036 WT 2009-01-31 54862.1 3.0 9.076 00090007033 WT 2009-01-31 54862.8 2.5 9.687 00030956037 WT 2009-02-01 54863.5 2.0 10.476 00090007035 WT 2009-02-02 54864.6 4.1 11.548 00030956038 PC 2009-02-03 54865.5 5.9 12.424 00030956039 PC 2009-02-04 54866.7 6.1 13.637 00030956040 WT 2009-02-05 54867.2 6.1 14.101 00030956042 WT 2009-02-07 54869.3 1.7 16.189 00090007036 WT 2009-02-12 54874.1 4.6 21.056 00090007037 WT 2009-02-22 54884.5 4.6 31.431 00090007038 WT 2009-03-04 54894.5 3.9 41.408 00090007039 WT 2009-03-13 54904.0 4.1 50.912 00090007040 WT 2009-03-24 54914.8 4.2 61.763 00030956054 WT 2009-09-30 55104.5 3.3 251.428 3.3 Analysis and Results 39 region and so those observations are not affected by dust scattering.

The spectra were fitted with a photoelectrically absorbed blackbody with an added power-law component. To determine NH, we fit observations having an exposure time greater than 3 ks jointly with a single NH. The parameters kT , Γ and their normalizations were allowed to vary 22 −2 in these fits. This resulted in NH = 3.24(5) × 10 cm which is consistent with the value +0.7 × 22 −2 of 3.1−0.8 10 cm reported in Gelfand & Gaensler (2007), though is somewhat lower than the value of 4.1(1) × 1022 cm−2 measured by Ng et al. (2011). All the Swift observations were subsequently fit with the column density fixed to our best-fit value. The 2008 data have been previously presented by Israel et al. (2010), whose results are generally consistent with those of our analysis for the same time period, so they will not be presented here. Figure 3.1 shows the results of fitting of the observations following the 2009 outburst. The split observations, affected by dust scattering, are the first 10 data points in Figure 3.1 following the trigger, and so should be regarded with caution. The two observations preceding the outburst were fit with only a blackbody and no power-law component. This is because the power-law index could not be constrained due to a paucity of counts. The fits in general were excellent; the goodness-of-fit

2 statistic χν ranged between 0.61 and 1.48 with a mean of 1.06.

The peak of the persistent emission occurred ∼6 hr after the BATfirst triggered on 1E 1547−5408 in 2009 January. The peak was almost 3 orders of magnitude higher in flux than the pre-outburst emission. This was accompanied by a hardening of the spectrum in the 1-10 keV band, as can be seen in the falling spectral index and rising kT . After the peak, the spectral index softened and kT fell as the flux dropped. To characterize the flux decay of the outburst, a power-law decay was fit to the data following the first day of the outburst. The first day was not included as the source decay is superimposed by delayed emission from the dust scattering rings. The power-law

α decay is described by F = A(t − t0) , where F is the unabsorbed flux, A is the normalization,

α is the power-law index, and t0 is the time of the BAT trigger. The decay was described by a − 2 power-law with an index of 0.24 0.02. Although the χν/ν of the fit was 4.1/23, a power-law model fit the data much better than an exponential decay. To determine the blackbody radius of the emitting region as shown in Figure 3.1, a distance of 3.91 0.07 kpc from Tiengo et al. (2010) was assumed. 40 3 The 2009 Outburst of Magnetar 1E 1547−5408 )

2 ¡

-9

cm 10

1 ¡ 10-10 Unabs Flux (ergs s 1.2

kT 0.8 (keV) 0.4 6 3 ¢ 0

(km) 2 BB Radius 0

0.2 Pulsed Fraction 0.0

20 10 -1 0 1 2

10 10 10 10 Days from first BAT Trigger

Figure 3.1: Properties of the persistent emission of 1E 1547−5408 surrounding the 2009 outburst event. The panels on the left show the two observations that preceded the event, on a linear time scale. The right-side panels are the post-event observations and are plotted on a logarithmic time scale. The dashed line in the top panel shows the power-law decay fit to the unabsorbed flux. The unabsorbed flux in the top panel and the pulsed fraction in the bottom panel are for the 1–10 keV range. The first ten points (the first day) after the BAT trigger are contaminated by dust scattering and should thus be regarded with caution. Some of the early PC mode observations had background regions that were contaminated by the dust scattering; these are marked with an open triangle. 3.3 Analysis and Results 41

Year 2008.8 2008.9 2009.0 2009.1 0.8

0.7

0.6 )

0.5 PCU 1

0.4 (s 0.3 RXTE Pulsed count rate 0.2

54750 54800 54850 54900 MJD

Figure 3.2: 2-10 keV RMS pulsed flux evolution of 1E 1547−5408 determined from Swift XRT and RXTE. The black crosses show the RXTE pulsed count rates and the red points are the Swift pulsed count rates, arbitrarily scaled to the RXTE values. The dotted vertical lines mark the onsets of the 2008 and 2009 outbursts.

To measure pulsed fractions and fluxes, the burst-removed time series (see Section 3.3.2) were folded at the rotational ephemeris derived from contemporaneous RXTE observations of 1E 1547−5408 (Dib et al., 2012). Specifically, we used spin frequency ν = 0.48259615(3) Hz, with frequency derivative ν˙ = −5.12(2) × 10−12 s−2 at reference epoch MJD 54854.0 or 2009 January 23. The pulsed flux was calculated using an RMS method according to the formula in Dib et al. (2008), with 7 harmonics. The pulsed fraction was determined by dividing the pulsed flux by the phase-averaged flux. A pulsed flux and fraction were measured for each WT observation with an exposure time > 3 ks for which the ephemeris was valid. As seen in Figure 3.1, the pulsed fraction decreased as the flux increased. After ∼40 days, the pulsed fraction had not yet recovered to its pre-burst level of ∼0.25.

The pulsed flux evolution around both the 2008 and 2009 outburst events is presented in Figure 3.2. The Swift data confirm the evolution that is observed in the RXTE data which are presented briefly in Ng et al. (2011) and in detail in Dib et al. (2012). The pulsed flux enhancement ∼11 days following the initial trigger of the 2008 event, although not noted by Israel et al. (2010), is clearly present in the Swift data. Thus, the 2009 event showed a much smaller increase in pulsed 42 3 The 2009 Outburst of Magnetar 1E 1547−5408

100

10-1 RMS Pulsed Fraction

-2 10 -11 10 10-10 1 2 Unabsorbed Flux (ergs s− cm− )

Figure 3.3: 1-10 keV RMS pulsed fraction as a function of 1-10 keV unabsorbed flux. See also Ng et al. (2011).

flux than did the 2008 event, while the opposite is true of the total flux.

Figure 3.3 shows an anti-correlation between pulsed fraction and unabsorbed flux. It includes observations from both the 2008 and 2009 outbursts. Ng et al. (2011) present this trend using Chandra and XMM data as well as the burst-removed Swift data (see Section 3.3.2) presented in this paper.

3.3.2 X-Ray Bursts

Bursts were identified in a manner similar to that described in Gavriil et al. (2004). The event lists were binned at a 1/16 s time resolution and a mean number of counts per bin was calculated

for each Good Timing Interval (GTI). The number of counts in each bin, ni, was compared to the 3.3 Analysis and Results 43

GTI mean counts, λ, according to the probability Pi of ni occurring randomly,

− λni e λ Pi = . (3.1) ni!

Time bins that had Pi ≤ 0.01/N, where N is the total number of time bins in the GTI being searched, were identified as part of a burst. Since the mean number of counts in a GTI can be overestimated due to contamination from bursts in other time bins, the procedure above was repeated iteratively, each time removing the bins that were identified as containing bursts, until no further bursts were identified. The above procedure was then repeated for 1/32 s and 1/64 s time resolutions to improve sensitivity to bursts of different durations. Since several bins identified with bursts can be part of the same burst, a burst was defined by its peak. The peak of a burst was determined by first finding the minimum time to accumulate 10 counts, using unbinned event data. The midpoint of the time spanned by these 10 counts was defined as the peak. A search for a peak was done within 0.5 s on each side of an identified bin. This definition of burst peak is independent of binning and, for bursts with durations shorter than 1 s, will merge all of the identified bins into a single burst. Bursts within 1 s of each other that were merged into a single burst were identified when selecting the background (see below) and their properties were measured separately. Once identified, to remove the bursts from the event lists, the lists were divided into full periods of the pulsar, starting with the first event of the observation as a reference point. The periods that contained bursts were identified and all counts which arrived in that interval were removed from the event list. This was done to ensure equal exposure to all pulse phases in the pulse profile.

Burst Statistics

For each burst, a fluence, T90, rise time (tr), and fall time (tf ) were measured with the same analysis as in Gavriil et al. (2004), using the unbinned event data. The fluence was determined by first measuring a background count rate in hand-picked regions on either side of the burst. The background region by default was between 1 s and 2 s from the burst peak to either side of the burst, but was manually adjusted for most bursts in order to avoid contamination from other nearby bursts. The cumulative background-subtracted counts were then fit with a step function, using data point from the hand-picked background region. The height of the step function in 44 3 The 2009 Outburst of Magnetar 1E 1547−5408

40 20

30 15

20 10 Counts Counts

10 5

0 0

30 30

20 20 Counts Counts

10 10

0 0

1.5 1.5 1.5 1.5

1.0 0.5 0.0 0.5 1.0 1.0 0.5 0.0 0.5 1.0

Time relative to peak (s) Time relative to peak (s)

Figure 3.4: Examples of bursts from 1E 1547−5408. Time series are binned on a 1/16 s timescale in the 0.5–10 keV energy range. They display a wide range of morphology.

counts corresponds to the fluence of the burst. The T90 duration of the burst is the time between when 5% and 95% of the fluence has been accumulated. The burst rise and fall times were determined using a maximum likelihood fit to a piecewise function with an exponential rise and an exponential decay. Peak fluxes in counts per second were determined by passing a 62.5 ms boxcar integrator through a 250 ms interval (4 boxcar widths) centered on the burst peak in steps of 1 ms. The highest count rate measured by the integrator was defined to be the peak flux.

In total, for the 2009 outburst, 424 bursts were identified in 86 ks of observations from 2009 January 22 to 2009 September 30 using 1/16 s time resolution. Thirteen additional bursts were identified using the 1/32 s and 1/64 s time resolutions for a total of 437 bursts. Of those identified, 34 had too few counts to permit a reliable measure of fluence, and for 32, the exponential rise and decay were not successfully fit. For 64 of the bursts, properties could not be measured because 3.3 Analysis and Results 45

40 45 35 40 30 35 30 25 25 20 20 15 15 10

Number of events 10 Number of events 5 5

0 2 1 0 3 2 1 00

10 10 10 10 10 10 10 T90 (s) tr (s) 50 60

40 50 40 30 30 20 20

Number of events 10 10 Number of events

0 3 2 1 0 2 1 0 1 02

10 10 10 10 10 10 10 10 10 tf (s) tr/tf

Figure 3.5: Top left: Distribution of T90 duration of bursts. Top right: Distribution of burst rise times. Bottom left: Distribution of burst fall times. Bottom right: Distribution of tr/tf . In all panels, the solid line is the best-fit log-normal function.

they were too close to another burst to allow a reliable background estimate between them. Four bursts were too close to the edge of a GTI to calculate a background count rate either before or after the burst. In summary, 303 bursts could be fully analysed and only these 2009 bursts will be considered henceforth. Examples of different bursts are shown in Figure 3.4. Only two bursts were found in the XRT observations of the 2008 event; their properties were similar to those during the 2009 outburst.

Figure 3.5 shows the distributions of the burst properties, grouped in logarithmic bins. The T90, rise time, fall time, and the ratio of rise to fall time distributions have been fit with log-normal distributions using maximum likelihood fitting. The T90 distribution has a mean of 305 ms and a range for one standard deviation of 140 - 662 ms. For the rise time distribution, we find a mean 46 3 The 2009 Outburst of Magnetar 1E 1547−5408

Table 3.2: Burst statistics of magnetars

a a Magnetar T90 tr tf Γ B P Reference (ms) (ms) (ms) (1014 G) (s)

SGR 1806−20 161.8 - - - 21 7.6 Göğüş et al. (2001) SGR 1900+14 93.4 - - - 7.3 8.0 Göğüş et al. (2001) 1E 2259+586 99.31 2.43 13.21 1.35 0.59 7.0 Gavriil et al. (2004) 1E 1547−5408 305 39 66 0.17 2.2 2.1 this work aFrom the McGill AXP/SGR catalogue at http://www.physics.mcgill.ca/∼pulsar/magnetar/main.html of 39 ms and a range for one standard deviation of 14 - 109 ms. For the distribution of fall times, we find a mean of 66 ms and a range of 24 - 182 ms for one standard deviation. The mean of the tr/tf distribution is 0.59 with a range for one standard deviation of 0.21 - 1.66. A summary of the measured quantities is provided in Table 3.2. There we also provide these quantities, when available, for the three other sources for which such statistical analyses have been done. We note in particular that the average burst duration for 1E 1547−5408 is longer than for all others measured thus far. This result is further discussed in Section 3.4.2.

Figure 3.6 shows the fluence and peak flux distributions, in counts and counts per second, respectively, which have been fitted with a power-law distribution using a least-squares method. For low fluences or peak fluxes, the number is underestimated since the burst detection algorithm is less sensitive to these bursts. Therefore, some of the points with low fluence or peak flux were not included in the fits. The best-fit power-law index for the fluence distribution is −0.6 0.1. For the peak flux distribution, the power-law index is −0.34 0.12. This index is quite shallow and, despite the omission of the first two points in the fit, may still be affected by the bias in the burst search.

For other AXPs, there is evidence that bursts tend to arrive on pulse (e.g. Gavriil et al., 2002, 2004). For 1E 1547−5408 this does not seem to be the case, as burst peaks are distributed randomly in phase (see Figure 3.7a). This is similar to what is observed in SGRs 1806−20 and 1900+14 (Palmer, 1999, 2002). However, when the individual photon arrival times that are part of bursts are folded, a strong pulse is observed. The peak of this ‘pulse’, shown in Figure 3.7b, is not aligned with the peak of the quiescent pulse profile. Figure 3.7e presents this quiescent pulse 3.3 Analysis and Results 47

2 2 1

Fluence (ergs cm ) Peak Flux (ergs cm s )

9 8 8

7 7

10 10 10 10 10 100 100

10 10 Number of events Number of events

101 102 103 102 103 1 Fluence (counts) Peak flux (counts s )

Figure 3.6: Left: Distribution of burst fluences. Right: Distribution of burst peak fluxes. The solid line is a linear fit to the filled circles. These distributions are based on burst counts from a 1– 10 keV energy band. The open circles are not included in the fits because of reduced sensitivity in detecting such bursts. The top axes show the fluence and peak flux in cgs units which are derived from a single conversion factor between counts and ergs cm−2. In using such a factor, the bursts are assumed to have the same spectrum which is an approximation as each burst has a slightly different spectrum. 48 3 The 2009 Outburst of Magnetar 1E 1547−5408

profile obtained using the burst-removed data. Since the pulsed fraction of the first two observations following the 2009 BAT trigger is significantly lower and the persistent flux is significantly higher than in the subsequent observations, including them in the profile reduces the pulse amplitude. Thus, in order to better show the persistent pulse profile, Figure 3.7e does not include those first two observations. In order to determine whether the burst count pulse was dominated by a handful of bright bursts, the 15 brightest bursts were removed and the counts were refolded. The profile did not change significantly and still displayed a pulse at a similar phase. Panels c and d of Figure 3.7 separate the symmetric bursts from slow-fall bursts. Symmetric

bursts were defined as bursts with 0.5 < tr/tf < 2. Bursts with tf greater than 2tr were defined as slow-fall bursts. Of the 303 well measured bursts, 158 were classified as symmetric and 116 as slow falls. The remainder, 29 bursts, were those with rise times greater than twice their fall times. Curiously, the folded slow-fall burst counts exhibit a much stronger pulse than do the

2 2 folded symmetric burst counts, with a χν = 43 for the null hypothesis, compared to χν = 6 for the folded symmetric bursts with 15 degrees of freedom. This symmetric/slow-fall definition is somewhat arbitrary and these two classes of bursts are by no means distinct populations. We use this distinction only to demonstrate that the more symmetric bursts tend to be less pulsed than those that are less symmetric.

Burst Spectroscopy

Spectra within the T90 interval of each burst peak were extracted and grouped with 20 counts per bin. Background spectra were taken from 1 min on either side of the burst peak extracted from the burst-removed event data. The 46 bursts with fluences over 200 background-subtracted counts

22 −2 were fitted with a photoelectrically absorbed power law with NH fixed to 3.24 × 10 cm as measured from the fit to the persistent emission (see Section 3.3.1). The spectra were fitted using XSPEC. The mean of the measured spectral indices of the bursts was found to be Γ = 0.17, with a standard deviation of 0.33, where N(E) ∝ E−Γ. Fitting with more complicated models was attempted, but parameters could not be successfully constrained because of the low number of counts. As shown in Table 2, the average Γ we measure is significantly harder than that measured in the only other magnetar outburst for which the value is reported. This is discussed further in Section 3.4.2. 3.3 Analysis and Results 49

40 (a) 35 30 25 20

Number of 15 burst peaks 10 (b) 4500 4200 3900 3600 Burst counts (c) 1800 1700 1600 1500 Symmetric burst counts 1400 (d) 1600 1400 1200 Tailed 1000

burst counts 800 (e) 2550 2400 2250 counts

Persistent 2100 0.0 0.5 1.0 1.5 2.0 Phase

Figure 3.7: (a) Folded profile of the times of the burst peaks. (b) Folded profile of photon counts from cycles of the pulsar that contain bursts. (c) Folded profile of photon counts from cycles containing symmetric bursts. (d) Folded profile of photon counts from cycles containing slow- fall bursts. (e) Folded profile of photon counts from cycles of the pulsar that do not contain bursts but not including the first two observations following the BAT trigger, illustrating the quiescent pulse profile. Profiles are all in the 0.5–10 keV energy range. 50 3 The 2009 Outburst of Magnetar 1E 1547−5408

In order to determine the effect of pileup on the bursts, power-law spectra were fit to the two bursts with the highest peak flux while excluding a central region ranging from 1 to 15 pixels in radius. The power-law indices from the fits were plotted against radius of exclusion region as per the prescription of Romano et al. (2006). The power-law index did not change significantly as a function of exclusion radius. Hence we concluded that the bursts were not significantly affected by pileup.

In order to probe the relation between hardness and fluence for the bursts, hardness ratios were determined for each burst by measuring fluences in the 0.5–4 keV and 4–10 keV bands. No significant correlation between 0.5–4 keV/4–10 keV hardness and fluence was observed for bursts from 1E 1547−5408. For the 46 most fluent bursts, there was also no observed correlation between the 0.5–4 keV/4–10 keV hardness or the spectral index of the power-law fit and the fluence. The lack of a detection of the correlation between hardness and fluence in the Swift data may be due to the limited spectral range of the XRT (0.5–10 keV). However, an anti-correlation between power-law index and average flux over T90 from the spectral fits was observed (Figure 3.8). This is consistent with a correlation between the hardness and the magnitude of a burst.

Spectral features in magnetar bursts have been reported for some sources (Strohmayer & Ibrahim, 2000; Ibrahim et al., 2002; Gavriil et al., 2002; Ibrahim et al., 2003; Woods et al., 2005; Kumar & Safi-Harb, 2010; Gavriil et al., 2011; An et al., 2014), although most of the features have been discovered above 10 keV. The individual burst spectra for 1E 1547−5408 showed no evidence for any spectral features in the 1-10 keV range. Since spectral features may be masked by the low count rates in the individual spectra, we combined the burst spectra into a single average spectrum. The burst and background spectra and response files were combined using the FTOOL addspec. Spectral bins were grouped with a minimum of 20 counts per bin. The average spectrum was fit with a blackbody, a power law, a blackbody with an added power law, and a Comptonized blackbody; all four models were photoelectrically absorbed. All of the models 2 ∼ gave acceptable fits with χν 1; thus, no significant spectral features were observed in any of the residuals.

Fluences and peak fluxes in counts and counts per second, respectively, were converted into cgs units using the results of the spectral fits. The fluxes from the power-law fits were multiplied 3.3 Analysis and Results 51

1.0

0.5 ¢

0.0

0.5 ¡

10-7

2 1

Flux (erg cm s )

Figure 3.8: Power-law index as a function of average absorbed flux over T90 from the spectral fits of the 46 most fluent bursts. The black points are the individual bursts and the blue open squares represent the weighted averages of the power-law indices for bursts in logarithmic fluence bins. 52 3 The 2009 Outburst of Magnetar 1E 1547−5408

by the burst durations and compared to the fluences measured in counts. The proportionality constant between the two was determined to be 2.23 × 10−10 ergs cm−2 counts−1. In using this single conversions factor between counts and ergs cm−2 we are effectively assuming an average spectral model for the bursts which is not generally true. The conversion from counts to cgs units in reality is different from burst to burst depending on their spectra. Values in cgs units, using this single conversion factor, are indicated on the top axes of the fluence and peak flux distributions in Figure 3.6.

3.4 Discussion

We have presented Swift XRT observations of the 2008 and 2009 outburst events of 1E 1547−5408. In particular, we considered the behaviour of this source’s persistent flux in its 2009 outburst, which was qualitatively different from that in 2008. Specifically, the 2009 event showed a much smaller increase in pulsed flux than in 2008, while the opposite is true of the total flux. In this work, we have shown that for the 2009 outburst, the source spectrum became harder (though the exact degree of hardening is difficult to know, due to the contaminating dust scattering) as the flux increased after the initial trigger, and we found an anti-correlation between the pulsed fraction and the flux.

We have also presented a detailed study of the several hundred X-ray bursts detected by Swift following the 2009 event. Noteworthy results we have found include a correlation between burst flux and hardness. We also note that burst counts tend to contribute very significantly to the pulsed fraction, even if the phases of burst peaks are randomly distributed in pulse phase.

Next we discuss our results in the context of the magnetar model, as well as in comparison with those for other similar outbursts.

3.4.1 Persistent Flux

Figure 3.1 shows that as the X-ray flux increased, the blackbody temperature increased and the power-law index decreased during the 2009 outburst. Such a hardness/flux correlation was seen also in the 2008 outburst (Israel et al., 2010) and ubiquitously in other magnetar outbursts (e.g. Kaspi et al., 2003; Woods et al., 2004; Israel et al., 2007). In the case of 1E 1547−5408, however, 3.4 Discussion 53 we regard the precise values of kT and Γ as shown in Figure 3.1 on the first day after the outburst with caution, as they are very likely biased by dust scattering.

The thermal emission of magnetars, in the twisted magnetosphere model (Thompson et al., 2002, and see Section 1.2.3), has as its origin heating from within the star, due to the decay of the strong internal magnetic field. The resulting thermal surface photons are thought to be scattered by currents in the magnetosphere, resulting in a Comptonized blackbody-like spectrum which is often modelled with a blackbody plus a power law (Lyutikov & Gavriil, 2006). The magnetospheric currents are present due to ‘twists’ in the field structure, either global (Thompson et al., 2002), or, more likely, in localized regions (Beloborodov, 2009). In either case, the current strength, hence degree of scattering, increases with increasing twist magnitude. Moreover, return currents provide an additional, external source of surface heating in addition to the internal source. The increase in flux during a magnetar outburst is thus theorized to be caused by an internal heat-releasing event that may significantly increase the surface temperature (see, for example, Özel & Guver, 2007), further twist the magnetospheric field, and increase the external return- current heating. Thus, a correlation between hardness and flux is generically expected in the twisted-magnetosphere model (Lyutikov & Gavriil, 2006), in agreement with observations of 1E 1547−5408 and other magnetars.

It is interesting to compare the hardness/flux correlations seen for 1E 1547−5408 with those observed for other magnetars to see if there exists a universal relationship between increase in X- ray flux and hardness, as might be expected in the above scenario. Figure 3.9 shows the fractional increase in the 4–10/2–4 keV hardness ratio determined from fluxes as a function of 2–10 keV unabsorbed flux fractional increase for six different magnetar outbursts in four different magnetars. We chose to consider a flux hardness ratio as a measure of hardness (rather than e.g. power-law index) as it is defined independent of spectral model, and also is instrument-independent. In order to determine the hardness of each source, spectral model parameters from the literature were compiled and input to XSPEC. The 4–10 keV and 2–4 keV fluxes were then determined using the XSPEC flux command and the hardness was calculated from their ratio. For references that did not report a 2–10 keV unabsorbed flux, one was determined using XSPEC using the reported model parameters. As is clear from the Figure, an overall trend is apparent, although there is 54 3 The 2009 Outburst of Magnetar 1E 1547−5408

12 1E 1048.1-5937 2007 1E 1048.1-5937 2002 1E 2259+586 2002 10 XTE J1810-197 2003 1E 1547-5408 2009 1E 1547-5408 2008

8 q 6 H/H

0 100 101 102 103 F/Fq

Figure 3.9: 4–10 keV / 2–4 keV flux hardness, H, as a function of 2–10 keV flux, F for magnetar outbursts. Both are normalised to their quiescent values, Hq, Fq. For 1E 1547−5408, the spectral fits used to determine the hardnesses and fluxes were from this work, and the first day of the 2009 outburst has been omitted due to contamination by the dust-scattered emission. For XTE J1810−197 the spectral parameters were taken from Gotthelf & Halpern (2007b). For 1E 1048.1−5937 they were taken from Tam et al. (2008). For 1E 2259+586 they were taken from Zhu et al. (2008). Uncertainties on the hardness ratios are shown only for 1E 1547−5408; determining those for other sources is difficult from the literature, however they are likely comparable to the scatter. 3.4 Discussion 55

significant variation from source to source. For example, for similar flux enhancements over the quiescent level, 1E 2259+586 became much harder than did 1E 1048.1−5937, with the behaviour of 1E 1547−5408 lying somewhere in between. Thus, though Figure 3.9 demonstrates that a hardness/flux correlation is indeed generically observed, there does not appear to exist a universal law linking the degree of flux increase over the quiescent level with the degree of flux hardening. This observation will require accommodation in any detailed model of magnetar outburst emission.

As shown in Figure 3.3, the flux of 1E 1547−5408 was anti-correlated with the pulsed fraction. While immediately preceding the 2009 outburst the pulsed fraction was over 20% (Figure 3.1), immediately afterward, it dropped to nearly negligible levels in the 1–10 keV range, likely due to the emission being dominated by the scattered emission from the dust scattering rings. However, following the first day, the pulsed fraction was still significantly lower than the preburst pulsed fraction. This anti-correlation between pulsed fraction and flux is presented with the addition of Chandra and XMM-Newton data in Ng et al. (2011), who suggest it could be due to an increase in the emitting area of a thermal hot spot, which would cause the emission to be observable during a greater portion of the phase of the pulsar. We note that both correlations (Gotthelf et al., 2004; Zhu et al., 2008) and anti-correlations (Israel et al., 2007; Tam et al., 2008) between pulsed fraction and flux have been observed in magnetar outbursts. Different behaviours can result depending on the location of the emission region and the viewing geometry. Although detailed modeling of spectral, pulse morphology and pulsed flux changes during magnetar outbursts is beyond the scope of this work, recent attempts at unified modelling of magnetar surface and magnetosphere emission geometries and emission mechanisms (Albano et al., 2010) could in principle use data like ours to constrain the hot spot location and size. This seems to us to be a good future avenue for investigation.

Interestingly, Kaneko et al. (2010) report a ∼55% pulsed fraction at ∼100 keV as observed by Fermi GBM ∼30–40 minutes before the BAT trigger. They report that this is the first time that pulsations unrelated to a giant flare have been observed at ∼100 keV for an SGR1. However, AXPs have previously been shown to exhibit pulsations at ∼100 keV with pulsed fractions as high

1Note that Kaneko et al. (2010) use the designation SGR 1550−5418 for 1E 1547−5408. 56 3 The 2009 Outburst of Magnetar 1E 1547−5408

as 100% (e.g. Kuiper et al., 2006). Thus it is possible that the measured 55% actually decreased from a higher pulsed fraction leading up to the outburst event, i.e. the ∼100 keV pulsed fraction may have behaved similarly to that in the 1–10 keV band. In recent years NuSTAR has opened a window on pulsed fraction of magnetars, and has shown that although high, magnetar pulsed fractions do not seem to rise to 100% within the 3–79 keV NuSTAR band (e.g. An et al., 2015).

3.4.2 Bursts

Previous studies of SGR bursts have shown that their energies, and thus fluences, follow a power- law distribution dN/dE ∝ E−α with α equal to ∼5/3 (Cheng et al., 1996; Göğüş et al., 1999, 2000). It has been noted that this is similar to the Gutenberg-Richter law for earthquakes and to energy distributions of solar flares (Crosby et al., 1993; Lu et al., 1993). Both 1E 1547−5408 and 1E 2259+586 also follow this distribution. In this work, the fluence distribution of 1E 1547−5408 is found to have a power-law index of −0.60.1 which corresponds to dN/dE ∝ E−1.6. Gavriil et al. (2004) find an α of 1.70.1 for 1E 2259+586, similar to the values found for SGRs, further reinforcing the similarity in this particular behaviour among AXPs and SGRs. For the 2009 outburst, INTEGRAL observations which cover an energy range of > 80 keV, show different burst properties from those determined using the Swift XRT observations. Savchenko et al. (2010) report a 68-ms mean duration derived from a log-normal distribution with a scatter of 30 - 155 ms. This is much shorter than the 305-ms duration determined in this work (see Table 3.2). This discrepancy may be due to the difference in energy coverage; perhaps bursts have different morphologies at different energies. However, the definition of duration used by

Savchenko et al. (2010) differs from the T90 definition used here. Savchenko et al. (2010) define the burst duration as the time between the moment when the count rate rises above 5σ to when the count rate drops below 3σ. When applying their definition of duration to the bursts identified in our study, we find, for a log-normal distribution, a mean duration of 101 ms and a range for one standard deviation of 59 - 173 ms, closer to but still somewhat longer than their measurement, suggesting a possible energy dependence of burst duration. We do not, however, detect any significant difference in the durations measured using 0.5–10 keV counts with those measured using 2–10 keV counts. The properties of bursts from the 2009 outburst event of 1E 1547−5408 are reminiscent of 3.4 Discussion 57 those from the outburst of 1E 2259+586 (Gavriil et al., 2004). Both have a significant number of short spikes like those found in SGRs, and a set of bursts with long pulsating tails like those found in burst studies of other AXPs. Although we do not find any bursts with long pulsating tails in the XRT observations, Savchenko et al. (2010) and Mereghetti et al. (2009) find two such bursts. These were not found in our analysis because Swift was not observing 1E 1547−5408 when they occurred. Table 3.2 compares the properties of bursts from 1E 1547−5408 to those from outbursts from other magnetars. We note that the average durations of bursts from 1E 1547−5408 appear to be longer than for those in other sources. However, this could be an artifact as the burst properties for the other tabulated sources were determined with RXTE. The larger collecting area of RXTE allows it to detect bursts that are fainter than those Swift can detect. If faint, short bursts are missed by the XRT, the mean burst duration (as well as tr and tf ) may be overestimated. Also, the energy range of RXTE (2–60 keV) probes higher energies and so differences may be due to the energy dependence of burst properties. A detailed statistical study of 1E 1547−5408 bursts with RXTE is needed to clarify this point.

Although Swift XRT is not ideal for probing the spectra of magnetar bursts, which have significant flux above 10 keV, we were still able to draw the following conclusions from our analysis. While we do not observe a hardness-fluence correlation for 1E 1547−5408, this could be due to our limited energy range. Indeed, there is a hint of a correlation between Γ and fluence, however is is not statistically significant. Note however that we do observe a significant Γ-flux correlation (Figure 3.8). Savchenko et al. (2010), using INTEGRAL data of the 2009 outburst, find a correlation between burst hardness and count rate. Their hardness ratio is defined as the ratio between the Anti-Coincidence Shield (ACS) flux, which is sensitive to photons above 80 keV, and a 20-60 keV flux from the ISGRI instrument. This is also consistent with a correlation between hardness and burst magnitude for 1E 1547−5408. Gavriil et al. (2004) also find a correlation between hardness and fluence for 1E 2259+586. For the SGRs, on the other hand, an anti-correlation between hardness and fluence has been observed (Göğüş et al., 1999, 2000). Table 3.2 also shows that the 1E 1547−5408 bursts from Swift are much harder than those from 1E 2259+586. In light of the observed hardness-fluence correlation in AXP bursts, this is not a surprising result. The 28 most fluent bursts from 1E 2259+586 for which spectral indices were measured, have fluences 58 3 The 2009 Outburst of Magnetar 1E 1547−5408 of ∼ 10−9 − 10−8 erg cm−2 (Gavriil et al., 2004). This is to be compared with the 46 most fluent bursts for which Γ was measured here for 1E 1547−5408, that span a fluence range of ∼ 10−8 − 10−7 erg cm−2. This may account for the harder average spectral index for bursts from 1E 1547−5408.

In the magnetar model, two mechanisms have been suggested for producing magnetar bursts. Thompson & Duncan (1995) suggest that stresses due to the strong magnetic fields present inside magnetars are able to crack the crust of the neutron star. This cracking releases a plasma fireball into the magnetosphere. The strong magnetic fields can hold the fireball above the fracture site. The suspended fireball can heat the surface thus causing an extended cooling tail. Since the strongest surface fields are located near the polar caps, these fracture events would occur preferentially near the poles which would result in an observed phase dependence of the bursts. Another mechanism, proposed by Lyutikov (2003), suggests that bursts are caused by reconnection events initiated by the development of a tearing mode instability in the magnetically dominated relativistic plasma in the magnetosphere. In this case, bursts occur randomly in phase. This mechanism should also produce shorter more symmetric bursts than in crustal fracture. Lyutikov (2003) states that the hardness-fluence anticorrelation found in SGRs is consistent with magnetic reconnection. For the surface-cooling model, the opposite is expected. As discussed by Lyutikov (2003), both mechanisms could easily be at work.

Woods et al. (2005) suggested that observationally, there are two types of magnetar bursts. Type A bursts are nearly symmetric and are typical of SGR bursts. Type B bursts have been observed in AXPs and are characterized by a short spike followed by a long tail, typically much longer than the rotational period of the pulsar. Pulsations have been observed in these tails. Since the Type B bursts observed in AXPs occur preferentially in phase and exhibit a hardness-fluence correlation, and the Type A bursts in SGRs are distributed randomly in phase and have a hardness- fluence anti-correlation, Woods et al. (2005) suggest the magnetic reconnection mechanism for type A bursts and the surface-cooling model for Type B bursts.

For 1E 1547−5408, none of the bursts detected by Swift XRT could be classified as Type B. However, the two bursts with long pulsating tails found in INTEGRAL data by Savchenko et al. (2010) and Mereghetti et al. (2009) have typical Type B morphology. For the bursts in this work, 3.5 Conclusions 59

over half of the bursts were classified as symmetric, which nominally corresponds to Type A (see top-right panel of Figure 3.4 for example). About 40% of the bursts were classified as slow-fall bursts, which are actually closer to Type A in morphology than Type B, although they are not very symmetric. Thus, the bursts from 1E 1547−5408 are not easily classified into Types A and B as described by Woods et al. (2005). Moreover, for both the symmetric and slow-fall bursts, the folded photon arrival times exhibited a clear phase dependence, although for the slow-fall bursts this ‘pulse’ is much stronger. That the symmetric bursts show some pulse modulation is suggestive of a difference with ‘classical’ Type A bursts, or that pulse phase analyses of the latter should be attempted using all burst counts, as they too may be pulsed. That the burst counts are pulsed indicates that burst emission comes from a preferred region in rotational phase, be it on or near the surface or high in the magnetosphere, even if the burst peaks arrive randomly in phase. The offset between the burst counts pulse peak and the persistent pulse peak seen when comparing Figures 3.7b and 3.7e demonstrates that the preferred burst emission region has location and geometry similar to, but distinct from, that producing the persistent pulsations.

The total energy released in the Swift-detected bursts was ∼ 1×1040 erg in the 1-10 keV range. This is much lower than the 1-10 keV energy released from the persistent emission between 2009 January 22 and 2009 September 30 of ∼ 9 × 1041 erg. For reference, the energy released from the spin-down in that same period is ∼ 5 × 1040 erg. Woods et al. (2004) find that for SGRs, the energy released in the bursts is higher than that released in the persistent emission, but for 1E 2259+586, the opposite is true. In this regard, the 2009 outburst of 1E 1547−5408 is more like that of AXP 1E 2259+586.

3.5 Conclusions

We have presented an analysis of the persistent radiative evolution of the 2009 January outburst of 1E 1547−5408 from Swift XRT observations. We found that ∼ 6 hr after the 2009 BAT trigger the observed persistent 1–10 keV unabsorbed flux reached a peak of ∼ 8 × 10−9 ergs cm−2 s−1, an increase of more than 500 times the quiescent flux leading up to the outburst. This flux evolution is not due solely to the source; in the first day, there is also emission from dust scattering rings that is delayed emission from an energetic event near the onset of the outburst. 60 3 The 2009 Outburst of Magnetar 1E 1547−5408

There was significant spectral hardening at the outburst as seen in other magnetar outbursts. Note that the absence of spectral variation reported by Ng et al. (2011) is consistent with our results, as they missed the bulk of the spectral changes which occurred in the first day of the outburst and their Chandra observations did not begin until the next day. The pulsed fraction showed an anti-correlation with the phase-averaged flux for both the previous 2008 and 2009 outbursts, with both sets of data following the same trend. We have compiled data from this and five other magnetar outbursts for four different sources and find a generic X-ray hardness/flux correlation overall, but with no clear universal quantitative relationship between the two. We have also presented a detailed statistical analysis of the several hundred bursts detected during the 2009 event. The bursts do not easily fall into the Type A/Type B classification put forth by Woods et al. (2005). We found that the peaks of the bursts were randomly distributed in pulse phase, but that when the individual photon counts were folded at the pulsar emphemeris, a clear pulse was present. This phase dependence is stronger for those bursts with longer decays than rise times than for those bursts that are symmetric. We also report a correlation between burst hardness and burst flux. In many ways, these observations yield more questions than answers. The range of observed phenomenology in magnetar outbursts seems to increase with each event, with few overall trends to assist in constraining models emerging. Nevertheless given the paucity of events studied in detail, we remain hopeful that through perseverance, eventually physical insight will emerge. The fast response of telescopes like Swift is crucial to this endeavor. For 1E 1547−5408, it allowed an analysis of the first day of the 2009 event. This is important as both the most significant spectral changes and the majority of the bursts occurred within this period. This highlights the necessity of prompt response to magnetar outbursts in understanding their nature. 4 Post-outburst X-ray Timing Evolution of Swift J1822.3−1606

The work presented in this chapter was previously published in the article: Scholz et al., 2012, Post-outburst X-Ray Flux and Timing Evolution of Swift J1822.3−1606, Astrophysical Journal, 761, 66. That work presents ∼ 1 year of observations following the 2011 July magnetar outburst that resulted in the discovery of Swift J1822.3−1606 (Livingstone et al., 2011). A follow-up paper, Scholz et al., 2014, The Long-term Post-outburst Spin Down and Flux Relaxation of Mag- netar Swift J1822.3−1606, Astrophysical Journal, 786, 62 presents a similar analysis but with over a year of additional observations following the outburst. As you will see, Scholz et al. (2014b) resolved an ambiguity in the timing solutions presented in Scholz et al. (2012) and other works (Rea et al., 2012). So it is beneficial to present the earlier work here for context. The text of this chapter has been adapted from Scholz et al. (2012), and includes the earlier timing analysis as well as sections describing results that are not presented in Scholz et al. (2014b). Chapter 5 is an adaptation of Scholz et al. (2014b) and includes some results from Scholz et al. (2012). This is because the flux and spectral evolution results in Scholz et al. (2012) overlap with those in Scholz et al. (2014b).

4.1 Introduction

The magnetar Swift J1822.3−1606 was first detected by Swift Burst Alert Telescope (BAT) on 2011 July 14 (MJD 55756) via its bursting activities (Cummings et al., 2011). It was soon identified as a new magnetar upon the detection of a pulse period P =8.4377 s (Göğüş et al., 2011). No optical counterpart was found, with 3σ limit down to a z-band magnitude of 22.2 (Rea et al., 2011). In Livingstone et al. (2011), we reported initial timing and spectroscopic results using follow-up X-ray observations from Swift, Rossi X-ray Timing Explorer (RXTE), and Chandra X- ray Observatory. We found a spin-down rate of P˙ = 2.54 × 10−13 which implies a surface dipole magnetic field B = 4.7 × 1013 G, the second lowest B-field among magnetars. Using an

61 62 4 Post-outburst X-ray Timing Evolution of Swift J1822.3−1606

additional 6 months of Swift and XMM-Newton data, Rea et al. (2012) present a timing solution and spectral analysis. They find a spin-down rate of P˙ = 8.3 × 10−14 which implies a magnetic field of B = 2.7 × 1013, slightly lower than that found by Livingstone et al. (2011). In this chapter, we present a timing solution and pulse profile analysis using RXTE, Swift, and Chandra observations from the first year following the 2011 July outburst. The additional two Chandra and 18 Swift observations provide a timing baseline that is over four times longer than in Livingstone et al. (2011). We also search for bursts in the Swift and RXTE observations. We report on an archival ROSAT observation to constrain the pre-outburst flux as well as image the field around the source. We discuss the effects of timing noise on our timing solution and the properties and implications of this outburst within the magnetar model.

4.2 Observations

4.2.1 Swift Observations

Following the 2011 July 14 outburst of Swift J1822.3−1606, the Swift XRT (see Section 2.1.3) was used to obtain 46 observations for a total exposure time of 175 ks. Data were collected in two different modes, Photon Counting (PC) and Windowed Timing (WT). While the former gives full imaging capability with a time resolution of 2.5 s, the latter forgoes imaging to provide 1.76-ms time resolution by reading out events in a collapsed one-dimensional strip. For each observation, the unfiltered Level 1 data were downloaded from the Swift quicklook archive1. For a summary of observations used, see Table 4.1. The standard XRT data reduction script, xrtpipeline, was then run using HEASOFT 6.11 and the Swift 20110725 CALDB. We corrected the event arrival times to the solar-system barycentre using the position of RA= 18h 22m 18s, Dec= −16◦ 04′ 26′′.8 (Pagani et al., 2011). Source and background events were extracted using the following regions: for WT mode, a 40-pixel long strip centred on the source was used to extract the source events and a strip of the same size positioned away from the source was used to extract the background events. For PC mode, a circular region with radius 20 pixels was used for the source region and an annulus with inner radius 40 pixels and outer radius 60 pixels was used as the background region. For the first PC mode observation (00032033001), a circular

1http://swift.gsfc.nasa.gov/cgi-bin/sdc/ql 4.2 Observations 63

Table 4.1: Summary of observations of Swift J1822.3−1606.

ObsID Mode Obs Date MJD Exposure Days since trigger (TDB) (ks)

Chandra 12612 ASIS-S CC 2011-07-27 55769.2 15.1 12.6 13511 HRC-I 2011-07-28 55770.8 1.2 14.2 12613 ASIS-S CC 2011-08-04 55777.1 13.5 20.5 12614 ASIS-S CC 2011-09-18 55822.7 10.1 66.1 12615 ASIS-S CC 2011-11-02 55867.1 16.3 110.5 14330 ASIS-S CC 2012-04-19 56036.9 20.0 280.4 ROSAT rp500311n00 1993-09-12 49242 6.7 – Swift 00032033001 PC 2011-07-15 55757.7 1.6 1.2 00032033002 WT 2011-07-16 55758.7 2.0 2.1 00032033003 WT 2011-07-17 55759.7 2.0 3.1 00032033005 WT 2011-07-19 55761.1 0.5 4.6 00032033006 WT 2011-07-20 55762.0 1.8 5.5 00032033007 WT 2011-07-21 55763.2 1.6 6.7 00032033008 WT 2011-07-23 55765.8 2.2 9.2 00032033009 WT 2011-07-24 55766.2 1.7 9.7 00032033010 WT 2011-07-27 55769.5 2.1 12.9 00032033011 WT 2011-07-28 55770.3 2.1 13.8 00032033012 WT 2011-07-29 55771.2 2.1 14.7 00032033013 WT 2011-07-30 55772.3 2.1 15.7 00032051001 WT 2011-08-05 55778.0 1.7 21.5 00032051002 WT 2011-08-06 55779.0 1.7 22.5 00032051003 WT 2011-08-07 55780.4 2.3 23.9 00032051004 WT 2011-08-08 55781.4 2.3 24.8 00032051005 WT 2011-08-13 55786.4 2.2 29.8 00032051006 WT 2011-08-14 55787.6 2.2 31.0 00032051007 WT 2011-08-15 55788.1 2.3 31.6 00032051008 WT 2011-08-16 55789.5 2.2 32.9 00032051009 WT 2011-08-17 55790.3 2.2 33.8 00032033015 WT 2011-08-27 55800.8 2.9 44.2 00032033016 WT 2011-09-03 55807.2 2.4 50.6 00032033017 PC 2011-09-18 55822.7 4.9 66.2 64 4 Post-outburst X-ray Timing Evolution of Swift J1822.3−1606

Table 4.0: Summary of observations of Swift J1822.3−1606. (cont.)

ObsID Mode Obs Date MJD Exposure Days since trigger (TDB) (ks)

00032033018 WT 2011-09-20 55824.5 1.5 68.0 00032033019 WT 2011-09-25 55829.1 2.3 72.6 00032033020 WT 2011-10-01 55835.1 2.6 78.5 00032033021 WT 2011-10-07 55841.7 4.2 85.2 00032033022 WT 2011-10-15 55849.2 3.4 92.7 00032033023 WT 2011-10-22 55856.2 2.2 99.7 00032033024 PC 2011-10-28 55862.2 10.2 105.6 00032033025 PC 2012-02-19 55976.4 6.2 219.8 00032033026 WT 2012-02-20 55977.0 10.2 220.5 00032033027 PC 2012-02-21 55978.1 11.0 221.6 00032033028 WT 2012-02-24 55981.9 6.7 225.4 00032033029 WT 2012-02-25 55982.8 7.0 226.3 00032033030 WT 2012-02-28 55985.0 7.0 228.5 00032033031 WT 2012-03-05 55991.1 6.8 234.5 00032033032 WT 2012-04-14 56031.1 4.3 274.6 00032033033 WT 2012-05-05 56052.6 5.1 296.0 00032033034 WT 2012-05-26 56073.0 4.9 316.5 00032033035 WT 2012-06-17 56095.5 5.6 338.9 00032033036 WT 2012-06-26 56104.1 6.2 347.6 00032033037 WT 2012-07-06 56114.2 6.8 357.6 00032033039 WT 2012-08-17 56156.1 4.9 399.6 00032033040 WT 2012-08-22 56161.5 5.0 405.0 RXTE D96048-02-01-00 2011-07-16 55758.49 6.5 1.96 D96048-02-01-05 2011-07-18 55760.81 1.7 4.28 D96048-02-01-01 2011-07-19 55761.57 5.1 5.04 D96048-02-01-02 2011-07-20 55762.48 4.9 5.95 D96048-02-01-04 2011-07-21 55763.42 3.3 6.89 D96048-02-01-03 2011-07-21 55763.64 6.0 7.11 D96048-02-02-00 2011-07-22 55764.62 6.1 8.09 D96048-02-02-01 2011-07-23 55765.47 6.8 9.94 D96048-02-02-02 2011-07-25 55767.60 3.0 11.07 D96048-02-03-00 2011-07-29 55771.35 6.8 14.82 D96048-02-03-01 2011-08-01 55774.35 6.9 17.82 D96048-02-03-02 2011-08-04 55777.85 1.9 21.32 D96048-02-03-04 2011-08-04 55777.92 1.8 21.39 D96048-02-04-00 2011-08-07 55780.49 6.9 23.96 D96048-02-04-01 2011-08-09 55782.58 6.5 26.05 4.2 Observations 65

Table 4.-1: Summary of observations of Swift J1822.3−1606. (cont.)

ObsID Mode Obs Date MJD Exposure Days since trigger (TDB) (ks)

D96048-02-04-02 2011-08-11 55784.97 3.7 28.44 D96048-02-05-02 2011-08-12 55785.03 3.3 28.50 D96048-02-05-00 2011-08-15 55788.05 5.9 31.52 D96048-02-05-01 2011-08-16 55789.96 6.0 33.43 D96048-02-06-00 2011-08-21 55794.46 6.6 37.93 D96048-02-07-00 2011-08-26 55799.61 6.8 43.1 D96048-02-08-00 2011-09-06 55810.38 6.0 53.8 D96048-02-10-00 2011-09-16 55820.24 6.7 63.7 D96048-02-10-01 2011-09-22 55826.18 5.6 69.6 D96048-02-09-00 2011-09-25 55829.38 6.2 72.8 D96048-02-11-00 2011-10-01 55835.90 7.1 79.4 D96048-02-12-00 2011-10-08 55842.23 5.9 85.7 D96048-02-13-00 2011-10-15 55849.67 5.6 93.1 D96048-02-14-00 2011-10-29 55863.11 6.7 106.6 D96048-02-16-00 2011-11-13 55878.90 5.9 122.4 D96048-02-17-00 2011-11-20 55885.21 6.0 128.7 D96048-02-15-00 2011-11-28 55893.18 6.7 136.6 region with radius 6 pixels was excluded to avoid pileup. For the subsequent PC mode observation (00032033017), a region with radius 2 pixels was excluded. We estimate the maximum pileup fraction of the remaining PC observations to be less than 5%.

4.2.2 RXTE Observations

Swift J1822.3−1606 was observed by RXTE (see Section 2.1.6) in 32 observations spanning an MJD range from 55758 to 55893, for a total of 174 ks of integration time. We downloaded the PCA data for those observations from the HEASARC archive. The data were collected in GoodXenon mode which records each event with 1-µs time resolution. The observations are summarized in Table 4.1. We selected events in the 2–10 keV energy range (PCA channels 6–14) from the top xenon layer of each PCU for our analysis, to maximize signal-to-noise ratio. The data from all the active PCUs were then merged. If more than one observation occurred in a 24-hr period, the observations were combined into a single data set. Photon arrival times were adjusted to the solar-system barycentre using the same position as the for Swift data. Events were then binned 66 4 Post-outburst X-ray Timing Evolution of Swift J1822.3−1606

into time series with resolution 1/32 s for use in the following analysis.

4.2.3 Chandra Observations

Following the outburst, we triggered our ToO program with Chandra. Five Chandra/ACIS CC- mode (see Section 2.1.4) observations were obtained between days 13 and 281 after the outburst, with exposures ranging from 10 to 20 ks. For imaging purposes, we also processed a short (1.2 ks) archival Chandra HRC-I observation taken 14 days after the outburst. The observation parameters are summarized in Table 4.1. All Chandra data were processed using CIAO 4.3 with CALDB 4.4.6. We extracted the source events with a 6′′-long strip region, and the remainder of the collapsed strip (∼7′ long), excluding the region within 1′ of the source in order to minimize any contamination from the wings of the PSF, was used for the background. We restricted the timing analysis to events between 0.3 and 8 keV. Photon arrival times were corrected to the solar-system barycentre. The source spectrum was extracted using the CIAO tool specextract.

4.2.4 ROSAT Observation

The only existing X-ray image that covers the field prior to the outburst is a 6.5-ks ROSAT PSPC

(Aschenbach, 1985) observation of the nearby H II region M17 (Omega Nebula, G15.1−0.8). The observation has a time resolution of 130 ms. We downloaded the filtered event list from the HEASARC data archive1 and carried out the analysis using FTOOLS.

4.3 Analysis & Results

4.3.1 Imaging and Archival Spectral Analysis

Figure 4.1 shows the ROSAT and Chandra images. Swift J1822.3−1606 is the only source detected in the Chandra HRC image and its radial profile is fully consistent with that of a model PSF. Hence, there is no evidence for any surrounding nebula or dust scattering halo. We find a source position of RA= 18h 22m 18.06s, Dec= −16◦ 04′ 25′′.55 from the HRC image which is consistent with the XRT position from Pagani et al. (2011) used above. We assume an error ra-

1http://heasarc.gsfc.nasa.gov/W3Browse/ 4.3 Analysis & Results 67 " 00 ’ 00 o -16 " 00 ’ 00 o -16 DEC (J2000) DEC (J2000) " " 00 ’ 00 ’ 20 o 20

10’ o -16 -16

h m s h m s 18 22 00 18 21 00 18h24m00s 18h22m00s RA (J2000) RA (J2000)

Figure 4.1: Left: ROSAT image of the field of Swift J1822.3−1606 in 0.1–2.4 keV range. The position of Swift J1822.3−1606 is marked by the cross, and the lines indicate the Chandra HRC

observation field of view. The large-scale diffuse emission is the Galactic H II region M17. Right: 1.2 ks 0.06–10 keV Chandra HRC exposure of Swift J1822.3−1606. Swift J1822.3−1606 is the only source detected.

dius of 0.6′′ which is the uncertainty in the absolute astrometry of Chandra for a 90% confidence interval 1. In the ROSAT image, an unresolved source is clearly detected at the position of the magnetar, as first reported by Esposito et al. (2011). Since the Chandra image shows no other bright X-ray sources in the field, we take this source to be Swift J1822.3−1606 in quiescence. Using a 4′ ×2′ elliptical aperture, we obtain 11311 total counts in 0.1–2.4 keV range, of which 48 7 counts are due to background. Finally, we note that the diffuse X-ray emission ∼20′ southwest of the magnetar is from M17, which contains the young stellar cluster NGC 6618 with over 100 OB stars (Lada et al., 1991). Spectral models were fit to the archival ROSAT observation using XSPEC2 v12.7. The quiescent flux of Swift J1822.3−1606 was determined by first extracting the source spectrum from the ROSAT data, then fitting it with an absorbed blackbody model. The absorption column den-

21 −2 sity, NH, was fixed during the fit at the best-fit value (4.53 × 10 cm ) determined from the Swift and Chandra spectra (see Section 5.3.2). We obtained a quiescent blackbody temperature

1According to http://cxc.harvard.edu/cal/ASPECT/celmon/ 2http://xspec.gfsc.nasa.gov 68 4 Post-outburst X-ray Timing Evolution of Swift J1822.3−1606

+7 of kT = 0.12 0.02 keV and a radius of 5−2d1.6 km, where d1.6 is the distance to the source in units of 1.6 kpc, the estimated distance as discussed in Section 4.4.2. We found an absorbed flux +20 × −14 −2 −1 ∼ of 9−9 10 erg cm s in the 0.1–2.4 keV range. This flux is a factor of 1000 lower than the peak flux reached in the outburst (Section 5.3.2).

4.3.2 Timing Analysis

Spin Evolution

Barycentred events were used to derive a pulse time-of-arrival (TOA) for each Swift WT mode, RXTE, and Chandra observation. For the RXTE observations, events were binned into time series with 31.25-ms resolution. The time series were then folded with 128 phase bins using the ephemeris from Livingstone et al. (2011). A TOA was then measured from each profile by cross- correlation with a template profile (see Section 2.3.2). We verified that the RXTE pulse profiles were consistent with each other except in one isolated observation which was handled accordingly (see below).

For Swift and Chandra observations, TOAs were extracted using a Maximum Likelihood (ML) method, as it yields more accurate TOAs than the traditional cross-correlation technique (see Livingstone et al., 2009, and Section 2.3.2). This method was not used for the RXTE observations as their high number of counts (due to the large collecting area and background count rates of the PCA) make the ML method computationally expensive. The ML method for measuring TOAs requires a continuous model of the template pulse profile for which we used a Fourier model. The discrete Fourier Transform of the binned template profile was first calculated. The template was ∑ n i2πjϕ th then fitted by f(ϕ) = j=0 αje where αj is the Fourier coefficient for the j harmonic, and ϕ the phase between 0 and 1. The number of harmonics used was optimized to account for the features of the light curve while ignoring small fluctuations caused by the finite number of counts. For Swift J1822.3−1606, we used five harmonics to derive the TOAs.

Using the Fourier profile model we measured TOAs using the ML method as described in Section 2.3.2. We estimated TOA uncertainties by simulating one-hundred sets of events drawn from the pulse profile of the observation and measured an offset for each set using the ML method. The standard deviation of the simulated offset distribution was then taken as the TOA uncertainty. 4.3 Analysis & Results 69

0.05

0.00

0.05

0.10

0.05

0.00 0.05

Residuals (Phase) 0.05

0.00 0.05

55750 55800 55850 55900 55950 56000 56050 56100 56150 56200 MJD

Figure 4.2: Timing residuals of Swift J1822.3−1606. The top panel shows the residuals for the timing solution with one frequency derivative (Solution 1); see Table 4.0. The middle panel shows the residuals with the addition of a second derivative (Solution 2). The bottom panel shows the residuals with three frequency derivatives fitted. Swift WT mode data are represented by crosses, red circles denote RXTE observations and Chandra observations are shown as blue triangles.

The ML derived TOAs were consistent with those derived for Livingstone et al. (2011) using the cross-correlation method.

Timing solutions were then fit to the TOAs standard pulsar timing techniques (see Section 2.3.3) using TEMPO1. Three solutions, one with a single frequency derivative, one with two frequency derivatives and one with three frequency derivatives, are given in Table 4.0 along with the derived parameters surface dipolar magnetic field, B, spin down luminosity E˙ , and characteristic age τc (see Section 1.1.4). The top panel of Figure 4.2 shows the timing residuals with just ν and ν˙ fitted (Solution 1), the middle panel shows the residuals with ν¨ also fitted (Solution 2), and the

1http://www.atnf.csiro.au/people/pulsar/tempo/ 70 4 Post-outburst X-ray Timing Evolution of Swift J1822.3−1606

Table 4.0: Spin Parameters for Swift J1822.3−1606.

Parameter Value

Dates (Modified Julian Day) 55759 – 56161 Epoch (Modified Julian Day) 55761.0 Number of TOAs - RXTE 31 Number of TOAs - Swift 40 Number of TOAs - Chandra 5 Solution 1 - one frequency derivative ν (s−1) 0.1185154253(3) ν˙ (s−2) −9.6(3) × 10−16 RMS residuals (ms) 52.2 2 χν /ν 5.02/72 B (G) 2.43(3) × 1013 E˙ (erg s−1) 4.5(1) × 1030

τc (kyr) 1963(51) Solution 2 - two frequency derivatives ν (s−1) 0.1185154306(5) ν˙ (s−2) −2.4(1) × 10−15 ν¨ (s−3) 1.12(8) × 10−22 RMS residuals (ms) 32.2 2 χν /ν 1.94/71 B (G) 3.84(8) × 1013 E˙ (erg s−1) 1.12(5) × 1031

τc (kyr) 784(33) Solution 3 - three frequency derivatives ν (s−1) 0.1185154343(8) ν˙ (s−2) −4.3(3) × 10−15 ν¨ (s−3) 4.4(6) × 10−22 ... ν (s−4) −2.2(4) × 10−29 RMS residuals (ms) 27.5 2 χν /ν 1.44/70 B (G) 5.1(2) × 1013 E˙ (erg s−1) 2.0(2) × 1031

τc (kyr) 442(33) Errors are formal 1σ TEMPO uncertainties. 4.3 Analysis & Results 71

... bottom panel shows the residuals with ν¨ and ν also fitted (Solution 3). Solution 1 is a poor fit with

2 a χν/ν of 5.02/72. This could be due to timing noise, a common phenomenon in young neutron stars including magnetars (e.g. Dib et al., 2008; Livingstone & Kaspi, 2011). The best-fit ν and ν˙ values for Solution 1 imply a surface dipolar magnetic field of B = 2.43 0.03 × 1013 G. So-

2 lution 2, with a significant non-zero ν¨, gives a better fit with a χν/ν of 1.94/71. An F -test gives a probability of 2 × 10−16 that the addition of a second derivative does not significantly improve the fit. The surface dipolar magnetic field implied by Solution 2 is B = 3.84 0.08 × 1013 G.

... 2 Solution 3, with a significant non-zero ν , provides still a better fit than Solution 2 with a χν/ν of 1.44/70. An F -test gives a probability of 3 × 10−6 that the addition of a third derivative does not significantly improve the fit. The best-fit parameters from Solution 3 imply a surface dipolar magnetic field of B = 5.1 0.2 × 1013 G.

Note that the fit is heavily influenced by the very high quality Chandra TOAs. However, omitting them and including only TOAs from Swift and RXTE still yields significant second and third derivatives and an implied B-field of B = 4.80.2×1013 G which is consistent with that of Solution 3. The above-quoted uncertainties in B and other derived quantities in Table 4.0 reflect only the statistical uncertainties in ν and its derivatives and do not include any contributions from the simplified assumptions in the standard formulae used to determine such quantities. Note that even with the addition of highly significant second and third derivatives, Solution 3 still does not provide an adequate fit. Adding additional derivatives reduces the χ2 with marginal significance and results in larger values of the spin-down rate and hence B. For example, including a fourth

2 2 frequency derivative does not result in significant improvement in χ (χν/ν = 1.31/69) and yields B = 6.0 × 1013 G.

To search for pulsations in the ROSAT observation, we applied a barycentre correction to the

2 event arrival times, then used the Zm test (Buccheri et al., 1983) to search for pulsations. We searched in the frequency range from zero to 3.8 kHz in steps of 1.3 µHz, oversampling the independent Fourier spacing by a factor of 10; however, we found no significant signal. By simulating a pulsar with a background subtracted count rate of that of the ROSAT observation, we find that the pulsar would be undetectable even with a pulsed fraction of 100%, therefore we cannot constrain the pulsed fraction. 72 4 Post-outburst X-ray Timing Evolution of Swift J1822.3−1606

Pulse Profile Analysis

Here we search for time and energy variability in the pulse profile of Swift J1822.3−1606 using the RXTE, Swift, and Chandra observations. We created pulse profiles for each RXTE observation for energy ranges of 2 – 6 keV, 6 – 10 keV (with photons selected from only the top xenon layer), 10 – 15 keV, 15 – 20 keV, 20 – 40 keV, and 20 – 60 keV (with photons selected from all three xenon layers) using the Solution 2 ephemeris. For the Chandra data we produced pulse profiles with the energy ranges of 0.5 – 6 keV, 0.5 – 2 keV and 2 – 6 keV. For the Swift data we created 0.5 – 10 keV profiles, using only WT mode observations as PC mode does not have sufficient time resolution.

As in Livingstone et al. (2011), we searched for time variability in pulse profiles but found that all the RXTE profiles are consistent with the template in each case except for the one profile from the very first observation after the outburst (D96048-02-01-00). The difference is due primarily to the off-pulse feature which had slightly different structure between the template profile and the first RXTE observation. We therefore did not use D96048-02-01-00 in the timing analysis.

The Chandra profiles, however, do show evidence for low-level variability. Figure 4.3 shows the 0.5 – 6 keV pulse profile for each Chandra observation of Swift J1822.3−1606. We produced residuals between each pair of Chandra profiles by normalizing each profile and taking the difference between each normalized pair. A comparison of the profile residuals between each set of profiles shows that there is significant low-level evolution of the small ‘pulse’ that precedes the main pulse. The main pulse does not exhibit any significant variation. The most significant variability is that between the first (MJD 55769) and last (MJD 56036) Chandra observations.

2 The residuals between those two profiles have a χν of 16.8 for 63 degrees of freedom. We note however that these low-level variations in the smaller component likely do not have a significant impact on the timing analysis, since the TOA extraction is heavily weighted toward the unchanging primary component. Indeed our simulations of the effects of such low-level profile variations on the TOAs (see below) strongly support this conclusion.

The Swift profiles also show evidence for low-level variability. As above, we produced residu-

2 als between each pair of profiles and calculated a χν for the null hypothesis. The measured values are not consistent with a χ2 distribution, so there is significant variation between profile pairs. A 4.3 Analysis & Results 73

MJD 55769

MJD 55777

MJD 55822

Pulsed Intensity MJD 55867

MJD 56036

0.0 0.5 1.0 1.5 2.0 Phase

Figure 4.3: Pulse profiles with 64 bins from each of the four Chandra observations. The profiles are for the energy band 0.5–6 keV. 74 4 Post-outburst X-ray Timing Evolution of Swift J1822.3−1606 closer look at the residuals shows that the variation is due primarily to the small interpulse, as in the Chandra data. To investigate the dependence of pulse morphology on energy, we created a single high significance profile by aligning and summing individual profiles for each energy range. Figure 4.4 shows a summary of the results, with the summed profiles for 0.5 – 2 keV (top panel, with 64 phase bins, Chandra data), 2 – 6 keV (middle panel, with 64 phase bins, Chandra data), 6 – 10 keV and 10 – 15 keV (bottom two panels, RXTE data, with 64 and 16 phase bins, respectively). No pulsations were detected above 15 keV with the PCA. We then calculated residuals between pairs of

2 profiles, and calculated χν values of the resulting residuals in order to identify energy dependence of the pulse morphology. The most significant variability is between the 0.5 – 2 keV Chandra profile and the 6 – 10 keV RXTE profile. This can been seen in Figure 4.4 as a change in the

2 phase of the interpulse, arriving later for higher energies. For this profile pair, the χν of the residuals is 46.2 (for 28 degrees of freedom), excluding the null hypothesis. The interpulse variability causes significant differences between each pair of profiles, except the 10 – 15 keV profile, likely because of the lower statistics of the latter.

Comparison to Previously Reported Results

Rea et al. (2012) present a timing solution with a spin-down implied magnetic field of B = 2.7× 1013 G for Swift J1822.3−1606. Their data set is similar to ours, although they use proprietary XMM-Newton data whereas we use proprietary Chandra data and our data set includes seven additional Swift observations. Their timing solution is similar to our Solution 1. They, however, do not find a significant second frequency derivative. A possible cause of this discrepancy could be the difference in TOA extraction methods. Instead of using a pulse profile template, Rea et al. (2012) fit the folded profile for each observation with two sine functions with periods equal to the fundamental and the first harmonic of the pulse period. They then assign the ascending node of the fundamental sine function as the time-of-arrival of the pulse. This method was used to attempt to account for pulse-profile changes. We implemented this method and derived an additional set of TOAs to compare to our ML derived TOAs. We found that the sine-model derived TOAs provided similar timing solutions as our ML TOAs and the addition of a second frequency derivative did

2 significantly improve the fit, reducing the χν/ν from 7.91/72 to 2.72/71. The addition of a third 4.3 Analysis & Results 75

Figure 4.4: Pulse profiles for Swift J1822.3−1606 from Chandra and RXTE data for four energy ranges: 0.5–2 keV and 2–6 keV (Chandra data, 64 phase bins), 6–10 keV and 10–15 keV (RXTE data, 64 and 16 phase bins). 76 4 Post-outburst X-ray Timing Evolution of Swift J1822.3−1606

2 derivative in this case, results in only marginal improvement with a χν/ν of 2.47/70. If we limit our dataset to the Swift and RXTE data used in Rea et al. (2012), we find that the addition of a second frequency derivative is not necessary, which is consistent with their findings. In order to investigate the effects of pulse profile changes on both TOA extraction methods, we simulated pulse profiles with an unchanging (other than noise) primary component and a varying secondary component, as is observed in the pulse profile evolution of Swift J1822.3−1606. We modelled the profile using two Gaussians and modified the amplitude of the smaller Gaussian in order to vary the secondary component. We found that for both the sine-model and the ML methods, as the amplitude of the secondary component was varied, the measured phase offsets varied by less than their uncertainties. Hence we conclude that the observed pulse profile variations do not have an appreciable affect on the TOA determination, independent of which TOA extraction method was used.

4.3.3 X-ray Bursts

To search for X-ray bursts in RXTE data of Swift J1822.3−1606, we created a time series for each active PCU from GoodXenon data for each observation, selecting events in the 2 – 20 keV range (PCA channels 6–24) and from all three detection layers (the same energy range as selected for similar searches for X-ray bursts from magnetars, e.g. Göğüş et al., 2001; Gavriil et al., 2004). For the Swift observations, binned time series were made for each Good Timing Interval (GTI) in an observation. For both Swift and RXTE, time series were made at 15.625-ms, 31.25-ms, 62.5-ms and 125-ms time resolutions to provide sensitivity to bursts on a hierarchy of time scales. Bursts were identified by comparing the count rate in the ith bin to the average count rate as described in Gavriil et al. (2004) and applied in Chapter 3 to the magnetar 1E 1547.0−5408. Because the background rate of the PCA typically varies over a single observation, we calculated a local mean around the ith bin for RXTE. For Swift data, a mean was calculated for each GTI. We then compared the count rate in the ith bin to the mean. If the count rate in a single bin was larger than the local/GTI average, the probability of such a count rate occurring by chance was calculated. For RXTE data, the probability of the count rate in the corresponding bin in the other active PCUs was also calculated (whether or not the count rate in that bin was greater than the local average). If a PCU was off during the bin of interest, its probability was set to 1. We then 4.4 Discussion 77

Table 4.1: RXTE-detected X-ray Bursts from Swift J1822.3−1606.

RXTE Obsid MJD Total counts Chance Probabilitya

D96048-02-01-01 55761.53224 15 4 7.8 × 10−7 D96048-02-01-01 55761.57082 36 6 8.6 × 10−33 D96048-02-01-02 55762.49919 21 5 1.1 × 10−13 D96048-02-03-04 55777.91627 12 3 4.5 × 10−5 D96048-02-04-01 55782.53122 13 4 2.4 × 10−5 D96048-02-05-01 55789.96209 11 3 2.2 × 10−4 aThe probability of the detected signal being due to noise.

found the total probability that a burst was observed by multiplying the probabilities for each PCU

together. If the total probability of an event was Pi,tot ≤ 0.01/N (where N is the total number of time bins searched), it was flagged as a burst.

We found six bursts in RXTE data of Swift J1822.3−1606. The burst properties are summarized in Table 4.1. In the Table are the MJDs of each burst, the number of counts in a 31.25-ms bin, and the probability that the burst would occur by chance given the local mean count rate. An insufficient number of bursts was detected to perform a detailed statistical analysis of the burst properties for Swift J1822.3−1606. The bursts found were very narrow, typically only one or two 31.25-ms bins wide, and not very fluent compared to typical magnetar bursts (see Göğüş et al., 2001; Gavriil et al., 2004; Scholz & Kaspi, 2011; Lin et al., 2011). No significant changes in the long-term flux decay were observed at the times of these bursts.

Although in certain Swift observations we detected several bursts, these had much softer spectra than typical magnetar bursts and were also seen in the background region. Therefore, we do not believe they originated from Swift J1822.3−1606. No other bursts were detected in any of the Swift data.

4.4 Discussion

We have presented Swift, RXTE, Chandra observations following the discovery of Swift J1822.3−1606 during its outburst in 2011 July. We presented a phase-connected timing solution which suggests a spin-down inferred B ∼ 5 × 1013 G, the second lowest measured for a 78 4 Post-outburst X-ray Timing Evolution of Swift J1822.3−1606

magnetar thus far, although we note that timing noise may significantly contaminate this estimate. Swift J1822.3−1606 also emitted several short bursts during its period of outburst. We also analysed an archival ROSAT observation from which Esposito et al. (2011) previously reported that Swift J1822.3−1606 is detected in quiescence. We note that the source had a similar absorption

column density to the nearby Galactic H II region M17. In the following we discuss the above results.

4.4.1 Timing Behaviour

In Section 4.3.2 we presented a timing solution for Swift J1822.3−1606 with just ν and ν˙ fitted (Solution 1). However, this solution appears significantly contaminated by timing noise, a common phenomenon in pulsars. Most pulsars seem to display some unexplained ‘wandering’ in their spin evolution (Hobbs et al., 2010). A measure of the amount of timing noise displayed

8 3 by a pulsar is ∆8 and is defined as ∆8 = log[(1/6ν)|ν¨|(10 s) ] (Arzoumanian et al., 1994). ˙ Hobbs et al. (2010) measured a correlation between P and ∆8 using timing solutions for 366 rotation-powered pulsars. Magnetars are very noisy timers, generally having more timing noise,

as measured by ∆8, than those rotation-powered pulsars of similar properties (Gavriil & Kaspi,

2002; Woods et al., 2002). Here, for Swift J1822.3−1606, we measure ∆8 = 2.8 (using ν¨ from Solution 3) which is much higher than the value predicted from the correlation in Hobbs et al.

(2010) of ∼ −2. However, we caution that in general the ν¨ used to calculate ∆8 is measured 8 for a data span of 10 s, whereas our data span in much shorter. The large value of ∆8 we measured may be biased by the short span, or by unmodelled relaxation following a hypothetical glitch that could have occurred at the BAT trigger (see Chapter 5). Glitches are commonly seen to accompany radiative outbursts from magnetars (e.g. Kaspi et al., 2003; Dib et al., 2009). Due to the presence of timing noise, we take the timing and derived parameters of Solution 3 not as the ‘true’ spin-inferred values, but as a ‘best guess’ given the data thus far. As such, the uncertainties in the parameters presented, which do not take into account the effect of contamination by timing noise, likely underestimate the true uncertainties. The B-field measured by Solution 1 would be the second lowest measured for a magnetar to date, higher than only SGR 0418+5729 (Rea et al., 2010). Solution 3, although still the second lowest yet measured, gives a higher value of B that is close to that of magnetar 1E 2259+586 and 4.5 Conclusions 79

the magnetically active rotation-powered pulsar PSR J1846−0258. It is also similar to the quan-

13 tum critical field of BQED = 4.4 × 10 G(Thompson & Duncan, 1996) which has been viewed in the past of being an approximate lower limit on the magnetic field of magnetars, although SGR 0418+5729 has shown that it is not a necessary condition for magnetar-like activity.

4.4.2 Distance Estimate and Possible Association

′ As shown in the ROSAT image (Figure 4.1), the Galactic H II region M17 is located ∼20 southwest of Swift J1822.3−1606. It has a distance of 1.6 0.3 kpc (Nielbock et al., 2001) and an

21 −2 absorption column density NH = 4 1 × 10 cm (Townsley et al., 2003) which is consistent with our best-fit value of 4.53 0.08 × 1021 cm −2 (see Sections 4.3.1 and 5.3.2). This suggests that Swift J1822.3−1606 could have a comparable distance to that of M171. If so, then Swift J1822.3−1606 would be one of the closest magnetars detected thus far. The above argument does not necessitate a direct association between M17 and Swift J1822.3−1606. However, if Swift J1822.3−1606 is associated with M17, then its angular separation of 26′ from the cluster centre, where the X-ray emission peaks in the ROSAT image, implies a physical distance of 12 pc. For a pulsar age of 105 yr, this requires a space velocity of only ∼100 km s−1 (corresponding to a proper motion of 0′′.016 yr−1). This would make a direct proper motion measurement difficult. From timing, the characteristic age appears to be larger than 105 yr which would further reduce the implied proper motion. On the other hand, characteristic ages can be large overestimates of the true age. However, even if the true age were as low as 104 yr, the proper motion would be difficult to measure even with Chandra. Additionally, if the magnetar was born near an edge of the cluster, the angular separation from its birthplace could be larger or smaller by up to ∼ 10′.

4.5 Conclusions

We have presented an analysis of the post-outburst timing behaviour of Swift J1822.3−1606, following its discovery on 2011 July 14. We estimate the surface dipolar component of the B- field to be ∼ 5 × 1013 G, slightly higher than that inferred in Livingstone et al. (2011). However,

1While there are two molecular clouds surrounding M17 (Wilson et al., 2003), they are confined to the north and west,

such that they should not contribute to the NH of either M17 or Swift J1822.3−1606. 80 4 Post-outburst X-ray Timing Evolution of Swift J1822.3−1606

as this measurement is contaminated by timing noise, the true value of the magnetic field could be well outside of the uncertainties quoted in Table 4.0. Further monitoring of Swift J1822.3−1606 as it fades following the outburst will allow us to better account for the timing noise and measure more robust timing parameters (see Chapter 5). The quiescent flux of Swift J1822.3−1606 measured using a 1993 ROSAT observation of M17 was found to be roughly three orders of magnitude lower than the peak flux during the outburst.

Based on the similarity in NH to that of the H II region M17, we argue for a source distance of 1.6 0.3 kpc. If so, then this source would be one of the closest magnetars yet known. 5 The Long-term Post-outburst Behaviour of Magnetar Swift J1822.3−1606

The work presented in this chapter has previously been published in the article: Scholz et al., 2014, The Long-term Post-outburst Spin Down and Flux Relaxation of Magnetar Swift J1822.3−1606, Astrophysical Journal, 786, 62. This presented a similar analysis but with over a year of additional observations compared to what was presented in Scholz et al. (2012), the basis for the previous chapter. Chapter 5 resolves the ambiguity in the timing solutions found in Scholz et al. (2012, and presented in Chapter 4) and Rea et al. (2012). The text of this chapter has been adapted from Scholz et al. (2014b), but also includes some of the flux and spectral results from Scholz et al. (2012). Note that the work on models of thermal relaxation presented in Section 5.4.3 was preformed by Dr. Andrew Cumming and he was the primary author of that section.

5.1 Introduction

The magnetar Swift J1822.3−1606, was discovered when an X-ray burst was detected by the Swift Burst Alert Telescope (BAT) on 2011 July 14 (Cummings et al., 2011). It was found to be a pulsar when an 8.43-s periodicity was identified using RXTE (Göğüş et al., 2011). Livingstone et al. (2011) reported on initial timing and spectroscopic results from Swift, RXTE, and Chandra and showed that the flux of the source was decaying from its peak at the onset of the outburst. A spin-down rate of P˙ = 2.54 × 10−13 was measured which implied a surface dipolar magnetic field of B = 4.7 × 1013 G. The characteristic post-outburst decay and high magnetic field value confirmed that Swift J1822.3−1606 was a new magnetar that had experienced an outburst on 2011 July 14. Subsequent studies of the post-outburst timing evolution of Swift J1822.3−1606 found that the spin-inferred magnetic field may be lower than that measured in Livingstone et al. (2011). Rea et al. (2012) presented a timing solution in which the spin-inferred magnetic field was measured to be 2.7×1013 G. In Chapter 4 several timing solutions were fit to the post-outburst Swift, RXTE,

81 82 5 The Long-term Post-outburst Behaviour of Magnetar Swift J1822.3−1606

and Chandra observations and it was found that a model with only P and P˙ (similar to what was presented in Rea et al., 2012) was not a good fit to the data and that the addition of higher-order period derivatives improved the fit. The best fit utilized three significant period derivatives and the measured P˙ in that case implied a spin-inferred B-field of ∼ 5 × 1013 G. There has thus been some ambiguity in the best timing solution, and parameters, like B, derived from those solutions for Swift J1822.3−1606.

Nearly every magnetar outburst has been accompanied by a change in the timing properties of the pulsar (Dib & Kaspi, 2014). The most common timing change that is observed is a spin-up glitch contemporaneous with the outburst onset. Following a glitch, the spin period of a magnetar can exponentially recover, although sometimes only partially, to its pre-glitch value. In some cases the recovery has overcompensated for the spin-up glitch and the net effect is a spin down (Livingstone et al., 2010; Gavriil et al., 2011). In the cases where a spin-up glitch has not been observed, other timing changes and anomalies have been noted, such as enhanced spin down and an increase in timing noise (e.g. Dib et al., 2009, 2012).

The flux and spectral evolution of Swift J1822.3−1606 was also presented in Rea et al. (2012) and Scholz et al. (2012). They found that the flux decayed rapidly following the outburst and that the spectral parameters softened. A correlation between the X-ray hardness and flux is generally expected in the twisted-magnetosphere model (Thompson et al., 2002; Lyutikov & Gavriil, 2006; Beloborodov, 2009) and observed in many other magnetars (e.g. Israel et al., 2007; Scholz & Kaspi, 2011). The magnetospheric twist model also makes specific predictions for the flux and spectral evolution. In particular the twist relaxation time scale depends in a well defined way on the stellar magnetic moment, the electric voltage sustaining magnetospheric discharge, as well as on the emitting area, and can be tested if these parameters are constrained (Beloborodov, 2009). Also, the thermal luminosity is predicted to vary as the emitting area squared, which can also be tested. On the other hand, it was found that a model of the thermal relaxation of the magnetar crust reproduced the observed luminosity decay well. Both Rea et al. (2012) and Scholz et al. (2012) reported that, in these models, the late time decay was not well constrained and depended on parameters of the inner crust. X-ray flux observations at late times, when the source is closer to quiescence, could better constrain the models and thus implied parameters of the neutron star 5.2 Observations 83

crust in this picture.

In this paper we present updated timing solutions for Swift J1822.3−1606 with a baseline that is over twice as long as in Chapter 4, using an additional ∼ 400 days of data from the Swift X- ray Telescope (XRT). From this we attempt to resolve the previous ambiguity regarding the true value of the spin-down rate and hence the magnetic field. We also present the up-to-date flux and spectral evolution. We discuss how the timing and spectral evolutions have changed since previous studies and the implications of the new results in the context of the magnetar model.

5.2 Observations

5.2.1 Swift Observations

Since the 2011 July 14 (MJD 55756) outburst of Swift J1822.3−1606, Swift/XRT (Burrows et al., 2005) has been used to obtain 61 observations of the source for a total exposure time of 297 ks. The exposure times for each individual observation ranged from 0.5 to 18 ks. A list of these observations can be found by querying NASA’s HEASARC archive1. Data were collected in two different modes, Photon Counting (PC) and Windowed Timing (WT; for more information see Section 2.1.3). As the PC mode time resolution is insufficient for our timing analysis, those data are used only for our spectral work.

For each observation, the unfiltered Level 1 data were downloaded from the Swift quicklook archive2. The standard XRT data reduction script, xrtpipeline, was then run using the source position of RA= 18h 22m 18s, Dec= −16◦ 04′ 26′′.8 (Pagani et al., 2011) and the best available spacecraft attitude file. Events were then reduced to the solar-system barycenter using the above source position. Source and background events were extracted using the following regions: for WT mode, a 30-pixel long strip centered on the source was used to extract the source events and a 50-pixel long strip positioned away from the source was used to extract the background events. For PC mode, a circular region with radius 20 pixels was used for the source region and an annulus with inner radius 40 pixels and outer radius 60 pixels was used as the background region. For the first (00032033001) and second (00032033017) PC mode observation, circular regions with

1http://heasarc.gsfc.nasa.gov/ 2http://swift.gsfc.nasa.gov/cgi-bin/sdc/ql 84 5 The Long-term Post-outburst Behaviour of Magnetar Swift J1822.3−1606

radii of 6 and 2 pixels, respectively, were excluded to avoid pileup. For WT mode data, exposure maps, spectra, and ancillary response files were created for each individual orbit. The spectra and ancillary response files were then summed to create a spectrum for each observation. For the PC mode data, exposure maps, spectra and ancillary response files were created on a per observation basis. We used response files for spectral fitting from the 20130313 CALDB and version 6.13 of HEASOFT. In Swift/XRT observations, there are columns of bad pixels that can disrupt the source PSF. Orbits were not used in an observation if the bad columns were found to be within 3 pixels of the source position.

5.2.2 RXTE and Chandra Observations

We downloaded 32 RXTE observations from the HEASARC archive. These data spanned the MJD range from 55758 to 55893 (2011 July 16 to 2011 Nov 28), for a total of 174 ks of integration time. The data were collected in GoodXenon mode which records each event with 1-µs time resolution. Following the outburst, our ToO program with the Chandra X-ray Observatory was triggered. Five ACIS Continuous Clocking (CC) mode (see Section 2.1.4) observations were obtained between MJD 55769 and 56036 (2011 July 27 and 2012 April 19), with exposures ranging from 10 to 20 ks. The RXTE and Chandra sets of observations are identical to those used in Chapter 4 and are summarized in Table 4.1.

5.3 Analysis & Results

5.3.1 Timing

For each Swift and Chandra observation, a pulse time of arrival was extracted using the maximum likelihood method described in Section 2.3.2. RXTE TOAs were measured using cross-correlation with a template profile, as the maximum likelihood method is too computationally expensive for these data due to the high number of counts. We then fit timing solutions to the TOAs using the TEMPO1 pulsar timing software package.

1http://tempo.sourceforge.net 5.3 Analysis & Results 85

Year 2011.5 2012.0 2012.5 2013.0 2013.5 2014.0 0.10

0.05

0.00

0.05

0.10

0.05 Residuals (Phase) 0.00

0.05

0.10

0 200 400 600 800 Days from BAT Trigger (MJD 55756)

Figure 5.1: Timing residuals of Swift J1822.3−1606. The top panel shows the solution in Table 5.1 before the glitch recovery is fit. The bottom panel shows the residuals for the solution with the glitch recovery fit out. In both panels, black crosses represent Swift observations, red circles indicate RXTE observations, and Chandra data are shown as blue triangles. The gray band represents the data that were excluded when the long-term spin down was fit prior to attempting to fit the glitch recovery. The vertical dotted line shows where the longest previous published timing solution ended (Chapter 4). 86 5 The Long-term Post-outburst Behaviour of Magnetar Swift J1822.3−1606

We first fit a timing solution that included only a frequency and frequency derivative as was done by Rea et al. (2012) and for Solution 1 in Chapter 4 (Table 4.0). The TOAs were fitted to a standard Taylor series model (see Section 2.3.3) in which the phase ϕ at time t is given by

1 ϕ(t) = ϕ + ν (t − t ) + ν˙ (t − t )2 , (5.1) 0 0 0 2 0 0 where ϕ0, ν0, and ν˙0 are the phase, frequency, and frequency derivative of the pulsar at the reference epoch t0. This single frequency derivative model did not fit the data well, with reduced 2 χν = 7.38 for 83 degrees of freedom. In order to be sensitive to only the long-term spin down of the pulsar, we then fit the same model to all TOAs from observations taken later than approximately two months (MJD ≥ 55800) from the onset of the outburst. The two month timescale was chosen to be longer than the time that most magnetars are observed to take to return to their

2 pre-outburst spin-down rate. We found that this provided an acceptable fit (χν/ν = 1.19/41), and that it was much improved from the ν and ν˙ fit to the entire data set. We noted that the excluded TOAs appeared to form an exponential decay in the phase residuals (top-panel of Figure 5.1). We therefore added an exponential glitch recovery to our model with the glitch epoch at the time of the Swift/BAT burst trigger (MJD 55756). This is represented by

 ( )  − t−tg  τ ϕ(t) + ∆νdτd 1 − e d t ≥ tg ϕexp(t) =  (5.2)  ϕ(t) t < tg ,

where ϕ(t) is given in Equation 5.1, ∆νd is the amplitude of the frequency decay, τd is the decay timescale, and tg is the glitch epoch. The glitch recovery model provided an excellent fit with 2 χν/ν = 0.97/81. Table 5.1 shows the results of this fit and the bottom panel of Figure 5.1 shows the best-fit residuals. In addition to the exponential recovery model, we tried some alternative models. We attempted to fit the residuals with higher derivatives similar to Scholz et al. (2012). We found that in order

2 to produce a fit with a similar χν, five frequency derivatives were needed. However, since the long-term spin down is well fit by the simpler ν and ν˙ timing solution, and extra derivatives are not needed if the first two months following the outburst are ignored, it is clear that the multi- derivative solution is not representative of the true spin down of the pulsar and was only an artifact 5.3 Analysis & Results 87

Table 5.1: Timing Parameters for Swift J1822.3−1606.

Parameter Value

Observation Dates 16 July 2011 - 04 Nov 2013 Dates (MJD) 55758 − 56600 Epoch (MJD) 55761 Number of TOAs 86 ν (s−1) 0.1185154135(9) ν˙ (s−2) −3.0(3) × 10−16 Post-Outburst Glitch Recovery Glitch (Burst) Epoch (MJD) 56756.000 −1 −8 ∆νd (s ) 2.7(1) × 10

τd (days) 40(6) RMS residuals (ms) 24.3 2 χν /ν 0.97/81 Derived Parameters B (G) 1.35(6) × 1013 E˙ (erg s−1) 1.4(1) × 1030

τc (kyr) 6300(600) Numbers in parentheses are TEMPO reported 1σ uncertainties. 88 5 The Long-term Post-outburst Behaviour of Magnetar Swift J1822.3−1606

due to the contamination of the enhanced spin down at early times. We also compared the two models by fitting them to all of the data excluding the last three months and seeing how well they predicted the excluded TOAs. The single-derivative glitch recovery model predicted the last three months within 5% in phase, i.e. comparable to the TOA errors, and the measured parameters were fully consistent with the fit to the whole data set. The multi-derivative model, however, did not predict the later data with the last three months of TOAs wandering up to 30% in phase. We also attempted to fit the post-outburst TOAs with a change in ν at MJD 55900 as the timing residuals from the simple ν and ν˙ fit indicated a deviation in the rotation from the long-term spin down prior to that epoch. This did not provide an acceptable fit, so we also tried a change in ν˙.

2 This gave a slightly higher χν/ν (1.22/81) than in the exponential recovery model. Aside from the poorer fit, this latter solution seems contrived given the absence of precedence for such behaviour post-outburst in magnetars. As discussed in Section 5.4.1, there are many examples of glitches accompanied by exponential recoveries in magnetar outbursts. For these and the aforementioned reasons, we conclude that the glitch recovery model is by far the most likely. Although we model the post-glitch spin down with a glitch recovery, we cannot conclusively say that a glitch occurred. This is because timing observations of the source pre-outburst are not available. However, if the pre-detection spin-down frequency was the same as its long-term post- outburst value (i.e. the exponential recovery perfectly compensated for the spin-up glitch), the fractional magnitude of the hypothetical glitch would be ∆ν/ν = (2.3 0.1) × 10−7 which is in the typical range of glitch magnitudes observed from magnetars (∆ν/ν ∼ 10−7 − 10−5; e.g. Dib & Kaspi, 2014). An under-recovery wound imply a larger glitch, whereas an over-recovery implies a smaller glitch.

5.3.2 Flux and Spectral Evolution

We fit a photoelectrically absorbed blackbody plus power-law model to each Swift and Chandra spectrum using XSPEC1 v12.8. We used the XSPEC phabs model with abundances from An- ders & Grevesse (1989) and photoelectric cross sections from Balucinska-Church & McCammon

(1992). The hydrogen column density, NH, was measured from a joint spectral fit of the early (first ∼ 400 days) Chandra and Swift data when the source was bright to be 4.53 × 1021 cm−2.

1http://xspec.gfsc.nasa.gov 5.3 Analysis & Results 89

For observations later than MJD 55975, sets of observations nearby in time were fit with joint kT and Γ. This was done as the spectral parameters were not well constrained for individual observations and for each set kT and Γ were consistent from observation to observation. The flux was left free to vary from observation to observation as significant flux evolution was still

2 present. The reduced χν values from the spectral fits ranged from 0.81 to 1.5. Figure 5.2 shows the results of the spectral fits. The flux is seen to decay following the outburst and the kT and Γ spectral parameters soften. The blackbody temperature, kT , remained approximately constant at ∼ 0.75 keV, or perhaps even increased, in the first 10 days following the outburst onset at the BAT trigger. It then decreased to ∼ 0.6 keV between 10–100 days from the trigger. Since MJD 55900, the blackbody temperature has remained roughly constant. The photon-index, Γ appears to have increased (softened) following the outburst. This is most evident from the Chandra observations where the photon-index softened from ∼ 2.0 to ∼ 2.5 between 10 and 300 days from the trigger. The bottom panel of Figure 5.2 shows the ratio between the blackbody and power-law components of the spectral model. The ratio is of order unity, i.e. the blackbody and power-law components contribute about the same amount of flux in the 1–10 keV spectral range. This ratio makes sense in the context of the magnetar model where surface thermal photons are scattered to higher energies by the high magnetic field (e.g. Lyutikov & Gavriil, 2006). In order to characterize the flux relaxation we fit exponential decay models to the fluxes measured from the X-ray spectra. We first attempted a double-exponential decay model,

−(t−t0)/τ1 −(t−t0)/τ2 F (t) = F1 exp +F2 exp +Fq. (5.3)

2 This did not provide an acceptable fit, as the reduced χν/ν was 2.26/56. So, we then fitted a triple exponential model,

−(t−t0)/τ1 −(t−t0)/τ2 −(t−t0)/τ3 F (t) = F1 exp +F2 exp +F3 exp +Fq. (5.4)

In both cases, t is the time in MJD, t0 is the MJD of the BAT trigger, Fi are the absorbed 1–

10 keV fluxes of each component at t0, and τi are the decay timescales in days of each exponential −14 −2 −1 component. Fq is the quiescent 1–10 keV flux, 3×10 erg cm s , implied from the 0.2–2.4 90 5 The Long-term Post-outburst Behaviour of Magnetar Swift J1822.3−1606

-10 )

1 10

2 -11

Empirical models 10-12 Double-exponential Decay

(ergs cm -13 Triple-exponential Decay

1-10 keV Abs. Flux 10

-10 )

1 10

2 -11

Thermal Relaxation models 10-12 Cooling of 15% of surface at magnetic pole

(ergs cm -13 Cooling of entire surface

1-10 keV Abs. Flux 10 3.0

¡ 2.5 2.0 1.5 0.75

kT 0.65 (keV) 0.55 2 1 PL Flux BB Flux 0 100 101 102 103 Days from BAT Trigger (MJD 55756)

Figure 5.2: Spectral evolution of Swift J1822.3−1606. The top two panels both show the 1– 10 keV flux evolution, but are fitted with two different sets of models. Black crosses denote Swift WT mode observations, open circles represent Swift PC mode data, and blue triangles show Chandra observations. In the spectral fits, for some observations kT and Γ are fit jointly in sets that are nearby in time, and so are represented by a single point in their respective plots. The horizontal error bars on kT and Γ respresent the extent in time of such sets. The bottom panel shows the ratio of the 1–10 keV unabsorbed fluxes from the power-law (PL) and blackbody (BB) components of the spectral fit. 5.4 Discussion 91

Table 5.2: Empirical Models of the Flux Evolution of Swift J1822.3−1606.

2 Model τ1 (days) τ2 (days) τ3 (days) χν /ν Double Exponential 16.8 0.4 260 10 ... 2.26/56 Triple Exponential 6 1 27 2 320 20 0.95/54

keV flux and spectral model measured from a 1993 ROSAT observation (Chapter 4). The triple

2 exponential model provides a much better, and acceptable, fit with χν/ν = 0.95/54. The best-fit exponential decay timescales for both models are listed in Table 5.2.

5.4 Discussion

We have presented the results of RXTE, Chandra, and Swift/XRT observations of Swift J1822.3−1606 spanning a baseline of over two and a half years. This has allowed us to better measure the pulsar’s timing and spectral evolution. Importantly, we have presented a more straightforward timing model than that in Chapter 4 as well as evidence for a glitch at the epoch of the outburst onset. Our new timing model implies a long-term spin-down rate that is significantly lower than previous estimates. We have also updated the post-outburst flux and spectral evolution of Swift J1822.3−1606 and show that it is well fit by a triple-exponential model that is decaying to the ROSAT measured quiescent flux. Below we discuss the implications of these findings.

5.4.1 Post-outburst Spin-down Behaviour

Previous studies of the timing evolution of Swift J1822.3−1606 did not find a consistent timing solution. Livingstone et al. (2011) first presented a timing solution with just ν and ν˙ fit to the first ∼ 80 days following the outburst and measured B = 4.7 × 1013 G. This was followed by Rea et al. (2012) who, with 275 days of observations, found a lower value of B = 2.7 × 1013 G. Both studies found that there was an unmodelled trend in their residuals, possibly attributed to timing noise. In Chapter 4 we attempted to fit the trend with higher frequency derivatives. We found that as higher derivatives were added, the value of B increased. The best fit was found with three frequency derivatives (Solution 3) and B = 5.1 × 1013 G, larger than the Rea et al. (2012) estimate. 92 5 The Long-term Post-outburst Behaviour of Magnetar Swift J1822.3−1606

Here we find that in the initial ∼ 100 days following the onset of the outburst, the timing behaviour of Swift J1822.3−1606 was not representative of the long-term spin down of the pulsar. Specifically, it was spinning down more rapidly, likely due to a recovery from a glitch. By using the data from the initial post-outburst epochs, the previous studies measured higher spin-down rates because of contamination from the early enhanced spin down. This is shown by the fact, pointed out by Tong & Xu (2013), that as the solutions were derived from longer timing baselines, the measured spin-down rate became lower.

Glitches in pulsars and magnetars have been known to show exponential recoveries. Magne- tars 1RXS J170849.0−400910 and 1E 2259+586 showed clear exponential recoveries following their 2001 and 2002 glitches (Kaspi & Gavriil, 2003; Woods et al., 2004) and 4U 0142+61 showed a slight over-recovery following its 2006 glitch (Gavriil et al., 2011). The magnetically active rotation-powered pulsar PSR J1846−0258 showed a spin-up glitch with a large over-recovery (Livingstone et al., 2010). The decay timescale measured for Swift J1822.3−1606 (40 days; see Table 5.1) is comparable to the analogous timescale for the 2001 glitch of 1RXS J170849.0−400910 (43 days) and somewhat longer than was observed in 1E 2259+586 (17 days) and 4U 0142+61 (12–17 days; Dib & Kaspi, 2014). We note that in the single well sampled anti-glitch, during the 2012 outburst of magnetar 1E 2259+586, no exponential recovery was seen (Archibald et al., 2013). Without knowledge of the pre-outburst spin down of Swift J1822.3−1606, we cannot conclusively argue for the occurrence of a glitch, but given the exponential form of the post- outburst spin down and the prominence of exponential glitch recoveries in other magnetars, it seems extremely plausible.

However, the occurrence of enhanced spin down without the occurrence of a glitch following a magnetar outburst has also been observed. Following the the 2002 outburst of 1E 1048.1−5937 no glitch was observed and the magnitude of ν˙ increased as the pulsed flux decreased (Dib et al., 2009). The magnetars 1E 1547.0−5408 and SGR 1745−2900 showed similar behaviour after their 2008 and 2013 outbursts, respectively (Dib et al., 2012; Kaspi et al., 2014). The same behaviour is clearly not present in the post-outburst timing of Swift J1822.3−1606. In its case, as the flux of the magnetar decreased, the magnitude of ν˙ decayed. Thus, the post- outburst timing behaviour of Swift J1822.3−1606 looks like a glitch recovery as observed from 5.4 Discussion 93

1RXS J170849.0−400910, 1E 2259+586, and 4U 0142+61 and does not resemble the more unusual enhanced spin-down behaviour seen in 1E 1048.1−5937 and 1E 1547.0−5408.

The enhanced spin-down rate following the outburst of Swift J1822.3−1606 was a factor of several larger than its long-term spin-down rate. The instantaneous post-glitch spin-down rate

at the glitch epoch for an exponential recovery can be quantified by ∆νd/τ (Dib et al., 2008).

For Swift J1822.3−1606, this quantity is ∆νd/τ = (26 5)ν ˙ where ν˙ is the value we report in Table 1. This is higher than in previous magnetar glitches, the next highest being the 2002 glitch of

1E 2259+586 with a ∆νd/τ = (8.20.6)ν ˙. For radio pulsars, the post-glitch recoveries usually result in spin-down enhancements of only a few percent (e.g. Flanagan, 1990; Wong et al., 2001).

Since many magnetars are observed frequently after their outburst, but are not followed up with long-term timing campaigns as has been Swift J1822.3−1606, it is possible that the measurements of their spin-down rates are not representative of their long-term timing evolution. For example, the magnetic field of CXOU J164710.2−455216 was measured to be ∼ 1 × 1014 G using phase- coherent timing in the first 100-200 days following its 2006 outburst (Israel et al., 2007; Woods et al., 2011), but An et al. (2013) placed an upper limit on the long-term spin-down rate and hence inferred magnetic field of < 7 × 1013 G using a timing baseline of ∼ 6 years.

The magnetic field measured from the long-term spin down of Swift J1822.3−1606 is 1.35 × 1013 G. This is the second lowest spin-down inferred magnetar dipolar magnetic field and is about a factor of two higher than the lowest measured value, 6.1×1012 G of SGR 0418+5729 (Rea et al., 2013). However, since pulsar timing is only sensitive to the surface dipolar component of the field, the true magnetic field of the magnetar could be significantly higher than the value measured from pulsar timing if the toroidal component is much higher than the poloidal component or if the polodial field has significant multipolar contributions (Thompson & Duncan, 1996).

The exponential glitch recovery model fit here is an empirical model that does not address the physical origin of the behaviour. Because of the prevalence of exponential recoveries following spin-up glitches in pulsars and magnetars, we view it as a recovery following a glitch. How- ever, more generally, it is a exponentially decreasing spin frequency that follows an outburst. Such an exponentially decreasing spin frequency requires an exponentially decreasing torque on the neutron star. Assuming the pre-outburst long-term spin-down rate was similar to the current 94 5 The Long-term Post-outburst Behaviour of Magnetar Swift J1822.3−1606

long-term rate, an increase of torque near the epoch of the outburst is also required. This change in torque could be provided by an internal source such as a sudden spin-up torque, followed by a relaxation, originating from the interior superfluid transferring angular momentum to the solid outer crust (Anderson & Itoh, 1975), i.e. the standard model of pulsar glitches. The torque could also be provided by an external source, such as a particle wind or magnetospheric untwisting (Beloborodov, 2009). The magnetar wind-braking model of Tong et al. (2013), applied to Swift J1822.3−1606 by Tong & Xu (2013), theorizes that the change in spin-down frequencies observed in magnetars is due to a particle wind with a variable luminosity. Such a particle wind may be expected to cause a nebula around the magnetar. Tong et al. (2013) predict a particle luminosity from such a wind comparable to that of the X-ray luminosity of the magnetar. In Chapter 4 we detected no evidence for a deviation from a point source in a 2 ks Chandra High Resolution Camera (HRC) image taken on 2011 July 28, two weeks after the outburst. From this same observation, here we place an upper limit on the 1–10 keV X-ray flux of an outflow of 2% of the source flux at this epoch. The limit was placed using Chandra marx1 simulations assuming a 1.5′′ (the angular extent of a putative nebula expanding at c at a distance of 1.6 kpc) circular nebula with a Crab-like spectrum. As argued by Scholz et al. (2014a, and see Chapter 6), the presence of radiatively quiet glitches in magnetars favours an internal mechanism for their glitches. From an external mechanism we would expect observable external changes, such as a flux increase or pulse profile changes. Al- though this is certainly seen in the case of the 2011 outburst of Swift J1822.3−1606, if we assume that all magnetar glitches (and thus the exponential recoveries that sometimes follow) originate from the same physical mechanism, then that mechanism must be able to produce a radiatively quiet event. Hence, we favour an internal mechanism for magnetar glitches, and therefore for the exponential recovery seen here.

5.4.2 Flux and spectral evolution

In the twisted-magnetosphere model of magnetars, the thermal emission is thought to originate from heating within the star, caused by the decay of strong internal magnetic fields (Thomp- son et al., 2002). Currents in the magnetosphere, which are due to twists in the magnetic field

1http://space.mit.edu/ASC/MARX/ 5.4 Discussion 95

1.0

0.8

0.6

0.4 4-10 keV / 2-4 Hardness Ratio

10-11 10-10 2-10 keV Unabsorbed Flux

Figure 5.3: Spectral hardness as a function of unabsorbed flux for Swift J1822.3−1606. The Swift WT mode observations are shown as grey crosses, the Swift PC mode data are denoted by open circles, and the blue triangles respresent the Chandra observations.

(Thompson et al., 2002; Beloborodov, 2009), scatter the thermal surface photons to higher energies. In addition to scattering, the currents provide a source of surface heating in the form of a return current. The flux increase that accompanies a magnetar outburst is theorized to be due a rapid heating which could originate from magnetospheric, internal, or crustal reconfiguration of the neutron star. This release may result in a significant increase in the surface temperature, in the return-current heating, and in the twisting of the magnetic field. Thus, an increase in flux due to an internal heat release should result in an increase of the hardness of the emission. This hardness-flux correlation is in agreement with observations of several magnetars (Gotthelf & Halpern, 2007a; Tam et al., 2008; Zhu et al., 2008; Scholz & Kaspi, 2011).

In Chapter 3 the hardness-flux correlation for magnetar outbursts was explored by comparing the relation between fractional increase in 4–10/2–4 keV hardness ratio and fractional increase in 96 5 The Long-term Post-outburst Behaviour of Magnetar Swift J1822.3−1606

2–10 keV unabsorbed flux for six different outbursts in four different magnetars (Figure 3.9). We present a similar plot here in Figure 5.3 for Swift J1822.3−1606. Here, however, the hardnesses and fluxes are absolute quantities and not fractional increases over quiescent values as in Scholz & Kaspi (2011), as there is no quiescent observation of Swift J1822.3−1606 with the appropriate spectral coverage (ROSAT is only sensitive to X-rays between 0.1 and 2 keV). Figure 5.3 shows that Swift J1822.3−1606 softens as the flux decreases following the outburst and so is in broad agreement with the hardness-flux correlation observed in other magnetar outbursts. This spectral softening with flux decline is clear also in Figure 5.2, where kT declines and the power-law index Γ increases as the flux drops.

Magnetars in Quiescence

The quiescent flux of Swift J1822.3−1606 measured by ROSAT in 1993 is about 3 orders of magnitude lower than the peak flux measured following the outburst (see Section 4.3.1). Such large flux variations have been observed in several other magnetars (e.g. 1E 1547−5408, XTE J1810−197, AX J1845−0258; Ibrahim et al. 2004; Gotthelf et al. 2004; Tam et al. 2006; Scholz & Kaspi 2011; Bernardini et al. 2011). Other magnetars, such as 1E 1841−045 (Zhu & Kaspi, 2010; Lin et al., 2011), 4U 0142+61 (Gonzalez et al., 2010), and 1RXS J170849.0−400910 (den Hartog et al., 2008) have not exhibited large flux variations, but are much brighter in quiescence than are the magnetars with large outbursts. The cause of this difference is unclear. Pons & Rea (2012) suggest that there is a maximum luminosity that can be reached by a magnetar during an outburst due to neutrino cooling dominating at high crust temperatures. This helps to explain the differences in outburst magnitudes, but does not address the wide range of quiescent luminosities. Case in point, the magnetar 1E 2259+586 has spin properties that are likely quite similar to those of Swift J1822.3−1606 but has a much higher quiescent luminosity. The magnetic field measured from spin-down for 1E 2259+586 is 5.9×1013 G(Gavriil & Kaspi, 2002), close to B = 5.1×1013 G for Swift J1822.3−1606 as estimated by our Solution 3. 1E 2259+586 also went into a period of outburst on 2002 June 18 where the flux increased by a factor of ∼> 20 (Woods et al., 2004). However, in quiescence, 1E 2259+586 is much brighter than Swift J1822.3−1606 with a

34 −1 31 −1 quiescent 2–10 keV luminosity of 2×10 erg s (Zhu et al., 2008) compared to ∼< 10 erg s for Swift J1822.3−1606. 5.4 Discussion 97

One possibility is that the ‘true’ magnetic fields of the more luminous magnetars are higher than those of the fainter magnetars. The spin-down of the neutron star is only sensitive to the dipole component of the magnetic field. If the magnetic field had significant components in higher multipoles or a toroidal component (Thompson & Duncan, 1996; Pons & Perna, 2011), the true magnetic field could be higher. Another possibility is that neutrino cooling in the core is setting a long-term luminosity limit, and that the neutrino cooling properties of the stars are different, e.g. due to different masses. For example, consider first the case where the neutrino emission in the core is due to the modified ∼ 20 −3 −1 8 URCA process, with an emissivity ϵν 10 erg cm s T9 (Yakovlev et al., 2003). If we take the magnetic-field decay time to be τ = 104 yrs, then the luminosity from magnetic field

2 3 34 −1 14 decay is roughly LB = (B /8π)(4πR /3)(1/τ) = 10 erg s for B = 10 G. Balancing 3 8 this with the neutrino losses Lν = (4πR /3)ϵν, we find a core temperature Tc = 2.5×10 K or, using the core temperature-luminosity relation from Potekhin & Yakovlev (2001), a luminosity L ≈ 4 × 1033 erg s−1. On the other hand, if the neutrino emission is by the direct URCA ∼ 26 −3 −1 6 process, with ϵν 10 erg cm s T9 (Yakovlev et al., 2003), we find a core temperature 7 31 −1 Tc = 1.5 × 10 K, corresponding to a surface luminosity of ≈ 2 × 10 erg s . This shows

that we might reasonably expect a factor of ∼> 200 in luminosity between different stars if one has slow neutrino emission in the core, and the other fast, for example if the mass of one of the stars is large enough for direct URCA reactions to occur in the core. Even in the case where external currents dominate the quiescent luminosity, thermal emission from the neutron star provides a baseline luminosity, so that the low quiescent luminosity of Swift J1822.3−1606 suggests a low core temperature which implies either a low heating rate or efficient neutrino emission.

5.4.3 Models of Flux Relaxation

Thermal Relaxation of the Neutron Star Crust In addition to the empirical model fits in Section 5.3.2, we fit the light curve with a model of crustal cooling. In these models, the neutron star crust is heated by a sudden deposition of energy, and the subsequent thermal relaxation and cooling is followed by integrating the thermal diffusion equation in time. Rea et al. (2012) were able to fit the first 100 days of the light curve by depositing ∼ 1042 erg in the outer crust at densities ∼ 109–1010 g cm−3. The late time lightcurve 98 5 The Long-term Post-outburst Behaviour of Magnetar Swift J1822.3−1606

is sensitive to a number of physics inputs such as the neutron contribution to the heat capacity near neutron drip, thermal conductivity of the inner crust, and angular distribution of the heating

around the star. We investigate this here, utilising the new flux measurements at times ∼> 500 days after outburst.

We follow the evolution of the crust temperature profile by integrating the thermal diffusion equation. The calculation and microphysics follow Brown & Cumming (2009) who studied tran- siently accreting neutron stars, but with the effects of strong magnetic fields on the thermal conductivity included (Potekhin et al., 1999). To take into account the effect of the outer envelope of the neutron star, we have reproduced the detailed magnetized envelope models of Potekhin & Yakovlev (2001), rather than use their analytic flux-temperature relations, which are strictly correct only in the high density isothermal part of the crust. This allows us to match the envelope to the correct density at the top of our numerical grid (we typically follow the temperature on a grid in density extending from the crust/core boundary to ≈ 6 × 108 g cm−3). Because the temperature profile is not fully isothermal at these depths (deeper in the crust, the temperature profile is close to isothermal in steady-state because of the large thermal conductivity), using the analytic flux-temperature relation leads to a tens of percent underestimate of the flux and corresponding overestimate of the energy deposited. Second, we have improved our treatment of the magnetic field geometry. We calculate the cooling curve at the magnetic pole, where the magnetic field is radial, and then rescale that light curve appropriately for each local patch on the neutron star surface given the local magnetic field direction (a time-dependent extension of Greenstein & Hartke, 1983).

Two models that reproduce the first 100 days of the light curve are shown in the second panel

of Figure 5.2. We assume a distance of 1.6 kpc, neutron star mass 1.6 M⊙, radius R = 11.2 km, core temperature 1.5 × 107 K, and magnetic field strength at the pole 1014 G. The mass and radius correspond to the particular equation of state chosen by Brown & Cumming (2009). A different choice of mass and radius primarily changes the cooling timescale by a factor of 1/g2, where g is the gravity, because the crust thickness is ∝ 1/g. The core temperature is chosen so that the luminosity at late times is 2 × 1031 erg s−1. We then vary the energy injected and depth of heating to match the lightcurve. In the models shown in Figure 5.2, we deposit ≈ 3 × 1042 erg 5.4 Discussion 99

in the outer crust down to a density of ≈ 1011 g cm−3, either over the whole surface assuming a dipole field geometry or over 15% of the neutron star surface at the magnetic pole. Both models predict the same flux evolution for times ∼< 100 days, but differ at late times. Heating a small region near the pole gives better agreement with the shape of the late time light curve. In this case the field is close to radial everywhere in the heated region, leading to more rapid cooling at late times which more closely matches the observed luminosity decrease.

Both models underpredict the luminosity at times ∼> 200 days by about a factor of two. There are several properties of the inner crust that can change the late time part of the light curve. A small amount of heat deposited in the inner crust can bring the late time lightcurve into agreement

with the data. The shape of the decay at times ∼> 200 days is sensitive to the heat capacity of the layer of normal neutrons just below neutron drip. The thickness of this layer is determined by

how quickly the critical temperature Tc for superfluidity increases with density (Page & Reddy, 2012). We find that the best fits are obtained when we do not include the neutron heat capacity at all, i.e. Tc rises very rapidly with density below neutron drip; a slow rise in Tc leads to a slower decline in the light curve at late times. Another important parameter is the impurity parameter

Qimp in the inner crust which determines the thermal conductivity. We set Qimp ≈ 10 in the models shown in Figure 5.2.

It is rather remarkable that the models we have computed with standard assumptions for the inner crust physics reproduce the shape of the observed decay so well. It would be interesting to carry out a comprehensive survey of the parameters such as gravity, critical temperature for neutron superfluidity, inner crust thermal conductivity, magnetic field geometry and angular size of the heated region (e.g. see the similar study by Page & Reddy, 2013, for the accreting neutron star XTE J1701−462). The good agreement is especially interesting given the uncertainties in comparing the models with the data. These include the fact that the models predict the surface bolometric luminosity of the star, whereas the X-ray flux is measured in the narrow bandpass 1– 10 keV, although we note that the bolometric correction to the thermal component of the spectrum is of order unity, as the peak of the spectrum lies within the 1–10 keV bandpass. Furthermore, the thermal part of the spectrum that is observed decreases in flux primarily due to a decreasing emitting area rather than a decreasing temperature as might be expected for a cooling surface. Ex- 100 5 The Long-term Post-outburst Behaviour of Magnetar Swift J1822.3−1606

plaining the observed decrease in emitting area is the major challenge for crust cooling models. Addressing the spectral evolution requires detailed modelling of the formation of the spectrum (Özel & Guver, 2007). Here we have assumed that while there can be significant modification of the spectrum, due to for example resonant Compton scattering in the magnetosphere, the luminosity remains largely unaffected, at least over the bulk of the evolution.

Untwisting of the Magnetosphere

The magnetospheric untwisting model detailed by Beloborodov (2009) also makes specific predictions regarding the flux and spectral evolution of magnetars post-outburst. In this picture the post-outburst magnetosphere has been twisted due to crustal motions originating from stresses induced by the strong internal magnetic field. The twist is carried by a bundle of current-carrying field lines (the “j-bundle”) which is anchored in the crust on a footpoint of area A. This footpoint, bombarded by current particles, radiates thermal emission and both fades and shrinks as the j-bundle dissipates during relaxation and untwisting. The evolution time of the X-ray lumi- ≃ 7 −1 nosity is predicted to be tev 10 µ32Φ10 A11.5 s (Beloborodov, 2009; Mori et al., 2013), where 32 3 −1 µ32 is the magnetic moment in units of 10 G cm , Φ10 is the electric voltage sustaining e 10 discharge in the magnetosphere in units of 10 V, and A11.5 is the j-bundle footpoint area in units of 1011.5 cm2. For Swift J1822.3−1606, the relation predicts an evolution time scale of ∼ 6 ∼ −1 10 s, or 10 days assuming Φ10 = 1, reasonable given expectations (Beloborodov, 2009). This is roughly consistent with the time scale (∼ 6 days) we found for the fastest-decaying exponential component (see Section 5.3.2) but inconsistent with the second two time scales in the

three-component decay model, unless Φ10 is significantly smaller than unity. It could be that the j-bundle untwisting time scale corresponds to the shortest exponential decay, with overall crustal cooling corresponding to the latter two.

The untwisting model further predicts that the thermal X-ray luminosity from the heated footpoint should vary with A2. Figure 5.4 shows the thermal X-ray flux of Swift J1822.3−1606 plotted against the emitting area as inferred from our blackbody fits. Here we compare the expectation of the magnetospheric twist model, namely f ∝ A2 with our data and find that this is not a good description of the data. Rather, our best-fit relation has f ∝ A3/2. The observed prefactor is larger than the model predicts even when the twist is maximal (of or- 5.4 Discussion 101

10-9 F =kAn

n =1.50 0.03 ¡ n =2 ) 1 -10 s 10

(erg cm(erg F

10-11

10-12 1-10Absorbed keV Flux,

10-13 10-2 10-1 100 101 Blackbody Area, A (km2 )

Figure 5.4: 1–10 keV absorbed flux as a function of the emitting area of the blackbody component of the spectral fits. To these data, we have fit the function F = kAn. The solid line shows our best fit when allowing n to vary, The best fit line in that case, in terms of luminosity (assuming a distance of 1.6 kpc), is L = 1.5 × 1034 erg s−1(A/1 km2)3/2. The dotted line shows the case n = 2, as predicted by Beloborodov (2009). For that case, the best-fit line is given by L = 1.3 × 1034 erg s−1(A/1 km2)2. 102 5 The Long-term Post-outburst Behaviour of Magnetar Swift J1822.3−1606

der unity) and the voltage drop is ∼ 10 GeV (Φ10 ≈ 1). Beloborodov (2009) predicts L ≈

34 −1 −3 2 2 10 erg s B14R6 ψΦ10(A/km ) , where ψ is the twist angle. The observed relation has 34 −1 2 L = 1.5 × 10 erg s for A = 1 km and d = 1.6 kpc. However, Φ10 = 1 is on the upper end

of the 0.1−1 Φ10 range set by pair creation given by Beloborodov (2009), and the magnetic field we infer from spin down is significantly smaller than 1014 G, reducing the expected luminosity. In addition, the absorbed 1–10 keV flux is an underestimate of the true bolometric flux.

The shallower scaling of luminosity with area could arise from a systematic change in the shape of the thermal spectrum compared to a blackbody as the flux decreases. Then the inferred area from blackbody fits would systematically change with flux, modifying the underlying L ∝ A2 scaling. An alternative physical explanation is that the field geometry is more complex than the dipole geometry assumed by Beloborodov (2009). The luminosity is L ≈ IV where I is the

current, given from Ampère’s law by I ∝ Bϕa where a is the radius of the flux bundle at the surface of the star. Following the bundle of field lines from one pole to the other through the magnetosphere (see Beloborodov, 2009, Appendix A for a more detailed treatment), the twist

angle is ψ ≈ (rmax/a)(Bϕ/BP ), where BP is the poloidal field strength, Bϕ the toroidal field

in the twist, and rmax is the maximum radial extent of the flux tube. For a dipole field, rmax ≈ R(R/a)2, giving L ∝ a4 ∝ A2 as found by Beloborodov (2009). A different field geometry

3 changes the scaling. For example, a quadrupole field has rmax ≈ R(R/a), giving L ∝ a ∝ A3/2, in agreement with the observed scaling in Figure 5.4. It may therefore be of interest to explore magnetospheric untwisting with a more complex field geometry.

5.5 Conclusions

We have presented an up-to-date analysis of the post-outburst flux and timing evolution for Swift J1822.3−1606. We find that the spin down following the outburst is well described with an exponential glitch recovery and that the long-term spin-down inferred magnetic field is lower than previously estimated. From this, we conclude that a glitch likely occurred near the outburst onset as has been seen in several other magnetar outbursts. We also find that the post-outburst flux evolution is consistent with thermal relaxation of the neutron star crust, particularly if heat was deposited internally in a small region close to neutron drip depth and near the magnetic axis. We 5.5 Conclusions 103 find that flux relaxation due to magnetospheric untwisting may also be consistent if the poloidal magnetic field is more complicated than a simple dipole. 104 5 The Long-term Post-outburst Behaviour of Magnetar Swift J1822.3−1606 6 On the X-ray Variability of Magnetar 1RXS J170849.0−400910

The work presented in this chapter has previously been published in the article: Scholz et al., 2014, On the X-Ray Variability of Magnetar 1RXS J170849.0−400910, Astrophysical Journal, 783, 99. The text of this chapter has been adapted from that work.

6.1 Introduction

1RXS J170849.0−400910 (hereafter referred to as RXS J1708 for brevity) was first identified as an X-ray source in the ROSAT all-sky survey (Voges et al., 1999). It was first discovered as a pulsar by Sugizaki et al. (1997), using ASCA data, who suggested that it was an AXP based on its X-ray spectrum and 11-s spin period. Israel et al. (1999) measured a period derivative typical of AXPs for RXS J1708, confirming that the source is an AXP, and thus a magnetar. Rotational glitches in magnetars have been observed both with and without associated radiative changes (Dib & Kaspi, 2014, and Section 1.2.2). It is important to determine whether or not there is a generic connection between magnetar glitches and radiative events because it can help us determine the physical origin of these phenomena. It seems reasonable that magnetospheric mechanisms, because of their external nature, are likely to be accompanied by radiative changes whereas internal mechanisms could produce radiatively quiet glitches. RXS J1708 was the first magnetar observed to glitch (Kaspi et al., 2000). It has since been found to glitch several more times (Israel et al., 2007; Dib et al., 2008; Dib & Kaspi, 2014). Note that some of the glitches reported in Israel et al. (2007) are considered to be glitch candidates in Dib et al. (2008) as they could be consistent with timing noise. Rea et al. (2005) first suggested that RXS J1708 exhibited post-glitch X-ray flux variability based on a 2003 XMM-Newton observation. They reported an XMM-Newton flux that was significantly lower than preceding Chandra and BeppoSAX observations. Further evidence for flux variability was claimed based on additional Swift and INTEGRAL observations (Campana et al., 2007; Götz et al., 2007; Israel et al.,

105 106 6 On the X-ray Variability of Magnetar 1RXS J170849.0−400910

2007). However, puzzlingly, variability at the level claimed in these studies was not seen in the pulsed count rate as measured by frequent observations with RXTE (Dib et al., 2008; Dib & Kaspi, 2014). In this chapter we analyze all the available Swift XRT data from the period of the claimed variability to present day. We also use one XMM-Newton and one Chandra observation that were performed prior to the start of the Swift observations. We then use the measured spectral and flux values to constrain the level of source variability. We also present an up-to-date timing solution which continues the RXTE timing of Dib & Kaspi (2014) using Swift. We then discuss the occurrence of radiatively quiet glitches in magnetars.

6.2 Observations

6.2.1 Swift Observations

RXS J1708 was observed by the Swift XRT (see Section 2.1.3) frequently between 2005 and 2010. Beginning in 2011 July RXS J1708 was observed as a continuation of the RXTE timing campaign summarized by Dib & Kaspi (2014). Here we use all available archival Swift data in that time period in both Windowed Timing (WT) and Photon Counting (PC) modes. There were 80 observations for a total exposure time of 268 ks. Table 6.1 shows a summary of the Swift observations used in this work. We downloaded the unfiltered Level 1 data from the HEASARC data archive and ran the standard Swift data reduction script xrtpipeline using the source position of 17h 08m 46.87s, −40◦ 08′ 52.44′′ (Israel et al., 2003) and the best available spacecraft attitude file. Events were then corrected to the solar-system barycenter using the same position. For WT mode, a 30-pixel long strip centred on the source was used to extract the source events and a 50-pixel long strip positioned away from the source was used to extract the background events. For PC mode observations, an annular region with inner radius 3 pixels and outer radius 20 pixels was used. The inner region was excluded to avoid pileup of the source. An annulus with inner radius 40 pixels and outer radius 60 pixels was used as the background region. For WT mode data, exposure maps, spectra, and ancillary response files were created for each individual orbit. The spectra and ancillary response files were then summed to create a spectrum 6.2 Observations 107

for each observation. For the PC mode data, exposure maps, spectra and ancillary response files were created on a per observation basis. We used response files for spectral fitting from the 20120209 Swift CALDB.

The use of exposure maps when creating the ancillary response files is especially important for Swift data, as there are columns of bad pixels which can disrupt the PSF of the source for parts of certain observations. Orbits were not used in the observation if the bad columns were found to be within 3 pixels of the source position.

For WT mode data we selected only Grade 0 events for spectral fitting as higher Grade events are more likely to be caused by a background event (Burrows et al., 2005). In PC mode we used the standard Grade 0-12 selection.

6.2.2 Chandra and XMM-Newton Observations

In this study, we also reprocessed archival data taken with Chandra and XMM-Newton. To avoid pileup, we used the Chandra continuous-clocking (CC) mode observation (ObsID 4605) and the XMM-Newton pn small-window mode data (ObsID 0148690101). The former was taken on 2004 July 3 with the ACIS-S detector in CC mode, which has a time resolution of 3 ms. The total exposure was 29 ks. The XMM-Newton observations were made on 2003 August 28. The pn and MOS detectors were run in small and large window modes, with 6-ms and 0.9-s time resolution, respectively. As the source is bright, the low time resolution of the MOS data results in significant pileup. Therefore, we focused only on the pn data. After filtering for periods of high background, we were left with 35 ks of exposure in the pn observation. This is equivalent to 24 ks of live time since the XMM-Newton-pn small-window mode has an efficiency of 70%.

We processed the Chandra and XMM-Newton data using CIAO 4.4 and SAS 11, respectively. The source spectrum was extracted using a 6′′-wide region from the Chandra observation and a 40′′-radius aperture from the XMM-Newton pn data. For the Chandra observation, the background spectrum was extracted from the entire 1D CC-mode strip excluding the inner 1′ closest to the source. For the XMM-Newton observation, the background spectrum was extracted from two 40′′-radius circular regions placed away from the source. 108 6 On the X-ray Variability of Magnetar 1RXS J170849.0−400910

Table 6.1: Summary of Swift observations of RXS J1708

Sequence Mode Observation date MJD Exposure time Set Set exp. time Set counts (TDB) (ks) (ks)

00050701001 PC 2005-01-30 53400.2 2.3 00050702001 PC 2005-02-02 53403.0 4.6 00050702002 PC 2005-02-23 53424.0 2.0 2005 23.1 10947 00050701002 PC 2005-02-24 53425.1 11.9 00050700006 PC 2005-03-23 53452.2 2.3 00035318001 PC 2006-09-20 53998.4 2.7 2006 11.8 5081 00035318004 PC 2006-10-09 54017.3 9.2 00035318005 PC 2007-02-25 54156.3 1.3 00035318006 PC 2007-02-28 54159.0 1.8 00035318007 PC 2007-03-05 54164.9 2.3 00035318008 PC 2007-03-13 54172.7 1.2 2007 12.4 5537 00035318010 PC 2007-03-18 54177.8 2.0 00035318012 PC 2007-03-23 54182.6 2.0 00035318011 PC 2007-03-26 54185.4 1.7 00035318013 PC 2008-02-23 54519.2 15.9 2008-PC 20.9 10169 00090025001 PC 2008-05-13 54599.0 5.0 00090057001 WT 2008-04-02 54558.0 3.0 00090057002 WT 2008-04-03 54559.6 2.1 00090057003 WT 2008-04-04 54560.5 3.2 00090057004 WT 2008-04-08 54564.1 1.2 2008-1 27.1 26586 00090057005 WT 2008-04-11 54567.0 3.8 00090057006 WT 2008-06-05 54622.2 6.4 00090057007 WT 2008-06-06 54623.4 7.5 00090057008 WT 2008-08-13 54691.3 7.4 00090057009 WT 2008-08-14 54692.1 1.4 2008-2 16.4 15260 00090057010 WT 2008-10-03 54742.0 7.0 00090057011 WT 2008-10-10 54749.7 0.6 00090057012 WT 2009-02-06 54868.3 2.2 00090057013 WT 2009-02-08 54870.1 3.8 00090057014 WT 2009-02-15 54877.1 12.7 2009-1 42.9 42616 00090057015 WT 2009-03-20 54910.0 16.5 00090213001 WT 2009-04-26 54947.1 7.7 00090213002 WT 2009-06-28 55010.9 8.7 00090213004 WT 2009-09-02 55076.2 8.7 2009-2 22.3 21748 00090213005 WT 2009-10-11 55115.0 4.9 00090213006 WT 2010-02-03 55230.0 8.6 00090213007 WT 2010-02-04 55231.7 5.4 2010 23.8 23038 00090213008 WT 2010-03-25 55280.0 9.8 6.2 Observations 109

Table 6.0: Summary of Swift observations of RXS J1708. (cont.)

Sequence Mode Observation date MJD Exposure time Set Set exp. time Set counts (TDB) (ks) (ks)

00035318014 WT 2011-07-28 55770.3 0.9 00035318015 WT 2011-08-04 55777.4 1.0 00035318016 WT 2011-08-11 55784.0 2.3 00035318017 WT 2011-08-18 55791.2 1.9 00035318018 WT 2011-08-25 55798.3 2.0 00035318019 WT 2011-09-01 55805.4 2.1 00035318020 WT 2011-09-08 55812.5 2.2 00035318021 WT 2011-09-15 55819.2 2.2 2011 27.8 27744 00035318022 WT 2011-09-22 55826.1 2.3 00035318023 WT 2011-09-29 55833.9 2.4 00035318024 WT 2011-10-06 55840.8 2.3 00035318025 WT 2011-10-13 55847.0 1.6 00035318026 WT 2011-10-20 55854.3 0.9 00035318027 WT 2011-10-22 55856.3 1.8 00035318028 WT 2011-10-27 55861.1 2.0 00035318029 WT 2012-01-25 55951.5 2.0 00035318030 WT 2012-02-01 55958.3 2.1 00035318031 WT 2012-02-08 55965.8 2.2 00035318032 WT 2012-02-15 55972.2 0.3 00035318033 WT 2012-02-22 55979.8 0.4 00035318034 WT 2012-02-29 55986.4 2.2 00035318035 WT 2012-03-07 55993.3 2.2 2012-1 21.0 21056 00035318036 WT 2012-03-16 56002.6 2.2 00035318037 WT 2012-03-21 56007.5 1.0 00035318038 WT 2012-03-28 56014.9 1.6 00035318039 WT 2012-04-13 56030.2 1.6 00035318040 WT 2012-04-26 56043.1 1.5 00035318041 WT 2012-05-10 56057.3 1.3 00035318042 WT 2012-05-25 56072.0 0.5 00035318043 WT 2012-06-07 56085.6 2.0 00035318044 WT 2012-06-22 56100.2 1.5 00035318045 WT 2012-07-05 56113.4 0.6 00035318047 WT 2012-07-15 56123.5 1.1 00035318048 WT 2012-08-16 56155.0 1.7 2012-2 10.8 11423 00035318049 WT 2012-09-06 56176.1 2.0 00035318050 WT 2012-09-27 56197.1 1.7 00035318052 WT 2012-10-23 56223.4 0.3 00035318053 WT 2013-01-24 56316.3 1.0 00035318054 WT 2013-02-13 56336.8 1.9 00035318055 WT 2013-03-06 56357.1 2.0 2013 7.1 7380 00035318056 WT 2013-03-27 56378.6 0.7 00035318057 WT 2013-03-31 56382.2 1.5 110 6 On the X-ray Variability of Magnetar 1RXS J170849.0−400910

6.3 Analysis & Results

6.3.1 Flux and Spectra

We first fit the spectra for each individual observation with a photoelectrically absorbed power-

law model. The spectra were fit with a single NH using the XSPEC tbabs model with abundances from Wilms et al. (2000), and photoelectric cross-sections from Verner et al. (1996). We used XSPEC1 with Cash statistics (Cash, 1979) to fit the spectra because of the low number of counts in the Swift observations (see Section 2.2). The grey points in Figure 6.1 show the results of the spectral fits to the individual observations. The typical uncertainties in the spectral parameters vary widely due to the large range in exposure times. In order to place the best constraints on the variability, we consider PC and WT modes separately. This is because the two modes are calibrated to within only 10% of each other (A. Beardmore, private communication). The mean and standard deviation of the 1–10 keV absorbed flux for the PC mode data are 4.0 × 10−11 erg cm−2 s−1 and 1.9 × 10−12 erg cm−2 s−1, respectively. The PC mode photon index has a mean and standard deviation of 3.1 and 0.08. For WT mode the mean and standard deviation are 4.0 × 10−11 erg cm−2 s−1 and 2.1 × 10−12 erg cm−2 s−1 for flux and 3.2 and 0.07 for the photon index. In order to better constrain the variability, we then separated the Swift spectra into sets of observations nearby in time (see Table 6.1). Within each set, the 1–10 keV flux and photon-index were consistent with being constant (i.e. the χ2 values of fits to a mean value in each set were consistent with being drawn from a χ2 distribution). We fit the sets of Swift observations as well as the XMM-Newton and Chandra spectra with a photoelectrically absorbed power law. Each Swift set was fitted with the same model with all spectral parameters the same from observation to observation within the set. All parameters were allowed to vary from set to set except for NH which was tied to the same parameter for all sets and was measured to be (2.434 0.008) × 1022 cm−2. We did not fit the conventional but more complicated blackbody plus power-law model because the addition of the extra blackbody component did not improve the goodness-of- fit significantly for any of the Swift sets. Although additional components are significant for the XMM-Newton and Chandra spectra, we opted to use a single component model because only Swift

1http://xspec.gfsc.nasa.gov 6.3 Analysis & Results 111 )

1 5.0 s 2 4.5 Chandra

4.0 XMM ergscm 11

3.5 1-10 keV Abs. Flux (10 3.0

3.6

3.4

3.2 XMM ¡ Chandra 3.0

2.8

2.6 53000 53500 54000 54500 55000 55500 56000 MJD

Figure 6.1: Top Panel: Absorbed 1–10 keV flux of RXS J1708 over a ∼10-yr period. Note that the zero on the y-axis is suppressed. Bottom Panel: Photon indices from fitting a power-law model to the 1–10 keV spectrum. Grey points are from spectral fits to individual observations. Black triangles are sets of Swift PC mode observations, and white circles are sets of Swift WT mode observations (see Table 6.1 for definitions of sets). XMM-Newton and Chandra observations are labelled. The dark grey bands represent the 90% error in the mean and the light grey bands represent the level of previously claimed variability (∼ 50% in 1–10 keV flux and ∼ 30% in spectral index; Götz et al. 2007). The solid vertical lines represent the epochs of glitches and the dashed lines indicate the epochs of glitch candidates. All error bars are 90% confidence intervals. 112 6 On the X-ray Variability of Magnetar 1RXS J170849.0−400910

data are used here to constrain the variability (see Section 6.4.1) and using a single-component model simplifies the comparison of spectral properties. The joint power-law fit to the sets of observations provided a Cash statistic of 32806 and a Pearson χ2 of 37191 for 33571 degrees of freedom. This corresponds to a reduced χ2 of 1.1.

Figure 6.1 shows the 1–10 keV absorbed flux and power-law index as a function of time resulting from the spectral fit to the sets. The mean and standard deviation of the flux for the PC mode sets are 4.0 × 10−11 erg cm−2 s−1 and 8.4 × 10−13 erg cm−2 s−1, respectively. The PC mode photon index has a mean and standard deviation of 3.1 and 0.07. Thus for PC mode, the maximum variability allowed by 3σ confidence intervals (3 times the standard deviation divided by the average value) is 6.3% for the flux and 7.5% for the photon index. In WT mode, the mean flux is measured to be 4.1 × 10−11 erg cm−2 s−1 with a standard deviation of 5.9 × 10−13 erg cm−2 s−1 for a maximum variability of 4.3%. For the photon index, the mean and standard deviation are 3.2 and 0.04 for a maximum variability of 4.0%. Compared to the standard deviations measured for the individual observations above, the constraints here from fitting the sets of observations improved as little as a factor of 1.2 (PC mode photon-index) and as much as a factor of 3.5 (WT mode flux). A greater improvement is achieved with WT mode than PC mode, which makes

sense given that the individual WT mode observations have a large number of short (∼< 2 ks) observations.

The probability of the data being constant can be estimated from the χ2 of each data set. For

2 the PC mode observation sets, the reduced χν/ν for the flux is 2.4/3 which corresponds to a 2 × −7 6.7 % probability of being constant and for the power-law index the χν/ν is 11/3 (5.1 10 2 probability). The sets of WT mode observations have a χν/ν of 2.3/8 (0.021 probability) for 2 × −8 flux and a χν/ν of 6.1/8 (6.3 10 probability) for power-law index. So, in both modes, the fluxes are consistent with being constant (i.e. within 3σ), although the power-law indices are only consistent within a 5σ tolerance. This could be due to unknown systematic sources of error or possibly low-level spectral variations, possibly due to the neglected blackbody component. Regardless, these variations are much lower than the ∼ 30% previously claimed (Rea et al., 2005; Campana et al., 2007; Götz et al., 2007). 6.3 Analysis & Results 113

Residuals [s]

1.0 0.5 0.0

0.5

1.0

Residuals [s]

55700 55800 55900 56000 56100 56200 56300 56400 56500 Modified Julian Date

Figure 6.2: Timing residuals, the difference between the predicted and measured TOAs for the timing model shown in Table 6.1. The top panel shows residuals before fitting for a glitch, and the bottom panel after. In both panels, open circles indicate data from RXTE, and black triangles indicate Swift. The vertical dashed line represents the glitch epoch and the grey band represents the uncertainty in that epoch.

6.3.2 Timing

A phase-coherent timing solution for RXS J1708 has been maintained using RXTE since 1998 (see Dib & Kaspi, 2014). In order to continue to maintain a timing solution for RXS J1708, we began a monitoring campaign using the Swift/XRT on 2011 July 28, overlapping with the RXTE campaign, until RXTE’s demise in December, 2011. Monitoring observations were typically 2-ks long. Barycentred events were used to derive a pulse time of arrival (TOA) for each observation. For a given observation, a TOA was obtained using a maximum likelihood (ML) method, as described by Livingstone et al. (2009) as well as in Section 2.3.2. The ML method compares a continuous model of the pulse profile, derived from taking aligned profiles of all the pre-glitch Swift/XRT observations, and creating a template composed of the first five Fourier components. The TOAs were fitted using standard pulsar timing techniques (Section 2.3.3) using the TEMPO2 (Hobbs et al., 2006) pulsar timing software package.

In Figure 6.2 we show the timing residuals for RXS J1708 starting on 2011 July 28 and show the overlap between the RXTE and Swift monitoring epochs. The data are well fit by a single 114 6 On the X-ray Variability of Magnetar 1RXS J170849.0−400910

Table 6.1: Timing Parameters for RXS J1708.

Parameter Value

Observation Dates 28 July 2011 - 29 May 2013 Dates (MJD) 55770.396 − 56441.770 Epoch (MJD) 56000.000 Number of TOAs 61 ν (s−1) 0.090851264(3) ν˙ (s−2) −1.638(3) × 10−13 Glitch Glitch Epoch (MJD) 56019(11) −1 −8 ∆νd (s ) 7.5(5) × 10

τd (days) 111(15) ∆ν ˙ (s−2) 1.4(3) × 10−15 RMS residuals (ms) 229.07 χ2/ν 64.94/55 Numbers in parentheses are TEMPO2 reported 1 σ uncertainties.

spin frequency and frequency derivative (Table 6.1). However, we identified one notable timing event which we report as a new glitch. The event occurred within 11 days (1σ uncertainty) of MJD 56019 with a decaying ∆ν/ν = (8.3 0.6) × 10−7. The glitch displayed an exponential recovery with a timescale of 11115 days, 2.60.3 times longer than the 432 day decay time of the other reported decaying glitch in the source (Dib et al., 2008). This glitch was accompanied by a ∆ν ˙ of (1.4 0.3) × 10−15 Hz/s.

6.4 Discussion

In this chapter, we have reported on the flux and spectral properties of RXS J1708 over a ∼ 10 year period from 2003 to 2013. We show that there is no significant flux variability and that only low-level spectral variations are seen. We have also presented an up-to-date timing solution and we report on a glitch that occurred on MJD ∼ 56019. Below we compare our findings with previous results and discuss the significance of the lack of variability in RXS J1708. 6.4 Discussion 115

6.4.1 Flux Variability of RXS J1708

In this work, we do not use measured flux and spectral properties between different X-ray telescopes to constrain the variability of RXS J1708. This is because cross-calibration between instruments onboard the Swift, Chandra, and XMM-Newton telescopes is such that the flux and spectral index can differ by up to 20% and 9%, respectively (e.g. Tsujimoto et al., 2011). As seen in Figure 6.1, the XMM-Newton and Chandra observations are consistent with one another within those tolerances. Additionally, each Swift XRT mode (PC and WT) is considered separately, as the two modes are cross-calibrated only to within 10% in flux (A. Beardmore, private communication).

Previous studies have claimed that RXS J1708 displayed variability following glitches that occurred between 2002 and 2005. Using a multi-component blackbody plus power-law model, Götz et al. (2007) measure a low 1–10 keV absorbed flux of ∼ 3 × 10−11 erg cm−2 s−1 for the 2003 XMM-Newton observation and 2006 set of Swift observations. They measured a higher flux for the 2004 Chandra observation and the 2005 set of Swift observations. Their highest flux measured is ∼ 4.5 × 10−11 erg cm−2 s−1 for the 2005 Swift set. This gives a total claimed variability of ∼ 50%.

Because we used a single-component model in Section 6.3.1, the values in Figure 6.1 are not directly comparable to those in Götz et al. (2007). For the Swift data, additional spectral components do not significantly improve the fit. However, additional components for Chandra and XMM-Newton observations do provide a much better fit and so here we apply a blackbody plus power-law model for direct comparison with Götz et al. (2007). With a multi-component model we measure 1–10 keV absorbed fluxes of (3.83 0.04) × 10−11 erg cm−2 s−1 for the XMM-Newton spectrum and (4.29 0.08) × 10−11 erg cm−2 s−1 for the Chandra observation. This 11% discrepancy in flux between the two observations is within the 20% cross-calibration error. As in Götz et al. (2007), we find that the temperature of the blackbody component of the model is consistent between the two observations and is 0.46 0.01 keV. For the photon index we measure 2.630.03 and 2.500.07 for the XMM-Newton and Chandra observations, respectively. This compares to Γ ∼ 2.8 for both observations in Götz et al. (2007). Reassuringly, the Chandra flux that we measure is higher than the XMM-Newton flux and the Chandra spectral 116 6 On the X-ray Variability of Magnetar 1RXS J170849.0−400910

index is harder as found in cross-calibration studies (e.g. Tsujimoto et al., 2011). In order to attempt to reproduce previous Swift results, for which only PC mode data were used (Götz et al., 2007), we processed the PC mode data from 2005-2007 without using exposure maps and without removing orbits with bad columns within 3 pixels of the center of the PSF. We found the same trend as in previous studies: the flux of the 2005 set of observations was higher than the 2006 and 2007 sets and the flux of the 2007 set was slightly higher than that of the 2006 set. We also observed an apparent correlation between the flux and power-law index. However, the level of variability in the three flux points was only about 30% compared to ∼ 50% claimed in Götz et al. (2007). Still, this is much higher than the < 10% that we find in our more detailed analysis. So, the majority of the discrepancy can be explained by a failure to correct for the effect of bad columns. The lack of variability found here using soft X-ray imaging telescopes is consistent with what has been found by non-focusing telescopes in other regimes. Using INTEGRAL data, den Hartog et al. (2008) found no significant variability in the hard X-ray flux or spectral index for data spanning from 2003 to 2006. With RXTE, Dib et al. (2008) found that the pulsed count rate showed evidence for only low-level variability (< 15%) and they concluded that the glitches of RXS J1708 appeared to be “quiet”, i.e. unassociated with significant changes in the radiative properties of the magnetar.

6.4.2 Radiative Activity and Glitches in Magnetars

Radiative activity in magnetars is almost always associated with changes in timing behaviour (e.g. glitches or increased timing noise; Dib & Kaspi, 2014). Of the 26 known magnetars and magnetar candidates, only five have long-term (>10 yr) phase-connected timing solutions that can be used to unambiguously detect glitches. These five magnetars are 1E 1841−045, 1E 2259+586, 4U 0142+61, 1E 1048.1−5937, and RXS J1708. Of the three glitches each that have been detected from 1E 2259+586 and 1E 1048.1−5937, five were radiatively loud, with the 2006 glitch of 1E 2259+586 being the exception. The magnetars 1E 1841−045, 4U 0142+61, and RXS J1708 have not displayed any significant flux increases associated with their glitches, although 4U 0142+61 emitted short X-ray bursts near the epoch of its 2006 candidate glitch (see Dib & Kaspi, 2014, and references therein). 6.4 Discussion 117

It is therefore clear that glitches are not always accompanied by radiative changes. Because changes in the magnetosphere would likely manifest as pulse profile or flux variations, it seems more likely that radiatively quiet magnetar glitches have their origin in the interior of the neutron star. If we assume that radiatively quiet and loud glitches have the same origin, a mechanism must exist to allow magnetars to exhibit prompt X-ray flux increases in some cases and no significant flux increases in others.

One possible way to achieve both radiatively loud and quiet glitches in an interior model is to vary the depth at which the glitch-inducing event occurs. Eichler & Cheng (1989) showed that if energy is injected into the crust of a neutron star it can travel outward, and manifest as a prompt outburst, or travel inward and heat the core of the neutron star. The direction of travel depends on the size and depth of the energy deposition. In the inward case, the heat is released slowly over a time scale of thousands of years. The flux decays of magnetars following prompt outbursts are indeed reasonably well modelled by crustal cooling (Lyubarsky et al., 2002; Scholz et al., 2012; An et al., 2013; Scholz et al., 2014b). If the mechanism that causes glitches in magnetars injects energy at a shallow depth, a radiatively loud glitch would occur.

An additional possible limit to the occurrence of radiative outbursts from magnetars at glitch epochs is the predominance of neutrino emission at high temperatures in neutron star crusts (Eich- ler & Cheng, 1989; van Riper, 1991). We expect neutron stars to have a limiting luminosity which occurs when the emission of neutrinos dominates as a cooling mechanism over the emission of photons. We would thus expect the brightest magnetars to be unable to increase their luminosity beyond ∼ 1035 erg s−1 (Thompson & Duncan, 1996). The five brightest magnetars, for which long-term timing solutions are available, have luminosities ∼ 1035 erg s−1 (though see below for caveats on luminosity measurements). So, flux increases for these magnetars should either not occur or be small. Indeed, of the five, only 1E 2259+586 and 1E 1048.1−5937 have displayed significant flux increases at glitch epochs (Woods et al., 2004; Gavriil & Kaspi, 2004; Tam et al., 2008) and those flux increases were much smaller than those from outbursts observed in fainter transient magnetars (e.g. Israel et al., 2007; Scholz & Kaspi, 2011).

However, magnetar luminosities are not well constrained since the source distances are hard to determine. There exist in the literature several disagreements in the distances to magnetars that 118 6 On the X-ray Variability of Magnetar 1RXS J170849.0−400910

lead to a discrepancy of up to a factor of ∼ 30 in luminosity (e.g. see An et al., 2012 versus Durant & van Kerkwijk, 2006 for 1E 1048.1−5937). Even when the distance is agreed upon there are discrepancies. For example, for RXS J1708, the only distance estimation is from Durant & van Kerkwijk (2006) but the 2–10 keV luminosity has been reported to be as low as 4.2×1034 erg s−1 (Olausen & Kaspi, 2014) and as high as 1.4 × 1035 erg s−1 (Rea & Esposito, 2011). From the model given by our best-fit mean flux and spectral indices, we get a 2–10 keV unabsorbed flux of 3.9 × 10−11 erg cm−2 s−1, which corresponds to a 2–10 keV luminosity of 6.8 × 1034 erg s−1, closer to that listed in the magnetar catalog (Olausen & Kaspi, 2014). Discrepancies such as this could be caused by the difference in spectral models used or differences in the instruments used to measure the flux (as mentioned above, X-ray detector cross-calibration can be discrepant up to 20%). We therefore cannot say conclusively whether magnetar luminosity is inversely correlated with the size of radiative activity as discussed here and as previously proposed in Pons & Rea (2012).

If we do assume that fainter magnetars are able to have larger flux increases coincident with glitches, this suggests a rough luminosity order for the five brightest magnetars. RXS J1708, 1E 1841−045, and 4U 0142+61 have experienced only radiatively quiet glitches whereas 1E 1048.1−5937 and 1E 2259+586 have shown significant flux increases during some (or all for 1E 1048.1−5937) of their glitches. That suggests that RXS J1708, 1E 1841−045, and 4U 0142+61 are intrinsically more luminous than the other two.

Pulsars with higher B-fields are expected to be more luminous and have higher surface temperatures than pulsars with lower magnetic fields because of energy deposition from the decay of their magnetic fields. Indeed, it has been shown that high-B radio pulsars are systematically hotter than similarly aged pulsars with lower magnetic fields (Zhu et al., 2011; Olausen et al., 2013). We may also expect that magnetar-like activity in such sources could arise due to energy from the magnetic field being deposited at shallow depths. Case in point, the high-B rotation-powered pulsar PSR J1846−0258 displayed a magnetar-like outburst in 2006 (Gavriil et al., 2008). In recent years, two magnetars, SGR 0418+5729 and Swift J1822.3−1606, were discovered with magnetic fields lower than several high-B rotation-powered pulsars and have had clear X-ray outbursts (Rea et al., 2010; Livingstone et al., 2011). It is thus becoming increasingly clear that 6.5 Conclusions 119 high-B rotation powered pulsars and magnetars are related and form a spectrum of objects rather than two distinct groups. Therefore, the mechanism that causes X-ray outbursts at glitch epochs could be active in all high-B field pulsars.

6.5 Conclusions

We have presented an analysis of all of the Swift WT and PC mode data of RXS J1708 in the period 2005–2013. We show that the maximum variability for both the 1–10 keV X-ray flux and spectral index is constrained to < 10%. This is much less than claimed by previous studies and is consistent with the flux being constant. We also report on a newly discovered glitch at MJD∼ 56019 which has a fractional amplitude of ∆ν/ν = (8.3 0.6) × 10−7, typical of magnetar glitches. The occurrence of both radiatively quiet and loud glitches in magnetars, sometimes from the same source, shows that the mechanism that causes these glitches must be able to produce prompt flux increases in some cases and no significant increases in others. Here we have discussed the possibility that the glitches originate internally to the neutron star, with the deciding factor the depth of the energy deposition associated with the glitch. We note that these conclusions have been drawn from a sample of only five magnetars and therefore increasing the number of magnetars for which we can unambiguously detect glitches would be beneficial in answering the questions posed here. 120 6 On the X-ray Variability of Magnetar 1RXS J170849.0−400910 7 Summary and Conclusions

In this thesis, three different magnetars were studied:

• 1E 1547.0−5408: The fastest spinning magnetar, and therefore likely one of the youngest, which, in 2009 January, had the largest persistent flux increase yet found for any magnetar and emitted hundreds of short X-ray bursts (Chapter 3). This outburst followed another in 2008 October. Based on the power-law fit to its flux recovery 1E 1547.0−5408 does not seem to be returning to its lowest previously observed state any time soon (see below).

• Swift 1822.3−1606: A low-magnetic-field magnetar that was discovered in 2011 when it entered a period of outburst. In terms of flux and spectral behaviour, it is likely cooling as expected from crustal cooling models to its ROSAT measured quiescent state. In terms of timing its spin-down is well characterized by a simple ν and ν˙ model after correcting for a glitch recovery following the outburst (Chapter 5). So, after the outburst the magnetar seems to be returning to its quiescent state in a relatively well behaved fashion in both flux and timing properties.

• 1RXS 170849.0−400910: One of the original so-called “anomalous X-ray pulsars”, it is persistently much brighter than the transients Swift 1822.3−1606 and 1E 1547.0−5408 are in quiescence. It has experienced several glitches over the past two decades which were shown to be radiatively quiet in Chapter 6. We showed conclusively that it has not had any observed radiative variability despite previous claims.

The level and type of radiative activity among these three sources is markedly different. 1E 1547.0−5408 is very active, having experienced two outbursts within three months in 2008/2009 and another in 2006–2007 (Halpern et al., 2008). It has also emitted hundreds of short X-ray bursts. In contrast, Swift 1822.3−1606 displayed a much more well behaved post-outburst recovery and emitted only a handful of short X-ray bursts (Chapter 4). Following a putative glitch,

121 122 7 Summary and Conclusions

its timing properties stabilized to a degree unusual in magnetars and it seems to be approaching its quiescent flux state. In terms of radiative variability, 1RXS 170849.0−400910 is the most well behaved of the three with no observed radiative variability, but it also has by far the brightest quiescent X-ray flux state. It is a frequent glitcher, and therefore experiences significant timing variability. Here we attempt to place these three objects in the context of the larger magnetar population.

Note that in the following, properties of magnetars, unless otherwise noted, are from the McGill Magnetar Catalog (Olausen & Kaspi, 2014)1.

7.1 Emerging Trends in the Magnetar Population

Before we discuss the magnetar population from the perspective of the three objects in this thesis, we must recall a few things regarding magnetars and the magnetar model. First, the quiescent X-ray luminosities of magnetars seem to be correlated with their magnetic fields (Pons et al., 2007; An et al., 2012). This makes sense within the magnetar model as the high magnetic field is thought to provide the extra energy reservoir that powers both the activity and anomalously high X-ray luminosities of magnetars (see Section 1.2.3).

Secondly, characteristic ages from pulsar timing (Section 1.1.4) are not accurate measures of the true ages of magnetars and often greatly overestimate their ages. For example, the characteristic age of the magnetar 1E 2259+586 is ∼ 230 kyr but it is located in the supernova remnant CTB 109 which has an estimated age of 14 kyr (Sasaki et al., 2013). In most cases, ages measured from other methods are significantly smaller for magnetars than their characteristic ages (see Olausen & Kaspi, 2014). This implies that magnetars spin down more rapidly than what would be predicted for the simplified pulsar model of a pure dipole spinning in a vacuum (see Chapter 1). However, in general it is reasonable to assume that slower spinning pulsars with lower P˙ ’s are older than the faster ones. So, here we will assume that faster spinning magnetars are younger than those at long periods.

We must also note that the magnetic field measured by pulsar timing is only the dipolar, surface component of the total magnetic field. If the toroidal component of a neutron star’s magnetic field

1http://www.physics.mcgill.ca/~pulsar/magnetar/main.html 7.1 Emerging Trends in the Magnetar Population 123

is significant compared to its poloidal component, the true magnetic field could be higher than that implied by pulsar timing. It is therefore possible that the magnetic field, the energy source that is both heating the surface of magnetars and causing magnetar activity, could be significantly higher than measured from pulsar timing due to a “hidden” toroidal magnetic field. As discussed in Section 5.4.1, the low-magnetic-field magnetars may have toroidal B fields much larger than their spin-down measured dipolar magnetic fields (Thompson & Duncan, 1996; Pons & Perna, 2011). It is therefore possible that a high toroidal component of the magnetic field provides the energy reservoir necessary for magnetar activity.

If we take a broader view of magnetars, and consider objects other than the three studied here, we see that these three objects are in many ways “typical” of the objects near them in P – P˙ parameter space (Figure 7.1). At the long period, high-magnetic field end of the magnetar population, are the bright AXPs which have been monitored for the past 20 years using RXTE and Swift (Dib & Kaspi, 2014). These five magnetars, 1RXS 170849.0−400910, 1E 1841−045, 1E 2259+586, 4U 0142+61, and 1E 1048.1−5937, have high persistent X-ray luminosities (∼ 20 − 200 × 1033 erg s−1 in the 2–10 keV band) and when they have outbursts their flux increases are modest (< 10× over quiescence; and note that 1RXS 170849.0−400910 and 1E 1841−045 have not displayed outbursts).

Contrast this with 1E 1547.0−5408 and its neighbours. The lowest X-ray luminosity yet observed for 1E 1547.0−5408 is ∼ 40 times lower than that of 1RXS 170849.0−400910 and its outbursts have been anything but modest with a > 1000× flux increase in 2009. The two magnetars closest to 1E 1547.0−5408 in P –P˙ space are SGR 1627−41 and Swift J1834.9−0846. SGR 1627−41 had two outbursts in 1998 and 2008 which had flux increases of ∼ 20 and ∼ 100 times respectively (An et al., 2012). Swift J1834.9−0846 was discovered in 2011 following an outburst which raised its X-ray flux by at least a factor of 1000 based on a Chandra non-detection in 2009 (Kargaltsev et al., 2012).

The low-magnetic-field magnetar Swift 1822.3−1606 has behaved more similarly to 1E 1547.0−5408 than to 1RXS 170849.0−400910 in that it had a large flux increase (∼ 1000 times that of the ROSAT measured quiescent level; see Chapter 4) but is located in a very different location in P –P˙ space. What clearly separates Swift 1822.3−1606 and its fellow low-magnetic- 124 7 Summary and Conclusions

-9 10

3 r 10 y 34.8 -10 10 34.2 1E 1841 045 1015 1E 1048.1 5937 − G 1E 1547.0 5408 − − 1RXS J170849.0 40091 SGR 1627 41 − -11 − 33.6 10 XTE J1810 197 PSR J1846 0258 Swift J1834 0845 − − − 5 r 10 y 33.0 )

) 4U 0142+61 X s

/ -12 L s 10 ( ( 32.4

1E 2259+586 g ˙ 14 P 10 G o l 31.8 -13 10

7 r 31.2 10 y Swift J1822.3 1606 − -14 10 30.6

13 SGR J0418+5732 10 G 30.0 -15 10 0.2 0.5 1.0 2.0 5.0 10.0 20.0 P (s)

Figure 7.1: P –P˙ diagram focussed on the long period, high P˙ region to highlight magnetars. Certain objects of interest, discussed in the text, are labelled in black. The three magnetars studied in this thesis are labelled in red. Black points are pulsars from the ATNF catalog. Squares denote magnetars and are coloured by their X-ray luminosities from the Magnetar Catalog. Gray squares represent those magnetars that do not yet have a quiescent X-ray luminosity measured. Green circles mark X-ray dim isolated neutron stars (XDINs). 7.1 Emerging Trends in the Magnetar Population 125

field magnetar SGR 0418+5729 from the rest of the magnetar population is a low P˙ and thus spin-down implied magnetic field1. Like Swift 1822.3−1606, SGR 0418+5729 also experienced an outburst that led to its discovery from which it recovered smoothly to its quiescent state (Rea et al., 2013). Also, like Swift 1822.3−1606, the spin-down of SGR 0418+5729 is well fit by a simple ν, ν˙ spin-down model over a timescale of over three years (Rea et al., 2013), although, unlike Swift 1822.3−1606 (Chapter 5), its spin-down model does not require a post-outburst glitch recovery. This is unusual for magnetars which generally require multiple spin-down derivatives to time. The low-B magnetars seem to be relatively better behaved than other magnetars post- outburst. As was pointed out above, the long-period magnetars tend to be more luminous than those with shorter periods for a given B and their outbursts are modest in comparison to that of 1E 1547.0−5408 and the other transient magnetars. As discussed by Pons & Rea (2012) and mentioned in Section 5.3.2 this could be due to a maximum luminosity for neutron stars due to the dominance of neutrino cooling at high temperatures. So, for a fixed size of energy deposition into the neutron star crust, a less luminous magnetar, such as 1E 1547.0−5408 or Swift 1822.3−1606, will be able to have a larger outburst than one that is near the limiting luminosity in quiescence. Although this is a satisfactory explanation for the relative magnitudes of the outbursts, an open question is why these more luminous magnetars tend to be at longer spin periods. Naively, one may expect magnetars to cool as they age, and thus the opposite behaviour, i.e. that longer period magnetars would be cooler, would be expected. One possibility is that if the younger transient magnetars have outbursts more often than those at longer periods, there may be undetected, low-luminosity magnetars at long periods that would be found if they enter outburst and their non-detection is just due to their lower outburst rate. Indeed, 6/9 of the magnetars, excluding the low-magnetic-field magnetars, with periods > 6 s were discovered due to their bright persistent emission and not due to radiative activity. Further, two of the three that remain, SGR 0526−66 and SGR 1806−20 do have high X-ray luminosities, but were discovered from their bursts and giant flares in 1979, in an era when we did not have

1Note that two other magnetars, CXOU J164710.2−455216 and 3XMM J185246.6+003317, have upper limits to their magnetic fields, < 7 × 1013 G(An et al., 2013) and < 4 × 1013 G(Rea et al., 2014) respectively, that suggest that they are also likely low-magnetic-field magnetars. 126 7 Summary and Conclusions sensitive all-sky X-ray surveys that would have discovered them from their persistent emission.

We, of course, do know of long-period magnetars with low quiescent luminosities: the low- magnetic-field magnetars. Swift 1822.3−1606 and SGR 0418+5729 were discovered due to their

30 −1 outbursts and their quiescent 2–10 keV luminosities are both ∼< 10 erg s (Scholz et al., 2012; Rea et al., 2013), much lower than in other magnetars. If there are undetected sources with luminosities comparable to the transient magnetars and if magnetar activity scales with age and magnetic field, then why would a population of low-B sources emerge due to their outbursts before a, presumably more active, high-B population? This seems to argue against such a selection effect.

If the lack of slow, low-luminosity, high-B magnetars is not a selection effect due to outburst rate then there must be a mechanism in magnetar evolution that biases long period sources to high luminosities. The source of both activity and crustal heating in the magnetar model is the decay of the high magnetic field (Chapter 1). Energy could be deposited in the crust promptly, so perhaps the outburst activity that a magnetar experiences earlier in its lifetime causes the crust of the neutron star to be heated. Alternatively, the magnetic field decay could heat the neutron star in a secular fashion over a long timescale and so the heating and activity could be correlated due to a common origin, rather than being causally related.

In this context, it is also worth noting the flux history of 1E 1547.0−5408. The lowest flux state yet recording for it occurred in 2007 when its 0.5–10 keV flux was found to be ∼ 3 × 10−13 erg cm−2 s−1. Following its 2009 outburst, the flux has been decreasing according to a power-law with index −0.24 (Section 3.3.1). If the flux decay continues to follow this form, the time to reach the 2007 flux level is ∼ 1 Myr. The new flux state may therefore be effectively permanent on the timescale of the active lifetime of the magnetar. If another outburst occurs in the intervening time, that could result in yet another enhancement of this new “quiescent” state. Perhaps, therefore, 1E 1547.0−5408 is showing us that outburst activity heats the neutron star crust in a prompt way resulting in a flux enhancement that could persist over the timescale it takes to evolve to longer periods. Note, however, that plateaus in post-outburst flux decays of magnetars have been observed (e.g. An et al., 2012). Further monitoring of 1E 1547.0−5408 will reveal whether or not this enhancement persists as predicted by the power-law decay model. Also, 7.1 Emerging Trends in the Magnetar Population 127

building up a larger sample of long-term magnetar outburst flux decays, especially those from transient magnetars like 1E 1547.0−5408, will show whether such a long-term flux enhancement is unique to 1E 1547.0−5408 or does indeed represent a feature of magnetar evolution.

We then arrive at a picture of magnetar evolution where the short period magnetars with relatively low quiescent luminosities experience large outbursts and, whether directly through this activity or though a more secular process, they are heated as they spin down to longer periods. If the more luminous magnetars also have outbursts of similar magnitude to those displayed by the transient ones, their flux increases will be modest or non-detectable due to the prevalence of neutrino cooling at high crustal temperatures. These luminous long-period magnetars, over a timescale of several tens to hundreds of thousands of years then cool and experience magnetic field decay until they become low-magnetic-field magnetars that may be detected when they experience rare outbursts. In this picture, the fact that we have detected a significant number of these rare low-B magnetar outbursts points to a large hidden population of quiescent, low-luminosity, low-B magnetars.

This picture is supported by magnetothermal evolution models of high-magnetic field neutron stars. In Figure 7.2, we show paths of magnetar evolution in the P –P˙ plane based on simulations from Viganò et al. (2013). These simulations take into account the Hall term in equations of the coupled evolution of magnetic field and neutron star temperature. This term is best illustrated by the Hall effect where a voltage is induced across an electrical conductor due to a perpendicular magnetic field. In neutron stars, magnetic field lines are moved due to feedback from the electron fluid in the crust. This term was previously ignored due to its negligibility at B < 1013 G as well as its complexity. The main effect of the Hall term is to transfer magnetic energy between toroidal and poloidal components. These simulations show that on a timescale of ∼ 104 years, the transient, short period, magnetars evolve through magnetic field decay to periods ∼ 10 s. These magnetars then experience magnetic field decay on a timescale of several hundreds of thousands of years that evolves them to the low-magnetic-field magnetars. Note that the simulations in Viganò et al. (2013) predict that longer-period magnetars should be cooler than their younger, faster counterparts, the opposite of what was noted in the discussion above. However, they do note the excess luminosities than predicted in their simulation for those sources. 128 7 Summary and Conclusions

(#'$9@8>$

(#'$9A88$ !,%$$9?9<$ 9"$9=$ 9"$9@<9$ 9"$98<@$ 9',($$9?8@$ (#'$9>:?$$ !,%$$8988$ ,)"$$9@98$ &('$$999A$ (#'$8=89$ &('$$9?9@$ <*$89<:$ &('$$9?<8$ !,%$$9>

&('$ :;;<$ &('$$8?:>$ 9"$::=A$ +.2-$ (51/$$9@::$ &('$ 9?8>$ ',$$9;8@$ ',$$8?:8$ ',$$8<:8$ ',$$8@8>$ &('$ 8>=>$ ',$$:9<;$ ',$$9@=>$ #.3140-$ (#'$8<9@$ &('$ 98==$

&('$$8=;@$

Figure 7.2: Evolutionary tracks in the P –P˙ diagram with mass and radius according to the magnetothermal evolution model of Viganò et al. (2013) Asterisks mark the model ages t = 103, 104, 105, 5 × 105 years, while dashed lines show the tracks followed in absence of magnetic field decay. Figure from Viganò et al. (2013). 7.2 Relation to Other Classes of Neutron Stars 129

7.2 Relation to Other Classes of Neutron Stars

It is worth noting that there are several high-B field rotation-powered pulsars (RPPs) that overlap in P − P˙ space with the magnetars. What sets these objects apart from magnetars, if anything? First of all, they lack two defining characteristics of magnetars: they have X-ray luminosities that ˙ can be explained solely from rotational spin down (i.e. LX ≪ E) and they have not displayed any activity typical of magnetars, i.e. X-ray outbursts or short X-ray bursts. However, as we have seen for the objects in this thesis, these “defining” characteristics are not all that defining. The ˙ LX ≫ E criteria is only met by many magnetars during outburst (e.g for 1E 1547.0−5408; ˙ see Chapter 3), and several magnetars with LX ≫ E have never showed an outburst (e.g. 1RXS 170849.0−400910; see Chapter 6). Moreover, the low-magnetic-field magnetars have shown that a high spin-down inferred magnetic field is not required to display magnetar-like activity.

Indeed, an object originally classified as high-B field RPP,PSR J1846−0258, showed magnetar- like activity in 2006 when it displayed an X-ray outburst and emitted a handful of short X-ray bursts. This illustrated (before low-B magnetars were discovered and while transient magnetars ˙ were still just emerging) that magnetar activity is not exclusive to those sources with LX ≫ E and high magnetic fields. The period of PSR J1846−0258, 0.327 s, is also very atypical of magnetars so it is unclear how it fits into the picture presented in the previous section. Is it a young magnetar that will evolve into the main magnetar population? Or will it evolve along constant magnetic field lines before experiencing significant magnetic field decay as predicted by Viganò et al. (2013)? In the latter case, its descendants would be the high-B pulsars located between PSR J1846−0258 and the low-B magnetars on the P − P˙ diagram. Are these sources also able to show magnetar-like activity? Monitoring of these sources in the X-ray could place limits on or detect such activity.

How do these high-B RPPs differ from quiescent transient magnetars (i.e. those with LX ≪ E˙ )? It appears that magnetars have systematically higher quiescent blackbody temperatures than high-B RPPs (Figure 14 of Olausen & Kaspi, 2014). So, those high-B objects that we label as magnetars have hotter surfaces than those that we do not label as such. If magnetar activity causes, or is correlated with, the heating of the neutron star surface we would expect those objects 130 7 Summary and Conclusions

that display activity to be hotter than those that don’t. There is also a possible selection effect here: objects that display magnetar activity more often are more likely to be detected due to their activity, and, assuming an activity-temperature correlation, these objects would therefore be more heated. As we detect more outbursting objects, we may find that the gap in blackbody temperature between magnetars and high-B pulsars disappears. Indeed, Perna & Pons (2011) present simulations of long-term evolution of magnetic stresses in the crusts of neutron stars, and find that magnetar activity could arise from any high-B pulsar, but that the frequency of outbursts decreases as a function of increasing age and decreasing magnetic field. So, those objects that we call magnetars may be just the extreme of a spectrum of activity. Also recall that the pulsar- timing-measured magnetic field is only the dipolar component and that a “hidden” toroidal field could be present in some sources to fuel activity and raise the temperature of the neutron star.

Another class of neutron star that may be related to magnetars are the so-called “X-ray dim isolated neutron stars” or XDINSs (marked with green circles in Figure 7.1). These sources are located conspicuously between the low-magnetic-field magnetars and the rest of the magnetar population on the P − P˙ plane. Further, in the magnetothermal models of Viganò et al. (2013) (Figure 7.2) they lie along the evolutionary curves linking the low-magnetic-field magnetars and the main magnetar population. This suggests that they could be quiescent low-magnetic-field magnetars. They are well fit by blackbody spectral models with temperatures ∼ 0.1 keV similar to Swift 1822.3−1606 which was found to have a kT = 0.12 keV in the archival ROSAT observation (see Chapter 4). However, the lowest blackbody temperatures observed in other low-magnetic-field magnetars (∼ 0.3 keV for SGR 0418+5729; Rea et al. 2013, ∼ 0.6 kerV for 3XMM J185246.6+003317; Rea et al. 2014, ∼ 0.5 keV for CXOU J164710.2−455216; An et al. 2013) seem to be significantly higher. Perhaps these other sources will cool further in the future.

7.3 Concluding Remarks

This thesis has presented studies of three different magnetars, two following their outbursts, and one (1RXS 170849.0−400910) which has not displayed any radiative activity. This concluding chapter speculated on the locations within the magnetar population of these three objects based on the differences in their behaviour. We are in an era where the magnetar population is emerging. 7.3 Concluding Remarks 131

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