An Anti-Glitch in a Magnetar

Robert F. Archibald

Master of Science

Department of Physics

McGill University Montreal,Quebec 2013-08-15

A Thesis submitted to McGill University in partial fulﬁllment of the requirements for the degree of Master of Science c Robert Frederic Archibald, 2013 DEDICATION

For the family.

ii Abstract

Magnetars are neutron stars showing dramatic X-ray and soft γ-ray outbursting behaviour that is thought to be powered by their intense internal magnetic fields. Like conventional neutron stars in the form of radio pulsars, magnetars show sudden changes in their rotation rate, called “glitches,” during which angular momentum is believed to be transferred between the solid outer crust and the superfluid component of the inner crust. Hitherto, the several hundred observed glitches in radio pulsars and magnetars have involved a sudden spin-up of the star, due presumably to the interior superfluid rotating faster than the crust. In this thesis, we report on X-ray timing observations of the magnetar 1E 2259+586 , using the Swift X-ray Telescope, which we show exhibited a clear “anti-glitch” – a sudden spin down. We show that this event, like some previous magnetar spin-up glitches, was accompanied by multiple X-ray radiative changes and a significant spin-down rate change. This event, if of origin internal to the star, is unpredicted in models of neutron star spin-down and is suggestive of differential rotation in the neutron star, further supporting the need for a rethinking of glitch theory for all neutron stars.

iii ABREG´ E´

Les magnétarssont des étoilesàneutrons caractériséespar une émissionvio- lente de rayons X et de rayons gamma doux. Cette émissionpar sursauts serait alimentéepar leur puissants champs magntiques internes. A` l’instar des étoilesà neutrons conventionnelles se trouvant sous la forme de pulsars radios, les magnétars affichent des changements soudains dans leur vitesse de rotation, appelés‘glitches’. Durant ces changements, un transfer de moment angulaire se ferait entre la croûte solide extérieureet la composante superfluide de la croûteintérieure. A` ce jour, les quelques centaines de ‘glitches’ observésdans les pulsars radios et les magnétarsse sont transformésen accélérationsoudaine de l’étoile,un phénomènevraisemblable- ment dûau fait que la rotation du superfluide intérieurest plus rapide que celle de la croûte.Dans ce travail, nous rapportons des observations du magnétar1E 2259+586 réalisées l’aide du Télescope àrayons X Swift démontrant clairement un comportement d’anti-glitch, c’est-à-direun ralentissement abrupt de la vitesse de rotation de l’étoile.Nous montrons que cet évènement, tout comme d’autres ‘glitches’ observés précédemment, a étéaccompagnépar de multiples changements dans l’émissionde rayons X et par une décroissancedu spin de l’étoile.Ce comportement, s’il est caus par des mécanismesstellaires internes, n’est pas préditpar les modèlesde varia- tion de vitesse de rotation des étoilesàneutrons et suggèrel’existence de rotation différentielle, ce qui supporte l’idéeque la thèorie du ‘glitch’ dans les étoilesàneu- trons doit êtrerepensée.

iv TABLE OF CONTENTS

DEDICATION...... ii Abstract...... iii ABREG´ E´...... iv LIST OF TABLES...... vii LIST OF FIGURES...... viii PREFACE...... ix STATEMENT OF ORIGINALITY AND CONTRIBUTION OF AUTHORS.x ACKNOWLEDGEMENTS...... xi 1 Neutron Stars...... 1 1.1 Theoretical Objects...... 1 1.2 Observational Confirmation of the Existence of Neutron Stars..2 1.3 Canonical Pulsar...... 2 1.4 Observational Classes of Pulsars...... 5 1.5 Soft Gamma-ray Repeaters and Anomalous X-ray Pulsars.....5 1.6 Unification: The Magnetar Model...... 8 2 Pulsar Timing...... 11 2.1 Timing...... 11 2.1.1 TEMPO2...... 15 2.2 Glitches...... 16 2.2.1 The Starquake Model...... 18 2.2.2 The Superfluidic Coupling Model...... 19 2.3 Glitches in Magnetars...... 21

v 3 X-ray Astronomy...... 22 3.1 X-ray Spectroscopy...... 23 3.2 Mission History...... 24 3.3 The Swift Gamma-Ray Burst Mission...... 27 4 An Anti-Glitch in 1E 2259+586...... 30 4.1 Introduction...... 30 4.2 Observations...... 33 4.2.1 Swift X-ray Telescope Observations...... 33 4.2.2 Expanded Very Large Array Observation...... 41 4.2.3 Chandra X-ray Observation...... 42 4.3 Discussion...... 42 4.3.1 Previous Evidence for Anti-Glitches...... 42 4.3.2 Physical Origins of the Anti-Glitch...... 43 5 Outlook and Conclusions...... 46 References...... 49

vi LIST OF TABLES Table page 4–1 Properties of 1E 2259+586...... 32 4–2 Timing parameters for 1E 2259+586...... 38

vii LIST OF FIGURES Figure page 1–1 P − P˙ diagram...... 6 2–1 Typical pulse profiles...... 13 2–2 Pulsar Glitches...... 16 3–1 The Swift Satellite...... 29 4–1 XMM image of CTB 109...... 31 4–2 Pulse profiles of 1E 2259+586...... 36 4–3 Timing and X-ray flux properties of 1E 2259+586 around the 2012 event...... 39 4–4 Timing residuals for 1E 2259+586...... 40

viii PREFACE

This thesis contains a manuscript published in Nature. This work was done in collaboration with other authors at various institutions. Acknowedgements from the original manuscript follow. Acknowledgements for “An Anti-Glitch in a Magnetar” (Chapter4), Archibald et al. 2013: Victoria Kaspi acknowledges support from the Natural Sciences and En- gineering Research Council of Canada Discovery Grant and John C. Polanyi Award, from the Canadian Institute for Advanced Research, from Fonds de Recherche Nature et Technologies Qu´ebec, from the Canada Research Chairs Program, and from the Lorne Trottier Chair in Astrophysics and Cosmology. David Tsang was supported by the Lorne Trottier Chair in Astrophysics and Cosmology and the Canadian Institute for Advanced Research. Kostas N. Gourgouliatos was supported by the Centre de Recherche en Astrophysique du Qu´ebec. We thank Heidi Medlin and Joseph Gelfand for help with the EVLA observation. We thank D. Eichler, B. Link, M. Lyutikov and C. Thompson for useful discussions. We acknowledge the use of public data from the Swift data archive.

ix STATEMENT OF ORIGINALITY AND CONTRIBUTION OF AUTHORS

The university guidelines for a manuscript-based thesis state that “ candidates have the option of including, as part of the thesis, the text of one or more papers submitted, or to be submitted, for publication, or the clearly duplicated text of one or more published papers.” In accordance with the above, the results presented in this thesis is original work that was published in the following refereed article: The manuscript “An Anti-Glitch in a Magnetar” (Chapter4), Archibald et al. 2013. The paper discribes the discovery of an “anti-glitch” in a magnetar and dis- cusses possible physical origins of such an event. I performed the data analysis on the Swift data and wrote portions of the analysis software. Victoria Kaspi designed the study, was the project leader for the Swift data, proposed for the Chandra data, assisted with the interpretation of the data analysis, as well as with the theoretical implications. C.Y. Ng proposed for the VLA data and reduced them and the Chandra data. Kostas N. Gourgouliatos and David Tsang assisted with the theoretical implications. Paul Scholz wrote signiﬁcant portions of the Swift analysis software. A. P. Beardmore, N. Gehrels, & J. A. Kennea assisted with Swift observations and data analysis. I wrote the paper with guidance from Victoria Kaspi and with signiﬁcant input from all co-authors.

x ACKNOWLEDGEMENTS

I would like to thank my supervisor Victoria Kaspi for taking me on as a student, her guidance throughout the past two years have been invaluable. I would also like to extend my gratitude to the other members of the group for many enlightening conversations, and general merriment during my time here. I would also like to thank Gabrielle Simard for translating the abstract.

xi CHAPTER 1 Neutron Stars 1.1 Theoretical Objects

In the early 1930s, Fritz Zwicky & Walter Baade were struggling to explain the massive amounts of energy given oﬀ by supernovae – the sudden appearance of objects

10 in the sky which reached ∼ 10 L . At the same time physicists were unraveling the mysteries of the inner workings of the atom, and had just experimentally conﬁrmed the existence of the neutron (Chadwick, 1932). Zwicky and Baade postulated that the energy of a supernova could then come from the compacting of a stellar core from normal stellar densities into a gas of neutrons forming a “neutron star”- and in so doing, convert ∼ 10% of the stellar-core rest mass into energy (Baade and Zwicky, 1934). Lev Davidovich Landau also postulated the existence of “dense stars that look like one giant nucleus” (Landau and Peierls, 1931; Yakovlev et al., 2013), and later about the possible existence of “neutron cores” at the centre of stars (Landau, 1938). Neutron stars are now indeed known to be the compact remnants left over from supernovae resulting from the death throes of stars between a few to a few tens of

M (Shapiro and Teukolsky, 1983). They are stars held from gravitational collapse by neutron degeneracy pressure. Neutron stars are extremely dense objects with typical densities of ∼ 1015 g cm−3, about three times nuclear density. They have radii that are ∼ 10 − 14 km, and contain masses between ∼ 1 − 3M , although

1 the exact mass-radius relation for super-nuclear matter is not known (eg. Potekhin, 2010). 1.2 Observational Conﬁrmation of the Existence of Neutron Stars

Neutron stars were not observed until more than forty years after their initial predicted existence. The first neutron star observed was Scorpius X–1 in 1962 (Giac- coni et al., 1962; Bowyer et al., 1964). It was not, however, until 1967 that Scorpius X–1 was positively identified as an accreting neutron star (Shklovsky, 1967). This coincided within the detection of an incredibly stable periodic signal at the Mullard Radio Astronomy Observatory by Hewish et al.(1968). Originally dubbed LGM–1, for ‘little green men’, the new objects were called pulsars, a portmanteau of “PUL- Sating stARs.” It was quickly realized that due to the extreme stability of the pulse periods, and the needed compactness of the objects, these pulsars must be neutron stars (Gold, 1968). The first detection of pulsars in the X-ray band came soon after with a rocket launched on the 23rd of December, 1968 which detected pulsations from the direction of the Crab Nebula (Ducros et al., 1970). Since then, pulsars have been observed in nearly every waveband – from radio to gamma-ray (Abdo et al., 2010). 1.3 Canonical Pulsar

The canonical pulsar is rotation powered, with its emission coming from magnetic dipole radiation (Gold, 1968; Ostriker and Gunn, 1969). The principle energy source available to a pulsar is then its total rotational kinetic energy:

1 E = IΩ2 (1.1) 2

2 2π where Ω is its angular frequency (Ω = 2πν = P ), and I the pulsar’s moment of inertia. Since the mass of an isolated pulsar, and more generally the exact equation of state is unknown (Potekhin, 2010), the exact moment of inertia is unknown. To gain insight, and to have a standard measure with which to compare pulsars, generally

‘average’ pulsar parameters are assumed, with M = 1.4M and R = 10 km (Lyne and Graham-Smith, 2005). Given these parameters and assuming a pulsar is a sphere

2 2 45 2 of constant density, one can calculate I = 5 MR = 10 g cm . Given that isolated pulsars are observed to be spinning-down, one can calculate the power available at a given time by taking the derivative of equation 1.1, giving:

2 E˙ = IΩΩ˙ = ΩΩ˙ MR2 (1.2) 5

Since pulsars are highly magnetized and spinning, they will emit electromagnetic radiation by magnetic dipole radiation (eg. Lyne and Graham-Smith, 2005). In this case, the power emitted by the pulsar can be given by:

2m2Ω4 E˙ = 0 sin2 α, (1.3) 3πc3 where m0 is the magnetic moment, Ω the rotational frequency, and α the misalign- ment between the magnetic and rotational axis.

−3 With this, and using the approximation of a point dipole, Bs = m0R , and if we assume all power lost is emitted via magnetic dipole radiation we can equate the spin-down power (equation 1.2), and dipole radiation (equation 1.3), and solve for

Bs:

3 1 1 1 3Mc3 2 −ν˙ 2 −ν˙ 2 B = = 3.2 × 1019 G. (1.4) s 20πR4 sin2 α ν3 ν3

Bs is referred to as the spin-down inferred magnetic field of the pulsar, and is often used as a proxy for the actual magnetic field. It is thought to be representative of the true equatorial surface magnetic field to within a factor of a few, depending on the alignment angle between the magnetic and rotation axis, α, among other factors.

As well, with the above assumptions, we can determine a characteristic age, τc, for a pulsar: 1 ν τ = . (1.5) c 2 ν˙ This equation has built in the assumption that the initial spin period was much faster than the current spin period, and that the pulsar spins down only via magnetic dipole radiation. For a few young pulsars, one can test the assumption that pulsars can be well modelled as a magnetic dipole in a vacuum. One can do this by measuring the braking index of of pulsar, deﬁned as

νν¨ n = . (1.6) ν˙ 2

Magnetic dipole radiation predicts that n = 3, while the measured values are all lower than this, between 0.9–2.91 (eg. Lyne et al., 1988; Livingstone et al., 2005; Espinoza et al., 2011a). This indicates there is more physics involved in pulsar spin down than just simple dipole radiation.

4 1.4 Observational Classes of Pulsars

Pulsars are often classiﬁed based on their periods, and period derivatives. This is often displayed in the form of a P -P˙ diagram, as in Figure 1–1. In the lower left hand side of the diagram reside the millisecond pulsars (msps), named for their incredibly short spin period. They are believed to be formed by the spinning up of an old, slow pulsar by accretion from a companion and, as such, are often found in binary systems. This recycling process weakens the pulsar’s magnetic ﬁeld, leaving

8 millisecond pulsars with Bs ∼ 10 G (eg. Paczy´nski, 1971; Urpin et al., 1998). The majority of pulsars fall in the centre of this diagram, with periods ranging from approximately a tenth of a second to a second and a magnetic ﬁeld between 1011 and 1013 G. These pulsars, as well as the msps are believed to be powered by magnetic dipole radiation (Ostriker and Gunn, 1969), as discussed in Section 1.3. Magnetars, the focus of this work, occupy the upper right-hand side of this diagram, and are discussed in detail in the following section. 1.5 Soft Gamma-ray Repeaters and Anomalous X-ray Pulsars

What we now generally refer to as magnetars were originally discovered and classiﬁed as two sets of objects: the Soft Gamma-ray Repeaters and the Anomalous X-ray Pulsars. Soft Gamma-ray Repeaters (SGRs) were named after their repeated output of soft gamma ray bursts. Such a repetitive behaviour was ﬁrst detected from FXP 0520−66 (now called SGR 0526−66) by Golenetskij et al.(1979). Recurrent bursts were seen soon after from another source, B 1900+14 (now called SGR 1900+14) by Mazets et al.(1979).

5 Figure 1–1 The P −P˙ diagram. Pulsar period derivative is plotted against pulsar spin period. Magnetars are highlighted as red circles, with the position of 1E 2259+586 indicated by the star. Isochrones are represented by dot-dashed lines, and lines of isomagnetism are dashed. Data from the ATNF pulsar catalogue, code to generate the diagram was provided by P. Scholz.

-8 10 -9 10 Other Pulsar -10 10 Magnetar -11 10 1E 2259+586 14 -12 10 10 G kyr -13 1 10 13 ) -14 10 s G / 10 yr s k

( 00

-15 1 ˙

P 10 12 -16 10 10 G Myr -17 10 10 11 -18 10 10 G -19 10 -20 10 -21 10 -3 -2 -1 0 1 2 10 10 10 10 10 10 P (s)

6 SGRs are also known for their giant flares, in which their luminosity can reach a million times the Eddington luminosity for a neutron star. On the 5th of March, 1979 the first such giant flare was detected with a short (∼ 200 ms) intense (∼ 5 × 1042 erg/s) burst, followed by emission with strong periodicity at 8 seconds by Venera 11 & 12, and other spacecrafts from (what is now called) SGR 0526−66 (Cline et al., 1980). The emission was originally thought to be from a Gamma-ray Burst, but the unusual periodic nature of the burst hinted at other explanations. The position of this burst was consistent with the location of the supernova remnant N49 in the Large Magellanic Cloud, a known soft X-ray source, and led to the (correct) speculation that this event could be linked to a neutron star (Barat et al., 1979) as it had been proposed that neutron stars could produce soft gamma-ray bursts (Tsygan, 1975). To date only three giant-flares from SGRs have been seen - the above mentioned in SGR 0526-66, one on the 27th of August 1998 with SGR 1900+14 (Woods et al., 1999), and SGR 1806−20 (Hurley et al., 2005) on the 27th of December 2004. It took 15 years before quiescent emission from an SGR was seen, with the detection of an X-ray point-source at the location of SGR 0526−66 (Rothschild et al., 1994). That same year, persistent X-rays were also seen from SGR 1806−20 (Sonobe et al., 1994). Persistent pulsations from SGRs were first seen by Kouveliotou et al. (1998) from SGR 1806-20, where a period and period derivative could be measured, implying a magnetic field of 8 × 1014 G, higher than any other known pulsar at that time. Another group of neutron stars, with spin periods of a few seconds, and high X- ray to optical flux ratios were grouped together by Mereghetti and Stella(1995), and

7 later dubbed the “Anomalous X-ray Pulsars”(AXPs) (Mereghetti et al., 1998). The AXPs were noted as anomalous primarily as their X-ray luminosity exceeded the E˙ available from normal pulsar spin-down. These AXPs shared many other properties amongst themselves. They had a softer spectra than most X-ray pulsars, as well as being less luminous than the persistent emission of Low Mass X-ray Binaries. Unlike the other X-ray pulsars, these AXPs had relatively constant ﬂux over months to years. These AXPs also appeared to be young objects, as two of them were associated with supernova remnants. Originally, it was proposed that the AXPs were accretion powered pulsars with ultra-low mass companions. With further observations of these sources, however, the parameter space available to a companion star became more and more excluded (Mereghetti et al., 1998), suggesting that these were instead a type of isolated neutron stars. 1.6 Uniﬁcation: The Magnetar Model

Duncan and Thompson(1992) presented a model to explain the giant SGR ﬂares as outbursts from a highly magnetized neutron stars. In their model, neutron

17 Pi stars can become highly magnetized, up to 3×10 1ms G through convective dynamo action as differential rotation in the star is smoothed by magnetic stress (Duncan and Thompson, 1992). This model was expanded on with a series of papers (Thompson and Duncan, 1995, 1996) in which mechanisms for the persistent emission properties, as well as the giant flares were put forth. In the magnetar model, the excess X-ray emission, as well as the bursts come from the decay of enormous magnetic fields. In the initial magnetar model, the differentiation point between a regular pulsar and a magnetar occurred when the magnetic field of the pulsar exceeded BQ, the magnetic

8 ﬁeld strength at which the ﬁrst electron Landau level matches the electron rest-mass (Thompson and Duncan, 1995).

2 3 mec 13 BQ = = 4.4 × 10 G. (1.7) e~

Thompson and Duncan(1996) also suggested that AXPs might be different observational incidences of the magnetar class, due to their similar periods and spin-down rates as well as similar soft X-ray spectra and a similar Galactic distribution. In doing so, they made a testable prediction that SGR-like bursts would be seen from AXPs. In October of 2001, two SGR-like bursts from 1E 1048.1−5937 (Gavriil et al., 2002) were detected. Since the current AXP accretion models could not account for these SGR like bursts, this provided strong evidence that the magnetar model is the correct description for these sources. Further evidence that SGRs and AXPs seem to be well, and uniquely, explained by the magnetar model came with the detection of a major SGR-like outburst from the AXP 1E 2259+586 (Kaspi et al., 2003). The distinction between magnetars and nominally rotation powered high magnetic field pulsars has become blurred in recent years. The most telling such event came with the detection of magnetar-like emission from a formally ‘well-behaved’ rotation powered pulsar PSR J1846−0258 in the Kes 75 supernova remnant (Gavriil et al., 2008). PSR J1846−0258 had had a stable flux during seven years of monitoring, and had been rotationally stable enough to measure a braking index (Liv- ingstone et al., 2010). However, in 2006, its 2-10 keV X-ray flux increased by a

+4.5 factor of 5.5−2.7, and it emitted several SGR-like bursts. After this magnetar-like

9 outburst, PSR J1846−0258 went back to behaving like a normal rotation-powered pulsar (Livingstone et al., 2010). As well, the recent discovery of magnetars with low magnetic fields, such as SGR 0418+572 with a magnetic field of only 6 × 1012 G, (Rea et al., 2010, 2013), comparable to that of an average pulsar, and Swift J1822.3−1606, with a magnetic field between 2 − 5 × 1013 G(Scholz et al., 2012; Rea et al., 2012) challenge the original magnetar definition of having a magnetic field greater than BQ. Taking these recent discoveries into account, it seems more probable that magnetars are part of a continuum of neutron stars rather than a distinct class. The working definition for magnetars seems to be any pulsar which displays behaviour that is magnetically powered.1 There are currently ∼ 26 known magnetars, and an up-to-date list can be found at the McGill Magnetar Catalogue,2 currently maintained by McGill PhD student Scott Olausen, and to soon appear as Olausen & Kaspi, in prep.

1 Deﬁnition used by Dr. Nanda Rea at her talk at NS2013 2 http://www.physics.mcgill.ca/ pulsar/magnetar/main.html

10 CHAPTER 2 Pulsar Timing In order to do much of the interesting time-domain science with pulsars such as tests of general relativity (eg. Lyne et al., 2004), gravity wave detection (eg. Manchester et al., 2013), and glitch studies, see Section 2.2, one must be able to precisely time pulsars. The best known method to accomplish this is known as phase coherent timing (Manchester and Taylor, 1977). In this timing method, the number of phase turns a pulsar undergoes can be uniquely determined between any two times. In this section, we will explain how to go from raw X-ray event data, to a phase connected timing solution. 2.1 Timing

In order to properly time a pulsar, one must take into account any time delays which occur between the emission of a photon from the pulsar, to its measurement at an observatory. To do so, one must take into account eﬀects such as the motion of the observatory around the Earth, as well as the motion of the Earth relative to the Sun. Photon arrival times are corrected to arrive at the barycentre of our solar

11 system. This is typically done in our analysis using barycorr, part of the standard X-ray analysis software HEASOFT1 . With barycentred photon arrival times, one can find the pulsar spin period. If the pulsar spin period is completely unknown, a Fourier transform can be used to find a peak in the power spectra associated with the pulsar spin period. Complications arise if the pulsar is in a binary, however, since this thesis deals with only isolated pulsars, binary orbital effects will not be discussed. For pulsars where a rough period is already known, the rotation period can be better estimated the H-test (de Jager et al., 1989), which would be too computationally extensive for use in blind searches. The photon arrival times are then folded at the period of the max H-test score to create a pulse profile. To build a high signal-to-noise pulse template, the profiles from multiple observations are aligned and added together to decrease fluctuations caused by a limited number of photons. To illustrate, a sample single observation, and high signal-to-noise pulse template are presented in Figure 2–1. In order to find the phase offset between the standard profile and a given observation, a continuous model for the pulse profile is required. This is done by taking the discrete Fourier transform of the binned pulse profile to create a profile:

n X i2πjφ f(φ) = αje (2.1) j=0 where φ is the pulse phase between 0 and 1, and αj is the the Fourier component of the jth harmonic. For a given observation, a TOA was obtained using a maximum

1 Available from http://heasarc.nasa.gov/lheasoft/

12 Figure 2–1 The top panel shows the pulse proﬁle for a typical Swift monitoring observation of 1E 2259+586 in the 0.5–10 keV range. The bottom shows the standard template built up over multiple observations. The solid line is the Fourier based continuous model used to determine the phase of arrival to create the TOA. In both panels, two pulse cycles are shown for clarity.

0.0 0.5 1.0 1.5 2.0 Pulse Phase

13 likelihood method, as described in Livingstone et al.(2009) and Scholz et al.(2012). The number of harmonics used is optimized to capture the persistent features of the pulse profile, while not capturing features only present due to a finite number of counts. In this method, the probability distribution for an observation being offset by a phase φoff is given by:

N Y P (φoff ) = f(φi − φoff ) (2.2) i=0

th where φi is the arrival phase of the i photon in the observation. The area under the normalized probability distribution function between two points represents the total likelihood for the true phase to be between said points. As such, the uncertainty of a phase offset was estimated by integrating this normalized probability distribution function from the maximum until 34 %, one σ, of the area under the probability distribution function had been encompassed on either side of the maximum. Residuals, the differences between the actual TOA and the TOA predicted by the model are defined as:

R = φoff mod 2π (2.3) where φoff here is the most probable φoff , as determined above. Typically, most timing analysis is done in this residual space using the TEMPO2 software package (Hobbs et al., 2006). In residual space, an error in ν presents itself as a change in slope, and an error inν ˙ as a parabola. In order to set-up and maintain a phase coherent timing solution, one must have observations suﬃciently frequently that the integrated error in phase given by the

14 error in ν,ν ˙, and other timing parameters is less than one half of a phase turn. This ensures that the number of phase turns can be uniquely determined. 2.1.1 TEMPO2

TEMPO2 is a pulsar timing software package developed by George Hobbs and Russell Edwards as part of the Parkes Pulsar Timing Array project (Hobbs et al., 2006). It was based on the original TEMPO2 software package written by J. H. Taylor, R.N. Manchester, D. J. Nice, and others. TEMPO2 takes in two input files, a ‘tim’ file which contains pulse TOAs for all observations, and a ‘par’ file, which contains the parameters for the pulsar spin model. For the case of X-ray data, the ‘tim’ file contains solely pre-barycentred TOAs. The ‘par’ file contains the best-known pulsar spin frequency and frequency derivatives at a reference epoch, as well as any changes in these parameters due to glitches. The TOAs are then fit to a Taylor expansion of pulse phase as a function of the pulsar spin frequency, ν, and time from a reference epoch, t.

1 1 φ = νt + νt˙ 2 + νt¨ 3 + ... (2.4) 2 6

The diﬀerence between the predicted pulse arrival time and the measured TOA, referred to as timing residuals, are minimized using a χ2 minimization.

2 http://www.atnf.csiro.au/people/pulsar/tempo/

15 Figure 2–2 Typical pulsar glitches in ν space (top) and timing residual space (bottom). The left panels shows a simple glitch in ν, and the right panels show a glitch in both ν andν ˙. The dashed line indicates the glitch epoch. ν ν

t t φ φ

t t

2.2 Glitches

A sudden increase in a pulsar’s spin frequency is referred to as a “glitch.” While some glitches are characterized solely by a sudden jump in ν, many glitches have been seen to be accompanied by an increase inν ˙, or to decay by some portion of the initial jump in an exponential manner. Glitches can then be modelled as:

−(t−tg)/τd ν(t) = ν0(t) + ∆ν + ∆ν ˙(t − tg) + ∆νde (2.5)

where ν0 is the expected frequency given the pre-glitch timing behaviour, ∆ν and

∆ν ˙ are permanent changes to the timing parameters occuring at time tg, and ∆νd is a change in frequency which decays with a characteristic timescale τd. Figure 2–2 shows the eﬀect of a glitch in ν and both ν andν ˙ on the observables of a pulsar, in both frequency and residual space.

16 The ﬁrst glitch was observed in 1968 from the Vela pulsar about a year after the initial discovery of pulsars. In the Vela glitch, the period of the pulsar was observed to suddenly decrease by 134 ns, with the glitch being limited to having a timescale less than a week, as it was conﬁned between two weekly observations (Radhakrishnan and Manchester, 1969; Reichley and Downs, 1969). A later observation of Vela during a glitch has since limited the time over which a glitch occurs to less than two minutes (McCulloch et al., 1990). Since then, more than 300 glitches have been seen in over 100 pulsars (Espinoza et al., 2011b; Yu et al., 2013). On the other hand, some Crab pulsar glitches have been fully resolved to have occurred on longer time scales (Lyne et al., 1992). The fractional sizes of these glitches spans many orders of magnitude,

∆ν −11 −5 with ν ranging from 10 to 10 . Since glitches are thought to be due to an interaction between the outer crust, which is tightly coupled to all pulsar observables, and the pulsar’s interior, studying glitches is one of the few methods we have to learn about the interior structures of neutron stars (Link et al., 1992). The link between glitches and the internal structure in neutron stars is drawn mainly from the observation that, in general, rotation powered pulsars do not display any radiative changes following a glitch. However magnetars, whose glitch behaviour is elaborated in the following section, and two normal rotation powered pulsar, PSR J1119−6127 (Weltevrede et al., 2011) and PSR J1846−0258 (Gavriil et al., 2008), have shown radiative changes following a glitch, which could indicate some glitches occur by other methods. With this in mind, we shall brieﬂy discuss the internal structure of a neutron star. The general structure of a neutron star is thought to be as follows: the very surface

17 of the star is a several centimetre thick atmosphere, composed mainly of hydrogen and helium. Below the atmosphere is an outer crust that is ∼ 0.1 − 1 km thick. The outer crust is a solid lattice of heavy elements, like iron, with a degenerate Fermi sea of electrons (Page et al., 2006). It is only the rotation of the outer crust which can be directly observed. Below the outer crust is the inner crust. The inner crust is ∼ 0.5−3 km thick, and starts at the neutron drip density, ∼ 4−8×1011 g cm−3. The neutron drip density is the density at which the neutron chemical potential exceeds its rest mass energy, making it energetically favourable for neutrons to ‘drip’ out of their nuclei (Pethick and Ravenhall, 1991). The inner crust is composed of a solid lattice with a relativistic Fermi gas of superﬂuidic neutrons. The lattice is thought to be strongly coupled to the core’s rotation whereas the superﬂuidic component can rotate independently. Beyond this lies the core. The core, beginning at a density of∼ 2 × 1014 g cm−3 contains the vast majority of the mass of a neutron star (Pines and Alpar, 1985). Its composition, however, depends strongly of the equation of state of dense matter, which is currently not well constrained, and could contain several varieties of exotic particles (Hebeler et al., 2013). 2.2.1 The Starquake Model

The ﬁrst model put forth to attempt to explain glitches is known as the “starquake” model (Baym et al., 1969a). In this model, neutron stars are originally oblate due to their spin period at birth. As the star slows down, it becomes energetically favourable for the crust to become less oblate, however the solid crust cannot grad- ually deform. This builds a strain in the crust until the strain exceeds the breaking

18 point of the crust, at which point a starquake occurs. With the starquake, the neutron star suddenly becomes less oblate, reducing the moment of inertia. Assuming I ∝ MR2 then we can say (Lyne and Graham-Smith, 2005):

∆I ∆ν 2∆R = − = . (2.6) I ν R

In the starquake model, this means in a 10 km neutron star for a typical glitch of

∆ν −9 −5 ν ∼ 10 , the radius would need to change by only ∼ 10 m. This model however predicts it would take hundreds to thousands of years to build up strain between starquakes (Baym and Pines, 1971), which is at odds with the observation of a glitch in Vela every two to three years on average (Dodson et al., 2007). 2.2.2 The Superﬂuidic Coupling Model

The dominant model for glitches currently is a transfer of angular momentum from the superﬂuidic inner crust to the solid outer crust (Baym et al., 1969b; Packard, 1972). In a superﬂuid, angular momentum is quantized into vortex lines with an area

2mΩ density of nvortices = h . These vortex lines become pinned to the crustal lattice, as it is energetically less favourable for the vortex line to pass through the lattice (Anderson and Itoh, 1975). As long as the vortices remain pinned, their number remains constant, and therefore so does the angular momentum contained in the superfluid. The solid portion of the crust, however, is constantly spinning down due to the energy lost to dipole radiation. This leads to a differential rotation between the solid crustal lattice and crustal superfluid, with the superfluid always spinning faster than the solid crust. As the differential rotation becomes greater and greater, a Magnus force acts on the vortices which increases the stress on the pinning sites (Link

19 and Epstein, 1991). This force builds up until the pinning breaks down, allowing the vortices to rearrange themselves to correct the differential rotation (Pines and Alpar, 1985). In doing so, they transfer angular momentum to the solid crust, resulting in an apparent increase in spin frequency of the neutron star. In the simplest form, this model predicts that after a glitch, the crust should exponentially relax back to its original spin behaviour, and the exponential recovery timescale should always be the same for a given pulsar (Shapiro and Teukolsky, 1983; Ruderman et al., 1998). This behaviour is seldom seen, and in some pulsars multiple timescales are seen (Alpar et al., 1993). Link et al.(1999), using the glitch history of Vela and six other pulsars, showed that to explain the observed glitches with the superfluidic model, the superfluid reservoir must contain ∼ 1% of the moment of inertia of the neutron star. Recently, it has been suggested that the crustal superfluid cannot provide enough angular momentum to explain observed glitches (Anderson et al., 2012; Chamel, 2013). It is suggested that there exists a coupling between the superfluid and the crust, known as entrainment. This entrainment restricts the superfluid, causing it to, at least partially, rotate with the crust, decreasing the amount of angular momentum that can be transferred to the solid crust an unpinning event. With this effect taken into account, the crustal superfluid cannot provide a large enough store of angular momentum to explain the observed glitches.

20 2.3 Glitches in Magnetars

Magnetars also glitch (Kaspi et al., 2000), generally with glitch amplitudes com-

∆ν −7 parable to normal pulsars in terms of ∆ν, and trending higher in terms of ν (10 - 10−5 vs 10−11-10−5)(Dib et al., 2008a). Unlike the vast majority of glitches in normal pulsars, however, magnetars sometimes display radiative changes at the times of glitches such as SGR-like bursts, long-term X-ray flux increases, spectral changes, and/or pulse profile changes. In a long term monitoring study of 5 magnetars, Dib and Kaspi(2013) observed 22 distinct timing events. Of these, only approximately ∼ 20% displayed changes in their radiative behaviour contemporaneous to the timing behaviour. In fact, in a single source, 1E 2259+586, both radiatively loud and radiatively silent glitches have been observed (Kaspi et al., 2003; I¸cdemet al., 2012). There does not, however, appear to be a clear correlation between glitch size and radiative changes, yet in this study other correlations were noted. First, all observed flux increases have an associated change profile change. As well, most, but not all, (5/6) observed SGR-like bursts have been associated with a change in timing behaviour. All flux increases observed have an associated timing event, however this can be delayed by months; see Archibald et al. in prep. Only 5 magnetars have been monitored regularly for timing anomalies, and these are, by necessity, the brightest magnetars, those originally dubbed the AXPs.

21 CHAPTER 3 X-ray Astronomy Fortunately for living beings, and unfortunately for us, the X-ray astronomers, Earth’s atmosphere is optically thick to X-rays, the part of the electromagnetic spectrum with energies between ∼ 0.1−200 keV. This means that in order to observe celestial objects in the X-ray bands, we must escape the surly bonds of mother Earth. Thus, no celestial X-ray sources were known until after the rapid development of rockets developed for more sinister uses during the second great war. With this in mind, the first X-ray source, the Sun, was detected with a photon counter tube aboard a V–2 rocket in September of 1949 (Friedman et al., 1951). For the following decade, the Sun remained the only known X-ray source in the heavens. The next X-ray source, the first detected from outside our solar system, was found in the constellation Scorpius with the flight of another rocket in April 1963, and later named SCO X-1 (Giacconi et al., 1962). Even when above our atmosphere, whenever we observe an object to determine its true properties, we must take into account the photoelectric absorption caused by all the material between our telescopes and our source (Morrison and McCammon, 1983). The effect is due to atomic absorptions in the K and L electron shells. The amount of absorption depends on the relative abundances of heavy elements, which change the cross section of interaction. We quantify this effect into an equivalent neutral hydrogen column density along the line of sight, denoted NH . The total

22 −NH σ(E) absorption can be calculated by Fo = Fee , where σ(E) is the energy dependent cross section of interaction, Fo is the source flux observed, and Fe is the source flux before absorption. The net effect of this X-ray absorption is to preferentially absorb softer (lower energy) X-ray photons, making it harder to detect soft sources which are further away, and generally making X-ray sources appear harder, since the Universe is more transparent at higher energies. 3.1 X-ray Spectroscopy

While ideally we would be able to build perfect instruments with infinite spectral resolution, in reality we must use telescopes that can be built with current technology. Such realistic telescopes have finite spectral resolution, strongly energy dependent effective areas, and other instrumental effects. These effects are calibrated for each separate instrument, and are stored as response files.1 The telescopes’ responses are applied to the raw data by means of processing using parts of the HEASOF T 2 software package. At this point we now have a calibrated file in a standard format, FITS,3 which contains a list of every detected photon, with its energy channel, time of arrival, and detector position tagged. With this information, we can select source and background regions, typically using xselect, another HEASOF T tool, from which we can obtain

1 Response ﬁles for the Swift telescope can be found here: http://swift.gsfc.nasa.gov/proposals/swift responses.html. 2 Available from http://heasarc.nasa.gov/lheasoft/. 3 Flexible Image Transport System, see Wells et al.(1981).

23 spectra. The background region is typically taken from a region near the source to minimize instrumental effects due to position dependent instrument responses. To fit spectra, spectrum files are created which contain the number of photons which arrived in an energy channel during the observation. Spectral models are then fit to the background subtracted data, taking into account the exposure times, and effective areas of the source and background regions. All spectral fitting in this work was done using the XSPEC software package (Arnaud, 1996). In XSPEC, theoretical models are convolved with the instrument response files, and spectral parameters are adjusted to optimize a goodness of fit parameter, eg. a χ2 minimization, when comparing theoretical predictions to the observed spectra. 3.2 Mission History

Uhuru was the ﬁrst dedicated X-ray astronomy satellite, and was active from December 1970 - March 1973. The main objective of this mission was to survey the 2-20 keV X-ray sky down to a sensitivity of half a milliCrab4 , with an angular resolution of a few arcminutes (Giacconi et al., 1971). It had two proportional counters, each with 840 cm2 of eﬀective area. A proportional counter consists of a container of inert gas, with a charged wire running through the centre. When an X- ray photon interacts with a particle of this gas, it ionizes an atom there within, and, if the X-ray photon has enough energy, each free electron generated can continue to knock loose more free electrons, proportional to the photon’s X-ray energy. The

4 A Crab is an X-ray ﬂux unit equivalent to 2.4×10−8 erg cm−2s−1 in the 2–10 keV regime.

24 electrons are drawn to the charged wire, and generate an electric pulse, which is the signal of detection. The major result of this mission was the 4U catalogue, the first comprehensive catalogue of X-ray sources (Forman et al., 1978). Unbeknownst at the time, this marks the discovery of the first magnetar, 4U 0142+61, one of the 339 sources in this catalogue. The next major X-ray mission was the Einstein X-ray observatory, launched in November of 1978 (Giacconi et al., 1979). Einstein was the first focusing X-ray telescope, and as such was able to get arc-second resolution. Before this mission, positional information was gained first by the simplest optic, the cos(θ) effect of reduction of projected area as a source goes off axis, and later by the use of collimators, metal tubes which block the light except that from a reduced angular range which can go directly down the line of the pipe. The Einstein telescope used a Wolter 1 mirror to focus. Unlike visible light, X-rays can only be reflected at small angles, approximately 1 deg relative to the reflection surface for X-rays between 0.1-10 keV. In the Wolter I mirror design, each layer of the mirror contains two focusing elements; a paraboloid followed by a hyerboloid. Each of these layers, however, can only focus light from a small area, the cross section of the parabolic mirror when viewed from above, so multiple layers are nested to order to increase the effective area. In the case of the Einstein telescope, four such layers were used. The Wolter I mirror design is the dominant design now used in X-ray telescopes, and is now in use on the Chandra, XMM Newton, Swift, and NuSTAR missions. The Einstein mission discovered three more magnetars, 1E 1048.1−5937, 1E 1841−045, and 1E 2259+586,

25 ROSAT, or Röntgensatellit, launched in June of 1990, and was active until 1999. During its first two years of operation, it conducted an all sky survey in which 18 811 bright sources were catalogued (Voges et al., 1999). Like Einstein before it, ROSAT used a Wolter I mirror, with four nested layers. The most common X-ray sources seen by ROSAT were stellar coronae, active galactic nuclei, galaxy clusters, and X-ray binaries. The Advanced Satellite for Cosmology and Astrophysics (ASCA) was launched in February of 1993, and was active until 2001 (Tanaka et al., 1994). ASCA, once again used Wolter I type optics, but more importantly it was the first X-ray satellite to use a Charge Coupled Device (CCD) as the X-ray detector, allowing an energy

E resolution of ∆E ∼ 50 at 6 keV. The Rossi X-ray Timing Explorer (RXTE) was launched in December of 1995 and was in operation until January of 2012. RXTE was designed to explore the time domain of astronomy, rather than having the angular resolution of prior missions (Bradt et al., 1993). One of its main science instruments was the Proportional Counter Array (PCA), with 6500 cm2 of collecting area, sensitive from 2–60 keV, and a ∼ 1◦ ﬁeld of view. RXTE was unique in having microsecond time resolution. RXTE was an incredibly capable instrument for studying the time variable X-ray sky, of which magnetars are a vital part. In 1999, two X-ray observatories were launched: the X-ray Multi-Mirror Mis- sion (XMM–Newton) and the Chandra X-ray observatory. XMM has three co-aligned X-ray telescopes, each with a 58-layered Wolter I mirror (Jansen et al., 2001), giving XMM a larger collecting area than Chandra, while Chandra has better angular

26 resolution. The Chandra X-ray observatory is one of NASA’s Great Observatories (Weisskopf et al., 2000). It has the best angular resolution of any X-ray mission ever launched,or currently planned, with a ∼ 0.5 arcsecond half-power diameter, approximately one tenth that of XMM. Both XMM and Chandra are still it operation. 3.3 The Swift Gamma-Ray Burst Mission

The Swift Gamma-Ray Burst Mission (Burrows et al., 2005) is the principle observatory used to obtain the data used in this work. A diagram of Swift can be seen in Figure 3–1. As the name implies the principle purpose of the Swift mission is to study Gamma-ray Bursts (GRBs) and their afterglows. The Swift mission was launched into a low-Earth orbit on November 20, 2004, and is still in operation. The Swift mission consists of three instruments: the Burst Alert Telescope (BAT), the UV/Optical Telescope (UVOT), and the X-Ray Telescope (XRT). The BAT (Barthelmy et al., 2005) is a hard X-ray telescope, sensitive to photons having energies between 15-150 keV. The BAT has a 1.4 sr ﬁeld of view, and can localize sources to within a few arcminutes. It determines the location of a source by the use of a coded aperture mask, whereby a source at any point in the ﬁeld of view of the telescope will project a unique pattern on the detectors. The UVOT (Roming et al., 2005) is designed to see photons with wavelengths between 170-600 nm. It has a limiting sensitivity of 24th magnitude in 1 ks. It can achieve a positional accuracy of 0.3 arcseconds, useful for ground follow-up observations of GRBs. The Swift X-Ray Telescope (XRT) consists of a 3.5-m focal length Wolter-I telescope (originally built for the JET-X mission), and a 600 by 600 pixel XMM-Newton

27 EPIC-MOS CCD22 detector, sensitive in the 0.2 -10 keV range. The XRT has a field of view of 23.6 arcminute by 23.6 arcminute with angular resolution of 18 arcseconds. The XRT could initially operate in four modes: image mode, photon counting mode, windowed timing mode, and photodiode mode. Image mode is designed for fast lo- calization of GRBs. At the cost of all spectral resolution, it produces an image of the source region, without event classification solely for the purpose of refining the position of a GRB. Photon counting mode (PC) has the best spectral, and spatial information of all operational modes available to the XRT. This optimal spectral and spatial resolution is obtained by reading off each pixel of the CCD individually, at the cost of time resolution. It has time resolution of 2.5 s, and is useful for sources dimmer than ∼ 1 mCrab, as sources brighter than this will lead to pileup.5 Win- dowed timing mode (WT) collapses the read-out of the CCD into one dimension, giving better time resolution than PC mode, 1.76 ms, at the cost of a dimension of spatial information, and slight loss of spectral information. Photodiode mode is optimized for time resolution with 0.14 ms, but to obtain this, all spatial resolution is lost as the entire CCD is read off at once as a single pixel, and much of the spectral information is lost. Photodiode mode can no longer be used after damage by a micrometeorite on the 27th of May, 2005.

5 Pileup occurs when more than one photon reach an X-ray detector during the same read-out time. This leads to the apparent detection of one photon with high energy, instead of two lower energy photons, leading to inaccurate ﬂux and spectral measurements.

28 Figure 3–1 The Swift Satellite. The two tubes protruding from the top are the UVOT and XRT. The bottom of the satellite contains the BAT. Image from NASA GSFC.

When a burst is detected by the BAT, Swift is designed to slew to the burst position within 75 s. While this slewing was intended for GRBs, it has proved invaluable at detecting and following up bursts from other transient sources, including magnetars.

29 CHAPTER 4 An Anti-Glitch in 1E 2259+586 This chapter contains a modiﬁed version of the manuscript which ﬁrst appeared as “An Anti-glitch in a Magnetar,” published in Nature (Archibald et al., 2013). 4.1 Introduction

1E 2259+586 is a magnetar located near the centre of Galactic supernova remnant CTB 109 (Gregory and Fahlman, 1980), also called G109.1−1.0. CTB 109 was first seen as an unidentified radio source by Wilson and Bolton(1960), and identified as a supernova remnant by Hughes et al.(1981) using the Westerbork Synthesis Ra- dio Telescope, and concurrently by Gregory and Fahlman(1980) using the Einstein X-ray Observatory. 1E 2259+586 was first identified as an X-ray point source by Gregory and Fahlman(1980), again using the Einstein X-ray Observatory. Shortly thereafter, X-ray pulsations were discovered by Fahlman and Gregory(1981) with a period of ∼ 3.5 s. Later analysis showed the spin period was actually double this, ∼ 7 s (Fahlman and Gregory, 1983). Figure 4–1 shows a later X-ray image of the magnetar and surrounding supernova remnant. The observed and spin-down-inferred properties of 1E 2259+586 are compiled in Table 4–1. It was quickly realized that the X-ray luminosity greatly exceeded the power available from spin-down (Koyama et al., 1987) which is believed to power normal pulsars. Thus, 1E 2259+586 was initially believed to be the accretion-powered component of a low-mass close binary system with a possible orbital period of ∼ 2300s

30 Figure 4–1 A false colour X-ray Multimirror Mission (XMM) image of CTB 109 from Sasaki et al.(2004). Taken with the European Photon Imaging Camera. The colours represent energy bands with red being 0.3-0.9keV, green 1.5-4.0 keV, and blue 1.5- 4.0 keV. The image has been smoothed to a resolution of 4 ”. 1E 2259+586 is the bright blue object at centre-right.

31 Table 4–1 Measured and spin-down-derived properties of 1E 2259+586 Parameter Value RA 23h01m07.900s DEC 58◦52046.0000 Epoch (MJD) 55, 380.000 ν (s−1) 0.143, 285, 110(4) ν˙ (s−2) −9.80(9) × 10−15 B 5.9 × 1013G E˙ 5.6 × 1031ergs/s 33 * 2 − 10 keV Lx 1.3 × 10 erg/s τc 230 000 years 3 † τSN 8.8(9) × 10 years * Assuming a distance of 3kpc (Sasaki et al., 2004) † Age implied by supernova remnant, see Sasaki et al.(2004)

(Fahlman et al., 1982; Fahlman and Gregory, 1983). This binary interpretation of the source continued to be the dominant explanation, leading to the classification of this source with similar sources as very low mass X-ray binary pulsars (Mereghetti and Stella, 1995), later dubbed the Anomalous X-ray Pulsars (AXPs) (Mereghetti et al., 1998). . In 16 years of monitoring with the Rossi X-ray Timing Explorer (RXTE), 1E 2259+586 has shown a very stable spin-down rate and pulsed flux, with the exception of three timing events. The first timing event, a glitch accompanied by a large radiative event, occurred on the 18th of June, 2002 (Kaspi et al., 2003). This

∆ν −6 −14 glitch had a magnitude of ν = 4.24(11) × 10 , and a ∆ν ˙ = −1.09(7) × 10 , which decayed over the subsequent weeks (Dib and Kaspi, 2013). During four hours

32 of observation time at this epoch with RXTE, over 80 short, (from 2 ms to 3 s), X-ray bursts were detected, as well as a factor of ∼ 20 increase in pulsed flux, and a short-term change in pulse profile. The flux decayed following a power law with α = −0.69(3), with a strong correlation between spectral hardness and flux (Zhu et al., 2008). It was this soft gamma-ray repeater like outburst which led to the prevailing opinion that 1E 2259+586, along with all AXPs and SGRs, belong to the magnetar class (Kaspi et al., 2003; Gavriil et al., 2004). A second glitch occurred in 1E 2259+586 on the 25th of March, 2007 (Dib et al.,

∆ν 2008b; I¸cdemet al., 2012; Dib and Kaspi, 2013). It had a magnitude of ν = 8.80(3) × 10−7, and ∆ν ˙ = −6(2) × 10−16 (Dib and Kaspi, 2013). This glitch was not observed to be accompanied by any radiative events. A third timing anomaly in January 2009 has also been reported (I¸cdemet al.,

∆ν −8 2012; Dib and Kaspi, 2013), with an apparent ν = −8.2(2.1) × 10 , and a ∆ν ˙ = +2.3(1.6) × 10−16. However, as the surrounding TOAs can be fit by a polynomial of degree 3, it is possible this may have been an extended event, rather than a sudden glitch. This timing anomaly was accompanied by a small change in pulsed flux, and a possible pulse profile change (Dib and Kaspi, 2013). 4.2 Observations

4.2.1 Swift X-ray Telescope Observations

We began monitoring 1E 2259+586 with NASA’s Swift X-ray Telescope (XRT) (Burrows et al., 2005) in July 2011. For details on the Swift XRT, please see section 3.3. The XRT was operated in Windowed-Timing (WT) mode for all observations, which gives 1.76-ms time resolution. Swift monitoring was initiated at this

33 time as the RXTE mission was scheduled to end at the end of 2011, and Swift was uniquely positioned to take over its role in magnetar monitoring. Swift observations of 1E 2259+586 have been made every 2-3 weeks, with typical exposure times of 4 ks. From each observation, we obtained a pulse time-of-arrival (TOA) by folding the X-ray time series at the current pulse period and aligning this folded light curve with a high signal-to-noise template. The X-ray flux was measured by processing level 1 data products which were obtained from the HEASARC Swift archive, reduced using the xrtpipeline standard reduction script, and reduced to the barycentre using the position of 1E 2259+586, using HEASOFT v6.12 and the Swift 20120209 CALDB. A 40-pixel long region centred on the source was extracted, as well as a background region of the same size located away from the source. To investigate the flux and spectral behaviour of 1E 2259+586, spectra were extracted from the selected regions using xselect, and fit to an NH -absorbed blackbody and power-law model using XSPEC package version

22 −2 12.7.0q (Arnaud, 1996). NH was fixed at the value of 0.97 × 10 cm , determined by co-fitting all the pre-glitch spectra. The spectra were grouped with a minimum of 20 counts per energy bin. Ancillary response files were created using the FTOOLS xrtmkarf and the standard spectral redistribution matrices. We fitted the pulse TOAs to a long-term timing model which keeps track of every rotation of the neutron star. This model predicts when the pulses should arrive at Earth, taking into account the pulsar rotation as well as astrometric terms. We compared the observed TOAs with the model predictions, and obtained best-fit parameters by χ2 minimization, using the TEMPO2(Hobbs et al., 2006) software

34 package. Until the observation on 14 April, 2012 (MJD 56,031.18) the Swift TOAs were well fitted using only a frequency and first frequency derivative as shown in Figure 4–3. The subsequent data, however, clearly were not predicted by this simple model. TOAs starting on the 28th of April, 2012 (MJD 56 045.01) showed an apparently instantaneous change of the frequency – which we dub an ‘anti-glitch.’ On the 21st of April, 2012 (MJD 56 038), consistent with the epoch of this sudden spin down, a 36 ms hard X-ray burst was detected by the Fermi Gamma-ray Burst Monitor (GBM) (Foley et al., 2012), with a fluence of ∼ 6 × 10−8 erg/cm2 in the 10 − 1000 keV range. No untriggered GBM bursts were seen within three days of the observed burst (Foley et al., 2012). As well, on the 28th of April, 2012 (MJD 56 045.01), coincident with the nearest post-anti-glitch observation, we detected an increase in the 2 -10 keV flux by a factor of 2.00 ± 0.09 (see Figure 4–3). The flux increase was also accompanied by a change in the spectral hardness ratio, defined as the ratio of the 4-10 keV to the 2-4 keV fluxes, from 0.10 ± 0.02 to 0.18 ± 0.02. This flux increase subsequently decayed following a power-law model with α = −0.38 ± 0.04 (see Figure 4–3). The flux increase was accompanied by a moderate change in the pulse profile: the addition of a sinusoid centred between the usual two peaks in the pulse profile. This modified pulse profile relaxed back to the usual shape on a timescale similar to that of the flux. We verified that this profile change did not affect the TOAs determined near the anti-glitch epoch. The evolution of the pulse profiles from the Swift monitoring campaign can be seen in Figure 4–2.

35 Figure 4–2 The evolution on the 0.5–10 keV pulse profile of 1E 2259+586. In all panels two pulse cycles are shown for clarity. Panel a: profile before the flux increase (MJD 55 765 - 56 032), Panel b: profile at epoch of maximal flux (MJD 56 045 - 56 050), Panel c: profile from MJD 56 050-56 100, Panel d: profile from MJD 56 100-56 400.

36 This remarkable spin-down event was immediately followed by an extended period of enhanced spin-down rate. This anti-glitch and spin-down rate change can be well modeled by an instantaneous change in the frequency and frequency derivative, followed by a second sudden event. We have found two possible timing models to describe the pulsar’s behaviour, described in full in Table 4.2.1. In the first, there is an instantaneous change in frequency and frequency derivative by ∆ν = −4.5(6) × 10−8Hz (∆ν/ν = −3.1(4) × 10−7) and ∆ν ˙ = −2.7(2) × 10−14Hz/s on 18 April (MJD 56,035(2)). This enhanced spin-down episode ended with a second glitch, this time a spin-up event, of amplitude ∆ν = 3.6(7)×10−8Hz (∆ν/ν = 2.6(5)×10−7) and ∆ν ˙ = 2.6(2) × 10−14Hz/s. In the second model, the spin evolution can be described by two anti-glitches, instead of an anti-glitch/glitch pair. In this model, a change of ∆ν = −9(1)×10−8Hz (∆ν/ν = −6.3(7) × 10−7) and ∆ν ˙ = −1.3(4) × 10−14Hz/s occurred on 21 April (MJD 56,038(2)). This period ended with a second anti-glitch of amplitude ∆ν = −6.8(8) × 10−8Hz (∆ν/ν = 4.8(5) × 10−7) and ∆ν ˙ = 1.1(4) × 10−14Hz/s. Note the absence of any apparent change in the X-ray flux at the epoch of this second putative anti-glitch The full timing parameters for both possible models are presented in Table 4.2.1, as well as the timing residuals in Figure 4–4. Note that neither model is preferred on statistical grounds, however models involving a single initial anti-glitch and subsequent relaxation with no second impulsive event are ruled out to high confidence. Also note that no significant radiative, or profile changes can be associated with either of the possible second impulsive events.

37 Table 4–2 Timing parameters for 1E 2259+586. Numbers in parentheses are TEMPO-reported 1 σ uncertainties. Parameter Value Observation Dates 23 July 2011 - 1 January 2013 Dates (MJD) 55 765.829 − 56 293.332 Epoch (MJD) 55 380.000 Number of TOAs 51 ν (s−1) 0.143 285 110(4) ν˙ (s−2) −9.80(9) × 10−15 Model 1 Glitch Epoch 1 (MJD) 56 035(2) −1 −8 ∆ν1 (s ) −4.5(6) × 10 −2 −14 ∆ν ˙1 (s ) −2.7(2) × 10 Glitch Epoch 2 (MJD) 56 125(2) −1 −8 ∆ν2 (s ) 3.6(7) × 10 −2 −14 ∆ν ˙2 (s ) 2.6(2) × 10 RMS residuals (ms) 56.3 χ2/ν 45.4/44 Model 2 Glitch Epoch 1 (MJD) 56 039(2) −1 −8 ∆ν1 (s ) −9(1) × 10 −2 −14 ∆ν ˙1 (s ) −1.3(4) × 10 Glitch Epoch 2 (MJD) 56 090(3) −1 −8 ∆ν2 (s ) −6.8(8) × 10 −2 −14 ∆ν ˙2 (s ) 1.1(4) × 10 RMS residuals (ms) 51.5 χ2/ν 38.1/44

38 Figure 4–3 Timing and flux properties of 1E 2259+586 around the 2012 event. Panel a shows 1E 2259+586’s spin frequency as a function of time, determined by short- term fitting of typically 5 TOAs. The grey horizontal errorbars indicate the ranges of dates used to fit the frequency, and the vertical error bars (generally smaller than the points) are standard 1σ uncertainties. The red and blue solid lines in panel a represent the fits to the pulse TOAs, as displayed in Table4.2.1, with red representing model 1, and blue model 2. Panel b shows the timing residuals of 1E 2259+586 after fitting only for the pre-anti-glitch timing solution. The inset shows the same timing residuals, zooming in on the anti-glitch epoch. Panel c shows the absorbed 2-10 keV X-ray flux. The error bars indicate the 1σ uncertainties, and the green line is the best-fit power-law decay curve with an index of −0.38 ± 0.04. The dashed vertical lines running through both panels indicate the glitch epochs, the black being the anti-glitch, and blue and red the second event in the models shown in Table 4.2.1. Year 2011.6 2011.8 2012.0 2012.2 2012.4 2012.6 2012.8 2013.0

-0.1 a ]

z -0.2

H -0.3 µ [ -0.4 ν

∆ -0.5 -0.6 5 30 2 b 4 [Phase] Residuals 1 20 [s] 3 0 0 25 50 75 2 10 [MJD-56000] 1 Residuals [s] ]

2 0 0 −

m c

c 3.0

− 2.5 s

r 2.0 e 1 1 1.5 − 2-10 keV Flux 0 1 [ 55800 55900 56000 56100 56200 56300 Date [MJD]

39 Figure 4–4 Timing residuals for 1E 2259+586. Panels a, b, and c show timing residuals, the difference between the predicted and measured TOAs for the timing models shown in Table 4.2.1. Panel a takes into account only the long-term pre-anti- glitch timing model, with the inset showing the phase jump and significant slope change that indicates the anti-glitch. Panel b shows these residuals after fitting Model 1, the anti-glitch and the glitch, and Panel c for Model 2, the two anti-glitch model. The dashed vertical lines indicate glitch epochs – the black line the common anti-glitch epoch, the red line the glitch epoch in model 1, and the blue the second anti-glitch epoch in model 2.

Year 2011.6 2011.8 2012.0 2012.2 2012.4 2012.6 2012.8 2013.0

30 a 2 4.0

1 [Phase] Residuals 20 [s] 3.0 0 2.0 0 25 50 75 10 Residuals [s] [MJD-56000] 1.0

0 0.0

0.4 Date [MJD] b 0.06 0.04

0.2 [Phase] Residuals 0.02

0.0 0.00

0.02

Residuals [s] 0.2 0.04

0.4 0.06

0.4 c 0.06 0.04

0.2 [Phase] Residuals 0.02

0.0 0.00

0.02

Residuals [s] 0.2 0.04

0.4 0.06

55800 55900 56000 56100 56200 56300 Date [MJD]

40 Note that in either model a sudden spin down consistent with the epoch of the Fermi burst is unambiguously required to model the observed TOAs properly. While the amplitude of this anti-glitch in either model is not unusual, the fact that it is a sudden spin down is remarkable. The net eﬀect of this active period are changes to the spin frequency and its ﬁrst derivative ∆ν = −2.06(8) × 10−7Hz (∆ν/ν = −1.44(6) × 10−6) and a ∆ν ˙ = −1.3(4) × 10−15Hz/s. 4.2.2 Expanded Very Large Array Observation

Following the detection of the anti-glitch, we looked for evidence of particle outflow, proposed as a possible mechanism for the apparent spin down in SGR 1900+14 (Thompson et al., 2000)). We carried out radio imaging on the 21st of August, 2012 using the Expanded Very Large Array (EVLA).1 The EVLA is a radio array con- sisting of twenty-seven 25 m dishes, located in New Mexico, USA. The array was operated in the B-array configuration with a 240 minute integration time. This yielded images with effective angular resolution 1.200. We performed standard flagging, cali- bration, and imaging using the Common Astronomy Software Applications (CASA) package (International Consortium Of Scientists, 2011). No source was found at the position of 1E 2259+586, and we place a 3σ flux density limit of 7.2 µJy at 7 GHz for a point source. This is significantly lower than the previous upper limit of 50 µJy at 1.4 GHz (Kaspi et al., 2003). If a putative outflow were expanding at 0.7c as was the case for a radio outflow from SGR 1806−20 (Granot et al., 2006)) at the time of its outburst, we would expect a nebular radius of 400. For this radius, we obtain a

1 The EVLA observation and data analysis were carried out by Dr. C.-Y. Ng.

41 3σ ﬂux density limit of 0.46 mJy. Note that the limit is more stringent if the size is smaller, and reduces to 7.2 µJy if unresolved. 4.2.3 Chandra X-ray Observation

In X-rays, we also detected no evidence for such outflow in a 10-ks Chandra HRC-I image taken on the 21st August, 2012. Using simulations, we place an upper limit on X-ray flux from a putative outflow at 2% of the total 1-10 keV X-ray emission of the magnetar, for a 400 circular nebula with a Crab-like spectrum. 4.3 Discussion

4.3.1 Previous Evidence for Anti-Glitches

Sudden spin-down glitches have heretofore not been observationally demon- strated in any neutron star, though some magnetar events have been suggestive. In 1998, a spin-down in magnetar SGR 1900+14 (Woods et al., 1999) was reported at an epoch with a giant SGR ﬂare. If indeed a sudden event, it would be the largest

∆ν −4 sudden timing anomaly yet seen in a neutron star with ν ∼ 10 . Unfortunately, there were no observations of the source during the prior 80-days, so one cannot rule out that the event could have been a gradual slow down, instead of a sudden glitch. As discussed above, 1E 2259+586 also had a timing event in 2009 which appeared to be a spin-down event, but it could also be ﬁt by a gradual change in spin-down rate (I¸cdemet al., 2012; Dib and Kaspi, 2013)). Net spin downs have been seen in the high-magnetic-ﬁeld rotation-powered pulsar PSR J1846−0258 (Livingstone et al., 2010) and in the magnetar 4U 0142+61 (Gavriil et al., 2011)). In the case of PSR J1846−0258, in 2006 a spin-up glitch with

∆ν −6 +4.5 ν = 4.0(1.3) × 10 was seen coincident with a factor of 5.5−2.7 increase in the 2-10

42 keV flux, as well as several SGR like bursts (Gavriil et al., 2008). This glitch decayed with τd = 127(5)days, but over-recovered by a factor of 8.7(2.5) (Livingstone et al., 2010). For 4U 0142+61, the net spin-down event also occurred during a period of activity, during which several SGR-like bursts were detected, as well as significant pulse profile changes, although no significant long-term flux increase. At the start of this

∆ν −6 active period, a glitch with ν = 1.7(3)×10 , which decayed with τd = 17(1.7)days, ∆ν −8 until the result was a net spin-down with ν ∼ −8 × 10 (Gavriil et al., 2011). For both of the above cases, if the initial stages of the glitch had been missed, it would have appeared as an anti-glitch, similar to the SGR 1900+14 event. If the 2012 1E 2259+586 event were due to a spin-up glitch and subsequent over recovery, we place a 3σ upper limit on the recovery decay time of 3.9 days for a spin-up of size ∆ν/ν = 1×10−6. Even for an inﬁnitesimally small spin-up glitch, the decay time was less than 6.6 days, far shorter than any previously observed magnetar recovery time scales. 4.3.2 Physical Origins of the Anti-Glitch

There are two main possibilities for the origin of the anti-glitch: either an internal or external mechanism. As discussed in section 2.2, the generally accepted model for standard spin-up glitches involves an internal mechanism in which the glitch is due to a change in the coupling between the crustal lattice and crustal superﬂuid. Following the possible spin-down event in SGR 1900+14 discussed above, Thompson et al.(2000) examined the possibility that an anti-glitch could also be internally driven. This requires a

43 differential rotation of the crustal superfluid wherein some parts of this superfluid are rotating at a rate slower than the external crust. In a regular rotation-powered pulsar, we always expect the crust to be spinning slower than the superfluid. It has been suggested, however, that in a magnetar, since the decay of the extreme magnetic field is a power source dominant to the normal spin-down power, this magnetic field decay could drive the differential rotation needed for an internal anti- glitch (Thompson and Duncan, 1995). The theory that the large magnetic fields play a strong role in an anti-glitch mechanism is supported by the observational evidence that all the prior sudden spin-down candidates seen, as discussed above, occurred either in a magnetar, or a high magnetic field pulsar. As for the enhanced spin-down rate following the anti-glitch, this behaviour is not unusual in magnetar glitches, even being seen in 1E 2259+586 after a prior glitch. Kaspi et al.(2003) attributed the greatly enhanced spin-down after the glitch to a decoupling of the core superfluid, or to a rearrangement of the magnetosphere brought about by the glitch. The radiatively loud nature of the first anti-glitch, followed by a second radiatively silent either glitch or anti-glitch is also not a problem in the internal model, as both radiatively loud and silent glitches are seen in magnetars (Dib et al., 2008a), including both types seen in this very source, as discussed in the introduction. Another possible internal anti-glitch mechanism put forth by Thompson et al. (2000) is that the anti-glitch is the end result of a slow plastic deformation of the crust by the magnetic fields. This slow plastic deformation, however would have had two distinct observational signatures: a long-term decrease in the magnitude ofν ˙

44 prior to the anti-glitch, as well as a slow change in pulse profile prior to the anti- glitch, as seen in 4U 0142+61 prior to its over-recovery glitch (Gavriil et al., 2011). Neither of these signatures were seen, leaving this to be an unlikely possibility. External mechanisms that could explain the observed anti-glitch behavior in- clude particle outflows, and magnetospheric twists. An outflow of particles along the open field lines of the magnetosphere would lead to an increase in the external torque acting on a magnetar, thus spinning it down (Thompson and Blaes, 1998; Harding et al., 1999; Thompson et al., 2000). In a wind model, the spin-down torque can only ever be increased, so this model is unable to explain the timing solution with a sudden spin-up glitch. As well, in the wind model a second anti-glitch would also be expected to be accompanied by a radiative change, similar to the first. In a magnetospheric twist model, if the flare and initial anti-glitch were caused by a twist in the magnetosphere, that twist should be followed by a gradual untwisting, in which caseν ˙ should show a gradual relaxation, and not the two sudden jumps observed (Parfrey et al., 2012). In this model, it would also be difficult to explain as to why in two anti-glitches of similar magnitude, why there would be radiative changes in one, yet no observed changes in X-ray luminosity, or pulse profile associated with the second event. Coupled with the superfluidic entrainment problems in the standard glitch model discussed in section 2.2, this magnetar anti-glitch, X-ray outburst, and subsequent evolution lend support to the need for a rethinking of glitch theory for all neutron stars.

45 CHAPTER 5 Outlook and Conclusions In this work, we have reported the discovery of an anti-glitch in 1E 2259+586, with a magnitude of ∆ν/ν = −3.1(4) × 10−7 or ∆ν/ν = −6.3(7) × 10−7, depending on the model, as described in Chapter4. This anti-glitch was accompanied by a radiative outburst including a hard X-ray burst, and a factor of 2.00 ± 0.09 ﬂux increase in the 2–10 keV band which decayed following a power-law model with α = −0.38 ± 0.04. Pulsar glitches remain one of the few methods we have to study the internal structure of neutron stars, and therefore matter at super-nuclear density, it is critically to determine the exact nature of anti-glitches. Determining the nature of anti-glitches, including whether they have origin internal or external to the star could be accomplished in principle by better constraining the time scale on which the anti-glitch occurs, since an internal angular momentum transfer is likely to yield a near-instantaneous event, where as magnetospheric twists should have a longer evolution time scale (Parfrey et al., 2012). A sensitive all-sky X-ray monitor would be useful in this regard or a dedicated X-ray telescope. There are currently two proposed X-ray missions that ﬁt the bill. The Large Observatory for X-ray Timing(LOFT) (Hernanz and on behalf of the LOFT collaboration, 2013), a candidate for the M3 mission of the European Space Agency, and The Neutron star Interior Composition ExploreR (NICER) (Gendreau et al., 2012), a NASA explorer mission to be deployed on the International Space Station.

46 LOFT contains two main science instruments: the Wide Field Monitor (WFM) and the Large Area detector(LAD). The WFM can see ∼ 50% of the sky at any given time, and has 10 µs time resolution, reduced to 16 ms when telemetered to the ground. WFM is planned to be able to detect every X-ray source above ∼ 1 mCrab daily, allowing daily monitoring of the X-ray flux of every magnetar in the sy, allowing us to narrow the time range of flux increases. LAD will have the largest collecting area of any X-ray telescope, with 10 m2 of effective area at 8 keV, compared to the prior largest, RXTE, with 6500 cm2, or our current monitoring instrument, the Swift XRT with 110 cm2 at 1.5 keV. This would mean magnetars could be timed with the LAD in a fraction of time, leading to either more frequent observations of magnetars, and/or the ability to monitor more of them.1 While NICER is not an all sky monitor, it is a mission dedicated to the study of neutron stars. NICER’s primary science instrument is an X-ray Timing Instrument (XTI), sensitive from 0.2–12 keV. It is not a focusing X-ray telescope, but instead uses X-ray concentrators which give a ∼ 2000 cm2 effective area at 1 keV for a 15 arcmin2 field of view. NICER will also have an unprecedented absolute timing accuracy of ∼ 100 ns, compared to ∼ 1 µs of RXTE. As such, it will enable more frequent monitoring of currently monitored magnetars, and hopefully allow the timing of sources which are currently too dim to be monitored regularly with current generation telescopes.

1 As LOFT is in the proposal stage, these details are likely to change, however they are included here as a general guideline.

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