The Pennsylvania State University The Graduate School The Eberly College of Science

POPULATION SYNTHESIS AND ITS CONNECTION TO ASTRONOMICAL OBSERVABLES

A Thesis in Astronomy and Astrophysics

Michael S. Sipior

c 2003 Michael S. Sipior

Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

May 2003 We approve the thesis of Michael S. Sipior Date of Signature

Michael Eracleous Assistant Professor of Astronomy and Astrophysics Thesis Advisor Chair of Committee

Steinn Sigurdsson Assistant Professor of Astronomy and Astrophysics

Gordon P. Garmire Evan Pugh Professor of Astronomy and Astrophysics

W. Niel Brandt Associate Professor of Astronomy and Astrophysics

L. Samuel Finn Professor of Physics

Peter I. M´esz´aros Distinguished Professor of Astronomy and Astrophysics Head of the Department of Astronomy and Astrophysics Abstract

In this thesis, I present a model used for binary population synthesis, and 8 use it to simulate a starburst of 2 10 M over a duration of 20 Myr. This × population reaches a maximum 2–10 keV luminosity of 4 1040 erg s−1, ∼ × attained at the end of the star formation episode, and sustained for a pe- riod of several hundreds of Myr by succeeding populations of XRBs with lighter companion stars. An important property of these results is the min- imal dependence on poorly-constrained values of the initial mass function (IMF) and the average mass ratio between accreting and donating stars in XRBs. The peak X-ray luminosity is shown to be consistent with recent observationally-motivated correlations between the star formation rate and total hard (2–10 keV) X-ray luminosity. Recent calculations published by other groups fail to account for the aforementioned sustained high X-ray luminosity from different mass companions. Model cumulative luminosity functions show increasing steepness at the high end, as the most luminous systems die off. I also consider those XRBs with massive companions that survive the second supernova, and go on to become double compact object binaries. Depending upon the initial configuration at the time the second compact object is formed, the system may go on to experience a merger through

iii the loss of orbital energy to gravitational radiation. We show that with a detection threshold of h 10−21 for gravitational radiation (comparable to ∼ the expected sensitivity of LIGO I), a total merger rate of 6 10−3–10−2 yr−1 × can be expected. This means that detection of gravitational wave sources through this formation channel will have to wait for LIGO II, with an order of magnitude improvement in sensitivity, and a commensurate thousand-fold increase in search volume and event rates. In an attempt to compare model predictions with observations, I analyze a sample of 41 nearby mildly-active galaxies observed in a snapshot survey during Cycles 1 and 2 of the Chandra X-ray Observatory. Using the observed X-ray images, 33 nuclei are detected, and diffuse nuclear X-ray emission is found in 25% of the targets. Substantial XRB populations are detected in all but a few fields, many with luminosities in excess of 1039 erg s−1. Over four hundred sources were detected overall, with fourteen in the latter high luminosity category. All but one of these sources is found in a spiral host galaxy, implying that such sources are generally tied to higher star formation rates.

iv Contents

List of Figures vii

List of Tables x

1 Introduction 1 1.1 Historical Perspective ...... 1 1.2 The Physics of Binary Evolution ...... 10 1.2.1 Gravitational Waves ...... 12 1.3 Overview ...... 15

2 Simulating the X-ray luminosity evolution of a stellar pop- ulation 18 2.1 Introduction ...... 18 2.1.1 X-ray binaries revealed by Chandra ...... 18 2.1.2 Observables for reconstructing a star formation history 19 2.2 Population modeling ...... 22 2.2.1 History and authorship of the population synthesis code 22 2.2.2 Population code theory of operation, choice and extent of parameter space ...... 23 2.2.3 Implementation of mass transfer in the code ...... 31

v 2.2.4 Mass accretion and resulting X-ray luminosity . . . . 37 2.3 Simulation results ...... 44 2.4 Comparison with other theoretical work ...... 69 2.4.1 Numerical simulations by Van Bever & Vanbeveren . . 69 2.4.2 Analytic calculation by Wu (2001) ...... 72 2.4.3 Semi-analytical calculation by Ghosh & White (2001) 73 2.4.4 Comparison with observations ...... 74 2.4.5 Further applications of the simulation results . . . . . 76

3 A snapshot survey of nearby mildly-active galaxies with Chandra 84 3.1 Introduction ...... 84 3.2 Data analysis ...... 85 3.3 Results ...... 94 3.3.1 Target descriptions and notable trends ...... 97 3.4 Epilogue ...... 105

4 Nova Sco and coalescing low mass black hole binaries as LIGO sources 149 4.1 Introduction ...... 150 4.2 Example of Nova Sco ...... 155 4.3 Population synthesis ...... 158 4.4 Results ...... 160 4.5 Discussion ...... 165

Bibliography 176

vi List of Figures

2.1 Evolution of total X-ray luminosity ...... 56 2.2 Evolution of BH/XRB population, Salpeter IMF, low q . . . 57 2.3 Evolution of NS/XRB population, Salpeter IMF, low q . . . . 58 2.4 Evolution of BH/XRB population, Miller-Scalo IMF, low q . 59 2.5 Evolution of NS/XRB population, Miller-Scalo IMF, low q . . 60 2.6 Evolution of BH/XRB population, Salpeter IMF, flat q . . . 61 2.7 Evolution of NS/XRB population, Salpeter IMF, flat q . . . . 62 2.8 Evolution of BH/XRB population, Miller-Scalo IMF, flat q . 63 2.9 Evolution of NS/XRB population, Miller-Scalo IMF, flat q . . 64 2.10 Luminosity function at five epochs, Salpeter IMF, low q . . . 65 2.11 Luminosity function at five epochs, Miller-Scalo IMF, low q . 66 2.12 Luminosity function at five epochs, Salpeter IMF, flat q . . . 67 2.13 Luminosity function at five epochs, Miller-Scalo IMF, flat q . 68 2.14 Hα luminosity evolution for the first 2 Gyr after star formation 80 2.15 X-ray luminosity versus Hα compared to Ho et al...... 83

3.1 L vs. B and (B V ) ...... 106 X T − T 3.2 LX frequency by host galaxy type ...... 107

vii 3.3 Colour-magnitude diagram and luminosity function for NGC 253, 404, 660 and 1052 ...... 127 3.4 Colour-magnitude diagram and luminosity function for NGC 1055, 1058, 2541 and 2683 ...... 128 3.5 Colour-magnitude diagram and luminosity function for NGC 2787, 2841, 3031 and 3368 ...... 129 3.6 Colour-magnitude diagram and luminosity function for NGC 3486, 3489, 3623 and 3627 ...... 130 3.7 Colour-magnitude diagram and luminosity function for NGC 3628, 3675, 4150 and 4203 ...... 131 3.8 Colour-magnitude diagram and luminosity function for NGC 4278, 4314, 4321 and 4374 ...... 132 3.9 Colour-magnitude diagram and luminosity function for NGC 4395, 4414, 4494 and 4565 ...... 133 3.10 Colour-magnitude diagram and luminosity function for NGC 4569, 4579, 4594 and 4639 ...... 134 3.11 Colour-magnitude diagram and luminosity function for NGC 4725, 4736, 4826 and 5033 ...... 135 3.12 Colour-magnitude diagram and luminosity function for NGC 5055, 5195, 5273 and 6500 ...... 136 3.13 Colour-magnitude diagram and luminosity function for NGC 6503137 3.14 NGC 253, 404, 660 and 1052 ...... 138 3.15 NGC 1055, 1058, 2541 and 2683 ...... 139 3.16 NGC 2787, 2841, 3031 and 3368 ...... 140 3.17 NGC 3486, 3489, 3623 and 3627 ...... 141 3.18 NGC 3628, 3675, 4150 and 4203 ...... 142 3.19 NGC 4278, 4314, 4321 and 4374 ...... 143

viii 3.20 NGC 4395, 4414, 4494 and 4565 ...... 144 3.21 NGC 4569, 4579, 4594 and 4639 ...... 145 3.22 NGC 4725, 4736, 4826 and 5033 ...... 146 3.23 NGC 5055, 5195, 5273 and 6500 ...... 147 3.24 NGC 6503 ...... 148

4.1 a vs. e for BH-BH and BH-NS systems ...... 171 4.2 Two mass distribution histograms for bound BH-BH systems 172 4.3 Chirp mass distribution for merging systems ...... 173 4.4 Merger time vs. final binary velocity ...... 174

ix List of Tables

2.1 Simulation parameters summary ...... 46 2.2 Power-law index of model cummulative luminosity function at five epochs ...... 77

3.1 Observed sample of nearby LLAGN galaxies ...... 92 3.1 Observed sample of nearby LLAGN galaxies ...... 93 3.2 Summary of source properties ...... 108 3.2 Summary of source properties ...... 109 3.2 Summary of source properties ...... 110 3.2 Summary of source properties ...... 111 3.2 Summary of source properties ...... 112 3.2 Summary of source properties ...... 113 3.2 Summary of source properties ...... 114 3.2 Summary of source properties ...... 115 3.2 Summary of source properties ...... 116 3.2 Summary of source properties ...... 117 3.2 Summary of source properties ...... 118 3.2 Summary of source properties ...... 119 3.2 Summary of source properties ...... 120

x 3.2 Summary of source properties ...... 121 3.2 Summary of source properties ...... 122 3.2 Summary of source properties ...... 123 3.2 Summary of source properties ...... 124 3.2 Summary of source properties ...... 125 3.2 Summary of source properties ...... 126

4.1 Summary of source properties ...... 169 4.2 Summary of source properties ...... 170

xi Acknowledgements

It is my great pleasure to thank the members of my thesis committee for their insightful comments and accumulated scientific wisdom. Thanks go most especially to my advisor(s), Herr Doktor Professors Mike Eracleous and Steinn Sigurdsson. Without their encouragement and (ahem) stern discipline, I should likely still be writing this thesis, and only half as well at that. Comraderie is the bulwark of any graduate student’s morale, and I have been indeed fortunate to have had some exceptional peers during my tenure at Penn State. First and foremost among these is Dave Andersen, my drink- ing mentor, without whom I should today be completely sober, and utterly boring. But I have been truly blessed with many exceptional friends here at Penn State, and I should like to thank them all for making the trip worth- while. Johannes Ruoff and William Krivan for an enormous amount of fun auf Deutsch. Ann Hornschemeier for her razor wit, and exceptional insight into the human condition. Sarah Gallagher, for always being willing to chat, even if I am much younger than she. Her wisdom and beer-quaffing skills never failed to brighten my day. Chris Smeenk for being so damned clever, and always fascinating to talk to. Rajib Ganguly for always laughing at my jokes. Mike Weinstein for his enormous passion for pedagogy (and I have

xii almost forgotten that his father gave me a “B” in Thermodynamics all those years ago. . . ) Jason Best, for being inimitable. Eric Cardiff for breaking all my stereotypes about those crazy engineers (in a good way). Karen Lewis for being there (and letting me beat up her stuffed frog, which is a great stress reliever, if you ever get the chance). Anna Jangren and Bertil Olsson are still the very definition of European Cool for me, even if Bertil isn’t really an Arctic Ninja. John Debes for his hearty sense of humour, and for not telling me to piss off when I really, really deserved it. John Feldmeier for actually being willing to share an office with me (for more than one year, even!) The Sipior Distinguished Service Medal goes to John Wise, Britton Smith, Miroslav Micic and Simos Konstantinidis. Thank you, gentlemen, for taking in a stray graduate student, and for letting an old geezer drink with you young whippersnappers. Without my parents, none of this, quite literally, would have been pos- sible, and I thank them for their love and unfailing support for these seven years. Lastly, I should like to send my sincere thanks to the distant stars of aeons past that perished, casting their enriched atmospheres into the Void, allowing all this to come to pass. Special heartfelt thanks for all of the Silicon, which has made my work possible.

Michael S. Sipior Amsterdam April 2003

xiii Chapter 1

Introduction

1.1 Historical Perspective

X-ray astronomy began with the now-legendary rocket launch on 18 June 1962 at White Sands Missile Range, New Mexico (Giacconi et al., 1962). This provided the first cogent evidence for extra-solar X-ray sources. The field blossomed rapidly from this point, with Bowyer et al. (1964) making use of a lunar occultation to show clearly that the Crab Nebula was a distinct source of X-rays. By 1966, no less than eight distinct X-ray sources were known to exist (Fisher et al., 1966). A fresh surprise came with a rocket launch from Woomera, Australia in April 1967. A source was detected with a brightness comparable to that of Scorpius X-1 (the most luminous source known at that time), but which had not been seen on a previous flight (Harries et al., 1967); as well, the intensity of the source dropped off by nearly two orders of magnitude over the next four months (Chodil et al., 1968). The first X-ray nova had been discovered (and is now known as the X-ray transient source Cen X-2). A less dramatic variability (factors of several in intensity) was found in Sco X-1 on time scales of roughly ten minutes (Lewin et al., 1968). Interestingly,

1 this discovery could not be made by rocket flight observations, which share ten minutes or less of exposure time between several targets. Instead, the variability was found by a long ( 7 hours) balloon observation. ∼ The identification of these X-ray sources with binary systems came sev- eral years later, and required a great deal more ancillary data. With the launch of the Uhuru X-ray satellite in December 1970, dramatically im- proved positions (0.5◦ uncertainty, down from several degrees with previous detectors) were established for a number of X-ray sources. This made mul- tiwavelength source correlations much easier, leading to the discovery of a variable radio source in close proximity (less than the Uhuru resolution limit) to Cyg X-1 (Braes & Miley, 1971; Hjellming & Wade, 1971). The error in the radio position was on the order of a few arcseconds, and, remarkably, contained a brilliant B0 supergiant star. At this point, optical observations of the supergiant (Webster & Murdin, 1972; Bolton, 1972) determined that the star possessed a 5.6 day orbital pe- riod around an unseen companion. From the radial velocity curve a mass function was established, with a probable companion mass of more than 2

M . That a star this massive was undetected at the distance of the super- giant strongly implied that the companion was a compact object, possibly even sufficiently massive to be a black hole, heretofore a purely theoretical construct. Shortly thereafter, Schreier et al. (1972b) demonstrated the binary na- ture of the X-ray source Cen X-3 by showing that the source underwent an X-ray eclipse every 2.1 days, and that X-ray pulsations exhibited by the source every 4.8 seconds experienced a Doppler shift that could not be explained except as coming from one element of a binary system. Similar analyses were performed, with the same conclusion, on Her X-1, which is

2 also an X-ray eclipsing system (Tananbaum et al., 1972), as well as SMC X-1 (Schreier et al., 1972a), among others. Even before so many X-ray sources were shown to be in binary systems, theorists attempted to explain the mechanism by which this luminosity was produced. Shklovsky (1967) put forward the first neutron star binary model for the source Sco X-1, showing that the optical and X-radiation could not be from the same source. Moreover, he showed that the energy distribution of the X-rays was consistent with thermal bremstrahlung arising from the accretion of an optically-thin plasma onto a neutron star surface. Joy (1954) and Crawford & Kraft (1956) had already introduced models of accretion disks in binary systems, albeit in the context of CVs. Shakura & Sunyaev (1973) and Shakura (1973) extended this to detailed modeling of accretion disks around black holes. These theoretical milestones were rapidly followed by the discovery of X-ray sources with even more unusual properties. These were X-ray burst sources with recurrence time scales on the order of a few hours; however, all exhibited a dramatic softening of the X-ray spectrum after only a few minutes after each flash. Hoffman et al. (1977) showed that the typical emission radius for such objects were on the order of 10 km, comparable ∼ to the size of a neutron star. Later observations would uncover another class of bursting source, this time with recurrence times of only a few minutes (the accurately-named “Rapid Burster”, Lewin et al. 1976). These rapid bursts showed none of the spectral softening seen in longer bursts. Further study of this source, however, revealed that, in addition to these rapid bursts, it also exhibited the less frequent bursts seen elsewhere, and that these bursts did display spectral softening (Hoffman et al., 1978). This discovery, coupled with theoretical advances in the understanding

3 of helium thermonuclear flashes made by Joss (1978) led to a simple picture to describe both types of X-ray bursts. The bursts with longer recurrence times and spectral softening after the burst (type-I) were the result of helium flashes on the surface of the neutron star, made possible as the accreting material built up in sufficient quantities that the temperature and pressure allowed for a rapid burst of fusion. These bursts softened as the material cooled adiabatically after each burst. The short-period bursts (type-II) were attributed to rapid variations in the rate at which material was accreted onto the neutron star. No softening was observed because the change in the rate of thermal bremstrahlung varied the total power emitted, but not the power distribution. This picture has remained essentially unchanged to the present day. Another major result to come out of this period was the distinction between low-mass and high-mass X-ray binaries, referring to the mass of the companion (mass donor) star. This distinction was first clearly made by Canizares (1975), who noted the similarity between the optically-identified companions of X-ray sources in the galactic bulge and in several globular clusters. These sources, embedded in an old stellar population, contrasted strongly with many sources in the galactic disk with a luminous O- or B-star companion to the unseen compact object. It rapidly became clear that the X-ray properties of these two groups were similarly distinct. For example, all of the known X-ray burst sources belong to the former group of low- mass X-ray binaries (LMXBs), whereas high-mass X-ray binaries (HMXBs) frequently display pulsations which are rare in LMXBs. The spectra of HMXBs tend also to be harder than LMXBs, and are generally brighter. HMXBs include both systems that accrete via Roche-lobe overflow, and those systems accreting part of a strong stellar wind produced by a massive

4 companion. Generally speaking, HMXBs have companion stars with masses above

8 M , and LMXBs have companions lighter than 1.4 M . This latter ∼ ∼ requirement comes out of an accretion stability criterion for a neutron star primary. In this case, a more massive donor star would undergo accretion on a dynamical time scale, with a rapidly contracting orbit driving unstable mass transfer. However, for systems with a more massive black hole primary, this is no longer the case, and a class of medium- or intermediate-mass X- ray binaries (MMXBs) should also exist (though not many, given the initial stellar mass required to form a black hole). As well, Pylyser & Savonije (1988) showed that, provided the donor’s convective envelope doesn’t extend too deeply, accretion on a 1.4 M neutron star will be stable for donor masses up to 2 M . Tauris & Savonije (1999) later extended this result for giant ∼ stars below this limit. So MMXBs with neutron star primaries also exist, for borderline donor masses. Indeed, the binary Her X-1 is thought to be such a system, with a companion mass of 2.3 0.3 M (Reynolds et al., 1997). Such  systems may also play an interesting role in solving the “birthrate problem” regarding binary millisecond pulsars, further discussed below. In the galactic population, there are now over 200 known XRBs, two- thirds of which are LMXBs (Lewin et al., 1997). The number of MMXBs at present is unclear, as there is considerable confusion with the LMXB population. Accurate companion masses are not available for many LMXBs, making it difficult to segregate the two populations. For the reasons given above, not many MMXBs are expected, and only a handful are known, with Her X-1 being the primary example. The X-ray luminosity produced by each of these binaries, when active, runs from 1036–1039 erg s−1, making XRBs the principal contributors to the X-ray luminosity of normal galaxies

5 lacking an active nucleus. In 1974, a binary pulsar was discovered using the Arecibo radio telescope by Hulse & Taylor (1975a), which was quickly shown to have some unusual properties. Unlike every other pulsar in a known binary system at that time, no optical companion could be discerned. Pulsar timing analysis confirmed the mass of the pulsar PSR 1913+16 at 1.442 0.003 M , and the mass of the  companion at 1.386 0.003 M . The orbit of the system was later shown to  be contracting at precisely the rate predicted by Einstein’s General Theory of Relativity(Taylor & Weisberg, 1982), simultaneously demonstrating that the companion was itself a neutron star or black hole (most likely the former). While a powerful test of General Relativity, it also raised the question of how such a system came to form in the first place. It is unlikely that the pulsar has remained unchanged since its initial formation, given the spin period (59 ms) and the observed magnetic field strength ( 3 1010 G). The ∼ × most probable explanation for this is that, after the more massive primary evolved off the main sequence and became a pulsar, it received an infusion of mass from the companion, either from Roche-lobe overflow accretion or by passing through a common-envelope evolution phase. The resulting transfer of angular momentum will spin up (recycle) the central pulsar; however, this mechanism is not available to the second star, and it remains either an ordinary neutron star or a short-lived pulsar. A variant of this mechanism comes into play in the binary pulsar system PSR 1534 + 12, discovered by Wolszczan (1990). Interestingly, radio pulse timing indictates a pulsar mass of 1.32 0.03 M , with a companion mass  of 1.36 0.03 M ; that is, the pulsar and its companion are of comparable  masses. As in the case of PSR 1913 + 16, the pulsar period and weak magnetic field strongly indicate that the pulsar was recycled by an episode of

6 mass transfer. In this system, however, the pulsar progenitor seems to have evolved last, which raises the question of how the pulsar could experience mass transfer. The likely scenario in this case is analogous to that of a classic “paradox” of binary evolution, the evolution of the eclipsing binary Algol (β Persei). This system consists of a main sequence star orbiting an evolved sub-giant. The assumption was that the sub-giant was the more massive of the pair, as it had evolved off the main sequence first. Later measurements showed that this was not the case, and it was eventually understood that the system had experienced at least one episode of mass transfer, and that the sub-giant had initially been the more massive star. As departure from the main sequence is driven by the consumption of hydrogen in the stellar core, the loss of a sizable amount of its envelope did not significantly affect the amount of time the mass donor remained on the main sequence. For PSR 1534 + 12, the pulsar progenitor may initially have been more massive, evolving first even after transferring a significant amount of mass to it companion. After becoming a neutron star, the reverse occurred, with mass flowing from the evolving companion to the neutron star, spinning it up. Binary evolution is also critical to our understanding of the fastest- spinning pulsars currently known, the millisecond pulsars. Generally de- fined to have a spin period of around 10 ms or less, millisecond pulsars are overwhelmingly found in binary systems. Of those millisecond pulsars in the galactic disk, 90% are known to be members of a binary, along with ∼ about half of those discovered in globular clusters (see Bhattacharya 1997, and references therein). Contrast this with the binarity rate among the radio pulsar population as a whole, where the value is closer to 5%. In addition to their short spin periods, millisecond pulsars are characterised by weak

7 magnetic fields, typically on the order of 109 Gauss or less, compared with the 1011–1012 Gauss that is normal for slower pulsars. This weak field means both that the neutron star is old, and that it spins down slowly compared to stars with stronger fields. This implies that pulsar recycling has occurred at some point in the past, as the neutron star would have had a stronger field when newly-formed, and would not still be spinning with a millisecond period so long after formation. A fresh infusion of angular momentum onto an old neutron star from its companion could produce such systems, as the weaker magnetic field means that the star will not spin down quickly. Also, the weak field permits a higher initial (recycled) spin to be reached, since strong-field objects tend to abruptly terminate mass transfer upon reaching a critical spin period, becoming “magnetic propellers”, and rejecting further accretion. To spin a neutron star to such periods requires that an amount of mass on the order of 0.1 M be transferred. Even for systems accreting at or near −8 −1 7 the Eddington rate (M˙ 10 M yr ), it would take around 10 years Edd ∼ to transfer the requisite amount of material. Assuming the Eddington rate applies generally, this implies that HMXB systems cannot be the progenitors of such systems, as they do not transfer mass for a long enough period of time, and the companion stars do not themselves live long enough. LMXBs, on the other hand, can transfer mass stably for many hundreds of Myr, de- pending upon the companion mass. This has led to the commonly-held view that millisecond pulsars are an evolutionary end state of LMXB systems. The difficulty with the above scenario was pointed out by van den Heuvel et al. (1986) and Kulkarni & Narayan (1988), and is now known as the “birthrate problem”. Extrapolating from current observations, and adjust- ing for the opaque zone of avoidance towards the Galactic center, it is es-

8 timated that there are around 100 LMXB systems throughout the Galaxy. Extensive radio campaigns to locate millisecond pulsars have borne con- siderable fruit, and currently there are believed to be nearly 104 millisec- ond pulsars in our Galaxy. The typical lifetime of an LMXB is roughly τ 109 years. The correspinding lifetime for a millisecond pulsar LMXB ∼ is around 1010 years. Roughly, the formation rate of LMXBs, then, is 100/109, or 10−7 yr−1. For millisecond pulsars, the resulting formation rate is 104/1010 = 10−6 yr−1, an order of magnitude greater. A number of theories have been put forward to bring these rates into closer agreement.

For example, the estimate of τLMXB may be too large, if X-ray irradia- tion of the companion star during mass transfer substantially shortens the duration of mass transfer (Tavani, 1991). Other pathways for creating mil- lisecond pulsars may exist; for example, it may be that some neutron stars are naturally born with weak magnetic fields and fast spins. As mentioned above, medium- (or intermediate-) mass X-ray binaries may provide an ad- ditional formation channel. The lifetime of such systems is shorter than that of LMXBs by nearly an order of magnitude, but they still live long enough to transfer the required amount of mass. There is some evidence that this channel produces at least a few systems, with several binary millisecond pulsars discovered in the Parkes multibeam Galactic plane survey (Camilo et al., 2001) showing deviations from the canonical millisecond pulsar. Their companion stars are white dwarfs with unusually high masses, indicative of a CO star from a more massive progenitor than those found in LMXBs. Also, the spin periods are slightly longer than usual, indicating a smaller amount of mass transfer than what is typical. A theoretical discussion, including attempts to model the final evolved system can be found in Li (2002).

9 1.2 The Physics of Binary Evolution

A detailed discussion of the mechanics of evolving binaries will appear in Section 2.2, below. For this introduction, the principal concepts will be touched on, with the specifics of implementation delayed until the population synthesis model is detailed. There are four primary quantities that uniquely specify the future evolu- tionary sequence of a binary star system. The quantities are the mass of the primary star (M1), the mass ratio between the primary and its companion (q), the initial eccentricity of their mutual orbit (e), and the initial semi- major axis of the orbit (a). There are a number of other parameters that govern the physics of the model proper, such as the efficiency with which orbital energy can expel a common envelope, or the intensity of winds gener- ated by stars of varying brightness on the main sequence and giant branch. Once the rules of the physical environment have been established, however, the output is strictly a function of the four fundamental parameters. All of the binary star modeling considered in this work is carried out in the Newtonian regime, with the exception of merger timescales via gravita- tional radiation, a principal result from Chapter 4. As the binary systems of Chapter 2 evolve out to a maximum of 2 Gyr, graviational radiation is considered only abstractly, and is applied in a separate processing step on systems that have reached the evolutionary endpoint of two closely-bound compact objects. For a binary system described in a co-rotating reference frame, the total potential energy of the system can be written as the sum of the gravita- tional potential and a centrifugal term arising from the choice of reference frame. For a binary with stars of masses M1 and M2, at positions R1 and

10 R2, rotating with a common angular velocity ω, the potential field can be expressed as (Pringle, 1985)

(ω R)2 M M φ (R) = × G 1 + 2 (1.1) − 2 − R R1 R R2 !  | − | | − |  This relation defines a continuous series of equipotential surfaces. Of particular interest is the unique equipotential surface which encompasses both stars, and tapers to a single point at exactly one place along the line which joins the centers of the two stars. This is the first, or inner Langrange point, and the surface defines the Roche lobe of each star. If neither star fills its lobe, the system is detached (no mass transfer). If one star fills its lobe, material can travel along the Roche surface and through the L1 point, transferring from one star to the other. This is a semi-detached system. If both stars fill their respective Roche surfaces, the system is said to have a common envelope, with the outer layers of both stars commingling freely. The Roche surface is usually described by a Roche radius, which is de- fined as the radius of a sphere with the same volume as the Roche lobe. An approximation for this radius was derived by Eggleton (1983). In units of the semi-major axis of the orbit, a, the Roche-lobe radius is given by

R 0.49 q2/3 L = (1.2) a 0.6 q2/3 + ln(1 + q1/3) For semi-detached systems, the stability of mass transfer essentially de- pends on how the donor’s radius changes in response to mass loss (whether it is partially or fully convective, etc.), and the mass ratio between the donor and the accretor. If the star expands in response to mass loss, it will con- tinue to overfill its Roche lobe in a positive feedback loop, resulting in a rapid burst of mass transfer. This can quickly change the orbital radius of

11 the system, often resulting in a merger of the two stars. If the star contracts in response to mass loss, it will barely fill its Roche lobe, and will only transfer mass in response to external stimuli; e. g., the radius expands due to nuclear evolution, or the orbital radius shrinks via gravitational radiation and/or magnetic braking. In addition, if the donor is the more massive star of the pair, the orbit will contract if the mass transfer is conservative (no material is expelled from the system). This can quickly lead to a runaway mass transfer episode if the donor’s Roche lobe shrinks faster than the stellar surface contracts. In the case of common envelope systems, orbital parameters change rapidly and dramatically, as viscous drag rapidly diminishes the orbit. Many of these systems will end up merging during this phase. Those systems that survive end up in a very close orbit, with a greatly improved chance of undergoing a later phase of mass transfer. As well, if the end system is comprised of two compact objects, the narrow separation makes these pairs strong potential sources of gravitational radiation, with the potential for a merger in the distant future via this process.

1.2.1 Gravitational Waves

Gravitational radiation is a direct prediction of Einstein’s General Theory. Just as electromagnetic waves are generated by the acceleration of electrical charges, gravitational waves are produced from the acceleration of matter. Electromagnetic (EM) waves are self-sustaining oscillations of the electric and magnetic fields. Gravitational waves are oscillations in the space-time metric which defines local notions of distance. As gravitation is a vastly weaker force than electromagnetism, so too are gravitational waves much weaker than their electromagnetic counterparts. As such, only the most

12 powerful sources of gravitational radiation can potentially be detected. The small wavelength of EM radiation compared to the size of the emit- ting object allows them to be used to image the source in a detector. The smallest wavelength expected from astronomical sources of gravitational ra- diation is on the order of tens of kilometers, meaning that the size of the emitter is at best comparable to, but usually much smaller than the grav- itational waves. Thorne (1997) makes the interesting point that the infor- mation carried by these very different radiations will be largely orthogonal, as most sources detected via one radiation will be invisible in the other. From General Relativity, a gravitational wave has two quadrupole po- larisations, typically labelled “+” and “ ”. Associated with these are the × two amplitudes h+ and h×, each of which is a function of time and position that completely describe the wave. The effect of a gravitational wave is to change the distance between two points in space, which can be thought of as a “strain” acting on the space between the two reference points. This strain can be quantified in terms of the fractional change in the distance, so if the resulting length change is denoted by the function ∆L(t), then the corresponding strain parameter h is defined as

∆L(t) h(t) = = F h (t) + F× h×(t) (1.3) L + + where the F coefficients range from zero to unity and denote the projec- tion of each component onto an arbitrary distance vector (i. e., the detector, or one arm of the detector). The strength of a gravitational wave source is typically given in terms of the strain parameter it produces at the detector. Using the Newtonian approximation to the Einstein field equations allows us to estimate the order

13 of magnitude of the strain parameter. If the astrophysical source has a mass quadrupole moment denoted by Q, then this approximation gives a value for the strain parameter proportional to the second derivative of the quadrupole moment

G Q¨ h (1.4) ∼ r c4 Note that the strain is inversely proportional to the source distance, not to the square of the distance. This is an important point in calculating the expected rate of gravitational wave events and will be raised again in Chapter 4. Clearly, sources with a rapidly changing quadrupole moment yield the largest signal, and this gives a clue to the astrophysical systems that should comprise the bulk of the detector signal. The gravitational interaction of compact objects should provide the brightest sources. This includes not only the gravitational collapse of the object at formation, but closely orbiting neutron star and black hole binaries as well. As such a bound system loses orbital energy to gravitational radiation, the orbit will shrink and the quadrupole moment will vary even faster, resulting in more radiation. This cascade culminates in the merger of the two compact objects, an event which would project an enormous amount of gravitational energy. Of course, these brightest sources are also very short-lived (the final stage of inspiral may last only a few minutes), and so really luminous gravitational wave sources will be very rare. The canonical source would be a neutron star- neutron star coalescence, which would typically produce a strain h 10−21 ∼ at a distance of 200 Mpc. The detection of gravitational waves similar to those predicted by theory would be yet another verification of General Relativity, and has been the

14 focus of numerous intensive experimental efforts over the past four decades, beginning with the bar detectors developed by Weber (1960), a pioneer of gravitational radiation detectors. The passing of a gravitational wave causes the bar to oscillate in response to the external strain, which can then be calculated. Unfortunately, it is not clear that such techniques can obtain the sensitivity needed to detect strains on the order of 10−20. Recent advances over the last two decades in laser interferometry, how- ever, mean that detectors capable of detecting strains of 10−21 can now be constructed on size scales that, while not exactly compact, can at least be termed “fundable”. The LIGO laser interferometer is the best and most recent example of this technology, encompassing two remote sites with 4 km interferometer arms. Even at this scale, a strain of 10−21 represents an os- cillation on the order of several 10−16 cm, much smaller than an atomic × nucleus. Thus, efforts are underway to construct wave “templates” using numerical techniques to predict the waveforms seen in a variety of possible source configurations (binary coalescence, for example). By convolving these patterns with the data garnered from the interferometer, it is hoped that this will greatly enhance the signal-to-noise ratio, allowing clear detections to be made and increasing the available search volume, with a commensurate increase in observed event rates.

1.3 Overview

Chapter 2 talks about the assumptions that went into the binary model, and why they were chosen. After describing the process by which binaries are evolved from the zero age main sequence (ZAMS) through to the final end state, I detail the mass transfer procedure used by the code. Finally, I

15 show the results produced during a simulation of a starburst with a stellar −1 formation rate of 10 M yr , and a duration of 20 Myr. The focus of this simulation is on the time evolution of the X-ray luminosity produced by vari- ous classes of X-ray Binaries (XRBs), and the individual contributions made by high-mass (HMXB), low-mass (LMXB) and intermediate-mass (MMXB) populations. The onset time for each population to reach a peak luminos- ity is shown and the physical basis for that onset delay is discussed. A comparison is then made to a number of recent theoretical models of X-ray luminosity evolution, as well as observational data in the context of a re- lationship between star formation rate and the 2–10 keV luminosity of the host galaxy. Lastly, an application of the model investigating how the ratio between the hard X-ray and Hα luminosity of a star-forming galaxy changes with time. Chapter 3 details a snapshot survey of 41 nearby galaxies with the Chan- dra X-ray Observatory. The data reduction process is detailed, and a com- plete target list (host galaxies) and source list are given. A summary of the source populations in each host galaxy is included, along with plots showing that there is little or no correlation between the optical luminosity or B V − colour and the total X-ray luminosity of the host galaxy. Massive binaries can become interesting astrophysical sources again, long after their X-ray emission is over. If both members of a binary are sufficiently massive to become compact objects, and remain bound through the second supernova, there is a possibility that they may become significant sources of gravitational radiation in the distant future, after their orbital energy has been slowly dissipated emitting gravitational waves. Chapter 4 gives a dis- cussion of this process in terms of the evolutionary history of the system, and uses population synthesis to estimate merger rates. The role of natal kicks

16 is discussed in terms of the effect on merger rates, as well as the importance of the IMF, initial binarity fraction and assumptions about the fraction of mass retained by a black hole during collapse. Rates are couched in terms of detectability with the LIGO laser interferometer, the most sensitive to date. Alternative merger channels are briefly discussed.

17 Chapter 2

Simulating the X-ray luminosity evolution of a stellar population

2.1 Introduction

2.1.1 X-ray binaries revealed by Chandra

There is now a considerable corpus of evidence that, for “normal” galaxies (i. e. with no active nucleus), the principal component of the X-ray lumi- nosity above 2 keV arises from the associated population of X-ray binaries (XRBs). This is especially true in the presence of vigorous starburst activity, and has been further established with the advent of the Chandra X-ray Ob- servatory, where high-resolution imaging allows an accurate source census and luminosity function to be constructed for a diverse sample of host galax- ies. Specific examples of large, luminous XRB populations that have been revealed with Chandra include the vigorous starbursts in NGC 4038/4039 (the Antennae, Fabbiano et al., 2001), M82 (Zezas et al., 2001; Griffiths et al., 2000), and the ULIRG NGC 3256 (Lira et al., 2002). Perhaps more interesting, however, has been the discovery of sizable XRB populations

18 in non-starbursting galaxies, with inactive or mildly-active galactic nuclei, comparable to those found in some starbursts. The implication, given the generally slow stellar formation rate, is that a significant fraction of X-ray binaries can remain luminous for many gigayears affecting the X-ray emis- sion of a galaxy long after their formation. By way of example, NGC 1291 (Irwin et al., 2002), IC 5332, M83 (Kilgard et al., 2002), and NGC 4736 (Eracleous et al., 2002) all sport several dozen point sources with 2–10 keV X-ray luminosities well in excess of 1037 erg sec−1. The first two of these are undistinguished spirals; however, M83 is known to exhibit highly lo- calised starburst activity in the nucleus and bar regions (Telesco et al., 1993), though the observed XRB population is not limited to these areas. The nucleus of NGC 4736 is known to contain a LINER (Low-Ionisation Nuclear Emission Region, see Heckman 1980). While a commonly-held view is that some LINERs populate the low- power regime of the active nucleus continuum that encompasses QSOs, Seyferts and the like, many are also associated with starburst activity (e. g. NGC 404, NGC 4736, see Eracleous et al. 2002). I shall defer further dis- cussion of the LINER-XRB connection to the end of the present chapter, but raise the issue now both to emphasise the utility of the Chandra ob- servatory (allowing individual X-ray sources to be tabulated even when in close proximity) and to establish the role of star formation as the princi- pal determinant of a galaxy’s X-ray properties in the absence of a strong, presumably accretion-powered, nuclear source.

2.1.2 Observables for reconstructing a star formation history

More than any other quantity observable in the X-ray band, the luminosity distribution of an XRB population gives great insight into the star forma-

19 tion history of the host galaxy. It is true that measurements of soft X-ray superwinds provide a great deal of information on recent episodes of star for- mation; however, XRBs (specifically low-mass X-ray binaries, or LMXBs) are durable records of the distant past, and can be studied long after the star formation driving the superwind has faded. This is doubly true for quiescent galaxies, where a measurable superwind may simply never form. The shape of the luminosity distribution is determined primarily by two factors; namely, the age of the population, and the distribution of mass ratios between the system primary (accretor) and companion (donor) star. The normalisation of the luminosity distribution is directly proportional to the star-formation rate (SFR) of the population in question, save for noise resulting from counting statistics when there are few active sources. These points are borne out by recent observations. The analyses of Eracleous et al. (2002) and Kilgard et al. (2002), comparing the source luminosity functions of a number of starburst and non-starburst galaxies show two significant trends. Specifically, the luminosity function in starburst galaxies tends to be substantially flatter, with high-luminosity sources in greater abundance. Second, the slope of the luminosity function shows a strong correlation to the observed 60 µm and Hα luminosities, direct measures of star formation. This trend can be understood in terms of a stellar population’s age, which determines which elements of the population will become luminous at some epoch. The simulations undertaken here allow the variation of luminosity func- tion with Hubble type to be predicted directly, from fundamental principles of stellar evolution coupled with a sophisticated treatment of mass trans- fer. The generated luminosity functions can then be compared against data from the Chandra and XMM/Newton observatories. This is a new approach

20 and allows for substantial iteration, whereby the latest observational results inform the next, refined iteration of the code, enhancing its predictive capa- bilities and simultaneously improving our understanding of the underlying input variables. The relationship between the shape of the luminosity function and the age of the underlying population is driven by the timescale over which the donor star in the binary begins to transfer mass. For low-mass XRBs (LMXBs), mass transfer is driven by either the nuclear evolution of the donor (expanding to fill its Roche lobe), or the loss of angular momentum through gravitational radiation and magnetic braking processes (shrinking the Roche lobe of the donor). All three of these mechanisms develop over long timescales. In contrast, high-mass XRBs (HMXBs) begin mass transfer on the shorter nuclear timescale of the massive donor star. HMXBs pow- ered by Roche-lobe overflow tend to be brighter, on average, than LMXBs, as the accretor is more likely to be a black hole when the donor is massive (a consequence of the stellar mass function and mass ratio distribution). The result is a flat luminosity function (more numerous bright X-ray sources) for young stellar populations, which slowly becomes steeper as the short-lived HMXBs give way to long-lived LMXBs. To extract more physical insight from recent XRB data, it is natural to consider a simplified system; where, by taking a simple set of rules to govern star formation and evolution, and by inferring a set of input parameters from available observations, a “binary machine” can be constructed. Synthetic populations can be created and evolved in time, observables calculated and then fed back as input in further iterations. Once there is confidence that the machine can be made to closely match observed XRB populations, the next step is to investigate the long-term evolution of synthetic XRB populations.

21 In particular, the evolution of the X-ray luminosity of a galaxy can then be modeled. Star formation rates can be inferred from photometry in var- ious bandpasses (see, e. g., Condon, 1992; Kennicutt, 1998; Rosa-Gonz´alez et al., 2002). Coupled with a few other assumptions, detailed below, this is sufficient to generate an approximate picture of the XRB population at an arbitrary epoch. Periods of mild or intense starburst activity can be introduced, and the effect of these events quantified. Indeed, in its most general form, the population synthesis undertaken here can be viewed as an “integrator” of the SFR, itself a function of time, between the epoch of galaxy formation and the current lookback time. Thus, it provides a use- ful connection between the cosmological star formation rate as a function of lookback time, and the population of XRBs seen at increasing redshift. This problem has been approached in a seminumerical fashion by Ghosh & White (2001); Ptak et al. (2001); White & Ghosh (1998), in addition to an analytic formalism expressed in Wu (2001). Our goal is to approach the study of the evolution of galactic X-ray properties from a numerical stand- point, which requires fewer simplifying assumptions than a seminumerical or purely analytic formulation. Coupled with an understanding of the relation- ship between a galaxy’s current star-formation rate and its X-ray properties, this work enhances the power of modern X-ray observatories to document the historical star-formation rate.

2.2 Population modeling

2.2.1 History and authorship of the population synthesis code

We make use of a binary evolution code detailed in part by Pols & Marinus (1994), and modified for use in neutron star-neutron star (NS-NS ) systems

22 by Bloom et al. (1999). Our extension of the code allows for evolution to the black hole state, with assumptions about the mass function of such objects at the time of collapse; in addition, the technique for computing mass transfer rates was refined considerably, by coupling it more directly to the underlying physics, as discussed below. For purposes of the numerical model, an initial binary system is con- sidered to be completely described by four parameters: the mass of the system’s primary (more massive) star, M1, which is chosen from the spec- ified initial mass function; the primary to secondary mass ratio, q, defined to lie between zero and unity; the initial orbital eccentricity, e; and the ini- tial orbital semi-major axis, a. The code then evolves the binary in time, taking into account the orbital changes caused by mass transfer, wind loss, etc. These four quantities are tracked, as is the evolutionary state of each star, and any mass exchanges that take place. The code terminates when both stars have reached their respective evolutionary end points, which are a strict function of the initial core mass.

2.2.2 Population code theory of operation, choice and extent of parameter space

The evolution of a binary pair starts with the choice of a primary mass from an assumed initial mass function (IMF). For this work, we consider two power law IMFs (where dN = m−αdm); the first index is α = 2.35 − (the Salpeter IMF; Salpeter 1955), the second is α = 2.7, approximating − the high end of a Miller-Scalo IMF (Miller & Scalo, 1979). In both cases, we established a lower cutoff of 4 M for the primary star’s mass, confining the code to an interesting range of initial masses; i. e., where at least one supernova is possible in principle. This is because our interest is in systems

23 with a neutron star or black hole, as these are the potentially luminous X- ray sources. Our stellar models are taken primarily from Maeder & Meynet (1989). The helium star models used are a mix of models from Habets (1986) and Paczynski (1971), and the reader is referred to these for a detailed discussion and evolutionary tracks. We define the initial mass ratio q to be the initial mass of the secondary divided by that of the primary (hence 0 q 1). The distribution of q is a ≤ ≤ topic of some controversy, given the observational biases involved in studying systems with diverse mass ratios (Hogeveen, 1992). A “flat” distribution, where all values of q are equally likely, is often chosen given the difficulty in reconstructing the underlying function. An extensive inventory of obser- vational data was compiled by Kuiper (1935) in an attempt to address the mass ratio distribution question. These data, coupled with the more recent data of Batten et al. (1989), and the analysis found in Hogeveen (1992), point to two principal results. First, in the case of single-lined spectroscopic binaries, the distribution of q is a two-part function, where:

q−2 for q > 0.3 ψ(q) (2.1) ∝   1 for q < 0.3

For double-lined spectroscopic systems, the observed q distribution was found to be driven almost completely by selection effects, albeit consistent with the q-distribution of single-lined binaries above. See Elson et al. (1998) for a further discussion of this problem in the context of massive binaries in a young LMC cluster, where a q distribution biased towards companions of equal mass is found, but the detection limit prevents an accurate census of low-q systems. We consider both the flat and the low-skewed q-distributions in our simulations below, accepting that reality likely lies somewhere be-

24 tween these two points. The initial binary separation is chosen after Abt (1983), with a distribu- tion that is flat in the logarithm of the semi-major axis , and in the range 6 10 R < a < 10 R . This distribution fits well with existing spectroscopic surveys of nearby stars. Duquennoy & Mayor (1991), describe another sep- aration distribution, based upon a CORAVEL spectroscopic survey of 181 Gliese catalogue stars. The function they derive is Gaussian, with a mean 3 2 of 8 10 R and σ = 8 10 R . We use Abt’s prescription here, but × × wished to make clear that this is not a settled issue. Related population synthesis studies currently use the former distribution almost exclusively, often with little comment. If the Duquennoy & Mayor (1991) result holds when expanded to a larger survey size (preferably including a few non-local systems) then this issue will have to be revisited. Given the dramatically wider initial separations implied by the Duquennoy & Mayor (1991) distri- bution, one can at least make the prediction that far fewer X-ray binaries would result, since the common-envelope phase would be less likely to occur. This in turn would imply wider systems with larger Roche surfaces, making Roche-lobe overflow unlikely. The eccentricity is chosen from the standard thermal distribution, ξ(e) = 2e. This choice for the distribution of initial eccentricities is ubiquitous in binary population synthesis. The mathematics justifying this relation can be found in Heggie (1975), and interested readers are referred there for all of the details. Briefly, consider a phase space of fourteen dimensions defined by the positions q1, q2 of two particles, their velocities v1, v2 and their masses m1, m2. Let f be a function on this space that gives the number density of particle pairs (per unit volume of phase space) with the specified state. In general, the pair distribution function can be written in terms of the single

25 particle distributions as

f(q1, v1, q2, v2, m , m ) f(1, 2) = f(1) f(2) + g(1, 2) (2.2) 1 2 ≡ where g is a correlation function. If the particles do not interact at all, the function g goes to zero. Obviously this cannot be strictly true for real stars, but it is sufficiently accurate if the binary forms at a large distance, a very common case. If the ensemble of stars is in thermal equilibrium, the single particle distribution functions converge towards the Maxwell distri- bution. After some manipulation (Heggie, 1975), it can be shown that in the resulting f(1, 2), the eccentricity parameter is not correlated with any other variable, and is distributed according to the relation ξ(e) = 2e. After the initial parameters have been selected, each binary system is evolved along the stellar tracks referenced above until both components have reached their final degenerate form, accounting for mass-transfer-induced stellar regeneration and stellar winds. Stellar winds from helium stars are accounted for using the relation developed in Langer (1989), where the mass −8 2.5 −1 loss rate is M˙ = 5 10 M M yr . This wind lasts for the duration of × the star’s helium main sequence lifetime. When the more massive primary leaves the main sequence and ascends the giant branch, the rapidly-swelling star may engulf its companion with its outer envelope. This common-envelope phase will rapidly shrink the orbital radius of the binary on a timescale of only a few orbital periods. Those systems that avoid a merger event at the end of the CE phase will be more likely to engage in mass transfer, as the size of the companion’s Roche lobe shrinks along with the orbital separation. A CE phase can also result as the secondary leaves the main sequence, though systems are unlikely to

26 survive two such events without merging. For our purposes here, during the common-envelope phase, the orbit is circularised, and the orbital energy is reduced by the binding energy of the envelope divided by the common- envelope efficiency parameter, which we take to be 0.5. In other words, the orbital energy is reduced by twice the envelope binding energy. Neutron stars are formed from progenitors with zero-age main sequence

(ZAMS) masses of between 8 and 20 M , inclusive, and are always given a mass of 1.4 M . More massive stars end up as black holes. This boundary is unlikely to be a sharp one, as it is strongly coupled to the spin state of the pre-collapse object (Fryer, 1999). Even assuming this was known to perfect accuracy, the effects of magnetic fields and rotational support on the compact object’s end state are not well understood. This point also bears upon the magnitude and direction distribution of natal kicks received by the neutron star at birth, from an asymmetric emission of neutrinos or core material. The role of and justification for asymmetric natal kicks is discussed below, including the appearance of assymetric kicks during black hole formation. The black hole mass function (i. e., the post-collapse mass of a BH, given its mass just prior to the explosion) is highly speculative at this point, and is almost certainly not merely a function of initial mass, but also of angular momentum, to the extent that this determines the fraction of material falling back onto the collapsing star. In order to experience a kick, the black hole’s formation must be delayed somewhat, either due to rotational support, or because event horizon formation occurs only after delayed fallback of mass initially ejected from the core. Fryer (1999) has performed core-collapse simulations in order to explore the critical mass for black hole formation, and the final masses of the resulting black holes. As a best working scenario,

27 we have constructed a mass relation from a quadratic fit to the limited data set found in Fryer (1999). Our fit shows that the mass of the black hole at formation (MBH ) is related to the ZAMS mass of the progenitor (M0) by 2 M = (M /25M ) 5.2M . This relation is accurate to about 10% of the BH 0 × black hole initial mass at each of the values resulting from a hydrodynamic simulation. It should be noted that this relation is almost certainly depen- dent upon metallicity (see, for example, Fryer et al. 2002). The assumed relation is appropriate for systems with approximately solar metallicity, but would need to be adjusted to investigate metal-poor progenitors. The importance of the black hole IMF in XRB formation extends beyond the obvious effect on a system’s orbital elements. The maximum luminosity from future mass transfer onto the black hole is a function of the hole mass. 38 −1 The Eddington limit of L = 1.3 10 M/M erg s is frequently invoked E × × for this luminosity cutoff; however, this limit applies strictly only in the case of spherically symmetric accretion. The black hole IMF is important because it is one of two important factors that set the maximum luminosity of the most luminous XRBs (the other is the range of mass transfer rates from the companion star). Thus, the high-luminosity end of the resulting luminosity function depends quite sensitively on the black hole IMF. Of course, the Eddington assumption can be relaxed, allowing us to test the models that have been put forward to explain the significant num- ber of extremely-luminous XRBs now known to exist. Models that explain these events through bona fide super-Eddington accretion (Begelman, 2002) should result in a different distribution of luminosities and event rates (per unit SFR) than models involving randomly-directed relativistic beaming (King et al., 2001). Careful population synthesis can provide a means to discriminate between these hypotheses, and we hope to report the result in

28 the near future. Another relevant parameter concerns the magnitude of natal kicks to be imparted to a neutron star or black hole at formation. I discuss more fully the mechanism and justification for including natal kicks in Chapter 4, but a brief overview is warranted here. There are two mechanisms for natal kicks. Blaauw-Boersma kicks (Blaauw, 1961) result from a conservation of momentum after the supernova which gives birth to the compact object. In this scenario, the supernova ejecta are released approximately isotropically, in the rest frame of the explosion. The remaining mass in the system receives a kick in the direction opposite the velocity of the exploding star, with a resulting speed change comparable to the orbital velocity of the supernova progenitor (assuming roughly half of the total binary mass is expelled from the system), and proportional to the mass ratio of the ejecta to the binary (post explosion). Asymmetric kicks arise from the anisotropic emission of neutrinos and/or core material in the supernova event. Compared to symmetric Blaauw- Boersma kicks, a smaller amount of mass loss is needed to generate a compa- rable velocity change, and this is especially true if the bulk of the momentum is carried away in an anisotropic neutrino flux. For neutron stars formed in a supernova, this scenario is sufficient. However, if the star is massive enough to form a black hole, there is a potential problem for the natal kick scenario. Gourgoulhon & Haensel (1993a) convincingly demonstrate that, if the event horizon forms on the dynamical timescale of the collapsing core, an insufficient number of neutrinos escape to drive a supernova explosion through envelope heating. This implies a maximum mass for a supernova progenitor, above which the supernova is quenched by the event horizon before it begins. We have chosen a simple criterion for whether a black hole

29 will receive an asymmetric kick during collapse; namely, all objects below

40 M (referring to the ZAMS mass) experience a random kick. Above this limit, objects collapse directly to a black hole, with no kick. This is a simplification consistent with hydrodynamical simulations such as those of Janka & Mueller (1996), Fryer (1999) and Fryer & Heger (2000). The magnitude and direction of the asymmetric kick are still matters of considerable debate. One strong possibility is that of neutrino-induced convection, as discussed in Janka & Mueller (1994); Fryer & Heger (2000), and references therein. In this process, the angular momentum acts to sta- bilise the forming compact object, so that rapidly-rotating progenitors pro- duce substantially-weakened explosions. The neutrino convection in rapid- rotators is concentrated at the slowly-rotating poles, driving an asymmetri- cal supernova. It is interesting that the kick vector depends not only upon the rotation of the progenitor, but that an inverse correlation is posited between the magnitude of the supernova event and the asymmetry of the explosion. Unfortunately, the binary evolution code does not track the rota- tion state of the progenitor, and so while the above theoretical predictions are an interesting path for future investigations, they cannot be effectively applied here. Therefore, I take asymmetric kicks to be oriented randomly and isotropically. The imparted kick speed is selected from a Maxwellian distribution with an energy corresponding to a 1.4 M neutron star with a speed of 90 km s−1. The distribution is truncated at the high end, with a −1 maximum kick speed of 500 km s (again, for a 1.4 M neutron star). All kick speeds are scaled to the mass of the recoiling object; e. g., a 7 M black hole will receive a speed change one-fifth the size that would be imparted to the aforementioned neutron star. A more complete discussion of the effects natal kicks have on binary evo-

30 lution can be found in Chapter 4. For the present discussion, it is important to note that, in order for a system to become an XRB of any type, it must first survive the natal kick produced when the compact object is formed. The likelihood of this obviously drops dramatically as the imparted kick speed increases. Since the kick speed is inversely proportional to the mass of the compact object progenitor, an immediate prediction is that XRBs with a black hole accretor should be more common than the assumed IMF would indicate, as these systems will survive the first natal kick more easily than systems with a neutron star primary. A similar effect holds for the mass of the donor star, though in this case the effect is independent of the kick magnitude. Systems which retain a larger fraction of their total mass have a greater chance of surviving the first supernova; this implies that binaries with more massive secondaries are also more resistant to disruption. The overall effect is to increase the ratio of HMXB to LMXB systems compared to what would be predicted on the basis of the initial IMF alone.

2.2.3 Implementation of mass transfer in the code

The code itself tracks changes of state, which means that instead of evolving a binary system along a smoothly-flowing time axis, the next evolutionary “event” (for example, a star may leave the main sequence, or become a helium star after casting off its envelope through a stellar wind) is found from the input stellar evolution tracks, and the code advances the time in- dex accordingly. At this point the code extrapolates mass loss from winds for each star for the elapsed time, and recalculates orbital parameters ac- cordingly. Sudden mass loss (from supernova events) is handled identically, with the code writing out the evolutionary state and orbital parameters immediately before the explosion, and immediately after. If, after advanc-

31 ing to the next evolutionary state, the code determines that the two stars should have interacted via mass transfer at some point, the system is backed up to the immediately previous state, and the orbital parameters are set such that (at least) one star is barely in contact with its Roche-lobe. An episode of mass transfer is then resolved, ending with both stars inside their respective Roche-lobes (or with a spiral-in, if the system was undergoing common-envelope evolution and lost sufficient orbital energy to bring the stellar cores into contact, after ejecting the envelope). The code is modu- lar in the sense that the means by which mass transfer is resolved can be completely redefined without affecting any other aspect of the evolution. The original evolution code made use of a crude technique for mass transfer, insufficient for our purposes. After interpolating on the appropri- ate stellar evolution track, the donor’s core mass (mcd) was found. The difference between this and the total donor mass md gave the envelope mass of the donor, which was considered to be completely transferred to the accre- tor over a discrete number of mass-transfer steps (twenty, by default). The amount of mass transferred in any given step was constant, so in the default case 5% of the envelope mass was moved to the accretor each time. After each mass element was moved, the orbital elements were recalculated. This low-resolution method gives a reasonable first approximation of the orbital elements after mass transfer has concluded, but obviously is a poor choice for studying X-ray binaries, where mass transfer is the phenomenon under consideration. Settling on a mass transfer routine was easily the most difficult aspect of the simulation, and was the greatest single modification that I made to the original code base. A commonly-used technique in Cataclysmic Variable modeling (Meyer & Meyer-Hofmeister, 1983; Ritter, 1988) is the following:

32 Letting ρL1 be the density of the mass flow through the inner Lan- grangian (L1) point, vs the isothermal sound speed, and Q the effective cross- sectional area of the flow, then the mass transfer rate is given as (Pringle, 1985)

M˙ = ρ v Q (2.3) − L1 s Next, consider Bernoulli’s theorem, along a path from the donor photo- sphere, to the L1 point

1 L1 dP v2 + + Φ = constant (2.4) 2 ρ Zph where P is the pressure, Φ the gravitational potential, and v the flow velocity. The result is the flow density at the L1 point, given by

1 φ φ ρ = ρ exp L1 − ph (2.5) L1 √e ph v2 − s  and the isothermal sound speed can be expressed in terms of the mean molecular weight, gas constant, and photospheric temperature

Tph vs = R (2.6) s µ From the above, the mass transfer rate can then be expressed as

1 φ φ M˙ = ρ v Q exp L1 − ph (2.7) √ ph s 2 − e − vs  The above equation demonstrates the principal difficulty in employing this technique. Note that the mass transfer rate depends on an exponential function of the gravitational potential difference between the L1 point and the edge of the donor’s photosphere. This means that even a small error

33 in estimating the potential difference will result in a very large error in the resulting mass transfer rate. To know the precise extent of the photosphere would require detailed knowledge of the star’s physical and chemical struc- ture. Chemical structure is not tracked in any way by our binary evolution code, and physical structure is generally interpolated between points on the stellar evolution grids that are taken from a library. The result is that we cannot know the potential difference in the mass transfer rate equation to sufficient accuracy. While not usable directly, the mass transfer equation makes sense at an intuitive level. It essentially states that the resulting mass transfer rate is strongly dependent on the extent to which the donor’s photosphere exceeds its Roche radius. A star that just barely fills its Roche surface will exhibit a low mass transfer rate, while a donor that would otherwise be much larger than the resulting Roche surface will support a much higher transfer rate. The model used in the final version of the binary evolution code in- corporates the above principle, as described in Hurley et al. (2002), and references therein. To determine the stability and timescale of mass trans- fer, adiabatic coefficients are employed, which describe the response of the donor star’s radius to mass loss. These coeffiecients are defined in Webbink (1985), as follows:

∂ ln R ζad (2.8) ≡ ∂ ln M X,s d ln R ζ L (2.9) L d ln M ≡   ∂ ln R ζ eq (2.10) eq ∂ ln M ≡  X

ζad is a logarithmic derivative of the donor’s radius with respect to mass,

34 at a constant chemical composition and specific entropy. ζL is the logarith- mic derivative of the donor’s Roche lobe radius with respect to its mass, and

ζeq is the logarithmic derivative of the radius of the donor in thermal equi- librium, when held at a fixed chemical composition, with respect to mass. The mode of accretion can be determined from the following inequalities between the coefficients

ζL < (ζad, ζeq) Nuclear timescale mass transfer. Mass transfer is not self- sustaining, and is strongly dependent on the degree to which the Roche lobe is overfilled. The resulting mass transfer rate is

3 R2 −1 M˙ = f(M ) ln M yr (2.11) 2 2 R −  L 

where M2, R2, and RL refer to the mass, radius and Roche lobe radius of the donor star, and f(M) is given by

f(M ) = 3 10−6 min (M , 5.0)2 (2.12) 2 × 2

This relation is chosen to ensure steady mass transfer (Hurley et al., 2002, and references therein).

ζeq < ζL < ζad Mass transfer occurs on the thermal timescale of the donor’s

envelope. If M is the donor mass, Mc is the core mass of the donor, and

τkh is the Kelvin-Helmholtz timescale (in years) of the donor envelope, then the mass transfer rate is

M2 Mc −1 M˙ 2 = − M yr (2.13) − τkh

35 ζad < ζL Dynamical mass transfer. In this situation, the radius of the pri- mary expands more quickly than the Roche surface after transferring a mass element. Thus the mass-loss rate is limited only by the sound

speed in the envelope of the donor, and is a runaway process. If τdyn is the sound-crossing time of the donor (the donor’s radius divided by the envelope sound speed), then the mass loss rate is just

M2 Mc −1 M˙ 2 = − M yr (2.14) − τdyn

A number of HMXBs exhibit a very different mode of mass transfer; namely, accretion from a strong stellar wind coming off of a massive com- panion, typically a Be- or O-star. We do not consider these systems for a number of reasons. First, the X-ray luminosity of such an XRB is highly variable, and strongly tied to the positions of the two stars relative to the line of sight, as the absorption column density is far from isotropic. Second, these systems tend to be very faint (below 1035erg s−1), unless in a rare out- burst from an instability in the companion. While these sources have a hard X-ray spectrum, they are never present in sufficient numbers to dramatically alter the outcome of the simulation. Pulsars and the associated supernova remnants (SNRs) also contribute to the overall X-ray luminosity. While SNRs energised by a young, rapidly- spinning pulsar can attain luminosities of 1037erg s−1 and above, much of this radiation is emitted below 2 keV, while we are more interested in the hard X-ray emission from 2–10 keV. Van Bever & Vanbeveren (2000) have an interesting discussion about the small contribution of these objects in their own synthesis work, and claim that, for the SNR contribution to be significant, the bulk of newly-formed pulsars would require spin periods of

36 10 ms or less. Hence, we ignore this group of objects in our tally of X-ray photons.

2.2.4 Mass accretion and resulting X-ray luminosity

For the Roche-lobe overflow systems we are considering here, the accretion flow, collimated through the inner Lagrange point, naturally forms into a disk structure around the accretor, as it cannot shed angular momentum quickly enough to permit a direct impact onto the primary (Shakura & Sunyaev, 1973). A distinction must be drawn between the mass transfer rate (the rate of material passing through the inner Lagrange point), and the mass accretion rate (the rate of material accreting on to the compact object). Clearly, the X-ray luminosity depends strongly upon the latter. In a conservative mass transfer scenario, no matter is lost from the system, and the two transfer rates should be equal if the disk remains in equilibrium. This is not generally true, however, and we must quantify the extent to which mass transfer is non-conservative. We can establish a relation defined in terms of the Eddington luminosity limit of the accretor; so the mass transfer rate M˙ , and mass accretion rate M˙ , are related by − 2 1

M˙ = (α 1) M˙ (2.15) 1 Edd − 2 where

M˙ Edd αEdd = max 0 , 1 (2.16) − M˙ 2 !

The M˙ Edd term is the mass transfer rate that generates a luminosity equal to the Eddington luminosity of the accretor (assuming for the moment that M˙ = M˙ ). In other words, as the mass transfer rate climbs above 1 − 2

37 M˙ Edd, the mass transfer becomes increasingly non-conservative, as αEdd approaches unity. The procedure for converting a mass transfer rate into a bolometric lumi- nosity follows from energy conservation. If r1 is the radius of the accretor, and a is the semimajor axis of the binary, then the power generated by an accretion rate M˙ on to a compact object of mass M1 is the bolometric luminosity

1 1 L = GM M˙ (2.17) bol 1 r a  1 −  For accretion onto compact objects, it is safe to assume that a r , so  1 that

GM1M˙ 1 Lbol = (2.18) r1 Half of the potential energy liberated by the infalling material is re- leased in the accretion disk before making contact with the compact object (Pringle, 1985). Precisely where this energy is emitted becomes important when considering accretion on to a black hole, where energy crossing the event horizon is lost from the system. Consider that a mass element falling from infinity begins with zero binding energy. Upon reaching the innermost region of a circular, Keplerian disk, the binding energy for an element of mass m is just one half of the kinetic energy, with opposite sign

1 T = K + U = K = mv2 (2.19) − −2 m GM = (2.20) − 2 R GMm = (2.21) − 2R

38 1 = U( ) (2.22) 2 ∞ (2.23)

Thus, we introduce the efficiency parameter ηc, with a value of 0.5 for black hole accretors, representing the fraction of energy released before the “accreted” material disappears across the event horizon. For neutron star accretion, we take this value to be unity, with essentially all of the energy radiated from either the innermost ring of the accretion disk, or from the accretion column on to the neutron star proper. The amount of energy emit- ted from these two regions is equal only in the special case of an accretion disk that is truncated at the radius of the neutron star. As the magnetic field of the neutron star acts to truncate the disk at much larger radii, the bulk of the energy is in fact emitted from direct accretion on to the neutron star surface. A second efficiency factor that must be considered is the duty cycle of the accreting sources. In many X-ray binaries, the accretion disk is vulnerable to an instability analogous to the so-called “dwarf nova” instability seen in many cataclysmic variables. A thorough analysis of the physics that drives the instability can be found in Frank et al. (1992, p. 104). Recall that for a disk comprised of annuli with temperature T and surface density Σ, steady accretion across the annulus will only occur if the derivative ∂T/∂Σ is positive. The functional form of T (Σ) in each annulus is a solution of the diffusion equation, with an equilibrium solution T0(Σ0) for a specified mass transfer rate. If the derivative ∂T/∂Σ is positive at the equilibrium solution, then the mass accretion rate will equal the mass transfer rate, and steady accretion will occur, with no instability. If, however, the derivative at the equilibrium point fails this condition, the system can never achieve

39 equilibrium. As the mass accretion rate gets closer to the mass transfer rate, the surface density of the disk climbs (as there is still a net flow of material into the ring), with a corresponding increase in temperature. When the temperature no longer increases with surface density, the system jumps to a much higher temperature and mass transfer rate at the same Σ, and the temperature derivative is again positive. However, the mass accretion rate is now much higher than the mass transfer rate, and the ring steadily empties of material as the system again attempts to attain equilibrium. The disk cools until the temperature derivative reaches zero once more, at which point the system again drops into the previous low temperature, low viscosity (hence low mass accretion rate), and returns to the beginning of the cycle. Reproducing this process in our numerical simulation is difficult, as the physical parameters of the accretion disk are not tracked. As well, the accretor itself plays a significant role in determining whether instabilities will be seen. From a large volume of observations, it is known that LMXB systems with black hole accretors, for example, almost always exhibit the dwarf nova instability. For NS-LMXBs this is much less common. It is thought that significant X-ray emission from accretion on to the neutron star illuminates and heats the disk, maintaining the high-viscosity state and allowing stable accretion. For the purposes of our simulation, we have broken down this problem into three possible cases. The first, accretion onto a neutron star primary from a massive companion (either an NS/HMXB or NS/MMXB in the clas- sification scheme), is the simplest case. The generally high mass transfer rates from massive companions, coupled with the radiation from the surface of the neutron star, act to prevent the dwarf nova instability. We therefore take the duty cycle of such systems to be unity.

40 The second case is that of accretion onto a neutron star by a low-mass companion (NS/LMXB). Here, the lower mass transfer rate means less il- lumination of the accretion disk by accretion onto the neutron star. To determine if the instability manifests itself in a given system of this type, we employ a period criterion inferred from a plot in Li & Wang (1998). The critical period Pcrit is defined as:

M2 0.6 log Pcrit(days) = 6.5 − (2.24) M ×   where M2 is the donor mass, as before. If the donor mass is below

0.6M , the energy released by mass transfer is judged to be insufficient to stabilise the disk, regardless of the orbital separation of the system. If

0.6M < M2 < 0.8M , then the system is taken to be stable if the orbital period is less than the critical period Pcrit above. If M2 exceeds 0.8M , then the system is stable only if its period is less than twenty days. All systems with larger periods are assumed to exhibit the dwarf nova instability, and are assigned a duty cycle of 0.1, meaning that only ten percent of the luminosity from such systems is counted in the results showing the time evolution of the luminosity. The final case covers black hole accretors with a companion of any mass. Because there is no radiation from the accretion column illuminating the disk, a black hole system must be closely bound to avoid the disk instability. The criterion for this case is taken from King (2001), where it is derived from estimating when the luminosity required to suppress disk outbursts exceeds the Eddington luminosity. The critical period for the system in this case is

0.75 f −1.5 M˙ M 0.125 P 3.3 disk 2 1 days (2.25) crit 0.7 ˙ M '   0.5MEdd !  2  41 The fdisk term refers to the disk filling fraction, which is the ratio of the disk radius to the radius of the accretor’s Roche lobe. We estimate this radius as the point at which the disk is disrupted by the tidal forces exerted by the donor star. Those systems with periods above Pcrit are flagged as subject to the dwarf nova instability. The duty cycle of such systems is known to be dramatically shorter than for neutron star accretors with this disk instability. This is because, in the absence of illumination from accretion onto a stellar surface, more material must be added to the disk to raise the temperature to the point where steady accretion can occur, and this material takes more time to accumulate. Typical recurrence times are on the order of a decade or longer, implying duty cycles of 0.01 or lower. With such extended recurrence times, it is difficult to estimate a mean time between outbursts, as few transient systems have been observed in outburst more than twice. For now, we assume a duty cycle of 0.01, keeping in mind that this will likely change as more black hole transient systems are catalogued. The relationship between accretion mode and the observed luminosity and spectrum from a binary has been covered by numerous authors (see Lewin et al., 1997, and references therein). The dramatic high-luminosity, soft-spectrum and low-luminosity, hard-spectrum states observed in Galactic HMXBs such as Cygnus X-1 and GS 1124–68 can be understood as a tran- sition between a bright, optically-thick disk and a dim advection-dominated accretion flow structure (ADAF) (Meyer et al., 2000). Interestingly, from ob- servations of state changes in Galactic HMXBs it is commonly held that the transition occurs when the luminosity is in the neighbourhood of 1037 erg s−1 (Lewin et al., 1997, pg. 165); this corresponds to the maximum ADAF lu- minosity of a 5 M black hole, a representative mass for currently-known ∼ 42 black hole candidates. Irrespective of what causes the hard-soft variability in XRBs, whether from ADAF formation or other disk instabilities, the variation in luminosity must be accounted for in our calculation of XRB X-ray luminosities. For a population of XRBs, the luminosity fluctuations can be parameterised by a single duty cycle, the fraction of time a binary spends in its high/soft state. This duty cycle is, of course, the average of the duty cycles for each XRB in a population, each a function of at least the orbital elements of the system, along with poorly-understood quantities like disk viscosity. Therefore, when presenting model results in section 2.3 I make no attempt to adjust for the duty cycle. Results given therein are for systems which are in a continual high (soft) state, and it must be understood that another factor should be applied to account for this. Unfortunately, the number of XRBs for which detailed variability information is available (that is, nearby Galactic sources) is somewhat small; until a more detailed understanding of XRB variability is developed, the duty cycle will remain as one of the tunable parameters of the model. Equivalently, the results herein can be adjusted post facto by applying a duty cycle scaling factor. Note that this factor is in addition to that imposed by considerations of the dwarf nova instability discussed above. Note also that this correction factor will be different each binary considered, as it is the result of a convolution of many factors, including orbital period, orbital radius, variability in the donor star, and so forth. A final efficiency parameter is employed to convert the calculated bolo- metric luminosity to the power radiated between 2–10 keV. This factor varies with the type and spin of the accreting compact object. For simplicity (and because the code does not track spin), we assume that 40% of the bolometric luminosity from accreting onto a black hole is emitted in this band. For neu-

43 tron star accretion, that value is 20%. This adjustment is used everywhere that an X-ray luminosity is quoted herein.

2.3 Simulation results

Four simulation runs were performed, each simulating a 20 Myr episode of star formation, at a constant rate of 10M per year. Of the four simulations, two were performed using the Salpeter initial mass function (Salpeter, 1955), and two with the Miller-Scalo IMF (Miller & Scalo, 1979). For each IMF, one run was performed with a flat mass ratio (“q”) distribution, and the other draws the mass ratio from the distribution φ(q) = 2/(1 + q)2, which approaches the spectroscopically-determined distribution shown in equation 2.1. For ease of reference these shall be referred to hereafter as Salpeter/flat- q, Salpeter/low-q, MS/flat-q, and MS/low-q. The first question to address is the normalisation of the simulations; that is, how one converts from a desired star formation rate and duration to a total number of binaries generated. One difficulty is that the code draws the primary mass from an IMF that is truncated at 4M at the low end. This is done because two such stars combined have the minimum mass necessary to undergo a supernova; lighter primaries will never become XRBs and hence are not considered. We therefore need a weighting factor, w, which is the number of generated stars of all masses divided by the number of generated stars above the 4M cutoff. In other words,

∞ 0.1 dN w = ∞ (2.26) R4 dN where dN is the differential numbRer of stars with mass m. For example, dN = m−2.35 dm for the Salpeter mass function. Performing this integration

44 for a general power law IMF of the form dN = m−α dm gives w = 40α−1 = 145.5 for the Salpeter IMF. The value of w for the Miller-Scalo IMF can be found in an analogous fashion, by considering the three separate power laws, giving w = 69.2 for this case. Next, a definition of the binarity fraction is needed. We take the binarity fraction b to represent the fraction of systems that contain two stars. For example, if a sample of three stars exists as a binary pair and one single star, the binarity is taken to be one-half (as opposed to two-thirds).

If we let m¯ and q¯ represent the average primary mass (in M ) and binary mass ratio, respectively, and let n denote the total number of binaries formed in a 1 Myr period, then the total star formation rate for the 1 Myr interval is the sum of three parts; the mass contributed by the primary stars, the mass contributed by the companion stars (weighted by q¯), and the mass of the single stars which are not considered in the code but are generated according to the binarity b. Assuming a binarity of b = 0.5, we can then write

−1 1 b SFR M Myr = nwm¯ + nwm¯ q¯ + nwm¯ − (2.27)  b 
= nwm¯ (1 + q¯) + nwm¯ (2.28)

= nwm¯ (2 + q¯) (2.29)

m¯ and q¯ are functions of the IMF and mass ratio distribution, respec- tively. w is also a function of the IMF, and the values of each of these parameters for the four runs are shown in Table 2.1. The last column of the table shows the number of binary systems generated for each Myr of the −1 simulation, representing a constant 10 M yr star formation rate. The star formation rate varies linearly with the number of binaries formed in each

45 −1 Simulation m¯ (= m¯ /M ) q¯ w n (Myr ) Salpeter/flat-q 0.39 0.5 145.5 71300 Salpeter/low-q 0.39 0.386 145.5 74700 MS/flat-q 0.6 0.5 69.2 96300 MS/low-q 0.6 0.386 69.2 101000

Table 2.1 A summary of the parameters used to normalise the four starburst simulations. The first column gives the simulation identifier, which shows both the mass function and mass ratio distribution used. The other four columns are the mean mass of a star with the given IMF (in Solar units), the mean mass ratio of a companion to the primary, the conversion factor giving the total number of stars formed for every star formed above 4M , and the number of binary systems generated in each 1 Myr interval to give −1 a 10M yr formation rate. interval, allowing the results to be adjusted for an arbitrary SFR by simple proportionality. This proportionality breaks down at large times, however, when large scatter is introduced by small-number statistics, as only one or two sources are active at any given moment. Figures 2.1–2.13 detail the final output of the investigation. One of the principal results of the simulations are the curves showing the time evolution of the bolometric luminosity and population size of the X-ray luminous pop- ulation. The bolometric luminosity is the total amount of radiated power, over all wavelengths. To obtain the hard (2–10 keV) luminosity from this, we must apply a correction factor of 0.2 to the neutron star accretors and a factor of 0.4 to the black hole accretors. For this purpose, the population is subdivided into six categories, based on two intrinsic properties of the system. First, the accretor is classified as either a black hole or a neutron star. Second, the donor is placed in one of three mass categories. Donors with a mass less than 1.4M are low-mass X-ray binaries (LMXBs), donors with a mass between 1.4 and 8M (the minimum mass necessary to form a

46 neutron star) are considered to be medium-mass X-ray binaries (MMXBs), and more massive donors are, naturally, high-mass X-ray binaries (HMXBs). Plots showing the evolution of the luminosity and size of each population subset are shown, one set for each of the four possible parameter sets. Figure 2.1 gives the most important and directly observable result; namely, the total 2–10 keV X-ray luminosity for the population, evolved over the first 2 Gyr after the star formation episode. Panels (a) and (b) show the results for a Salpeter IMF, with a low-skewed and flat q-distribution, respectively. (c) and (d) show the analogous plots for a Miller-Scalo IMF. The first thing that is immediately apparent from Figure 2.1 is that the input IMF and mass ratio distribution have little or no effect on the X-ray luminosity evolution of the population. This is an interesting and important result, because it implies that the output depends little upon uncertainties in the IMF, or choice of q-distribution, both parameters with significant uncertainties. Conversely, however, this also means that it would be difficult to constrain these parameters through a comparison of the results with observational data. Along these lines, an important question is the overall robustness of the output in terms of several other variables that are not explicitly listed as input variables, but comprise assumptions made in the implementation of the population synthesis code. We now describe each of these in detail, along with probable effects on the output, and a justification for the choice of parameter value employed. As mentioned previously, our choice for mass loss through winds during the main sequence phase is taken from the work of Langer (1989). This is the canonical treatment of winds used in a majority of the literature. A more recent formulation by Hamann & Koesterke (1998) dramatically lowers the

47 wind-loss rate on the main sequence, and is used in the numerical simulations of Van Bever & Vanbeveren (2000). This has the consequence of keeping the orbital size smaller throughout main sequence evolution (as a larger mass loss would widen the system dramatically). As well, stars retain a larger fraction of mass prior to the supernova, resulting in larger compact object masses. The end result are closer, more massive systems that are better able to survive the first supernova without becoming unbound. This results in a greater number of potential XRBs, and a correspondingly larger X-ray luminosity. As an example, the Van Bever & Vanbeveren (2000) results are several times greater than our own, with wind mass loss reduced by a factor of four. The wind prescription of Hamann & Koesterke (1998) has only been applied to a few systems. Until confirmed by futher observations, the formulation of Langer (1989) is still the most reasonable choice for describing winds. The mapping between the mass of a black hole progenitor and the final mass of the hole (the black hole “IMF”) is another poorly-constrained quan- tity. We make use of the IMF derived by Fryer (1999), using hydrodynamic collapse models. Critical to the end result is the mass at which a progenitor will collapse directly to a black hole, with no intervening supernova (and hence no asymmetric kick, discussed below). This limit strongly influences the average resulting black hole mass, as objects above the limit tend to retain most or all of their pre-collapse mass, and objects below this limit lose a substantial fraction of this mass through a supernova. If the criti- cal collapse limit is high, most black holes will experience a supernova at formation, with a lower resulting mass. If it is set low, the average black hole mass will be much greater, with correspondingly narrower orbits and larger Eddington accretion limits. The results in Fryer (1999) do approxi-

48 mate the typical observed mass in black hole candidates (averaging around

6–7 M ). However, this observable is likely influenced by selection effects ∼ dependent on the mass of the black hole. The magnitude and distribution of natal, asymmetric supernova kicks strongly influences the survival of binaries past the first supernova. As the magnitude of the kicks increase, of course, the number of XRBs goes down, as more systems are disrupted by the initial supernova. But this effect also changes the relative numbers of black hole and neutron star accretors, as the lighter neutron stars will be more strongly affected by the kick. The orientation of the kick is also important as retrograde kicks will tend to keep the system intact (and, indeed, shrink the orbit significantly), whereas prograde kicks disintegrate the system optimally. It is likely that the kick orientation is influenced by the spin of the progenitor. However, this rela- tionship has yet to be worked out in any detail, and the code does not track spin information in any event. Chapter 4 discusses at length the effect of kick magnitude on the survival of a binary. Tables 4.1 and 4.2 show the change in the number of bound BH-BH, BH-NS and NS-NS systems as the average kick magnitude changes from 90 km s−1to 190 km s−1, and then 450 km s−1. As can be seen, systems with black hole progenitors are only mildly affected by even strong kicks, with bound system rates dropping by roughly 30%. Neutron star systems, however, almost completely vanish in the presence of strong (450 km s−1) kicks. The kick distribution chosen for our simulations approximates that of Podsiadlowski et al. (2002), where a mix of low ( 90 km s−1) and strong ∼ ( 450) kicks is shown to reproduce the distribution of observed neutron ∼ star velocities. The Eddington limit is a somewhat contentious restriction on the maxi-

49 mum accretion rate of a compact object. In our models, we assume that the Eddington rate applies weakly; that is, the mass transfer rate is throttled back dramatically above this limit, with no abrupt cutoff. Still, this only permits a minor violation (typically of a few tens of percent) of the Edding- ton limit. However, there is observational evidence of systems that exceed this boundary by factors of several. For example, three X-ray pulsars in the SMC are known to exhibit substantial super-Eddington accretion. Neverthe- less, most galactic XRBs are at or below this limit, so this is representative of most known sources. Lastly, consider the parameter governing the efficiency of common-envelope evolution. Webbink (1984) introduced the idea of simulating a phase of common-envelope evolution by decreasing the orbital energy by the binding energy of the envelope. The efficiency parameter was assumed to be unity, so that the two quantities were equal. Later work by de Kool (1990) showed that when compared against reasonable stellar models, the average efficiency parameter dropped to around 0.5, and this is the value we use. This value means that the orbit must lose twice the binding energy of the envelope in order to dissipate it. It is true, however, that the precise value of the efficiency parameter depends strongly on the structure of the evolving star. More recently, Dewi & Tauris (2000) showed that the efficiency value ranged between 0.2 and 0.8 for the vast majority of stellar evolution tracks. While we should technically make use of the more precise values provided in this paper, the code does not track the structure of the star closely enough for this to be practical. Nevertheless, it is clear that the mean parameter value is a good choice overall for calculating the end results of a common-envelope evolution phase. Increasing the parameter would result in wider systems, and hence fewer XRBs. However, the fact that fewer systems would merge

50 under these conditions would mitigate this somewhat. A lower value of the efficiency parameter would dramatically increase the number of mergers, with fewer systems surviving this phase to become XRBs. Figure 2.2 shows the evolution of XRBs with black hole accretors, given an initial Salpeter IMF, and a low q distribution after equation 2.1. Each point represents the luminosity and population size for a 1 Myr interval. Star formation progresses at a constant rate for 20 Myr; the end of star formation is shown as a vertical dashed line on each of the plots. The left three panels (a, c and e) show the luminosity evolution of the HMXB, MMXB and LMXB populations, respectively. The corresponding plots on the right side show the number of emitting systems of each type at the indicated epoch. The evolution of all systems was tracked out to a maximum of 2 Gyr, though massive systems evolve on more rapid timescales, and are only tracked until the second compact object is formed. Panel (a) shows the luminosity evolution for the BH/HMXB systems, with a peak at about 1041 erg s−1. More importantly, the peak coincides with the end of the star formation episode. This is understood to be the result of massive donor stars, with short main sequence lifetimes. HMXBs thus form vary quickly after the creation of the initial binary, as the second (donor) star leaves the main sequence. The HMXB population tracks star formation closely, with accreting systems accumulating until star formation stops, at which point the remaining systems quickly die off; 20 Myr after the end of the star formation episode, no HMXBs remain. One final point: comparing the peak luminosity in panel (a) with the peak BH/HMXB population size in panel (b) of the same figure, we see that the mean luminosity of a binary is around 6–7 1038 erg s−1. This corresponds to the Eddington luminosity limit for × an accretor of roughly five solar masses, a typical black hole mass given the

51 assumed IMF and the mapping, discussed above, between the pre-collapse mass of a black hole progenitor and the final hole mass. We conclude that the bulk of BH/HMXB systems accrete at or near the Eddington limit, as they are driven by massive stars with rapid evolutionary timescales. Continuing with figure 2.2, panels (c) and (d) detail the evolution of

BH/MMXB population, with companion masses ranging from 1.4–8 M . The first and most important thing to notice is the delay in the onset of this population. The first such systems do not appear until more than 10 Myr have elapsed, and their numbers do not peak until about 30 Myr after the end of star formation. This is due, of course, to the longer evolution- ary timescales of these less-massive companion stars. The black hole forms quickly, but the binary will only enter the accretion stage on the nuclear timescale of the donor star. The reader may wonder why, if this is true, that there is a concentration of sources at 40–50 Myr. What about lower ∼ mass companions? This peak is the result of two effects. First, because of the choice of mass ratio distribution, a primary massive enough to form a neutron star (at least 8 M ) is less likely to have a light companion. For a

flat mass ratio distribution, the average companion mass for an 8 M star is

4 M . For the low-skewed mass ratio distribution, this value drops to just under 3 M . So this is a selection effect of sorts, arising from the minimum mass necessary to form a neutron star. The second factor to consider is that the duration of a typical mass transfer episode occupies a larger fraction of the life of a massive star than one at the light end of the MMXB category

( 1.4M ). Since massive companions are formed on a timescale compara- ∼ ble to their main sequence lifetimes, they all tend to leave the main sequence and fill their Roche lobes in a similarly short period. This contributes to the luminosity peak in panel (c). Longer-lived stars are less likely to leave the

52 main sequence in closely-timed groups, spreading out the resulting X-ray bi- naries in time. These sources are not concentrated in time, but XRBs from this group continue to be formed even at very large times (several Gyr). One other feature of note in panel (c) is the bifurcation in the luminosity evolution that at occurs about 70 Myr into the simulation. This population oscillates rapidly between a low-luminosity and a high-luminosity state. A glance at the number evolution plot shows that, at this epoch, less than ten sources (and at times as few as two) comprise the entire MMXB group. The variation is therefore partly due to small number statistics, as single sources ficker in and out of mass transfer episodes. As well, the systems comprising the upper branch of the bifurcation are almost entirely XRBs being driven by a companion crossing the Hertzprung Gap, implying a rapid expansion and commensurately high mass transfer rate and luminosity. The lower systems tend to be accreting on the nuclear timescale of the companion, with a lower resulting luminosity per system. Panels (e) and (f) show the BH/LXMB systems. One might expect that no such systems would be present in the first 2 Gyr of the simulation, as the main sequence lifetime of even the most massive companions in this category (1.4M ) is significantly longer than that. These systems are not accreting because the companion has left the main sequence; rather, the companion is transferring mass on its nuclear timescale. This requires a very small orbital separation for the companion to fill its Roche-lobe, and is unlikely to occur ab initio given the choice in the distribution in initial orbital separations. These systems are all survivors of an episode of common envelope evolution, when the system primary ascended the giant branch, and enveloped the secondary star. The dramatic reduction in orbital separation during this phase meant that, after the primary went through a supernova,

53 the secondary was close enough to begin transferring mass onto the nascent neutron star. This explains the concentration of such XRBs seen 20–40 Myr after the end of star formation, the time necessary for the primary to ascend the giant branch and go supernova. The small probability of this outcome explains the relatively small number of systems in this catgeory. If sufficient resources had allowed the simulation to be extended to several Gyr, more BH/LMXBs would begin to appear as the donor stars evolve off the main sequence, in the usual fashion. Figure 2.3 is analogous to figure 2.2, and shows the evolution of popu- lations accreting onto a neutron star instead of a black hole. All run pa- rameters remain identical. Panels (a) and (b) are almost precisely the same as those of the previous figure, with the exception of a noticeable delay in the rise-time of the NS/HMXB population. This is directly related to the longer main sequence lifetime of the lighter neutron star progenitors. Panels (c) and (d) show the evolution of the NS/MMXB set. This is the most numerous population, and, at its peak value is the most luminous as well, for a brief period from roughly 40–80 Myr into the simulation. The evolution curves are quite regular, until around 200 Myr, when the XRB population size fluctuates rapidly between several and ten or twenty sources at a time, with a corresponding dramatic fluctuation in the luminosity. The slow decrease in the maximum luminosity as the population ages results from fewer accreting systems, and also lower mass transfer rates from in- creasingly lighter, longer-lived companion stars. It is interesting to note, however, that the luminosity of this subset of XRBs remains significant well beyond even 2 Gyr. This means that populations of NS/MMXBs formed in long-vanished starbursts continue to contribute to the X-ray luminosity of their host galaxy, long after the galaxy returns to quiescent star formation.

54 This also means that successive waves of rapid star formation may allow NS/MMXBs and NS/LMXBs to accumulate in a sort of hysteresis loop, so that the total number of such systems observed in the present era represents a number of individual starbursts taking place in the distant past. The rela- tionship between the high-mass and lower-mass XRB systems, could best be summarised as follows. The BH/HMXB and NS/HMXB popuations track the current, or recent star formation rate. MMXBs and LMXBs, however, better track the time-integrated star formation in a galaxy’s history, i. e., the total mass of stars formed. Panels (e) and (f) show the NS/LMXBs. Note that they also attain a significant luminosity, at a later epoch than the MMXB population. Like the BH/LMXBs at this early time, these systems are the result of common- envelope evolution. The offset in time is larger, again, because of the longer main sequence lifetime of the neutron star progenitor. There are many more systems here than in the BH/LMXB plot, as they are formed more frequently from the assumed IMF. Figures 2.10–2.13 show the luminosity function at five epochs (10 Myr, 20 Myr, 50 Myr, 100 Myr and 200 Myr) after the beginning of star formation. The luminosity function is expressed in terms of the fractional amount of the population that exists above the given luminosity. One interesting aspect of these functions is that, because they represent a time-slice of the luminosity evolution, longer-lived systems are more likely to be included. This makes them representative, but ignores the high-luminosity sources, which are only active for a short time. This means that the high end of all of the displayed luminosity functions is subject to a considerable amount of variability as short-lived, high-luminosity systems flicker on and off.

55 Figure 2.1 The evolution of the total X-ray luminosity of a simulated pop- −1 ulation over 2 Gyr, from a star formation rate of 10 M yr , extending for 20 Myr (vertical dashed line). Panel (a) shows the results of a Salpeter IMF with a low-skewed q-distribution. (b) also uses the Salpeter IMF, with a flat mass ratio distribution. Panels (c) and (d) use the Miller-Scalo IMF with a low-skewed and flat mass ratio distribution, respectively.

56 Figure 2.2 The evolution of the bolometric luminosity of the BH/XRB com- ponent of the population over 2 Gyr, from a star formation rate of 10 M yr−1, extending for 20 Myr (vertical dashed line). Note the short delay between the start of the simulation and maximum luminosity, roughly cor- responding to the nuclear lifetime of the secondary (donor) star. The lumi- nosity evolution for the BH/HMXB (a), BH/MMXB (b) and BH/LMXB (c) populations are shown, alongside the evolution track of each population’s size (d,e,f). 57 Figure 2.3 The evolution of the NS/XRB component of the population over −1 2 Gyr, from a star formation rate of 10 M yr , extending for 20 Myr. This is the analogue of figure 2.2. The luminosity evolution for the NS/HMXB (a), BH/MMXB (b) and BH/LMXB (c) populations are shown, alongside the evolution track of each population’s size (d,e,f).

58 Figure 2.4 Same as figure 2.2, but for a Miller-Scalo IMF (the mass ratio distribution remains the same).

59 Figure 2.5 Same as figure 2.3, but for a Miller-Scalo IMF (the mass ratio distribution remains the same).

60 Figure 2.6 Same as figure 2.2, but for a flat mass ratio distribution (all values of q equally likely).

61 Figure 2.7 Same as figure 2.3, but for a flat mass ratio distribution (all values of q equally likely).

62 Figure 2.8 Same as figure 2.2, but using the Miller-Scalo IMF, and replacing the low-skewed q with a flat distribution.

63 Figure 2.9 Same as figure 2.3, but using the Miller-Scalo IMF, and replacing the low-skewed q with a flat distribution.

64 Figure 2.10 The cumulative function for the population derived from the Salpeter IMF, and a low-skewed q distribution. The five epochs are 10 Myr (a), 20 Myr (b), 50 Myr (c), 100 Myr (d), 200 Myr (e). These were chosen to show the dramatic change as star formation ends and massive stars no longer dominate (a and b), as the X-ray luminosity becomes driven by increasingly lighter companions (c, d and e).

65 Figure 2.11 Same as for figure 2.10, but using a Miller-Scalo IMF in place of the Salpeter function.

66 Figure 2.12 Same as for figure 2.10, but using a flat mass ratio distribution.

67 Figure 2.13 Same as for figure 2.10, but using the Miller-Scalo IMF, and a flat q distribution.

68 2.4 Comparison with other theoretical work

Recently, a number of attempts have been made by various groups to use population synthesis techniques to estimate the X-ray luminosity of a star formation episode at various epochs. We discuss three of them here, and draw a comparison between the results and methodology.

2.4.1 Numerical simulations by Van Bever & Vanbeveren

The simulations of Van Bever & Vanbeveren (2000) are nearest to our own work in terms of technique. A sizable population of binary systems was generated, using a library of stellar evolution calculations detailed in Van- beveren et al. (1998a,b,c). Winds, in particular, receive a great deal of attention, as the precise mass loss formalism used can greatly affect the fi- nal evolutionary outcome of massive stars. In particular, the choice of wind strength will change the mass distribution of black holes seen in the popu- lation, as the black hole progenitor loses a different amount of mass prior to collapse. As mentioned above, our simulations make use of the wind mass loss formalism of Langer (1989). Van Bever & Vanbeveren (2000) make use of the mass loss rates of Hamann & Koesterke (1998), which are roughly four times smaller than those predicted by Langer, and include the effects of line blanketing and clumping in determining wind strengths. The result of these stronger winds should be wider binaries, but with a larger fraction surviving the initial supernova. More black hole mass measurements are needed to lend support to the low wind mass loss rates; in particular, a large population of black holes with confirmed masses above 10M would ∼ require winds considerably weaker than those predicted by Langer (1989). Another significant difference in the assumptions made by Van Bever &

69 Vanbeveren (2000) involves the final collapse of a massive star into a black hole. They assume that all such objects (those with an initial mass of above

25M ) collapse directly to a black hole, with no associated supernova event. This again has the effect of increasing the mean black hole mass, as no ma- terial can be lost from the system via a supernova. They themsevles note that there is observational evidence contravening this assumption; specifi- cally, the dramatic overabundance of O, S, Mg and Si in the atmosphere of the optical component of the LMXB GRO J1655-40, reported by Israelian et al. (1999a). The primary in this system is a strong black hole candidate, with an inferred mass of 6 2M . Our simulations assume that a star with  a zero age main sequence (ZAMS) mass of 20M or more will become a black hole. Those progenitors with a ZAMS mass of less than 40M will undergo a supernova upon black hole formation. Above this limit, the hole forms via direct collapse, with no explosion. The difference is important, because black holes that form through direct collapse should experience no natal kicks, which can act to disrupt the system. If no black holes receive kicks, then a greater fraction of systems with a black hole component will survive to become X-ray binaries. For the same reason, a greater fraction of the observed XRB population will comprise accreting black holes, since neutron stars will still experience kicks at the same rate as before. Van Bever & Vanbeveren (2000) generate a single burst of 3 105 stars, × selecting the masses of single stars and binary primaries from the Salpeter initial mass function. A flat mass ratio distribution is used to choose the mass for the companion star. Single stars are tracked in this model because the hard (2–10 keV) X-ray contribution from supernova remnants (SNRs) is included in the total. To do this, neutron stars are assigned a magnetic field strength and initial spin period chosen from a random distribution, which

70 allows the rotational energy loss rate to be calculated. A small fraction ( 0.03) is then used to determine the amount of this energy that comes ∼ out as X-rays. We do not include young supernova remnants in our own calculations, for two reasons. First, the assignment of a magnetic field and rotational period at formation ignores the importance of the evolutionary history of the progenitor star, and so is fairly arbitrary. Second, the contri- bution of remnants to the total X-ray luminosity should be quite small for all but the shortest period pulsars. Indeed, after completing their simulation, Van Bever & Vanbeveren (2000) come to very much the same conclusion, claiming that SNRs contribute to the total starburst X-ray luminosity only when most or all neutron stars are born with an initial period of less than 10 ms. Van Bever & Vanbeveren (2000) plot the X-ray luminosity evolution for the first 10 Myr after the starburst. The onset time for the X-ray luminous phase is 3–4 Myr, precisely the same as in our own simulations. The peak 33 −1 −1 luminosity of around 10 erg s M is reached shortly thereafter (around 5 Myr), and remains constant through the 10 Myr that are plotted. This is very different from our own results, which show that the X-ray luminosity continues to rise nearly 100 Myr after the end of star formation, though the rate of increase slows dramatically after star formation ends. By only tracking the population out to 10 Myr, Van Bever & Vanbeveren (2000) missed the important contribution of neutron star accretors to the overall X-ray luminosity over an extended period of time. Note that the luminosity is given in terms of a power per unit solar mass of stars generated. If we scale the luminosity results shown in Figure 2.1 by dividing the peak luminosity 8 by the total mass of stars formed, which is 2 10 M for each simulation, × 32 −1 −1 we obtain a “specific luminosity” of approximately 5 10 erg s M . × 71 Interestingly, this rate is almost exactly the peak rate given by Van Bever & Vanbeveren (2000). One last thing to note about both the results of Van Bever & Vanbev- eren (2000) and our own simulations is the strongly stochastic behaviour of the luminosity evolution. This is noticeable throughout the 10 Myr range considered by the former, and can be seen in our results at longer timescales (typically above 100 Myr). This is the direct result of small-number statis- tics, when few systems are in an active state at a given time. The Van Bever & Vanbeveren (2000) results are based on a relatively small initial population of 3 105 stars, many of which will not become XRBs. Our × larger population size of 2 106, and the fact that the star formation occurs × over a significant interval, helps to smooth out dramatic fluctuations in the luminosity until a much larger period of time has elapsed.

2.4.2 Analytic calculation by Wu (2001)

As an alternative to the population modeling shown heretofore, where indi- vidual systems are tracked from birth to evolutionary end state, Wu (2001) views a population of XRBs in terms of differential equations governing birth and death rates. Unfortunately, to formulate such a system of equations requires a slew of simplifying assumptions. In particular, Wu assumes per- fectly circular initial orbits to calculate gravitational radiation and magnetic braking timescales, and completely ignores the effects of natal kicks from su- pernovae. In addition, no allowance is made for disk instability effects. As well, the parameterisation of many input quantities make comparison with observables difficult, with no clear coupling to a star formation rate. Still, the method has the advantage of rapidly exploring a wide parameter space, as well as providing analytic relations between certain parameters that would

72 not be immediately obvious from numerical population synthesis. A comparison of the results from Wu (2001) is complicated by the fact that no easy way exists to adjust his results to a specific star formation rate. Wu presents a number of luminosity functions representing the distribution of XRBs at a given epoch, but no normalisation is possible. Nevertheless, it is interesting to note that the bulk of the curves display a distinct turnover at a luminosity of around 6 1037erg s−1, a turnover which is also clearly × visible in many of the luminosity functions to come out of our simulations, and roughly one-third of the Eddington luminosity of a typical neutron star. As more work making use of this technique appears, a better comparison of these two dramatically different approaches to population synthesis should be possible.

2.4.3 Semi-analytical calculation by Ghosh & White (2001)

Ghosh & White (2001) make use of a related methodology through which they use X-ray survey data to infer the long-term evolution of cosmic star formation rates. They also establish a system of differential equations de- scribing the population of X-ray binaries, though their approach is more rooted in experimental data, and is couched in terms of a real star forma- tion rate, as opposed to the parameterised version found in Wu (2001). The goal of this study is quite different from our own, and is focussed on the X-ray luminosity evolution over scales of a Hubble time. Our work is in rough agreement in a qualitative sense; that is, the relative contribution of the various XRB species is similar, and the shape of the luminosity curves are analogous. We differ in one major prediction, however. Ghosh & White predict that the LMXB population will not become a significant contributor to the total X-ray luminosity until several Gyr have passed; in other words,

73 when the companion stars either begin evolving off the main sequence, or lose sufficient orbital energy to magnetic braking and/or gravitational radiation. Our prediction is that a large number of LMXB systems will become active in the first 200 Myr or so after a vigorous star formation episode; e. g., panels (e) and (f) on any of figures 2.2–2.9. These systems are survivors of a stage of common-envelope evolution, which shrank the orbital radius and permitted Roche-lobe overflow to occur several billion years before it would otherwise be possible. Ghosh & White do not consider the effect of common-envelope evolution in their equation set, and so do not predict this feature.

2.4.4 Comparison with observations

Recently, Ranalli et al. (2002) extended the well-known correlation between a galaxy’s far-infrared (and radio) luminosities and the underlying star for- mation rate to the 2–10 keV energy regime. Making use of ASCA and Bep- poSAX observations of nearby actively-star forming galaxies, they proposed that the star formation rate could be expressed in terms of the 2–10 keV luminosity of the host galaxy as

−1 −40 SFRM yr = 2.0 10 L − (2.30) × 2 10keV −1 For our simulated galaxy experiencing an SFR of 10 M yr , we found that the peak hard X-ray luminosity, reached at the time star formation ceases and sustained for several tens of Myr, was around 4 1040 erg s−1. × As discussed earlier, this result is largely independent of the choice of IMF or binarity fraction. By the above relation, such a galaxy should have an −1 underlying star formation rate of 8 M yr , which is in good agreement with the actual rate used in the simulation. This reinforces our original

74 claim that the principal output of the code is in good agreement with reality, i. e., that the estimated luminosity and relative population sizes are robust results. Table 2.2 shows the measured slopes of the cumulative luminosity func- tions shown in Figure 2.10 and those immediately following. As can be seen from the Table, the principal determining factor for this quantity is the elapsed time since the end of star formation. This is because the luminosity function becomes dramatically steeper as the population ages and luminous X-ray sources die off. In principle, one could use this value to estimate the age of a stellar population. In practice, this would require a great deal of detailed information about the star formation history of the host galaxy, in order to segregate individual stars by the particular star-formation episode which spawned them. Grimm et al. (2002) show a number of cumulative luminosity functions based upon recent Chandra and ASCA observations of nearby starbursts. The cummulative luminosity functions of twelve noted starbursts were fit to a relation describing the fall off of the luminosity function at the high end. They derive a best-fit power-law index of 0.6, which can be compared to − our results in Table 2.2. Grimm et al. (2002) does not discuss the variation in this coefficient with time (as the stellar population evolves), and so it is important to compare the value of the coefficient at the appropriate epoch. As most of the objects in the study are still actively star-forming, we must compare these results to our 10 Myr and 20 Myr calculations, as these represent the model starburst when it is still active and the X-ray luminosity is dominated by BH-HMXB systems. While still slightly steeper than that of Grimm et al. (2002), the results at 10 Myr, especially for the Miller- Scalo IMF, are in reasonable agreement. It should also be noted that the

75 power-law indices measured for the individual galaxies have a substantial spread to them. Similar measurements for smaller sets of galaxies (Eracleous et al., 2002; Kilgard et al., 2002), are in closer agreement with our steeper cummulative luminosity function. Our cummulative LFs are qualitatively correct, as they become both steeper and fainter with increasing time. This point is at the heart of the observed discrepancy between the luminosity functions of spiral galaxies and ellipticals (Zezas et al., 2001).

2.4.5 Further applications of the simulation results

In addition to being a useful probe of long-term trends in a population’s X-ray luminosity, the technique we employ can give insight into the evolu- tionary trends of other observables. The Hα luminosity is a quantity strongly correlated with ongoing star formation, and can be predicted from the out- put of our population synthesis code. The Hα luminosity is driven by the recombination of electrons liberated from hydrogen atoms by the ionising radiation of O-stars,. Thus, coupled with the assumption of an IMF, the Hα luminosity leads to an estimate of the instantaneous star fomation rate. For calculation of the Hα luminosity, we made use of the stellar spectra by models of Kurucz (1991), implemented in the photoionisation program Cloudy (v. 96.0) (Ferland, 1996). All Kurucz models for stars with an effective temperature between 25000 K and 50000 K, and surface gravity between 103 and 105 cm s−2 were considered. For each of these models, an emission rate for ionising photons was calculated, for a fiducial bolometric magnitude of 10. The surrounding medium (i. e. the HII region) was − assumed to have an extremely large optical depth, so that all ionising pho- tons would eventually lead to a recombination. From atomic physics, it is well-established that roughly 30% of such recombinations will result in an

76 Table 2.2. Power-law index of model cummulative luminosity function at five epochs

Model 10 Myr 20 Myr 50 Myr 100 Myr 200 Myr

M-S / flat q 0.8 to 1.25 1.1 to 1.7 0.7 to 1.25 3.3 to 4.4 2 to 3.6 − − − − − − − − − − M-S / low q 0.8 to 1.1 1.1 to 1.5 1.1 to 1.8 2.9 to 5.7 2.9 to 5.7 − − − − − − − − − − Sal / flat q 1.2 to 2.5 1.3 to 1.9 1.4 to 3.6 2.9 to 5.7 2.9 to 5.0 − − − − − − − − − − Sal / low q 0.9 to 1.5 1.1 to 1.5 0.9 to 1.6 2.9 to 4.4 2.2 to 3.6 − − − − − − − − − − 77

Note. — The measured ranges of the slope of the tail-end a series of model luminosity functions. The model column refers to the assumed IMF and whether the mass ratio distribution is flat, or skewed towards low-mass companions. “Sal” = Salpeter IMF, “M-S” is the Miller- Scalo IMF formulation. Hα photon being produced (with a slight temperature dependence). From this, the Hα luminosity for the model (with a bolometric magnitude of 10) − results directly. For each star that falls within the limits calculated (which maps to spec- tral types O and B), the population synthesis code calculates the bolometric magnitude using the effective temperature derived from the stellar evolu- tion track. This is just the basic relation between effective temperature and bolometric luminosity: L = 4 π R2 σ T 4. Recast in terms of bolometric magnitudes (with the radius given in cm), this becomes:

M = 42.36 10 log T 5 log R (2.31) bol − eff − Once we have a bolometric magnitude for the star, we find the Hα lumi- nosity that Cloudy calculated for a star with the same effective temperature and gravity (but with a bolometric magnitude of -10), and then scale the result appropriately. The results are shown in figure 2.14. Panels (a) and (c) show the case of a Salpeter IMF with a low-skewed and flat q-distribution, respectively. Similarly, panels (b) and (d) use the Miller-Scalo IMF. The first thing to note is the significant difference (20–30%) between the two IMFs. This is not surprising, as the Salpeter IMF will result in a larger fraction of massive stars than the Miller-Scalo IMF; hence, a larger number of O-stars result, with a corresponding increase in ionising photons. Interestingly, the mass ratio distribution makes very little difference at all, probably because few secondary stars would have enough mass to be O- or B-stars, irrespective of the mass ratio distribution used. The unusual behaviour of L at large times (past 30 Myr), results Hα ∼

78 from a breakdown in a critical assumption in the calculation of the Hα luminosity. In particular, after the rapid decay of Hα due to the decline in the O-star population, the luminosity rebounds due to the contributions of a larger population of relatively hot post-AGB stars of lower mass. However, the HII region is generally dissipated by the strong winds and supernova activity of the previous population of O-stars and so the assumption of an infinite optical depth breaks down, so that one recombination requires many ionising photons. The bottom line is that the plots in Figure 2.14 are not valid beyond 30 Myr or so. The right axis of the plot, however, shows the rate of ionising photons, and is independent of the surrounding medium. This rate remains relatively constant over the remainder of the simulation, but is not effective in producing Hα photons.

79 Figure 2.14 These four plots show the time evolution of the ionising photon −1 rate for the first 2 Gyr after a star formation episode. SFR = 10M yr , with a duration of 20 Myr. Panels (a) and (c) use the Salpeter IMF, whereas (b) and (d) make use of the Miller-Scalo IMF. The top plots have a low- skewed q-distribution, and the bottom plots have a flat one. Note that choice of IMF is the biggest factor, whereas a change in the mass ratio distribution matters very little. This is due to the fact that few secondaries would have sufficient mass to be O- or B-stars with either distribution. For large optical depths (early times), the Hα luminosity is almost exactly 1011 times smaller than Qion. Beyond 30 Myr or so, the assumption of large optical depth to ionising photons breaks down, and the Hα luminosity deviates from what is predicted above.

80 The relationship between LHα and the star formation rate developed in Figures 2.14 and 2.15 has a direct application to LINERs, including those in a Chandra snapshot survey of nearby galaxies, further detailed in Chapter 3 and Ho et al. (2001). Ho et al. note that when plotting the log Hα luminosity of known, luminous active galactic nuclei (AGN) such as Seyfert galaxies and quasars, versus the log of their X-ray luminosity, the result is that most objects fall close to a well-defined line. Similarly, nuclei identified as LINERs and so-called “transition” or HII objects fall close to the same line, though at much lower luminosities. The implication, they claim, is that these objects are powered in precisely the same fashion as the more energetic quasars and Seyfert galaxies; namely, through accretion onto a supermassive black hole, and they simply occupy the low-power regime of this mechanism. One can ask, however, if there are different physical processes that could give a similar result. In other words, if this test for AGN membership could have an inherent degeneracy. XRBs resulting from vigorous star formation pose an interesting alternative explanation for the observed LX –LHα rela- tionship. By simulating a star formation episode, and then asking where on the LX –LHα plot the results appear, we can evaluate the relation shown by Ho et al. (2001).

Figure 2.15 shows a plot of LX versus LHα for a starburst with an SFR −1 of 10M yr , lasting 20 Myr, from a Salpeter IMF and a flat mass ratio distribution. The values from the first 40 Myr are plotted, with each point representing 1 Myr. The values rise rapidly to the left when the starburst begins, as massive O-stars turn on and begin ionising their HII regions. So starbursts will remain essentially on the right-most vertical line indicated for at least 40 Myr (at which point much of the ionised material has dispersed,

81 and our assumption of large optical depth is no longer valid). But this constant Hα scales with the SFR just as LX does (i. e., linearly). We can then ask what values of the SFR would bring the population into proximity of the line discussed in Ho et al. (2001). The expected locus of points −1 for two smaller SFRs, 1M and 0.2M yr are shown for comparison. Interestingly, star formation rates similar to that of our own galaxy result in values of LX and Hα that are not greatly out of line with the low-energy region that Ho et al. show is populated by LINERs and transition objects.

As shown previously, LX from a burst of star formation may remain high long after the burst ends, as LHα declines with the death of the last O- stars. A weak starburst could potentially cross the AGN locus of points at low LX as it evolves, directly after the end of star formation. This suggests that low-luminosity AGN are not automatically distinguishable from actively star-forming populations, and that the diagnostic put forward by Ho et al. does not give a complete picture.

82 Figure 2.15 The figure shows the X-ray and Hα luminosity evolution for −1 a population undergoing star formation at 10 M yr for 20 Myr, with a Salpeter IMF and flat mass ratio distribution. The diagonal dashed line shows the region that Ho et al. (2001) suggest implies a central AGN. The two vertical lines on the left show where results at lower star formation rates would fall. Note that for low SFRs, there is substantial confusion between a population of X-ray emitting binaries and the AGNs from the Ho et al. sample.

83 Chapter 3

A snapshot survey of nearby mildly-active galaxies with Chandra

3.1 Introduction

Among the most startling discoveries made by the Chandra X-ray Obser- vatory was the presence of large populations of luminous X-ray binaries in otherwise normal galaxies with inactive or mildly-active nuclei. Many of these galaxies are actively star-forming, such as the Antennae and M82 (Zezas et al., 2001), or had a recent bout of star formation, like NGC 4736 (Eracleous et al., 2002). Even normal elliptical galaxies sport significant XRB populations, albeit with a lower maximum luminosity than those seen in many spirals. NGC 4697, for instance (Sarazin et al., 2000, 2001), con- tains over 80 such sources. The natural question to ask, then, is how the XRB population relates to overall galactic properties such as Hubble type and nuclear activity. We can attempt to understand these differences from population synthesis tech- niques as described in Chapter 2. However, our imperfect understanding of

84 stellar evolution means that this approach must be informed by a compre- hensive observational program. To study the variation in these populations with different host galaxy properties, there are two attacks one may consider. The first is to choose a small number of canonical targets as archetypes and perform long observa- tions on these. A second approach requires a broad but shallow survey of host galaxies that are close enough for individual X-ray sources to be dis- tinguished given the resolution limits of the telescope. This does have the limitation of a higher minimum luminosity for sources to be catalogued, so that the completeness limit will vary dramatically with the distance to the host. Both approaches are being used with the Chandra observatory, and we describe in Section 3.2 the results from a comprehensive survey of the latter type.

3.2 Data analysis

A survey following the broad but shallow approach mentioned above was, in fact, undertaken by the Penn State ACIS team through guaranteed time observations in Cycles 1 and 2 (late 1999 through early 2001). The sample consists of 41 targets, drawn from the Palomar optical spectroscopic survey of nearby galaxies (Ho et al., 1997a,b), comprising a nearly complete subset of 486 northern galaxies with B 12.5 mag. The 41 targets were consid- T ≤ ered to be AGN candidates from optical studies and were chosen on that ba- sis. They range from Seyfert nuclei, to low-ionisation nuclear emission-line regions (LINERs; Heckman, 1980), and so-called LINER/HII “transition nuclei” (Ho et al., 1997b). All but six comprise a complete, volume-limited sample out to 13 Mpc. The remaining six were included because they were

85 archetypes of different classes. The original purpose of this survey program was, foremost, to resolve the issue of the power source in nearby emission-line nuclei. Detection of a single nuclear hard X-ray source, in the absence of a significant number of ancillary sources (XRBs) was to be construed as confirmation of a low-luminosity AGN (LLAGN). Spectral information from the brighter sources could be used to help further constrain the emission mechanism. Interestingly, of the 41 target galaxies, eight do not display an X-ray source within several arcseconds of the nucleus, and yet each of these was optically selected as a potential LLAGN. While the initial focus of the survey was on the nuclear sources, the benefits of Chandra’s spatial resolution apply equally well to the study of the X-ray sources associated with the host galaxy. The survey was carried out in snapshot mode, by the AXAF CCD Imag- ing Spectrometer (ACIS) with exposure time ranging from 1–3 kiloseconds. The standard 3.2 s readout time was used for all but six of the observa- tions. The remaining targets possessed a luminous nuclear source that had been noted in previous ROSAT and ASCA observations. To avoid the phe- nomenon of pile-up (where multiple photon events occur in a given pixel before a readout can be performed), a special subarray mode was used for these exposures that allowed a fraction of the chip to be read out much more 1 frequently. The 2 -chip subarray mode (half the chip is read every 1.6 s) was used for exposures of NGC 4278 (M98), NGC 4374 (M84), NGC 4639 and 1 NGC 5033. NGC 4579 and NGC 4594 both required 8 -chip mode to prevent pileup. For these targets, studies of the off-nuclear sources are impeded by the resulting smaller field of view. Table 3.1 summarises the major properties of each of the 41 fields. The morphological type and position (J2000.0 epoch) for each galaxy are given,

86 along with the distance in Mpc. These were mostly obtained from Cepheid measurements (Ferrarese et al., 2000) and surface brightness variability tech- niques (Tonry et al., 2001). All other distances come from Tully (1988), with −1 −1 the assumption that H0 = 75km s Mpc . The error in nuclear position is also shown, with references to the relevant astrometric survey. The last two table columns give the mean background for the field in counts per square arc-minute, and the minimum detectable source threshold in total counts. This last quantity is quite low because the short exposure times result in almost no background signal at all, allowing even five or six photon events to become statistically significant. Data reduction began with the level 1 event files supplied by the Chan- dra X-ray Observatory Center (CXC). These events have undergone a bare minimum of processing prior to delivery, as opposed to the level 2 event files (also supplied for most of the observations), which have gone through the complete CXC reduction pipeline. The choice to begin with the raw event files was made because the reduction process in use at Penn State includes a thorough correction for Charge Transfer Inefficiency (CTI) , an effect with a strong temperature dependence that is discussed in Townsley et al. (2000), and references therein. This approach also grants greater flexibility, as some assumptions made in producing the supplied level 2 files (for example, the introduced software position randomisation) are not necessary or appropri- ate for our situation. As well, starting with the low-level event files gives us better control over aspect glitches, and the effect they have on the final events list. The first correction applied removed the software dithering mentioned previously. We then inspected the events for the so-called “Bev grades”— flight grades 24,66,107,214 and 255. These events should be removed by the

87 ACIS camera itself, and should never appear in any event list; their presence strongly indicates a processing error. Next came the correction for CTI effects. By design, each of the chips in the ACIS array have one of two energy responses, depending on whether the chip is back- or front-illuminiated. This refers to the penetration depth which electrons liberated by the impacting X-ray must attain to be registered as a count by the detector. Back-illuminated chips have a much better response at lower energies than front-illuminated chips, due to the smaller required penetration depth. As differences in response exist even between chips of the same type, the CTI correction is unique for each of the ten chips in the array. All of our targets were centered on the fourth chip in the spectral array, S3, which is back-illuminated. However, several targets had significant source populations on neighbouring chips, so an accurate CTI correction was needed on these chips as well. The CTI effect is essentially a charge “stickiness” which prevents all of the charge contents of a register from moving from row to row during readout. As a result, events that occur further from a readout row appear fainter, because a larger fraction of the generated charge is lost before it can be read out. As CTI is strongly temperature-dependent, it follows that colder chips show less of an effect than warmer ones. During Chandra’s first observing cycle, the temperature of the ACIS array was lowered from 110◦C to around 120◦C. This dramatically reduced the CTI problem for − − later observations. Given the short observation lengths, and correspondingly low count totals, CTI for these later observations was judged to be of little significance to the overall result. Therefore, the CTI correction was only performed on those observations taken at the higher chip temperature. Following this, the event list was scanned for any flaring events that could

88 be seen. Flares are caused by cosmic ray impacts, that create a large amount of charge in pixels in the vicinity of the event. This charge is dissipated over the next several readings of the chip, and could be incorrectly interpreted as a rapidly-decaying X-ray source. These events were flagged and then removed after all other filtering had taken place. ACIS flight grades 0,2,3,4 and 6 were retained as good events, and the rest were discarded as probable cosmic ray events. Filtering on the 32-bit status flags provided for each event was limited to excluding events with bits 16–19 inclusive, as these are set when the event is flagged as a flare. The “flight timeline” distributed by the CXC for every observation de- tails the so-called Good Time Intervals (GTIs), during which the aspect solution of the satellite is well-known, and events can be counted. Outside of these GTIs, event positions may be suspect, and should be excluded from the final event lists. In addition, it is important to shorten the given expo- sure time to account for these glitches, to ensure that count rates remain accurate. Lastly, the S4 chip in ACIS exhibits a considerable amount of horizontal streaking (at constant CHIPY). This is a manifestation of readout noise and must be compensated for before a source search can begin. Fortunately, the CIAO tool destreak performs just this function. Streaking events have a status bit set which can be filtered against later. The resulting cleaned events file is now suitable for use by the source- detection algorithm wavdetect, detailed extensively in Freeman et al. (2002). The events are filtered for energies between 0.5 keV and 8 keV for front- illuminated chips, and 0.2 keV to 8 keV for the low-energy sensitive back- illuminated chips. From these events, four image files were constructed by changing the binning applied to the array. The first 1024 1024 image was × 89 just the S3 chip, “binned” by a factor of unity. The next two 1024 1024 × images were binned by factors of 2 and 4, and show an increasing fraction of the total field of view. The last image was a large 2048 2048 image × showing the entire array binned by a factor of 4. The wavdetect algorithm makes use of wavelets—sinusoidal functions with an average value of zero, and with a zero value outside of a very lim- ited region of space. This property allows them to be used as filters in both space and frequency. By choosing wavelets with appropriate size scales and correlating with an image, one will get large correlation coefficients only in the vicinity of a rapid change in the underlying data. The specific formu- lation for wavelets in wavdetect is the Marr, or “Mexican Hat” function, derived from the two-dimensional Gaussian. As a function of x and y, and the input gaussian parameters σx and σy, the Marr function is defined as

2 2 x y 1 x y 2 2 2 2 −(x /2σx)−(y /σy) W , = 2 2 2 e (3.1) σx σy ! 2πσxσy − σx − σy ! × There are a number of advantages to using this formulation. The for- mula is easily manipulated analytically, allowing a number of operations (for example, Fourier transforms) to be applied without computation, speeding execution time dramatically. As well, the correlation of this function with both linear and constant functions is zero, so that a flat or linear background will not affect source detection in any way. We chose five spatial scales for source detection: 1, 2, 4, 8 and 16 pixels. For each of these four images, the wavdetect algorithm was run with a sensitivity parameter of 10−6. The four resulting catalogues were merged so as to remove multiple detections of the same source. At this point, the results of wavdetect were confirmed by inspection, to ensure that no obvious source

90 was skipped, and so that an obviously spurious source could be removed. Source extraction was then performed on the resulting region list. Estimates of source counts made by wavdetect were not used directly, only the source positions. The decision of whether a source was, in fact, associated with the target galaxy, and not merely a foreground dMe star (or a luminous background AGN) was made by comparing the source’s off-nuclear distance to the pub- lished D25 diameter for each galaxy. Sources outside this distance were excluded, and the rest were deemed to be associated with the host galaxy. Finally, it should be noted that the source search was performed on a full-band (0.2–8 keV) image, rather than two separate searches in each band. The resulting background was correspondingly much higher than an image confined to a 0.2–2 keV range. However, the source count rate is only moderately larger in the full-band image, with the result that our source detection threshold is somewhat conservative, even given the very low background level seen on the full-band images.

91 Table 3.1. Observed sample of nearby LLAGN galaxies

Galaxy Nucleus ACIS observation

NGC Messier D Morph RA Dec δ Nucl. Obs. texp Bk Thresh. 00 (Mpc) (J2000) ( ) Type Date (ks) (cts/02) (cts)

253 · · · 2.4 SABc 00 47 33.10 −25 17 18.0 · · · · · · · · · 2000-08-16 2.160 106 6 404 · · · 2.4 SA0 01 09 26.90 +35 43 03.0 · · · · · · L2 2000-08-30 1.760 72 6 660 · · · 11.8 SBap 01 43 01.60 +13 38 23.1 0.40 T2/H 2001-01-28 1.940 75 4 1052 · · · 17.8 E4 02 41 04.80 −08 15 21.0 0.07 L1.9 2000-08-29 2.400 150 6 1055 · · · 12.6 SBb 02 41 45.20 +00 26 30.0 0.30 T2/L2 2000-01-29 1.150 338 10 1058 · · · 9.1 SAc 02 43 29.90 +37 20 27.0 · · · · · · S2 2000-03-20 2.440 107 6

92 2541 · · · 10.6 SAcd 08 14 40.40 +49 03 51.0 · · · · · · T2/H 2000-10-26 1.950 50 4 2683 · · · 5.7 SAb 08 52 41.20 +33 25 09.4 0.03 L2/S2 2000-10-26 1.760 67 5 2787 · · · 13.0 SB0 09 19 18.90 +69 12 10.5 0.05 L1.9 2000-01-07 1.160 49 4 2841 · · · 12.0 SAb 09 22 02.70 +50 58 35.0 · · · · · · L2 1999-12-20 1.770 20 5 3031 M81 1.4 SAab 09 55 33.20 +69 03 55.0 0.10 S1.5 2000-03-21 2.410 113 6 3368 M96 8.1 SABab 10 46 45.80 +11 49 11.0 0.30 L2 2000-11-20 2.010 57 6 3486 · · · 7.4 SABc 11 00 23.90 +28 58 30.0 · · · · · · S2 1999-11-03 1.780 17 6 3489 · · · 6.4 SAB0 11 00 18.10 +13 54 08.0 · · · · · · T2/S2 1999-11-03 1.780 142 5 3623 M65 7.3 SABa 11 18 55.60 +13 05 28.9 · · · · · · L2: 2000-11-03 1.760 77 5 3627 M66 6.6 SABb 11 20 14.90 +12 59 21.0 0.30 T2/S2 1999-11-03 1.780 257 4 3628 · · · 7.7 SAbp 11 20 16.20 +13 35 22.0 0.20 T2 1999-11-03 1.780 222 5 3675 · · · 12.8 SAb 11 26 08.00 +43 34 58.0 0.80 T2 1999-11-03 1.770 257 6 4150 · · · 9.7 SA0? 12 10 33.20 +30 24 12.8 · · · · · · T2 2000-10-29 1.760 86 5 4203 · · · 9.7 SAB0 12 15 05.00 +33 11 49.0 0.10 L1.9 1999-11-04 1.780 91 5 4278 · · · 9.7 E1 12 20 06.80 +29 16 50.0 0.10 L1.9 2000-04-20 1.430 33 4 4314 · · · 9.7 SBa 12 22 31.90 +29 53 43.0 · · · · · · L2 2000-07-07 1.960 70 6 4321 M100 16.8 SABbc 12 22 54.80 +15 49 20.0 0.60 T2 1999-11-06 2.530 884 4 4374 M84 16.8 E1 12 25 04.00 +12 53 14.0 0.30 L2 2000-04-20 1.110 · · · 4 Table 3.1 (cont’d)

Galaxy Nucleus ACIS observation

NGC Messier D Morph RA Dec δ Nucl. Obs. texp Bk Thresh. (Mpc) (J2000) (00) Type Date (ks) (cts/02) (cts)

4395 · · · 3.6 SAm 12 25 48.90 +33 32 48.0 0.10 S1.8 2000-04-17 1.260 · · · 5 4414 · · · 9.7 SAc? 12 26 26.30 +31 13 18.0 · · · · · · T2: 2000-10-29 1.760 70 6 4494 · · · 9.7 E1 12 31 24.30 +25 46 24.0 · · · · · · L2: 1999-12-20 1.780 · · · 5 4565 · · · 9.7 SAb? 12 36 20.70 +25 59 16.0 0.10 S1.9 2000-06-30 2.900 · · · 5 4569 M90 16.8 SABab 12 36 50.00 +13 09 46.0 0.30 T2 2000-02-17 1.710 · · · 4 4579 M58 16.8 SABb 12 37 43.50 +11 49 05.0 0.10 S1.9/L1.9 2000-02-23 2.950 · · · 5 4594 M104 20.0 SAa 12 39 58.80 −11 37 28.0 0.10 L2 1999-12-20 1.950 · · · 5

93 4639 · · · 16.8 SABbc 12 42 52.35 +13 15 26.4 0.10 S1.0 2000-02-05 1.470 · · · 4 4725 · · · 12.4 SABabp 12 50 26.60 +25 30 06.0 · · · · · · S2: 1999-12-20 1.780 · · · 6 4736 M94 4.3 SAab 12 50 53.00 +41 07 12.0 0.10 L2 2000-06-24 2.430 · · · 4 4826 M64 4.1 SAab 12 56 44.20 +21 41 05.0 0.80 T2 2000-03-27 1.820 · · · 5 5033 · · · 18.7 SAc 13 13 27.60 +36 35 39.7 0.10 S1.5 2000-04-28 2.970 · · · 5 5055 M63 7.2 SAbc 13 15 49.30 +42 01 45.0 · · · · · · T2 2000-04-15 2.450 · · · 6 5195 M51b 9.3 IA0p 13 29 58.70 +47 16 04.0 · · · · · · L2: 2000-01-23 1.150 · · · 4 5273 · · · 21.3 SA0 13 42 08.30 +35 39 15.0 0.10 S1.5 2000-09-03 1.760 · · · 5 6500 · · · 39.7 SAab 17 55 59.70 +18 20 18.3 0.10 L2 2000-08-01 2.130 · · · 4 6503 · · · 6.1 SAcd 17 49 27.00 +70 08 45.0 · · · · · · T2/S2 2000-10-27 2.040 145 4 3.3 Results

Table 3.2 shows the summary information for all 427 sources. The ID and position columns are self-explanatory; dnuc gives the distance in arc-seconds from the published position for the center of the host galaxy. Sources are sorted in order of increasing nuclear distance, with the prefix X for all non- nuclear sources. Nuclear sources are indicated by an N when confidently identified as such, with a question mark following if the source is only posited to be nuclear. Next, the count rate per kilosecond is given. Here, an impor- tant distinction must be made between exposure time (time on target) and the effective observation length. Because of the presence of aspect glitches and similar telemetric problems listed in the GTI file, the actual useful inte- gration time includes only those frames that are not flagged for this reason. The count rate column is the total number of source counts divided by this shorter, effective time. Next is the error in the count rate from Poissonian statistics. Because many of the sources in these shallow exposures are detected with only a few counts, the standard Gaussian approximation for determining the count rate error is no longer valid. Instead, we make use of the prescription of Gehrels (1986), who derives accurate analytic approximations for the up- per and lower error bounds in the low-count regime. Unlike the Gaussian approximation, the errors are not symmetric about the quoted rate, as the Poissonian distribution is skewed and one obviously cannot observe fewer than zero counts. The confidence level represented by the calculated errors must then be chosen; we chose an 84.13% confidence level, as this corre- sponds to the confidence of a 1-σ Gaussian error. At this confidence level, the upper bound on the number of counts (the measured number of counts

94 plus the positive error) is given by the expression

3 NU = N + (δN)U = N + N + + 1 (3.2) r 4 The above returns an error accurate to better than 1.4%, for any number of counts N (Gehrels, 1986). Similarly, the formula for the lower count limit is

1 1 3 N = N (δN) = N 1 (3.3) L L 9N √ −  − − 3 N  The total number of counts is broken down by energy into two groups, a soft band of 0.2–2 keV, and a hard band of 2–8 keV. This distinction allows for a hardness ratio to be calculated via the relation

F (2 8 keV) F (0.2 2 keV) HR = − − − (3.4) F (2 8 keV) + F (0.2 2 keV) − − H S HR = f (H, S) = − (3.5) H + S

Several sources show a hardness ratio of 1, meaning that they were not − detected at all in the hard band. The error in the hardness ratio resulting from counting statistics in each bin is shown in the next column. As in the above discussion, the small number of counts means that the standard determination of error, σ2 = n ( ∂f )2σ2, is not reliable. We invoke the i=0 ∂xi i more general procedure detailedP in Lyons (1991), to estimate the error in the hardness ratio. First, the hardness ratio is calculated for the measured values of hard and soft counts. The extent of the errors in both directions is estimated by calculating the hardness ratio with the extrema of both the hard and soft counts, and summing the square of the differences. In other words, letting δNU and δNL be the difference between the measured counts

95 N and the upper and lower count limits, respectively, the uncertainty σHR in the hardness ratio function can be expressed as

σ2 (+) = [f (H + δH , S) f (H, S)]2 + [f (H, S + δS ) f (H, S)]2 HR U − U − (3.6)

σ2 ( ) = [f (H δH , S) f (H, S)]2 + [f (H, S δS ) f (H, S)]2 HR − − L − − L − (3.7) The penultimate column gives the full 0.2–8 keV X-ray luminosity. This luminosity is derived indirectly, as most sources are too weak to provide an adequate spectrum to integrate. The technique we use involves forward modeling an X-ray spectrum for the column density to the target galaxy of interest. Power-law spectra with a wide variety of photon indices are adjusted for absorption through the column density for that Galactic lati- tude and longitude (Dickey & Lockman, 1990). The hardness ratio of each resulting artificial spectrum can then be computed, building a lookup table between hardness ratio and the power-law index for a specific column den- sity nH. This spectrum is easily integrated, and yields the full-band X-ray luminosity once normalised to the appropriate number of observed counts. A critical assumption for the above, of course, is that the column den- sity remains relatively constant for all sources in the target galaxy. Even assuming that variations in the intrinsic column are always comparable to the variation in our own galaxy, it should be remembered that many of the target galaxies are at a high Galactic latitude. This means that the absorp- tion from the Galactic column density is likely to be much smaller than the intrinsic absorption of the host galaxy, and may even be small compared

96 to the variation in the column density from one source to another. Un- fortunately, there is little more that can be done without invoking shaky assumptions about the properties of each individual source.

3.3.1 Target descriptions and notable trends

Ho et al. (2001) employ a simple scheme to broadly classify the observed source population cum nucleus, if any. The four broad classes are defined as follows. Class I galaxies have a clearly dominant nucleus, accompanied by a number of fainter sources. In class II objects, the luminosity of the nucleus is comparable to the brightest off-nulear sources. Class III objects have a nucleus embedded in an extended diffuse emission, possibly with a few fainter off-nuclear sources. Lastly, class IV targets have no discernible nucleus at the nuclear position. There is some overlap between classes II and IV, as the nucleus may not be easily discernible from a dense population of equally-bright sources in close proximity. Conversely, if such a population exists, it is not always possible to show that none of the sources is the nucleus (i. e., that the nucleus is truly undetected). Of the 41 galaxies, 33 have sources coincident with the published nuclear positions. While some galaxies had as few as three or four sources associated with them, still others had thirty sources or more, with 6 to 12 source being most common. Most sources were distributed approximately evenly around the host galaxy, with typical distances of 1 to 3 arcminutes. There were some notable exceptions, most obviously NGC 4736, where a large number of luminous sources exist in close proximity to the galaxy nucleus. Also, this measure is susceptible to source confusion, an increasing problem as the distance to the host galaxy increases. If two or more sources exist in close proximity (within tens of parsecs of each other), they could not be

97 spatially discerned by Chandra beyond a few Mpc. With multiple exposures at different epochs, variability information could be used to show that some sources are distinct. Unfortunately, the exposures in this snapshot survey cover each target only once, for a short duration. Figure 3.1 shows a comparison of the 0.2–8 keV luminosity of the entire sample of galaxies versus their respective BT (photographic) magnitudes (upper panel) and (B V ) colours (lower panel). One might anticipate − T a correlation between these quantities, arguing that bluer and/or brighter galaxies exhibit more rapid star formation, and hence should also show a marked increase in X-rays produced by high mass X-ray binaries (HMXBs), whose formation rate is closely tied to the local star formation rate (see Chapter 2). However, as can be seen from Figure 3.1, this correlation, if it indeed exists, is quite weak. Diffuse emission was significant in one-fourth of the total sample, though not enough to typically merit a Class III designation. Interestingly, this fraction is a function of Hubble type: one-third of the Elliptical and early- Spiral galaxies exhibit some diffuse nuclear emission, compared to only about one-sixth of later Spirals (and 1 Irregular). This suggests that the diffuse emission is not tied to current stellar formation. Of considerable interest are the numerous high luminosity off-nuclear sources, so-called Ultraluminous X-ray binaries (ULX, or UXB). These are generally taken to have 0.5–8 keV luminosities above 1039 erg s−1. Fourteen are seen in the current sample, though a few are sufficiently far from the nucleus of the host galaxy to raise questions about their association. With one exception, these sources are seen in spiral galaxies. Since the advent of Chandra, significant numbers of these objects have been found, most notably in actively star-forming galaxies like the Antennae (Zezas et al., 2001).

98 Figures 3.14–3.24 show each of the 41 targets, in an 180 180 region × centered on the nominal aim point. The following describes the environs of each host galaxy, whether a nucleus is identified, and the luminosity range of any other point sources. This is summarised by a class designation from the Ho et al. scheme detailed above. Any other interesting or unusual features are similarly noted.

NGC 253 Class III source, with a luminous nucleus embedded in a sub- stantial diffuse emission region approximately 1 kpc in extent. Nearly three dozen sources are detected, and are scattered liberally through- out the disk of the galaxy. There is no clear correlation between source distance from nucleus and the source luminosity. 0.2–8 keV lumi- nosities range from the detection threshold at around 1037 erg s−1to 3 1038 erg s−1. It should also be noted that the nucleus is not the ∼ × brightest source in the frame.

NGC 404 Class I. Three moderately-luminous sources (L 1038 erg s−1). X ∼ NGC 660 Class II/IV. Several sources are detected, but it is unclear if the nucleus is among them. A luminous source with L 5 1038 erg s−1 X ∼ × is seen about 50 pixles (25 arcseconds) from the published position of the nucleus. A luminous source exceeding 1039 erg s−1also occupies

the frame, but is just barely inside the D25 radius of the galaxy, and so any association with NGC 660 is somewhat tenuous.

NGC 1052 Class III. Nucleus clearly detected (L 1040 erg s−1). Sig- X ∼ nificant diffuse nuclear emission.

NGC 1055 Class IV. Only four sources detected, none near the published nuclear position. One very luminous source (L 4 1039 erg s−1) X ∼ × 99 is seen 4 arcminutes from the putative nuclear position.

NGC 1058 Class I. Several off-nuclear sources; none significant.

NGC 2541 Class IV. A handful of sources, none within an arcminute of the published nuclear position. One luminous (L 2 1039 erg s−1) X ∼ × source was found an arcminute away. Source are well-scattered through- out the galaxy disk.

NGC 2683 Class II/IV. Ten sources, all at or below 1038 erg s−1. Two sources are found within 10 arcseconds of the nuclear position, with the rest scattered evenly within the surrounding 4 arcminutes.

NGC 2787 Class I. No interesting sources.

NGC 2841 Class II. Clearly detected nucleus surrounded by several com- parably bright sources. Less-luminous sources are scattered through- out the disk.

NGC 3031 Class I. This is Messier 81, with a brilliant, easily segregated nucleus with a luminosity of around L 3 1040 erg s−1. This source X ∼ × is, of course, heavily piled-up, and the count rate was estimated from the counts present in the readout trail. Nearly three dozen sources found throughout the galaxy, all with luminosities below 1038 erg s−1. Source X-15 is actually the remnant of supernova SN1993J, which was the second-brightest supernova known.

NGC 3368 Class II. This is Messier 96, with a clearly-detected nucleus. It is surrounded by a dozen dispersed sources, many of which are as bright as the nuclear source (L 1038 erg s−1). X ∼

100 NGC 3486 Class IV. Three sources, two faint and one 1038 erg s−1 source one-half arcminute from the published nuclear position.

NGC 3489 Class II. Three sources, each of which have L 2 1038 X ∼ × erg s−1. One of these is clearly the galactic nucleus. The other two are found along the rim of the galaxy (not close to each other). Two

fainter sources were also detected, but lie well outside the galaxy’s D25 radius.

NGC 3623 Class II/IV. Messier 65. Nine sources, with two sources at 8 and 15 arcseconds from the published nuclear position. Source lumi- nosities range between about 1038 and 7 1038 erg s−1, with a relatively × flat distribution.

NGC 3627 Class II. A dozen sources, several with luminosities comparable to that of the nucleus (L 2 1038 erg s−1). X ∼ × NGC 3628 Class II/IV. Ten sources, with one about 5 arcseconds from the established position. This source is faint (L 7 1037 erg s−1), but X ∼ × there is another source that is twice as bright only ten arcseconds from the putative center. In addition, there is a much more luminous source (L 2 1039 erg s−1) only thirty arcseconds from the published X ∼ × nuclear coordinates. It is likely that one of these is the nucleus, but it is unclear which of the three holds that distinction.

NGC 3675 Class IV. Two sources of modest luminosity (L 6 1038 X ∼ × erg s−1). Neither is close to the nuclear position.

NGC 4150 Class II/IV. About five sources, all with a luminosity in the range between 1038 and 5 1038 erg s−1. One of these is twelve arc- ×

101 seconds from the nuclear position, and another is 17 arcseconds away. Neither is particularly likely to be the nucleus. Another seven sources

are seen in the frame, but are outside the D25 radius. Two of these sources are quite luminous, with L of about 6.6 1039 and 2.7 1039 X × × erg s−1.

NGC 4203 Class I. Brilliant nuclear source, with an L 1040 erg s−1. X ∼ Two other sources with L 1039 erg s−1are seen; one is just inside X ∼ the D25 radius, and the other is about 1.5 arcmin outside it.

NGC 4278 Class I. Messier 98. Clear nuclear source with L 1040 X ∼ erg s−1. Another source of comparable luminosity is found less than two arcminutes away. What appears to be a telescope aspect anomaly makes a precise luminosity comparison difficult.

NGC 4314 Class III. Eight faint sources (all less than 1038 erg s−1). One ∼ is within 6 arcseconds of the nuclear coordinates, with the next nearest being 1.5 arcminutes away. Nucleus is embedded in a considerable amount of diffuse emission and may be substantially obscured.

NGC 4321 Class I. Clear nucleus with a luminous source (L 3 1038 X ∼ × erg s−1) less than fifteen arcseconds away.

NGC 4374 Class I. Weak but distinct nucleus with two faint sources.

NGC 4395 Class I. Nucleus with L 4 1038 erg s−1, attended by X ∼ × another eight sources. One of these has a luminosity comparable to the nucleus, and is less than two arcminutes away.

NGC 4414 Class II/IV. A possible nuclear source is heavily obscured by diffuse emission. A number of moderately-luminous sources spread

102 through the galactic disk. One particularly luminous source (L X ∼ 4 1039 erg s−1) can be found in the frame, but it is about seven × arcminutes from the nucleus. As well, the object looks somewhat extended, though it is difficult to tell so far off axis. The distance from the nucleus, at any rate, makes an association with NGC 4414 unlikely.

NGC 4494 Class I. Nucleus detected with L 7 1038 erg s−1. Some X ∼ × diffuse emission noted in proximity to the nucleus. Two sources are detected on the outer edge of the galaxy, with luminosities only slightly less than that of the nucleus. Several other unremarkable sources also in the disk.

NGC 4565 Class II. Bright nucleus with a rich group of luminous sources distributed throughout the galaxy disk. One source is particular stands out, with a luminosity approaching 1040 erg s−1. This source is less than an arcminute away from the nucleus, and is located at the edge of the central bulge. At least four other sources appear to be moderately luminous (L afew 1038) halo sources. X ∼ × NGC 4569 Class II. Messier 90. Nuclear luminosity of about 2 1039 × erg s−1. Some diffuse emission noted. Surrounded by a dozen luminous sources, evenly distributed. Two of these sources have luminosities in excess of 1039 erg s−1.

NGC 4579 Class I. Messier 58. Brilliant nucleus with luminosity 1041 ∼ erg s−1. This observation utilised a 1/8 chip subarray to minimise the effects of pileup. A few other uninteresting sources.

NGC 4594 Class I. Messier 104. This observation also made use of a 1/8

103 chip subarray to reduce pileup. Nucleus has a luminosity of around 1040 erg s−1. A few luminous sources in the disk, with one exceeding 1039 erg s−1.

NGC 4639 Class I. Clear nucleus, with no other interesting sources. A small amount of diffuse emission is present.

NGC 4725 Class I. Distinct nucleus with seven other sources with 1 ∼ kpc.

NGC 4736 Class II. Messier 94. Ten sources seen, with several of the most luminous contained within half a kiloparsec of the nucleus. One source has a luminosity approaching 1039 erg s−1, with a projected distance of only a few hundred parsecs from the nucleus.

NGC 4826 Class II/IV. Messier 64. Several 1038 erg s−1sources noted throughout the frame. Considerable diffuse emission from the nuclear region.

NGC 5033 Class I. 1/2-subarray mode used to reduce pileup. Nucleus has L 6 1040 erg s−1. One source near the nucleus with luminosity X ∼ × greater than 1039 erg s−1.

NGC 5055 Class III. Messier 63. Considerable diffuse nuclear emission. Several dozen faint sources.

NGC 5195 Class IV. Messier 51b. Several luminous sources (L several X ∼ × 1038 erg s−1). No clear nucleus. Some diffuse nuclear emission.

NGC 5273 Class I. Bright nuclear source with L 1040 erg s−1. Several X ∼ uninteresting sources in the disk.

104 NGC 6500 Class I. Nucleus detected. Little else of interest.

NGC 6503 Class IV. Four sources inside the D25 diameter.

3.4 Epilogue

The most obvious direction to take to improve upon the results here is to obtain deeper observations of the entire 41 galaxy sample. Shallow 2–3 ks exposures mean that only the brightest tip of the X-ray binary luminos- ity function can be explored. Even slightly deeper 5 ks exposures would permit many more detections, and would make this work more valuable in comparing against theoretical results as above. While it is something of a common joke among astronomers that what is needed is always “better data”, it is clear that a 2 ks snapshot survey, while well-suited to the task of studying relatively luminous LLAGN (or demon- strating a non-detection of the central source), is not sufficient to effectively characterise the luminosity function of the ancillary X-ray sources of the host galaxy. Longer exposures, or, better still, multiple exposures at several epochs would not only yield more and fainter sources, it would also permit a limited study of source variability. As noted above, this could be helpful in ruling out multiple unresolved sources in some instances. With the im- position of a 1.5 ks per-target overhead begun in Chandra Cycle 2 however, broad surveys building on this program may no longer be pragmatic. Data mining of the growing Chandra archive may ultimately be the best way to achieve this breadth of coverage with sufficient depth.

105 Figure 3.1 The upper frame shows the relation between the 0.2–8 keV X-ray luminosity of each galaxy and its BT magnitude. The lower frame shows how the (B V ) colour changes with L . To a first approximation, one − T X would expect bluer galaxies to have a higher X-ray luminosity, due to a greater incidence of star formation. This anticipated correlation appears to be quite weak, if it exists.

106 Figure 3.2 The four diagrams above show the relative frequency of sources with varying luminosity, in four broad classes of galaxy represented in the sample. 107 Table 3.2. Summary of source properties

Source ID RA Dec ∆nuc Cnt Rate HR LX (0.2–8 keV) Γ − − − (J2000) (00) (10 3 s 1) (1038 erg s 1) (1) (2) (3) (4) (5) (6) (7) . +2.415 − . +0.31 NGC 253 N 00 47 33.19 -25 17 19.2 1.8 6 019−1.622 0 23−0.22 0.1785 0.707 . +2.079 − . +0.40 X-1 00 47 33.54 -25 17 21.3 7.4 3 704−1.250 0 25−0.26 0.1115 0.739 . +1.997 − . +0.44 X-2 00 47 34.30 -25 17 03.3 23.2 3 241−1.162 0 43−0.26 0.1105 1.053 . +1.919 . +0.47 X-3 00 47 33.01 -25 17 48.8 30.8 2 778−1.066 0 33−0.29 0.0734 0.500 . +1.823 − . +0.53 X-4 00 47 33.57 -25 18 16.0 58.5 2 315−0.963 0 60−0.25 0.0848 1.404 . +3.347 − . +0.14 X-5 00 47 36.40 -25 16 38.7 63.2 15 741−2.671 0 88−0.07 0.5047 2.352 +1.983 +0.44 108 . − . X-6 00 47 33.01 -25 18 46.4 88.4 3 241−1.164 0 71−0.19 0.1196 1.694 . +1.953 − . +0.42 X-7 00 47 28.03 -25 18 20.0 98.1 3 241−1.193 1 00−0.00 0.0127 5.000 . +1.983 − . +0.44 X-8 00 47 25.44 -25 16 42.9 120.2 3 241−1.164 0 71−0.19 0.1196 1.694 . +2.026 − . +0.38 X-9 00 47 35.29 -25 15 11.5 130.7 3 704−1.279 1 00−0.00 0.0146 5.000 . +2.225 − . +0.29 X-10 00 47 31.70 -25 15 05.7 134.0 5 093−1.510 1 00−0.00 0.0200 5.000 . +1.983 − . +0.44 X-11 00 47 26.48 -25 19 13.4 152.2 3 241−1.164 0 71−0.19 0.1196 1.694 . +2.891 − . +0.23 X-12 00 47 28.94 -25 14 58.5 152.8 10 185−2.135 0 36−0.17 0.3338 0.935 . +1.906 − . +0.48 X-13 00 47 23.55 -25 19 05.6 179.2 2 778−1.068 0 67−0.22 0.1027 1.565 . +5.035 . +0.11 X-14 00 47 43.11 -25 15 29.3 185.4 40 741−4.325 0 00−0.10 1.0765 0.500 . +1.997 − . +0.44 X-15 00 47 25.20 -25 19 44.7 188.6 3 241−1.162 0 43−0.26 0.1105 1.053 . +2.150 − . +0.38 X-16 00 47 24.51 -25 14 50.1 196.2 4 167−1.333 0 33−0.25 0.1338 0.882 . +8.267 − . +0.06 X-17 00 47 42.82 -25 15 01.8 199.5 124 537−7.583 0 17−0.06 3.5004 0.604 . +1.983 − . +0.44 X-18 00 47 40.73 -25 14 12.0 218.4 3 241−1.164 0 71−0.19 0.1196 1.694 . +3.464 − . +0.16 X-19 00 47 44.90 -25 14 56.5 226.6 16 667−2.749 0 61−0.12 0.6119 1.429 . +4.347 − . +0.12 X-20 00 47 45.60 -25 19 40.8 235.7 29 167−3.653 0 59−0.09 1.0646 1.375 . +1.906 . +0.48 X-21 00 47 17.61 -25 18 11.9 238.5 2 778−1.068 0 67−0.22 0.0734 0.500 . +2.026 − . +0.38 X-22 00 47 17.68 -25 18 26.2 241.1 3 704−1.279 1 00−0.00 0.0146 5.000 . +2.282 − . +0.34 X-23 00 47 49.14 -25 16 28.4 245.7 5 093−1.485 0 45−0.22 0.1762 1.102 Table 3.2 (cont’d)

Source ID RA Dec ∆nuc Cnt Rate HR LX (0.2–8 keV) Γ − − − (J2000) (00) (10 3 s 1) (1038 erg s 1) (1) (2) (3) (4) (5) (6) (7) . +3.208 − . +0.20 X-24 00 47 18.54 -25 19 14.3 247.5 13 426−2.461 0 24−0.16 0.4015 0.724 . +1.707 − . +0.64 X-25 00 47 22.64 -25 20 50.8 264.4 1 852−0.884 1 00−0.00 0.0073 5.000 . +6.481 − . +0.07 X-26 00 47 48.57 -25 15 02.9 268.5 73 611−5.824 0 67−0.06 2.7228 1.581 . +1.823 − . +0.53 X-27 00 47 44.82 -25 20 46.0 272.4 2 315−0.963 0 60−0.25 0.0848 1.404 . +2.630 − . +0.26 X-28 00 47 43.10 -25 13 22.6 279.0 7 870−1.868 0 53−0.17 0.2818 1.250 . +2.225 . +0.36 X-29 00 47 18.39 -25 21 37.7 340.8 4 630−1.410 0 00−0.25 0.1223 0.500 . +1.634 − . +0.66 X-30 00 47 23.30 -25 10 52.3 412.7 1 389−0.708 0 33−0.35 0.0446 0.882 +4.601 +0.11 109 . − . X-31 00 47 43.14 -25 09 58.5 464.6 33 333−3.908 0 56−0.09 1.2049 1.305 . +5.092 − . +0.10 X-32 00 48 00.95 -25 23 51.8 574.1 42 130−4.398 0 45−0.09 1.4542 1.095 . +1.983 − . +0.44 X-33 00 47 50.56 -25 08 42.1 578.6 3 241−1.164 0 71−0.19 0.1196 1.694 . +3.685 . +0.15 X-34 00 47 52.99 -25 07 34.9 655.0 19 444−2.974 0 57−0.11 0.5138 0.500 . +1.843 − . +0.64 NGC 404 N 01 09 26.97 35 43 05.7 2.9 2 000−0.954 1 00−0.00 0.3003 5.000 . +2.312 − . +0.38 X-1 01 09 24.73 35 46 01.6 181.6 4 500−1.440 0 56−0.22 0.9566 1.824 . +2.076 . +0.46 X-2 01 09 21.32 35 46 19.1 213.3 3 000−1.151 0 00−0.30 0.3503 0.724 . +2.732 − . +0.29 X-3 01 09 11.16 35 42 16.5 240.7 7 500−1.889 0 33−0.20 1.3014 1.336 . +2.824 − . +0.19 X-4 01 09 05.93 35 42 46.4 315.0 9 000−2.100 1 00−0.00 1.3515 5.000 . +1.872 − . +0.59 X-5 01 09 16.37 35 47 54.6 331.6 2 000−0.912 0 50−0.29 0.4059 1.690 . +1.872 . +0.59 X-6 01 09 01.47 35 46 18.5 428.7 2 000−0.912 0 50−0.29 0.1940 0.500 . +1.872 . +0.59 X-7 01 08 52.28 35 46 19.6 555.3 2 000−0.912 0 50−0.29 0.1940 0.500 + . +0.00 X-8 01 08 42.69 35 47 36.7 717.4 − 0 00−0.00 . +1.850 − . +0.40 NGC 660 X-1 01 43 02.38 13 38 44.3 24.3 3 333−1.127 0 75−0.17 0.4596 2.009 . +1.650 − . +0.51 X-2 01 43 03.87 13 39 55.2 98.2 2 083−0.865 0 20−0.31 0.2136 0.806 . +1.536 − . +0.64 X-3 01 43 01.20 13 40 03.4 100.5 1 667−0.795 1 00−0.00 0.0479 5.000 . +1.566 . +0.56 X-4 01 42 51.17 13 34 25.1 284.8 1 667−0.759 0 00−0.34 0.1409 0.500 Table 3.2 (cont’d)

Source ID RA Dec ∆nuc Cnt Rate HR LX (0.2–8 keV) Γ − − − (J2000) (00) (10 3 s 1) (1038 erg s 1) (1) (2) (3) (4) (5) (6) (7) . +2.811 − . +0.17 X-5 01 42 51.71 13 33 52.3 308.7 11 667−2.176 0 79−0.10 1.5948 2.136 . +1.450 − . +0.77 X-6 01 43 14.72 13 31 43.5 445.4 1 250−0.678 1 00−0.00 0.0359 5.000 . +1.727 − . +0.47 X-7 01 43 13.70 13 30 10.5 525.0 2 500−0.959 0 33−0.29 0.2875 1.040 . +7.552 . +0.06 NGC 1052 N 02 41 04.84 -08 15 20.2 1.0 115 833−6.938 0 23−0.06 9.5919 0.500 . +1.689 − . +0.47 X-1 02 41 01.46 -08 14 30.1 71.4 2 500−0.989 1 00−0.00 0.0488 5.000 . +1.650 − . +0.51 X-2 02 41 10.16 -08 17 13.0 137.9 2 083−0.865 0 20−0.31 0.2006 0.749 . +1.560 − . +0.59 X-3 02 41 07.02 -08 18 16.5 178.6 1 667−0.760 0 50−0.29 0.1989 1.293 +2.053 +0.34 110 . − . X-4 02 41 06.08 -08 12 20.2 181.8 4 583−1.336 0 45−0.22 0.5339 1.203 . +2.029 − . +0.32 NGC 1055 X-1 02 41 41.00 00 26 44.8 64.8 4 583−1.338 0 82−0.13 0.6999 2.176 . +2.162 − . +0.31 X-2 02 41 32.38 00 26 15.1 192.9 5 417−1.460 0 54−0.19 0.8216 1.372 . +2.893 − . +0.17 X-3 02 41 45.26 00 30 28.4 238.4 12 500−2.254 0 73−0.11 1.9739 1.869 . +1.471 . +0.66 X-4 02 41 40.43 00 30 50.0 269.7 1 250−0.637 0 33−0.35 0.1293 0.500 . +1.981 − . +0.51 NGC 1058 X-1 02 43 28.43 37 20 22.6 22.5 2 500−1.037 0 20−0.31 0.2749 0.822 . +1.880 . +0.56 X-2 02 43 27.40 37 20 58.9 49.2 2 000−0.910 0 00−0.34 0.1789 0.500 . +3.230 − . +0.23 X-3 02 43 23.28 37 20 42.1 100.4 12 000−2.412 0 17−0.17 1.2741 0.763 . +2.076 . +0.46 X-4 02 43 38.11 37 21 44.5 145.5 3 000−1.151 0 00−0.30 0.2683 0.500 . +1.843 − . +0.64 X-5 02 44 06.81 37 16 31.8 601.6 2 000−0.954 1 00−0.00 0.0793 5.000 . +3.209 − . +0.21 X-6 02 43 45.33 37 10 39.9 631.1 12 000−2.412 0 58−0.15 1.7555 1.583 . +1.765 − . +0.66 X-7 02 44 02.15 37 13 22.3 643.7 1 500−0.765 0 33−0.35 0.1860 1.061 . +3.587 − . +0.14 NGC 2541 X-1 08 14 37.03 49 03 26.6 56.2 21 250−2.954 0 57−0.11 2.8081 1.509 . +1.758 − . +0.42 X-2 08 14 42.42 49 05 51.1 123.9 2 917−1.073 1 00−0.00 0.0805 5.000 . +1.641 − . +0.53 X-3 08 14 51.36 49 04 57.7 177.4 2 083−0.867 0 60−0.25 0.2787 1.583 . +2.413 − . +0.25 X-4 08 14 33.54 48 59 15.5 294.1 7 500−1.732 0 56−0.17 0.9855 1.480 . +1.615 − . +0.54 X-5 08 14 32.03 49 12 58.7 561.9 2 083−0.898 1 00−0.00 0.0575 5.000 Table 3.2 (cont’d)

Source ID RA Dec ∆nuc Cnt Rate HR LX (0.2–8 keV) Γ − − − (J2000) (00) (10 3 s 1) (1038 erg s 1) (1) (2) (3) (4) (5) (6) (7) . +1.727 . +0.47 X-6 08 15 24.41 49 02 50.5 662.9 2 500−0.959 0 33−0.29 0.2105 0.500 . +1.615 − . +0.54 NGC 2683 X-1 08 52 41.32 33 25 18.2 9.0 2 083−0.898 1 00−0.00 0.0407 5.000 . +1.650 . +0.51 X-2 08 52 41.76 33 25 04.2 9.9 2 083−0.865 0 20−0.31 0.1719 0.500 . +1.885 − . +0.34 X-3 08 52 37.22 33 25 13.4 59.8 3 750−1.224 1 00−0.00 0.0732 5.000 . +1.996 − . +0.36 X-4 08 52 45.57 33 26 05.0 85.9 4 167−1.270 0 40−0.23 0.4728 1.116 . +2.187 . +0.27 X-5 08 52 40.67 33 27 05.0 115.9 5 833−1.520 0 86−0.11 0.4813 0.500 . +1.560 . +0.59 X-6 08 52 42.47 33 27 43.4 155.2 1 667−0.760 0 50−0.29 0.1375 0.500 +1.715 +0.48 111 . − . X-7 08 52 33.31 33 22 38.0 192.2 2 500−0.961 0 67−0.22 0.3170 1.691 . +1.987 − . +0.35 X-8 08 52 40.37 33 21 05.5 244.2 4 167−1.270 0 60−0.20 0.5210 1.526 . +1.730 . +0.46 X-9 08 52 34.07 33 21 13.1 259.4 2 500−0.959 0 00−0.30 0.2063 0.500 . +1.641 . +0.53 X-10 08 52 58.70 33 25 22.5 262.9 2 083−0.867 0 60−0.25 0.1719 0.500 . +1.730 . +0.46 NGC 2841 N 09 22 02.73 50 58 35.1 0.5 2 500−0.959 0 00−0.30 0.2009 0.500 . +1.641 − . +0.53 X-1 09 22 02.52 50 58 18.9 16.4 2 083−0.867 0 60−0.25 0.2398 1.459 . +2.053 − . +0.34 X-2 09 22 02.21 50 58 53.9 20.2 4 583−1.336 0 45−0.22 0.4998 1.162 . +1.536 − . +0.64 X-3 09 21 59.37 50 57 31.4 80.9 1 667−0.795 1 00−0.00 0.0210 5.000 . +1.450 − . +0.77 X-4 09 21 58.12 50 59 58.4 108.0 1 250−0.678 1 00−0.00 0.0158 5.000 . +1.536 − . +0.64 X-5 09 21 58.69 50 56 11.5 155.6 1 667−0.795 1 00−0.00 0.0210 5.000 . +1.536 − . +0.64 X-6 09 22 02.34 51 02 02.7 207.8 1 667−0.795 1 00−0.00 0.0210 5.000 . +1.536 − . +0.64 X-7 09 21 49.67 50 57 04.9 215.2 1 667−0.795 1 00−0.00 0.0210 5.000 . +2.029 − . +0.32 X-8 09 21 44.22 50 56 47.7 297.3 4 583−1.338 0 82−0.13 0.5038 2.092 . +1.536 − . +0.64 X-9 09 21 49.06 51 02 13.5 299.3 1 667−0.795 1 00−0.00 0.0210 5.000 . +2.162 − . +0.31 X-10 09 21 53.88 50 53 22.1 339.7 5 417−1.460 0 54−0.19 0.6126 1.326 . +1.798 − . +0.44 X-11 09 21 36.35 51 00 46.8 416.7 2 917−1.046 0 43−0.26 0.3138 1.113 . +1.641 − . +0.53 X-12 09 22 51.13 51 07 52.6 915.8 2 083−0.867 0 60−0.25 0.2398 1.459 Table 3.2 (cont’d)

Source ID RA Dec ∆nuc Cnt Rate HR LX (0.2–8 keV) Γ − − − (J2000) (00) (10 3 s 1) (1038 erg s 1) (1) (2) (3) (4) (5) (6) (7) . +2.226 − . +0.30 NGC 3031 N! 09 55 33.26 69 03 55.9 1.3 5 833−1.518 0 29−0.21 1000.6262 0.918 . +6.296 − . +0.04 X-1 09 55 34.86 69 03 42.1 28.1 80 000−5.762 0 93−0.03 8.5509 2.887 . +1.758 − . +0.42 X-2 09 55 35.41 69 03 52.8 33.3 2 917−1.073 1 00−0.00 0.0727 5.000 . +1.972 − . +0.34 X-3 09 55 31.23 69 04 19.1 38.1 4 167−1.272 0 80−0.14 0.5444 2.147 . +1.715 − . +0.48 X-4 09 55 35.19 69 03 15.7 49.3 2 500−0.961 0 67−0.22 0.3313 1.716 . +2.845 − . +0.20 X-5 09 55 34.60 69 04 53.9 62.5 11 667−2.176 0 36−0.15 1.3246 1.046 . +1.689 − . +0.47 X-6 09 55 27.91 69 04 08.3 80.4 2 500−0.989 1 00−0.00 0.0623 5.000 +2.544 +0.23 112 . − . X-7 09 55 27.70 69 04 00.2 82.6 8 750−1.876 0 62−0.15 1.1461 1.593 . +2.162 − . +0.24 X-8 09 55 27.03 69 04 14.9 94.6 5 833−1.538 1 00−0.00 0.1453 5.000 . +5.369 − . +0.04 X-9 09 55 27.16 69 02 47.7 112.8 56 667−4.846 0 97−0.02 4.5057 3.479 . +1.823 − . +0.38 X-10 09 55 42.11 69 03 36.2 134.9 3 333−1.151 1 00−0.00 0.0830 5.000 . +1.650 − . +0.51 X-11 09 55 34.38 69 06 21.6 147.6 2 083−0.865 0 20−0.31 0.2072 0.769 . +2.332 − . +0.23 X-12 09 55 22.07 69 05 10.5 183.2 7 083−1.683 0 88−0.09 0.8509 2.550 . +1.823 − . +0.38 X-13 09 55 21.82 69 05 22.0 191.6 3 333−1.151 1 00−0.00 0.0830 5.000 . +3.367 − . +0.16 X-14 09 55 32.90 69 00 33.2 201.9 17 917−2.709 0 16−0.13 1.7202 0.707 . +1.935 − . +0.38 X-15 09 55 24.72 69 01 13.2 205.8 3 750−1.199 0 33−0.25 0.4182 1.003 . +2.214 − . +0.29 X-16 09 55 21.83 69 06 38.0 235.9 5 833−1.519 0 57−0.18 0.7511 1.480 . +1.650 − . +0.51 X-17 09 55 47.01 69 05 49.4 236.6 2 083−0.865 0 20−0.31 0.2072 0.769 . +4.726 − . +0.10 X-18 09 55 49.79 69 05 31.9 267.1 40 833−4.109 0 53−0.08 5.1615 1.389 . +1.615 − . +0.54 X-19 09 55 52.98 69 05 20.3 308.7 2 083−0.898 1 00−0.00 0.0519 5.000 . +1.241 − . +1.30 X-20 09 55 53.19 69 02 06.4 319.0 0 417−0.344 1 00−0.00 0.0104 5.000 . +5.890 − . +0.08 X-21 09 55 53.12 69 01 13.0 339.9 67 083−5.275 0 39−0.07 7.8051 1.110 . +1.536 − . +0.64 X-22 09 55 10.24 69 05 02.2 350.9 1 667−0.795 1 00−0.00 0.0415 5.000 . +1.784 − . +0.44 X-23 09 55 49.32 69 08 11.7 352.7 2 917−1.048 0 71−0.19 0.3883 1.852 Table 3.2 (cont’d)

Source ID RA Dec ∆nuc Cnt Rate HR LX (0.2–8 keV) Γ − − − (J2000) (00) (10 3 s 1) (1038 erg s 1) (1) (2) (3) (4) (5) (6) (7) . +1.850 − . +0.40 X-24 09 55 58.47 69 05 25.6 389.8 3 333−1.127 0 75−0.17 0.4426 1.965 . +2.152 − . +0.30 X-25 09 55 09.72 69 07 01.6 398.6 5 417−1.461 0 69−0.16 0.7203 1.787 . +1.730 . +0.46 X-26 09 55 59.20 69 06 17.8 415.3 2 500−0.959 0 00−0.30 0.2106 0.500 . +2.002 − . +0.29 X-27 09 55 57.73 69 00 36.6 418.1 4 583−1.359 1 00−0.00 0.1142 5.000 . +2.394 − . +0.23 X-28 09 54 57.54 69 02 40.8 540.0 7 500−1.733 0 78−0.13 0.9891 2.063 . +1.536 − . +0.64 X-29 09 56 08.87 69 01 05.4 561.4 1 667−0.795 1 00−0.00 0.0415 5.000 . +1.353 − . +0.97 X-30 09 54 50.38 69 04 18.8 642.7 0 833−0.536 1 00−0.00 0.0208 5.000 +2.870 +0.19 113 . − . X-31 09 54 45.08 68 56 58.1 833.5 12 083−2.215 0 59−0.13 1.5649 1.514 . +11.065 − . +0.04 X-32 09 54 06.17 69 08 43.7 1337.0 262 917−10.460 0 21−0.04 26.5105 0.794 . +1.803 − . +0.43 NGC 3368 N 10 46 45.71 11 49 11.3 1.3 2 917−1.045 0 14−0.28 0.2662 0.658 . +1.935 − . +0.38 X-1 10 46 49.00 11 49 35.9 54.0 3 750−1.199 0 33−0.25 0.4003 0.976 . +1.885 − . +0.34 X-2 10 46 42.95 11 51 11.2 127.5 3 750−1.224 1 00−0.00 0.0692 5.000 . +1.972 − . +0.34 X-3 10 46 53.18 11 50 22.8 132.0 4 167−1.272 0 80−0.14 0.5066 2.089 . +1.536 − . +0.64 X-4 10 46 53.21 11 50 27.0 134.7 1 667−0.795 1 00−0.00 0.0308 5.000 . +1.715 − . +0.48 X-5 10 46 53.49 11 51 16.1 170.1 2 500−0.961 0 67−0.22 0.3118 1.670 . +1.566 . +0.56 X-6 10 46 44.64 11 52 06.8 176.6 1 667−0.759 0 00−0.34 0.1373 0.500 . +1.715 − . +0.48 X-7 10 46 57.96 11 49 38.1 184.4 2 500−0.961 0 67−0.22 0.3118 1.670 . +1.560 − . +0.59 X-8 10 46 38.89 11 45 53.8 222.8 1 667−0.760 0 50−0.29 0.1971 1.289 . +1.784 − . +0.44 X-9 10 46 36.17 11 45 25.6 267.7 2 917−1.048 0 71−0.19 0.3642 1.802 . +2.211 − . +0.22 X-10 10 46 36.98 11 44 59.2 284.5 6 250−1.594 1 00−0.00 0.1154 5.000 . +1.615 − . +0.54 X-11 10 46 41.93 11 54 01.2 295.9 2 083−0.898 1 00−0.00 0.0385 5.000 + . +0.00 X-12 10 46 24.66 11 47 58.7 325.3 − 0 00−0.00 . +1.850 − . +0.40 NGC 3486 X-1 11 00 22.23 28 58 16.2 28.6 3 333−1.127 0 75−0.17 0.3978 1.877 . +1.689 − . +0.47 X-2 11 00 22.41 28 59 23.4 57.9 2 500−0.989 1 00−0.00 0.0366 5.000 Table 3.2 (cont’d)

Source ID RA Dec ∆nuc Cnt Rate HR LX (0.2–8 keV) Γ − − − (J2000) (00) (10 3 s 1) (1038 erg s 1) (1) (2) (3) (4) (5) (6) (7) . +1.885 − . +0.34 X-3 11 00 30.22 28 56 32.4 151.1 3 750−1.224 1 00−0.00 0.0549 5.000 . +2.214 − . +0.29 NGC 3489 X-1 11 00 18.54 13 54 02.8 8.4 5 833−1.519 0 57−0.18 0.6852 1.406 . +2.332 − . +0.23 X-2 11 00 05.17 13 55 26.2 209.2 7 083−1.683 0 88−0.09 0.7388 2.421 . +2.099 − . +0.31 X-3 11 00 32.67 13 53 44.8 219.8 5 000−1.400 0 67−0.18 0.5983 1.631 . +1.641 − . +0.53 X-4 11 00 53.57 13 53 27.3 533.7 2 083−0.867 0 60−0.25 0.2467 1.470 . +1.939 . +0.38 X-5 11 00 48.26 13 48 45.6 555.5 3 750−1.199 0 11−0.26 0.3064 0.500 . +2.099 − . +0.31 NGC 3623 X-1 11 18 56.00 13 05 33.4 7.5 5 000−1.400 0 67−0.18 1.0406 2.054 +1.784 +0.44 114 . − . X-2 11 18 55.03 13 05 41.6 15.4 2 917−1.048 0 71−0.19 0.6229 2.206 . +1.689 − . +0.47 X-3 11 18 52.85 13 05 42.0 43.3 2 500−0.989 1 00−0.00 0.3034 5.000 . +2.850 − . +0.21 X-4 11 18 58.54 13 05 30.9 44.2 11 667−2.176 0 21−0.16 1.6413 1.055 . +1.927 − . +0.38 X-5 11 19 00.59 13 05 37.4 75.4 3 750−1.200 0 56−0.22 0.7238 1.754 . +2.285 − . +0.24 X-6 11 18 52.44 13 03 35.9 122.6 6 667−1.631 0 88−0.10 1.4553 2.954 . +1.560 − . +0.59 X-7 11 19 01.70 13 09 45.3 272.2 1 667−0.760 0 50−0.29 0.3079 1.623 . +2.109 − . +0.32 X-8 11 19 09.36 13 09 50.6 333.2 5 000−1.400 0 50−0.20 0.9238 1.623 . +2.423 − . +0.21 X-9 11 19 28.43 13 02 51.1 517.1 7 917−1.783 0 89−0.08 1.7050 3.099 . +3.263 − . +0.21 NGC 3627 X-1 11 20 15.12 12 59 27.8 7.5 12 500−2.463 0 52−0.15 1.4703 1.325 . +2.220 − . +0.40 X-2 11 20 14.25 12 59 27.0 11.4 4 000−1.353 0 75−0.17 0.4866 1.900 . +3.270 − . +0.17 X-3 11 20 14.56 12 59 46.0 25.5 13 000−2.514 0 85−0.09 1.4825 2.269 . +2.564 − . +0.28 X-4 11 20 18.30 12 59 00.3 55.1 6 500−1.755 0 85−0.11 0.7413 2.269 . +1.843 − . +0.64 X-5 11 20 13.57 13 00 16.1 58.6 2 000−0.954 1 00−0.00 0.0333 5.000 . +3.796 − . +0.14 X-6 11 20 18.20 12 59 58.9 62.3 19 000−3.053 0 79−0.09 2.2738 2.035 . +1.880 . +0.56 X-7 11 20 16.64 12 58 20.1 66.2 2 000−0.910 0 00−0.34 0.1633 0.500 . +3.043 − . +0.22 X-8 11 20 13.46 13 00 26.0 68.4 10 500−2.252 0 71−0.13 1.2858 1.792 . +2.312 − . +0.38 X-9 11 20 20.89 12 58 45.9 96.5 4 500−1.440 0 56−0.22 0.5369 1.400 Table 3.2 (cont’d)

Source ID RA Dec ∆nuc Cnt Rate HR LX (0.2–8 keV) Γ − − − (J2000) (00) (10 3 s 1) (1038 erg s 1) (1) (2) (3) (4) (5) (6) (7) . +3.786 − . +0.16 X-10 11 20 17.60 13 01 40.0 144.8 18 500−3.011 0 57−0.12 2.2166 1.426 . +2.109 − . +0.42 X-11 11 20 19.01 13 01 35.2 147.6 3 500−1.288 1 00−0.00 0.0584 5.000 . +2.761 − . +0.26 X-12 11 19 59.98 12 59 26.8 223.9 8 000−1.955 0 75−0.14 0.9731 1.900 . +2.395 − . +0.36 X-13 11 20 21.66 12 55 13.6 267.4 5 000−1.524 0 40−0.23 0.5517 1.093 . +2.141 − . +0.44 X-14 11 20 34.96 13 05 44.5 487.5 3 500−1.257 0 71−0.19 0.4286 1.792 + . +0.00 X-15 11 20 37.10 13 05 44.3 507.7 − 0 00−0.00 . +2.109 − . +0.42 X-16 11 20 46.56 12 54 28.3 557.8 3 500−1.288 1 00−0.00 0.0584 5.000 +1.803 +0.43 115 . . NGC 3628 N? 11 20 16.23 13 35 27.0 5.0 2 917−1.045 0 14−0.28 0.2380 0.500 . +1.798 − . +0.44 X-1 11 20 15.75 13 35 13.1 11.1 2 917−1.046 0 43−0.26 0.3247 1.136 . +5.438 − . +0.09 X-2 11 20 14.30 13 35 09.8 31.0 55 833−4.810 0 15−0.08 5.0460 0.660 . +1.864 − . +0.41 X-3 11 20 06.89 13 34 53.7 142.5 3 333−1.125 0 50−0.24 0.3852 1.274 . +1.987 − . +0.35 X-4 11 20 05.55 13 34 49.9 163.0 4 167−1.270 0 60−0.20 0.4995 1.488 . +2.423 − . +0.21 X-5 11 20 14.69 13 32 27.6 175.9 7 917−1.783 0 89−0.08 0.8180 2.522 . +2.169 − . +0.31 X-6 11 20 11.75 13 31 23.1 248.0 5 417−1.460 0 38−0.21 0.5872 1.055 . +3.749 − . +0.14 X-7 11 20 10.45 13 39 34.8 267.1 23 333−3.097 0 04−0.12 1.9043 0.500 . +2.544 − . +0.23 X-8 11 20 08.97 13 39 30.4 271.0 8 750−1.876 0 62−0.15 1.0536 1.532 . +1.927 − . +0.38 X-9 11 19 57.05 13 34 56.4 288.4 3 750−1.200 0 56−0.22 0.4434 1.390 . +1.987 − . +0.35 NGC 3675 X-1 11 26 07.32 43 34 06.2 52.8 4 167−1.270 0 60−0.20 0.5367 1.465 . +2.332 − . +0.28 X-2 11 25 48.11 43 32 11.1 341.9 6 667−1.628 0 12−0.21 0.6249 0.587 . +1.560 − . +0.59 NGC 4150 X-1 12 10 32.81 30 24 24.2 12.8 1 667−0.760 0 50−0.29 0.2986 1.613 . +1.560 . +0.59 X-2 12 10 33.75 30 23 58.0 17.0 1 667−0.760 0 50−0.29 0.1528 0.500 . +1.650 − . +0.51 X-3 12 10 34.77 30 23 58.3 27.7 2 083−0.865 0 20−0.31 0.2804 1.022 . +1.450 − . +0.77 X-4 12 10 34.80 30 23 21.4 56.8 1 250−0.678 1 00−0.00 0.1446 5.000 . +1.689 − . +0.47 X-5 12 10 32.37 30 21 20.9 172.3 2 500−0.989 1 00−0.00 0.2892 5.000 Table 3.2 (cont’d)

Source ID RA Dec ∆nuc Cnt Rate HR LX (0.2–8 keV) Γ − − − (J2000) (00) (10 3 s 1) (1038 erg s 1) (1) (2) (3) (4) (5) (6) (7) . +1.560 − . +0.59 X-6 12 10 17.84 30 25 49.7 249.9 1 667−0.760 0 50−0.29 0.2986 1.613 . +4.914 − . +0.08 X-7 12 10 16.04 30 23 59.5 257.7 45 000−4.315 0 69−0.07 9.1624 2.099 . +1.996 − . +0.36 X-8 12 10 49.88 30 26 13.1 277.7 4 167−1.270 0 40−0.23 0.6851 1.400 . +3.683 − . +0.14 X-9 12 10 15.08 30 21 28.7 317.5 22 500−3.041 0 41−0.11 3.7244 1.415 . +2.001 − . +0.36 X-10 12 10 11.59 30 24 29.5 324.6 4 167−1.269 0 20−0.25 0.5607 1.022 . +1.641 − . +0.53 X-11 12 10 52.35 30 30 03.7 453.5 2 083−0.867 0 60−0.25 0.4023 1.856 . +1.784 − . +0.44 X-12 12 11 05.73 30 26 12.3 502.3 2 917−1.048 0 71−0.19 0.6028 2.194 +1.641 +0.53 116 . − . X-13 12 10 51.94 30 31 27.3 517.5 2 083−0.867 0 60−0.25 0.4023 1.856 . +1.798 − . +0.44 X-14 12 11 07.13 30 26 33.4 528.0 2 917−1.046 0 43−0.26 0.4919 1.459 . +1.758 − . +0.42 NGC 4203 N 12 15 05.02 33 11 49.9 1.0 2 917−1.073 1 00−0.00 0.0351 5.000 . +2.099 . +0.31 X-1 12 15 09.89 33 11 28.8 76.1 5 000−1.400 0 67−0.18 0.4172 0.500 . +1.353 − . +0.97 X-2 12 15 07.19 33 13 44.0 119.6 0 833−0.536 1 00−0.00 0.0100 5.000 . +2.394 − . +0.23 X-3 12 15 09.20 33 09 54.6 130.6 7 500−1.733 0 78−0.13 0.8596 1.905 . +1.353 − . +0.97 X-4 12 15 14.33 33 11 04.5 146.8 0 833−0.536 1 00−0.00 0.0100 5.000 . +1.641 − . +0.53 X-5 12 15 15.61 33 10 12.4 186.2 2 083−0.867 0 60−0.25 0.2429 1.420 . +1.730 . +0.46 X-6 12 15 15.32 33 13 54.3 199.2 2 500−0.959 0 00−0.30 0.2086 0.500 . +8.376 − . +0.04 X-7 12 15 19.69 33 11 11.5 223.5 146 667−7.809 0 74−0.03 17.0590 1.796 . +2.378 − . +0.22 X-8 12 15 19.82 33 10 12.4 242.4 7 500−1.734 0 89−0.09 0.7481 2.397 . +1.715 − . +0.48 X-9 12 14 46.34 33 13 23.6 295.5 2 500−0.961 0 67−0.22 0.2939 1.580 . +8.276 − . +0.05 X-10 12 15 06.20 33 16 53.9 305.4 141 667−7.675 0 42−0.05 15.3883 1.064 . +1.641 − . +0.53 X-11 12 15 33.66 33 05 42.5 565.0 2 083−0.867 0 60−0.25 0.2429 1.420 . +1.536 − . +0.64 NGC 4278 X-1 12 19 46.80 29 15 50.3 305.8 1 667−0.795 1 00−0.00 0.2715 5.000 . +1.650 − . +0.51 X-2 12 19 45.32 29 11 34.4 451.0 2 083−0.865 0 20−0.31 0.3509 1.028 . +1.987 − . +0.35 X-3 12 19 39.44 29 11 41.1 513.6 4 167−1.270 0 60−0.20 1.0284 1.891 Table 3.2 (cont’d)

Source ID RA Dec ∆nuc Cnt Rate HR LX (0.2–8 keV) Γ − − − (J2000) (00) (10 3 s 1) (1038 erg s 1) (1) (2) (3) (4) (5) (6) (7) . +1.996 − . +0.36 X-4 12 19 35.70 29 13 00.2 520.1 4 167−1.270 0 40−0.23 0.8658 1.419 . +2.115 − . +0.32 X-5 12 19 37.62 29 11 54.3 528.2 5 000−1.399 0 33−0.22 0.9726 1.283 . +1.650 − . +0.51 X-6 12 19 31.90 29 14 11.3 547.0 2 083−0.865 0 20−0.31 0.3509 1.028 . +1.650 . +0.51 X-7 12 19 31.99 29 13 51.9 551.7 2 083−0.865 0 20−0.31 0.2383 0.500 . +2.044 − . +0.33 X-8 12 19 30.48 29 20 20.8 584.2 4 583−1.337 0 64−0.19 1.1613 1.993 . +2.964 − . +0.13 X-9 12 19 28.15 29 11 40.7 657.1 13 750−2.369 0 94−0.05 3.5049 3.615 . +1.864 . +0.41 X-10 12 19 24.00 29 19 26.3 660.7 3 333−1.125 0 50−0.24 0.3813 0.500 +2.301 +0.26 117 . − . X-11 12 19 22.30 29 20 17.9 699.1 6 667−1.629 0 75−0.14 1.8076 2.372 . +4.491 − . +0.05 X-12 12 19 20.62 29 18 59.8 704.8 37 917−3.960 0 98−0.02 7.7829 4.407 . +1.996 − . +0.36 X-13 12 19 19.38 29 19 53.7 734.7 4 167−1.270 0 40−0.23 0.8658 1.419 . +2.083 . +0.30 X-14 12 19 18.71 29 19 47.0 742.8 5 000−1.402 0 83−0.12 0.5720 0.500 . +2.736 − . +0.18 X-15 12 19 22.42 29 10 09.2 777.0 10 833−2.095 0 77−0.11 2.9616 2.449 . +2.264 − . +0.28 X-16 12 19 15.86 29 19 23.9 779.4 6 250−1.575 0 60−0.17 1.5426 1.891 . +1.939 . +0.38 X-17 12 19 14.62 29 19 13.6 795.7 3 750−1.199 0 11−0.26 0.4290 0.500 . +1.784 . +0.44 X-18 12 19 17.49 29 11 17.8 810.8 2 917−1.048 0 71−0.19 0.3337 0.500 . +2.083 − . +0.30 X-19 12 19 11.61 29 20 23.0 854.8 5 000−1.402 0 83−0.12 1.3880 2.751 . +1.784 − . +0.44 X-20 12 19 11.29 29 22 07.8 891.2 2 917−1.048 0 71−0.19 0.7764 2.240 . +4.597 − . +0.05 X-21 12 19 06.25 29 10 15.7 990.1 40 000−4.068 0 98−0.02 8.0965 4.447 . +5.515 − . +0.03 X-22 12 19 06.16 29 10 18.6 990.3 60 417−5.005 0 99−0.01 10.8845 4.756 . +5.705 − . +0.04 X-23 12 19 06.19 29 10 09.7 993.4 64 583−5.175 0 95−0.02 16.0211 3.745 . +4.087 − . +0.06 X-24 12 19 05.88 29 10 09.4 997.8 30 417−3.543 0 97−0.02 6.5988 4.240 . +1.689 − . +0.47 NGC 4314 N? 12 22 31.78 29 53 48.3 5.6 2 500−0.989 1 00−0.00 0.0354 5.000 . +1.803 − . +0.43 X-1 12 22 27.00 29 54 05.9 77.0 2 917−1.045 0 14−0.28 0.2616 0.643 . +1.471 − . +0.66 X-2 12 22 34.39 29 54 50.9 77.5 1 250−0.637 0 33−0.35 0.1303 0.955 Table 3.2 (cont’d)

Source ID RA Dec ∆nuc Cnt Rate HR LX (0.2–8 keV) Γ − − − (J2000) (00) (10 3 s 1) (1038 erg s 1) (1) (2) (3) (4) (5) (6) (7) . +1.566 . +0.56 X-3 12 22 28.90 29 54 49.7 80.4 1 667−0.759 0 00−0.34 0.1363 0.500 . +1.758 − . +0.42 X-4 12 22 27.21 29 52 37.2 96.3 2 917−1.073 1 00−0.00 0.0412 5.000 . +1.471 − . +0.66 X-5 12 22 23.90 29 53 11.5 124.1 1 250−0.637 0 33−0.35 0.1303 0.955 . +1.823 − . +0.38 X-6 12 22 40.55 29 57 20.8 253.5 3 333−1.151 1 00−0.00 0.0471 5.000 . +1.641 − . +0.53 X-7 12 22 18.26 29 49 17.8 335.0 2 083−0.867 0 60−0.25 0.2474 1.474 . +2.136 − . +0.28 NGC 4395 N 12 25 48.86 33 32 48.7 0.9 5 417−1.462 0 85−0.11 0.5656 2.200 . +2.214 − . +0.29 X-1 12 25 49.07 33 32 01.8 46.3 5 833−1.519 0 57−0.18 0.6554 1.386 +4.986 +0.10 118 . . X-2 12 25 47.30 33 34 47.9 122.3 45 833−4.355 0 20−0.09 3.6490 0.500 . +1.566 . +0.56 X-3 12 25 39.55 33 32 04.1 146.9 1 667−0.759 0 00−0.34 0.1327 0.500 . +1.471 . +0.66 X-4 12 25 59.90 33 33 21.2 168.3 1 250−0.637 0 33−0.35 0.0995 0.500 . +2.237 − . +0.25 X-5 12 25 55.18 33 30 16.1 178.8 6 250−1.577 0 87−0.10 0.6322 2.299 . +1.536 − . +0.64 X-6 12 25 43.89 33 29 60.0 184.1 1 667−0.795 1 00−0.00 0.0199 5.000 . +5.507 − . +0.04 X-7 12 26 01.46 33 31 30.7 203.6 60 000−4.988 0 97−0.02 3.5848 3.274 . +1.803 − . +0.43 X-8 12 25 43.77 33 28 54.2 246.2 2 917−1.045 0 14−0.28 0.2508 0.621 . +1.536 − . +0.64 X-9 12 25 42.67 33 40 00.4 442.3 1 667−0.795 1 00−0.00 0.0199 5.000 . +1.450 − . +0.77 NGC 4414 X-1 12 26 27.19 31 13 23.7 14.5 1 250−0.678 1 00−0.00 0.1590 5.000 . +2.260 − . +0.21 X-2 12 26 25.40 31 13 40.6 26.3 6 667−1.647 1 00−0.00 0.8482 5.000 . +1.566 . +0.56 X-3 12 26 19.52 31 13 02.8 102.8 1 667−0.759 0 00−0.34 0.1965 0.657 . +1.727 − . +0.47 X-4 12 26 15.95 31 13 10.8 155.4 2 500−0.959 0 33−0.29 0.4288 1.251 . +1.641 − . +0.53 X-5 12 26 24.62 31 10 33.2 166.8 2 083−0.867 0 60−0.25 0.4469 1.841 . +1.450 − . +0.77 X-6 12 26 37.48 31 15 14.4 204.1 1 250−0.678 1 00−0.00 0.1590 5.000 . +1.784 − . +0.44 X-7 12 26 24.74 31 17 12.2 235.3 2 917−1.048 0 71−0.19 0.6696 2.180 . +1.758 − . +0.42 X-8 12 26 35.00 31 09 51.0 244.7 2 917−1.073 1 00−0.00 0.3711 5.000 . +1.972 − . +0.34 X-9 12 26 10.16 31 15 41.4 281.4 4 167−1.272 0 80−0.14 0.9847 2.513 Table 3.2 (cont’d)

Source ID RA Dec ∆nuc Cnt Rate HR LX (0.2–8 keV) Γ − − − (J2000) (00) (10 3 s 1) (1038 erg s 1) (1) (2) (3) (4) (5) (6) (7) . +1.871 . +0.40 X-10 12 26 01.88 31 12 07.2 373.1 3 333−1.125 0 25−0.26 0.3449 0.500 . +4.326 − . +0.12 X-11 12 26 49.63 31 17 36.5 435.1 32 917−3.686 0 16−0.10 4.7248 0.940 . +1.912 − . +0.37 X-12 12 26 43.19 31 20 18.2 490.6 3 750−1.202 0 78−0.16 0.8820 2.417 . +1.471 − . +0.66 X-13 12 27 11.42 31 15 12.8 686.5 1 250−0.637 0 33−0.35 0.2144 1.251 . +2.524 − . +0.21 NGC 4494 N? 12 31 24.06 25 46 30.1 7.1 8 750−1.877 0 81−0.11 0.9808 2.050 . +1.566 . +0.56 X-2 12 31 23.49 25 45 58.2 28.5 1 667−0.759 0 00−0.34 0.1359 0.500 . +1.972 − . +0.34 X-3 12 31 29.57 25 46 21.3 79.1 4 167−1.272 0 80−0.14 0.4704 2.014 +1.471 +0.66 119 . − . X-4 12 31 25.95 25 44 52.8 94.5 1 250−0.637 0 33−0.35 0.1277 0.931 . +2.658 − . +0.20 X-5 12 31 28.55 25 44 57.0 107.8 10 000−2.010 0 75−0.12 1.1589 1.843 . +1.803 . +0.43 X-6 12 31 34.16 25 45 16.6 162.6 2 917−1.045 0 14−0.28 0.2378 0.500 . +2.449 − . +0.24 X-7 12 31 07.83 25 47 34.0 256.7 7 917−1.782 0 68−0.14 0.9283 1.654 . +1.560 − . +0.59 NGC 4565 N 12 36 20.78 25 59 15.7 1.3 1 667−0.760 0 50−0.29 0.1833 1.237 . +1.566 . +0.56 X-1 12 36 20.91 25 59 26.8 11.3 1 667−0.759 0 00−0.34 0.1334 0.500 . +1.566 . +0.56 X-2 12 36 19.01 25 59 31.3 29.6 1 667−0.759 0 00−0.34 0.1334 0.500 . +1.650 . +0.51 X-3 12 36 18.65 25 59 34.8 36.0 2 083−0.865 0 20−0.31 0.1667 0.500 . +1.864 − . +0.41 X-4 12 36 19.46 25 58 45.1 36.1 3 333−1.125 0 50−0.24 0.3666 1.237 . +5.370 − . +0.08 X-5 12 36 23.83 25 58 59.6 49.8 54 583−4.756 0 47−0.07 5.9100 1.170 . +2.348 − . +0.24 X-6 12 36 17.40 25 58 55.5 53.6 7 083−1.682 0 76−0.13 0.7959 1.886 . +1.727 . +0.47 X-7 12 36 19.02 26 00 27.2 75.6 2 500−0.959 0 33−0.29 0.2001 0.500 . +1.715 − . +0.48 X-8 12 36 25.95 25 59 31.9 80.4 2 500−0.961 0 67−0.22 0.2863 1.605 . +2.377 − . +0.27 X-9 12 36 28.12 26 00 00.9 120.1 7 083−1.681 0 29−0.20 0.6907 0.865 . +2.285 − . +0.24 X-10 12 36 14.60 26 00 53.0 133.3 6 667−1.631 0 88−0.10 0.6670 2.341 . +1.727 − . +0.47 X-11 12 36 27.39 25 57 32.8 143.9 2 500−0.959 0 33−0.29 0.2505 0.932 . +2.423 − . +0.21 X-12 12 36 31.27 25 59 37.4 159.9 7 917−1.783 0 89−0.08 0.7573 2.456 Table 3.2 (cont’d)

Source ID RA Dec ∆nuc Cnt Rate HR LX (0.2–8 keV) Γ − − − (J2000) (00) (10 3 s 1) (1038 erg s 1) (1) (2) (3) (4) (5) (6) (7) . +2.607 − . +0.19 X-13 12 36 08.05 25 55 25.3 298.7 9 583−1.967 0 83−0.10 1.0297 2.110 . +1.864 − . +0.41 X-14 12 36 14.22 25 50 25.2 539.6 3 333−1.125 0 50−0.24 0.3666 1.237 . +7.689 − . +0.05 X-15 12 35 42.76 25 56 54.3 586.5 121 250−7.099 0 59−0.05 13.7370 1.419 . +2.187 − . +0.27 NGC 4569 N 12 36 49.82 13 09 46.2 2.8 5 833−1.520 0 86−0.11 0.6625 2.324 . +1.650 − . +0.51 X-1 12 36 49.83 13 09 57.4 11.6 2 083−0.865 0 20−0.31 0.1987 0.742 . +3.462 − . +0.14 X-2 12 36 47.69 13 08 40.2 74.3 19 583−2.834 0 66−0.10 2.4194 1.641 . +1.471 − . +0.66 X-3 12 36 46.36 13 10 55.2 88.1 1 250−0.637 0 33−0.35 0.1329 0.970 +1.758 +0.42 120 . − . X-4 12 36 52.64 13 11 40.9 121.6 2 917−1.073 1 00−0.00 0.0496 5.000 . +1.730 . +0.46 X-5 12 36 53.05 13 11 40.0 122.8 2 500−0.959 0 00−0.30 0.2061 0.500 . +2.053 − . +0.34 X-6 12 36 53.67 13 11 54.0 139.3 4 583−1.336 0 45−0.22 0.5263 1.192 . +2.053 − . +0.34 X-7 12 36 40.11 13 10 08.8 150.0 4 583−1.336 0 45−0.22 0.5263 1.192 . +2.226 − . +0.30 X-8 12 36 37.98 13 10 51.1 191.6 5 833−1.518 0 29−0.21 0.5985 0.888 . +2.449 − . +0.24 X-9 12 36 39.62 13 11 38.2 192.0 7 917−1.782 0 68−0.14 0.9797 1.706 . +1.471 − . +0.66 X-10 12 36 38.84 13 12 34.2 237.2 1 250−0.637 0 33−0.35 0.1329 0.970 . +1.730 . +0.46 X-11 12 36 34.55 13 08 42.2 240.4 2 500−0.959 0 00−0.30 0.2061 0.500 . +1.803 . +0.43 X-12 12 36 43.41 13 15 13.1 341.7 2 917−1.045 0 14−0.28 0.2404 0.500 . +1.471 − . +0.66 NGC 4579 N 12 37 43.52 11 49 05.4 0.5 1 250−0.637 0 33−0.35 0.1323 0.970 . +25.847 − . +0.01 X-1 12 37 43.61 11 49 07.4 2.9 1626 9−25.274 0 55−0.01 183.2740 1.384 . +25.898 − . +0.01 X-2 12 37 44.41 11 49 10.1 14.5 1635 0−25.325 0 55−0.01 184.1871 1.390 . +1.689 − . +0.47 X-3 12 37 45.40 11 49 07.2 28.5 2 500−0.989 1 00−0.00 0.0422 5.000 . +1.369 . +0.76 X-4 12 37 41.48 11 49 05.5 30.3 0 833−0.487 0 00−0.41 0.0684 0.500 . +1.566 . +0.56 X-5 12 37 43.85 11 48 27.2 38.2 1 667−0.759 0 00−0.34 0.1369 0.500 . +1.369 . +0.76 X-6 12 37 45.74 11 49 31.3 42.7 0 833−0.487 0 00−0.41 0.0684 0.500 . +1.353 − . +0.97 X-7 12 37 41.50 11 49 54.6 58.0 0 833−0.536 1 00−0.00 0.0141 5.000 Table 3.2 (cont’d)

Source ID RA Dec ∆nuc Cnt Rate HR LX (0.2–8 keV) Γ − − − (J2000) (00) (10 3 s 1) (1038 erg s 1) (1) (2) (3) (4) (5) (6) (7) . +1.798 − . +0.44 X-8 12 37 42.20 11 48 09.0 59.3 2 917−1.046 0 43−0.26 0.3286 1.143 . +1.353 − . +0.97 X-9 12 37 45.10 11 51 20.2 137.3 0 833−0.536 1 00−0.00 0.0141 5.000 . +1.450 − . +0.77 X-10 12 37 43.71 11 46 44.2 140.8 1 250−0.678 1 00−0.00 0.0211 5.000 . +1.353 − . +0.97 X-11 12 37 41.87 11 51 30.1 147.1 0 833−0.536 1 00−0.00 0.0141 5.000 . +1.689 − . +0.47 X-12 12 37 41.68 11 46 11.3 175.9 2 500−0.989 1 00−0.00 0.0422 5.000 . +1.450 − . +0.77 X-13 12 37 45.37 11 44 38.8 267.7 1 250−0.678 1 00−0.00 0.0211 5.000 . +1.864 − . +0.41 NGC 4594 X-1 12 39 59.43 -11 37 23.5 10.5 3 333−1.125 0 50−0.24 0.4101 1.322 +8.533 +0.05 121 . − . X-2 12 39 57.36 -11 37 20.6 22.8 151 250−7.930 0 40−0.05 17.5225 1.125 . +2.725 − . +0.13 X-3 12 40 00.32 -11 37 24.0 23.2 11 250−2.150 1 00−0.00 0.2596 5.000 . +1.784 − . +0.44 X-4 12 40 00.05 -11 37 09.2 26.6 2 917−1.048 0 71−0.19 0.3822 1.844 . +1.864 − . +0.41 X-5 12 40 01.03 -11 37 24.6 33.6 3 333−1.125 0 50−0.24 0.4101 1.322 . +2.136 − . +0.28 X-6 12 40 00.95 -11 37 02.7 41.1 5 417−1.462 0 85−0.11 0.6704 2.337 . +2.405 − . +0.24 X-7 12 39 59.30 -11 38 29.1 61.5 7 500−1.732 0 67−0.15 0.9794 1.709 . +2.850 − . +0.21 X-8 12 39 59.86 -11 36 23.5 66.4 11 667−2.176 0 21−0.16 1.1682 0.797 . +1.912 − . +0.37 X-9 12 39 59.66 -11 35 25.4 123.3 3 750−1.202 0 78−0.16 0.4860 2.052 . +1.798 − . +0.44 X-10 12 40 00.67 -11 35 20.1 130.9 2 917−1.046 0 43−0.26 0.3443 1.180 . +1.650 − . +0.51 X-11 12 40 05.34 -11 35 00.5 177.1 2 083−0.865 0 20−0.31 0.2058 0.772 . +8.745 − . +0.05 NGC 4639 N 12 42 52.38 13 15 26.6 0.5 159 583−8.146 0 45−0.04 18.1161 1.183 . +1.823 − . +0.38 X-1 12 42 51.19 13 14 39.9 49.7 3 333−1.151 1 00−0.00 0.0545 5.000 . +1.784 − . +0.44 X-2 12 42 53.41 13 13 46.1 101.6 2 917−1.048 0 71−0.19 0.3563 1.785 . +1.560 − . +0.59 X-3 12 42 54.38 13 23 56.2 510.7 1 667−0.760 0 50−0.29 0.1939 1.278 . +2.893 − . +0.17 NGC 4736 N 12 50 53.03 41 07 12.4 0.6 12 500−2.254 0 73−0.11 1.4413 1.794 . +1.369 . +0.76 X-1 12 50 53.32 41 07 14.1 5.3 0 833−0.487 0 00−0.41 0.0673 0.500 . +1.471 . +0.66 X-2 12 50 52.71 41 07 19.2 8.4 1 250−0.637 0 33−0.35 0.1009 0.500 Table 3.2 (cont’d)

Source ID RA Dec ∆nuc Cnt Rate HR LX (0.2–8 keV) Γ − − − (J2000) (00) (10 3 s 1) (1038 erg s 1) (1) (2) (3) (4) (5) (6) (7) . +6.373 − . +0.06 X-3 12 50 52.56 41 07 02.1 11.9 80 417−5.777 0 61−0.05 9.2720 1.465 . +2.029 − . +0.32 X-4 12 50 53.70 41 07 18.5 12.3 4 583−1.338 0 82−0.13 0.5042 2.085 . +2.162 − . +0.31 X-5 12 50 53.31 41 07 00.0 12.8 5 417−1.460 0 54−0.19 0.6126 1.319 . +4.084 − . +0.08 X-6 12 50 52.10 41 06 54.9 21.8 30 000−3.518 0 92−0.04 2.7308 2.617 . +2.083 − . +0.30 X-7 12 50 50.31 41 07 12.3 40.4 5 000−1.402 0 83−0.12 0.5413 2.148 . +3.398 − . +0.14 X-8 12 50 47.60 41 05 12.4 144.5 18 750−2.772 0 69−0.10 2.1769 1.668 . +2.059 − . +0.34 X-9 12 50 04.00 41 05 16.0 744.1 4 583−1.336 0 27−0.23 0.4451 0.833 +1.641 +0.53 122 . − . NGC 4826 X-1 12 56 43.67 21 40 57.1 11.2 2 083−0.867 0 60−0.25 0.2603 1.495 . +2.001 . +0.36 X-2 12 56 45.81 21 41 03.2 24.2 4 167−1.269 0 20−0.25 0.3518 0.500 . +2.053 . +0.34 X-3 12 56 41.60 21 41 03.5 39.1 4 583−1.336 0 45−0.22 0.3870 0.500 . +1.641 − . +0.53 X-4 12 56 42.05 21 41 34.6 43.8 2 083−0.867 0 60−0.25 0.2603 1.495 . +1.560 . +0.59 X-5 12 56 43.95 21 39 57.2 67.9 1 667−0.760 0 50−0.29 0.1407 0.500 . +1.615 − . +0.54 X-6 12 56 32.88 21 40 58.4 170.0 2 083−0.898 1 00−0.00 0.0368 5.000 . +1.730 . +0.46 X-7 12 56 32.67 21 40 23.9 177.7 2 500−0.959 0 00−0.30 0.2111 0.500 . +1.641 − . +0.53 X-8 12 56 45.59 21 38 05.5 180.7 2 083−0.867 0 60−0.25 0.2603 1.495 . +1.945 − . +0.31 X-9 12 56 14.01 21 39 23.9 464.1 4 167−1.293 1 00−0.00 0.0736 5.000 . +1.536 − . +0.64 X-10 12 56 58.70 21 50 04.2 581.4 1 667−0.795 1 00−0.00 0.0295 5.000 . +1.871 − . +0.40 NGC 5033 N 13 13 27.48 36 35 38.1 2.4 3 333−1.125 0 25−0.26 0.3104 0.783 . +3.514 − . +0.15 X-1 13 13 29.65 36 35 23.0 35.0 20 000−2.865 0 33−0.12 1.9788 0.923 . +1.450 − . +0.77 X-2 13 13 29.45 36 35 17.3 35.7 1 250−0.678 1 00−0.00 0.0136 5.000 . +1.536 − . +0.64 X-3 13 13 25.18 36 35 43.5 36.4 1 667−0.795 1 00−0.00 0.0181 5.000 . +1.650 − . +0.51 X-4 13 13 24.78 36 35 03.7 55.6 2 083−0.865 0 20−0.31 0.1864 0.702 . +1.560 . +0.59 X-5 13 13 24.89 36 36 56.2 86.6 1 667−0.760 0 50−0.29 0.1326 0.500 . +14.574 − . +0.03 X-6 13 13 35.55 36 34 04.4 152.6 469 167−13.977 0 29−0.03 45.1615 0.855 Table 3.2 (cont’d)

Source ID RA Dec ∆nuc Cnt Rate HR LX (0.2–8 keV) Γ − − − (J2000) (00) (10 3 s 1) (1038 erg s 1) (1) (2) (3) (4) (5) (6) (7) . +3.090 − . +0.14 X-7 13 13 39.39 36 37 17.6 202.1 15 000−2.475 0 83−0.08 1.5628 2.121 . +1.803 − . +0.43 X-8 13 13 14.26 36 34 16.9 216.5 2 917−1.045 0 14−0.28 0.2489 0.612 . +2.367 − . +0.26 X-9 13 13 15.60 36 32 56.2 243.1 7 083−1.681 0 53−0.17 0.7761 1.284 . +1.850 − . +0.40 X-10 13 13 51.28 36 36 20.4 357.5 3 333−1.127 0 75−0.17 0.3694 1.822 . +1.471 − . +0.66 X-11 13 12 58.16 36 34 26.7 447.6 1 250−0.637 0 33−0.35 0.1237 0.923 . +1.727 − . +0.47 X-12 13 13 17.13 36 42 43.7 452.1 2 500−0.959 0 33−0.29 0.2474 0.923 . +1.689 − . +0.47 NGC 5055 N 13 15 49.28 42 01 46.6 1.6 2 500−0.989 1 00−0.00 0.0297 5.000 +1.871 +0.40 123 . − . X-1 13 15 49.57 42 01 27.1 18.4 3 333−1.125 0 25−0.26 0.3127 0.785 . +1.471 . +0.66 X-2 13 15 50.95 42 01 59.9 28.9 1 250−0.637 0 33−0.35 0.1000 0.500 . +1.650 − . +0.51 X-3 13 15 51.39 42 01 40.8 31.6 2 083−0.865 0 20−0.31 0.1875 0.703 . +3.416 − . +0.07 X-4 13 15 46.64 42 02 01.3 43.1 20 000−2.876 1 00−0.00 0.2379 5.000 . +2.203 − . +0.28 X-5 13 15 53.25 42 02 15.2 66.4 5 833−1.519 0 71−0.15 0.6633 1.729 . +1.758 − . +0.42 X-6 13 15 53.89 42 01 04.7 79.7 2 917−1.073 1 00−0.00 0.0347 5.000 . +1.784 − . +0.44 X-7 13 15 43.36 42 01 50.7 89.3 2 917−1.048 0 71−0.19 0.3317 1.729 . +2.838 − . +0.20 X-8 13 15 49.46 41 59 51.9 113.1 11 667−2.176 0 50−0.14 1.2779 1.232 . +1.996 − . +0.36 X-9 13 15 40.83 42 01 49.6 127.1 4 167−1.270 0 40−0.23 0.4337 1.044 . +1.689 − . +0.47 X-10 13 15 58.82 42 02 03.9 144.0 2 500−0.989 1 00−0.00 0.0297 5.000 . +1.641 − . +0.53 X-11 13 15 39.31 42 01 54.0 150.1 2 083−0.867 0 60−0.25 0.2358 1.442 . +2.280 . +0.29 X-12 13 15 39.49 42 02 27.0 153.1 6 250−1.574 0 20−0.21 0.4998 0.500 . +1.823 − . +0.38 X-13 13 15 39.25 42 00 30.7 168.1 3 333−1.151 1 00−0.00 0.0397 5.000 . +1.730 . +0.46 X-14 13 15 48.52 42 04 32.7 168.2 2 500−0.959 0 00−0.30 0.1999 0.500 . +7.594 − . +0.05 X-15 13 15 43.85 41 59 10.4 174.9 117 917−7.000 0 55−0.05 13.1847 1.344 . +2.801 − . +0.20 X-16 13 15 37.62 42 02 13.4 177.5 11 250−2.136 0 48−0.15 1.2222 1.196 . +3.032 − . +0.12 X-17 13 16 02.26 42 01 53.7 194.6 14 583−2.441 0 94−0.05 1.1481 2.841 Table 3.2 (cont’d)

Source ID RA Dec ∆nuc Cnt Rate HR LX (0.2–8 keV) Γ − − − (J2000) (00) (10 3 s 1) (1038 erg s 1) (1) (2) (3) (4) (5) (6) (7) . +1.730 . +0.46 X-18 13 15 36.34 42 01 24.7 195.5 2 500−0.959 0 00−0.30 0.1999 0.500 . +2.211 − . +0.22 X-19 13 15 37.31 42 03 32.0 209.2 6 250−1.594 1 00−0.00 0.0743 5.000 . +2.413 − . +0.25 X-20 13 16 05.68 42 01 15.0 247.6 7 500−1.732 0 56−0.17 0.8388 1.345 . +2.449 − . +0.24 X-21 13 15 30.17 42 03 13.6 300.3 7 917−1.782 0 68−0.14 0.9031 1.647 . +1.823 − . +0.38 X-22 13 15 19.50 42 03 02.2 453.7 3 333−1.151 1 00−0.00 0.0397 5.000 . +1.927 . +0.38 X-23 13 15 18.12 42 04 04.5 488.0 3 750−1.200 0 56−0.22 0.2999 0.500 . +1.536 − . +0.64 X-24 13 15 08.57 42 01 12.8 611.9 1 667−0.795 1 00−0.00 0.0198 5.000 +4.690 +0.08 124 . − . X-25 13 14 59.15 41 58 38.4 775.1 40 833−4.109 0 82−0.06 4.4129 2.067 . +1.972 − . +0.34 X-26 13 14 54.74 42 02 39.6 820.2 4 167−1.272 0 80−0.14 0.4567 2.005 . +1.369 . +0.76 NGC 5195 X-1 13 29 58.37 47 16 12.6 9.9 0 833−0.487 0 00−0.41 0.0691 0.500 . +2.226 − . +0.30 X-2 13 30 00.40 47 15 58.4 26.1 5 833−1.518 0 29−0.21 0.5763 0.824 . +1.641 − . +0.53 X-3 13 29 53.68 47 16 45.2 85.8 2 083−0.867 0 60−0.25 0.2429 1.426 . +1.996 − . +0.36 X-4 13 30 02.96 47 15 06.6 85.9 4 167−1.270 0 40−0.23 0.4450 1.024 . +1.784 − . +0.44 X-5 13 29 54.60 47 14 36.7 106.8 2 917−1.048 0 71−0.19 0.3428 1.716 . +2.059 − . +0.34 X-6 13 30 06.90 47 15 43.4 124.8 4 583−1.336 0 27−0.23 0.4481 0.802 . +1.471 − . +0.66 X-7 13 29 59.18 47 13 21.9 162.3 1 250−0.637 0 33−0.35 0.1278 0.906 . +2.378 − . +0.22 X-8 13 29 59.82 47 12 12.4 232.2 7 500−1.734 0 89−0.09 0.7560 2.413 . +2.285 − . +0.24 X-9 13 29 51.60 47 11 55.3 270.6 6 667−1.631 0 88−0.10 0.6918 2.332 . +1.560 − . +0.59 X-10 13 30 16.65 47 15 17.6 273.2 1 667−0.760 0 50−0.29 0.1877 1.214 . +3.514 − . +0.13 X-11 13 29 53.68 47 11 40.9 273.7 20 417−2.895 0 71−0.09 2.3996 1.716 . +2.466 − . +0.20 X-12 13 29 38.81 47 16 15.1 298.6 8 333−1.831 0 90−0.08 0.8167 2.483 . +4.751 − . +0.05 X-13 13 30 08.42 47 11 07.0 330.9 42 917−4.214 0 96−0.02 3.0775 3.077 . +1.715 − . +0.48 X-14 13 29 39.46 47 18 55.5 335.7 2 500−0.961 0 67−0.22 0.2944 1.587 . +2.053 . +0.34 X-15 13 29 40.87 47 12 38.0 337.5 4 583−1.336 0 45−0.22 0.3798 0.500 Table 3.2 (cont’d)

Source ID RA Dec ∆nuc Cnt Rate HR LX (0.2–8 keV) Γ − − − (J2000) (00) (10 3 s 1) (1038 erg s 1) (1) (2) (3) (4) (5) (6) (7) . +1.641 − . +0.53 X-16 13 30 18.32 47 13 17.6 338.1 2 083−0.867 0 60−0.25 0.2429 1.426 . +2.053 − . +0.34 X-17 13 29 44.30 47 11 35.4 344.7 4 583−1.336 0 45−0.22 0.5047 1.125 . +4.844 . +0.10 NGC 5273 N 13 42 08.35 35 39 14.6 0.8 42 917−4.214 0 26−0.09 3.4126 0.500 . +1.823 − . +0.38 X-1 13 42 08.99 35 39 28.7 17.1 3 333−1.151 1 00−0.00 0.0356 5.000 . +1.641 − . +0.53 X-2 13 42 08.43 35 43 33.5 258.5 2 083−0.867 0 60−0.25 0.2322 1.431 . +1.823 − . +0.38 X-3 13 41 54.06 35 36 07.6 284.1 3 333−1.151 1 00−0.00 0.0356 5.000 . +1.566 . +0.56 X-4 13 41 48.49 35 40 04.6 301.3 1 667−0.759 0 00−0.34 0.1325 0.500 +1.615 +0.54 125 . − . X-5 13 42 31.00 35 35 16.1 416.0 2 083−0.898 1 00−0.00 0.0222 5.000 . +2.099 − . +0.31 X-6 13 41 33.74 35 36 36.8 541.9 5 000−1.400 0 67−0.18 0.5610 1.588 . +1.715 − . +0.48 X-7 13 41 50.27 35 30 05.0 612.9 2 500−0.961 0 67−0.22 0.2805 1.588 . +3.890 − . +0.12 X-8 13 41 33.06 35 32 52.5 652.5 25 833−3.261 0 55−0.10 2.8422 1.320 . +3.065 − . +0.12 NGC 6500 N 17 55 59.78 18 20 17.9 1.3 15 000−2.476 0 94−0.04 1.8469 3.275 . +1.798 − . +0.44 X-1 17 56 01.58 18 20 22.8 28.6 2 917−1.046 0 43−0.26 0.3991 1.293 . +1.650 − . +0.51 X-2 17 55 56.44 18 19 10.5 83.6 2 083−0.865 0 20−0.31 0.2347 0.869 . +1.641 − . +0.53 X-3 17 55 52.78 18 20 35.6 105.3 2 083−0.867 0 60−0.25 0.3155 1.673 . +1.641 − . +0.53 X-4 17 56 03.76 18 22 23.4 139.1 2 083−0.867 0 60−0.25 0.3155 1.673 . +2.647 − . +0.19 NGC 6503 X-1 17 49 28.96 70 08 43.1 29.5 10 000−2.011 0 83−0.10 1.3018 2.304 . +2.099 − . +0.31 X-2 17 49 31.59 70 08 19.4 73.5 5 000−1.400 0 67−0.18 0.6771 1.735 . +1.715 − . +0.48 X-3 17 49 26.58 70 06 51.1 114.0 2 500−0.961 0 67−0.22 0.3385 1.735 . +2.524 − . +0.21 X-4 17 49 12.43 70 09 30.3 223.2 8 750−1.877 0 81−0.11 1.1593 2.201 . +2.002 . +0.36 X-5 17 48 51.64 70 07 48.6 533.5 4 167−1.269 0 00−0.25 0.3542 0.500 . +1.803 . +0.43 X-6 17 50 12.46 70 04 54.4 719.9 2 917−1.045 0 14−0.28 0.2479 0.500 . +1.945 − . +0.31 X-7 17 48 31.79 70 08 10.7 828.8 4 167−1.293 1 00−0.00 0.1051 5.000 . +1.798 − . +0.44 X-8 17 50 25.17 70 00 57.6 989.9 2 917−1.046 0 43−0.26 0.3567 1.204 Table 3.2 (cont’d)

Source ID RA Dec ∆nuc Cnt Rate HR LX (0.2–8 keV) Γ − − − (J2000) (00) (10 3 s 1) (1038 erg s 1) (1) (2) (3) (4) (5) (6) (7) . +2.521 . +0.25 X-9 17 50 56.12 69 58 56.8 1460.4 8 333−1.829 0 00−0.19 0.7084 0.500

Note. — (1) Gives the source identifier, ordered by increasing distance from the nucleus. An exclamation point indicates a source with heavy pileup. (2) J2000 coordinates for the source. (3) Source distance from nucleus. (4) Observed count rate per ks. and the Poissonian error in count rate (5) Hardness ratio, defined between 0.2–2 keV and 2–8 keV. and the error in hardness ratio from counting statistics. (6) Inferred source luminosity (see text), in 126 units of 1038 erg s−1. (7) The photon power law index that is inferred from the hardness ratio. Figure 3.3 “Colour magnitude” diagram, luminosity function and cumula- tive luminosity function for the targets NGC 253, NGC 404, NGC 660 and NGC 1052. The top panel plots source hardness ratio against luminosity, analogous to a colour-magnitude diagram127 from optical astronomy. For mea- suring the hardness ratio, a hard band (2–8 keV) and a soft band (0.2–2 keV) were used. Sources along the 1 hardness ratio line were not detected at all − in the hard band. The middle plot shows the distribution of sources with the 0.2–8 keV X-ray luminosity. The lower panel is a cumulative luminos- ity function derived from the middle panel. This plot shows the fraction of sources brighter than the corresponding luminosity (again using the full band, 0.2–8 keV). Figure 3.4 Identical to 3.3, but for the galaxies NGC 1055, NGC 1058, NGC 2541 and NGC 2683.

128 Figure 3.5 Identical to 3.3, but for the galaxies NGC 2787, NGC 2841, NGC 3031 and NGC 3368.

129 Figure 3.6 Identical to 3.3, but for the galaxies NGC 3486, NGC 3489, NGC 3623 and NGC 3627.

130 Figure 3.7 Identical to 3.3, but for the galaxies NGC 3628, NGC 3675, NGC 4150 and NGC 4203.

131 Figure 3.8 Identical to 3.3, but for the galaxies NGC 4278, NGC 4314, NGC 4321 and NGC 4374.

132 Figure 3.9 Identical to 3.3, but for the galaxies NGC 4395, NGC 4414, NGC 4494 and NGC 4565.

133 Figure 3.10 Identical to 3.3, but for the galaxies NGC 4569, NGC 4579, NGC 4594 and NGC 4639.

134 Figure 3.11 Identical to 3.3, but for the galaxies NGC 4725, NGC 4736, NGC 4826 and NGC 5033.

135 Figure 3.12 Identical to 3.3, but for the galaxies NGC 5055, NGC 5195, NGC 5273 and NGC 6500.

136 Figure 3.13 Identical to 3.3, but for the galaxy NGC 6503.

137 Figure 3.14 180 180 images of NGC 253, NGC 404, NGC 660 and NGC 1052. ×

138 Figure 3.15 Identical to 3.14, but for the galaxies NGC 1055, NGC 1058, NGC 2541 and NGC 2683.

139 Figure 3.16 Identical to 3.14, but for the galaxies NGC 2787, NGC 2841, NGC 3031 and NGC 3368.

140 Figure 3.17 Identical to 3.14, but for the galaxies NGC 3486, NGC 3489, NGC 3623 and NGC 3627.

141 Figure 3.18 Identical to 3.14, but for the galaxies NGC 3628, NGC 3675, NGC 4150 and NGC 4203.

142 Figure 3.19 Identical to 3.14, but for the galaxies NGC 4278, NGC 4314, NGC 4321 and NGC 4374.

143 Figure 3.20 Identical to 3.14, but for the galaxies NGC 4395, NGC 4414, NGC 4494 and NGC 4565.

144 Figure 3.21 Identical to 3.14, but for the galaxies NGC 4569, NGC 4579, NGC 4594 and NGC 4639.

145 Figure 3.22 Identical to 3.14, but for the galaxies NGC 4725, NGC 4736, NGC 4826 and NGC 5033.

146 Figure 3.23 Identical to 3.14, but for the galaxies NGC 5055, NGC 5195, NGC 5273 and NGC 6500.

147 Figure 3.24 Identical to 3.14, but for the galaxy NGC 6503.

148 Chapter 4

Nova Sco and coalescing low mass black hole binaries as LIGO sources

Abstract

Double neutron star (NS-NS ) binaries, analogous to the well known Hulse– Taylor pulsar PSR 1913+16 (Hulse & Taylor, 1975b), are guaranteed-to- exist sources of high frequency gravitational radiation detectable by LIGO. There is considerable uncertainty in the estimated rate of coalescence of such systems (Phinney, 1991; Narayan et al., 1991; Kalogera et al., 2001), with conservative estimates of 1 per million years per galaxy, and opti- ∼ mistic theoretical estimates one or more magnitude larger. Formation rates of low-mass black hole-neutron star binaries may be higher than those of NS-NS binaries, and may dominate the detectable LIGO signal rate. Rate estimates for such binaries are plagued by severe model uncertainties. Re- cent estimates suggest that BH-BH binaries do not coalesce at significant rates despite being formed at high rates (Portegies Zwart & Yungelson, 1998; de Donder & Vanbeveren, 1998).

149 We estimate the enhanced coalescence rate for BH-BH binaries due to weak asymmetric kicks during the formation of low mass black holes like Nova Sco (Brandt et al., 1995), and find they may contribute significantly to the LIGO signal rate, possibly dominating the phase I detectable signals if the range of BH masses for which there is significant kick is broad enough. For a standard Salpeter IMF, assuming mild natal kicks, we project that the

R6 merger rate (the rate of mergers per million years in a Milky Way-like galaxy) of BH-BH systems is 0.5, smaller than that of NS-NS systems. ∼ However, the higher chirp mass of these systems produces a signal nearly four times greater, on average, with a commensurate increase in search vol- ume. Hence, our claim that BH-BH mergers (and, to a lesser extent, BH- NS coalescence) should comprise a significant fraction of the signal seen by LIGO. The BH-BH coalescence channel considered here also predicts that a substantial fraction of BH-BH systems should have at least one component with near-maximal spin (a/M 1). This is from the spin-up provided by the ∼ fallback material after a supernova. If no mass transfer occurs between the two supernovae, both components could be spinning rapidly. The waveforms produced by the coalescence of such a system should produce a clear spin signature, so this hypothesis could be directly tested by LIGO.

4.1 Introduction

With the arrival of LIGO, and other planned gravitational radiation ob- servatories, the nascent field of gravitational radiation astronomy is set to prosper, if there are detectable sources in the local universe. A consider- able amount of effort has been directed towards identifying potential grav-

150 itational radiation sources, and the relative rate of contribution of these sources to the anticipated signals. The canonical scenario envisioned is the final coalescence of a binary neutron star system (NS-NS), where the pair’s orbital energy has been radiated away by gravitational waves. NS-NS merger can produce a copious signal for LIGO, if they occur at high enough a rate locally — current estimates for LIGO phase I place the maximum detection radius for such an event at 20 Mpc or less (Kalogera ∼ et al., 2001). The merger rate of NS-NS binaries can be estimated from observed systems (Phinney, 1991; Narayan et al., 1991), such estimates are plagued by small number statistics and possible observer biases (Kalogera, 1998; Kalogera et al., 2001). Alternatively, the rate can be estimated from ab initio theoretical models (see review by Grishchuk et al. 2000, also Portegies Zwart & Yungelson 1998; Belczynski et al. 2002; Fryer 1999; Bloom et al. 1999). A number of authors have explored binary population synthesis models, making a number of assumptions about the input physics, leading to rates consistent with observational constraints, but uncertain by 1–2 orders of magnitude (Portegies Zwart & Yungelson, 1998; Kalogera, 1998; Kalogera & Lorimer, 2000; Bloom et al., 1999; de Donder & Vanbeveren, 1998; Bel- czynski´ & Bulik, 1999; Lipunov et al., 1997; Brandt & Podsiadlowski, 1995; Belczynski et al., 2002; Fryer, 1999) . Conventionally, the rates are expressed in terms of R6, the merger rate per million years per Milky Way-like galaxy, assuming normal rates of star formation. Then the rate in the local universe is the integrated rate over the number density of galaxies, the rate per galaxy, scaled to the Milky Way rate, per detection volume. Kalogera et al. (2001) find a LIGO I event rate of 3 10−4 y−1 for NS-NS mergers within 20 Mpc, × assuming R6 = 1. For a given detector sensitivity, higher mass coalescences

151 are detectable to larger volumes, with the detection distance, d M 5/6 , L ∝ chirp 3/5 1/5 where Mchirp = (m1m2) /(m1 + m2) (Thorne, 1994). Since black holes are expected to have masses several times larger than neutron stars, and the 3 event rate scales as dL (for dL small compared to the size of the universe), a black hole coalescence rate of order R6 implies event rates 2–3 orders of magnitude higher. The problem of accurately estimating the coalescence rate of compact binaries can be appreciated by noting that the type II supernovae rate in the Milky Way is 1–2 per century, implying that the rate of type II supernova in binaries is about 10−2 y−1, given a 50% binarity rate. Estimates of the −6 −1 coalescence rate are canonically close to R6 = 10 y per Milky Way. So the branching ratio for type II supernovae to form merging systems is of the order 10−4. Calculating the mean rate, averaged over all scenarios for coalescence, in the local universe, is hard, with small errors of assumption about the physics of stellar evolution leading to large fractional changes in the branching ratios of particular channels for mergers. Theoretical models require a series of assumptions, about the mass func- tion of high mass stars, the cut-off points for which zero age masses lead to NS or BH formation, the binary fraction and mass ratio distribution, the amount of mass loss during (binary) stellar evolution, and the amplitude and distribution of natal kicks. Secondary assumptions, that are usually not explored in detail, include the dependence of all of the above on metal- licity and environment in which the massive stars form; and the possibility that the NS/BH cut-off, and the natal kick, may depend on stellar rota- tion and magnetic fields. In fact, it is not implausible that the NS/BH formation boundary is “fuzzy”, that there is not a sharp border in zero-age

152 mass between stars that form neutron stars and those which form black holes. A further potential confounding effect, is that natal kicks are gener- ally assumed to be random, but may in principle be correlated with some macroscopic property of the progenitor star, such as rotation (e.g. Spruit & Phinney 1998; Pfahl et al. 2002). There are two arguments against a high rate of coalescence of compact binaries: most high mass binaries become unbound during the near instan- taneous mass-loss at supernova; the second problem is that of the ‘kicks’ believed to be inflicted upon the NS from an asymmetrical supernova blast. While the range of energies imparted by the kick is a subject of intense de- bate (Lyne & Lorimer, 1994; Hansen & Phinney, 1997; Tauris & Savonije, 1999; Cordes & Chernoff, 1998; Fryer et al., 1998; Arzoumanian et al., 2002), the resulting velocity change is believed to be of the order 250 km sec−1 for a 1.4 M neutron star. A properly aligned kick can allow the system to remain bound, albeit with dramatically altered orbital parameters, but a random kick is unlikely to be directed so fortuitously, with the extra energy making a bound final state even less likely. An alternative to the NS-NS scenario is one in which both stars are of sufficient mass to end up as black holes. The minimum mass required for black hole formation is not well known, and is heavily influenced by the evolutionary history of the black hole candidate (see Fryer 1999; Fryer & Kalogera 2001). Accretion induced spin-up of the star prior to collapse could result in a higher minimum mass threshold, while the presence of strong winds could drop the progenitor mass below the required minimum. Finally, unless an unusually flat IMF is assumed (as apparently seen in certain starburst galaxies, see, for example, Doane & Mathews 1993), few of these objects will be produced in the first place.

153 Nevertheless, precursors to black hole binary systems are more likely to survive both supernovae due to the smaller fractional mass loss during the event. Depending upon the mass of the star, a significant amount of material can fall back upon it just after the blast. Indeed, a sufficiently massive progenitor may not undergo a supernova at all, reaching a point where nearly all of the material is quickly reabsorbed (Fryer, 1999). After losing a significant fraction of mass to stellar winds and (possibly) two supernovae, a typical bound binary system will have expanded considerably, with most

Porb > 10days. Long-period systems do not decay in less than a Hubble time from gravitational radiation, and hence will never reach a frequency range useful to LIGO. However, including asymmetric supernova kicks changes the picture significantly. Assuming that the total momentum change is approximately the same for all supernovae, the velocity imparted to the nascent black hole will be scaled to its mass, via ∆vBH = ∆vNSMNS/MBH

(see Grishchuk et al 2001 for review). For a typical 7 M hole, this gives a kick of the order 50 km s−1, comparable to or larger than the orbital ∼ speed, but not so large as to always rip the system apart. Systems that remain bound are generally in highly eccentric orbits, which expedites their merger through emission of gravitational radiation. Ultimately, the point is this: the trace of the metric perturbation from gravitational waves, varies as h M 5/6 . As the maximum detection radius ∝ chirp scales linearly with h, the maximum search volume scales as V M 5/2 . ∝ chirp The implied several hundred-fold increase in search volume means that, even if only a small fraction of these systems can merge in τ < 1/H0, they may dominate the detected signal. Our approach is to concentrate on estimating the event rate from one particular coalescence channel. The total branching ratio for coalescence is

154 of course the sum of all possible channels, and it is possible that other chan- nels contribute significantly to the event rate, possibly dominating the total rate; for example, dynamical evolution of cluster binaries may create new channels for merger with high coalescence rates (Sigurdsson & Hernquist, 1993; Portegies Zwart & McMillan, 2000), or accretion induced collapse of neutron stars with soft cores may lead to enhanced rates (Bethe & Brown, 1998). Here, rather than trying to estimate the total event rate, we make an observationally motivated estimate of the rate for one particular channel.

4.2 Example of Nova Sco

Nova Sco 1994 (GRO J1655-40) is a strong candidate for being a black hole binary (Bailyn et al., 1995; Orosz & Bailyn, 1997), with the primary being a

6.3 0.5M black hole (Greene et al., 2001; Shahbaz et al., 1999). Perhaps  its most remarkable feature is an unusually high space velocity, whose lower limit of 106 km s−1was, until recently, several times greater than any other known black hole transient (Shahbaz et al., 1999; Brandt et al., 1995). The likely true space velocity is greater by a factor of √3, adjusting for mean projection effects. A number of scenarios have been put forward to explain the unusual speed of Nova Sco. Brandt et al. (1995) point out that the momentum component of Nova Sco along the line of sight is comparable to that of a single 1.4 M neutron star, having received a natal kick in the range 300–700 km s−1. This is not an unreasonable value for a neutron star kick (Lyne & Lorimer, 1994; Cordes & Chernoff, 1998; Fryer et al., 1998), and so lends strength to the possibility that Nova Sco can be explained by the primary experiencing a natal kick prior to formation of the black hole. Invoking

155 Blaauw-Boersma kicks (Blaauw, 1961) as the sole acceleration mechanism invites difficulty, as the low mass of the secondary means that most Blaauw- Boersma kicks strong enough to give the observed speed would also disrupt the binary system completely (Brandt et al., 1995). This is not to say that such a scenario is impossible (see, for example, Nelemans et al., 1999). However, the space velocity measurement of the X-ray nova XTE J1118+480 has provided a further example of a black hole binary with a high-velocity Galactic-halo orbit. Mirabel et al. (2001) used the VLBA to obtain a precise proper motion for the system, calculating a speed of 145 35 km s−1, with  respect to the local standard of rest. The system primary has a mass function of 6.0 0.4M (McClintock et al., 2001), with a faint ( 19 mag) optical  ∼ counterpart. To accelerate this system to the observed peculiar velocity using Blaauw-Boersma kicks alone, roughly 40 M of material would have to be expelled during stellar collapse, an implausibly large amount of matter. This issue remains contentious, however, as calculations in Nelemans et al. (1999) show that the velocity of Nova Sco, at least, might be explained by a symmetric supernova where the black hole progenitor lost more than half of its mass. This is marginally possible, but becomes much more tenuous if Nova Sco turns out to have a significant transverse velocity. One principal difficulty with the natal kick premise is arranging for suffi- cient neutrinos to drive a supernova explosion prior to being trapped by the formation of an event horizon, ejecting neutrinos or other material asymmet- rically. Few neutrinos escape if the horizon forms over the dynamical time of the collapsing core (Gourgoulhon & Haensel, 1993b). The drop in the resulting neutrino heating of the envelope allows most or all of the envelope to fall back onto the nascent black hole (see, for example, the hydrodynam- ical simulations of Janka & Mueller 1996), hence preventing the supernova.

156 However, there is now strong evidence that a supernova must have taken place in the Nova Sco system, from estimates of metal abundances in the atmosphere of the secondary star. Israelian et al. (1999b) show that the sec- ondary, an F3–F8 IV/III star, possesses a dramatic enhancement (factors of six to ten) in α elements such as oxygen, magnesium, silicon and sulfur (and see also the discussion in Podsiadlowski et al. 2002). Interestingly, no significant enhancement in iron was found. The implication is that the pro- genitor of the black hole did experience a supernova during its formation, and a significant amount of the former atmosphere was captured by its com- panion. As most of the iron core went on to collapse to a singularity, no enhancement of this particular element is seen. The question is then how long after the supernova it took for the black hole to form. One possibil- ity is that the star, at the instant of the supernova, experienced sufficient rotational support to avoid collapse for an extended period of time, until spin-down allowed the system to collapse to a black hole some time later. Another possible scenario has some of the material cast off in the supernova explosion recaptured by the newly-formed neutron star, elevating its mass above the threshold for collapse. In either case, a supernova is seen, with a corresponding asymmetric natal kick. More massive progenitors would form a horizon directly, with no possibility for a kick. We discuss limits for this behaviour in the next section. Nova Sco 1994 and XTE J1118+480 provide strong evidence that black holes do, in fact, experience natal asymmetric kicks, at least under some conditions. The resulting orbital eccentricities tend to accelerate binary coalescence from the enhanced radiation emitted at every periastron passage.

157 4.3 Population synthesis

We make use of a binary evolution code developed by Pols & Marinus (1994), and modified for use in NS-NS systems by Bloom et al. (1999). Our extension of the code allows for evolution to the black hole state, with assumptions about the mass function of such objects at the time of collapse. Initially, the code chooses the mass of the primary from a given mass function. For this work, we have chosen two power law IMFs, with indices α of 2.0 and 2.35 (the latter, of course, being the Salpeter IMF). In − − both cases, we established a lower cutoff of 4 M , confining the code to an interesting range of initial masses; i. e., where at least one supernova is possible. Our primary stellar models are taken from Maeder & Meynet (1989). The helium star models used are a mix of models from Habets (1986) and Paczynski (1971). We assume that the mass ratio distribution between the two components is flat. After choosing an initial separation a and eccentricity e after Pols & Marinus (1994), the code evolves each binary system until both components have reached their final degenerate form, accounting for mass-transfer-induced stellar regeneration and stellar winds. During the common-envelope phase, the orbit is circularised, and the orbital energy is reduced by the binding energy of the envelope divided by the common-envelope efficiency parameter, which we take to be 0.5. In other words, the orbital energy is reduced by twice the envelope binding energy. Neutron stars are formed from progenitors with ZAMS masses of between 8 and 20 M , inclusive, and are always given a mass of 1.4 M . More massive stars end up as black holes. As noted in the Introduction, this boundary is likely to be “fuzzy”, i.e., not a monotonic function of the progenitor mass, as it is strongly coupled to the spin state of the star prior to collapse, a quantity

158 which our code simply does not track. Even assuming this was known to perfect accuracy, it is far from trivial to estimate the effects of magnetic field and rotational support vis-a-vis the compact object’s end state. The black hole mass function (i. e., the post-collapse mass of a BH, given its mass just prior to the explosion) is highly speculative at this point, and is almost certainly not merely a function of initial mass, but also of angular momentum, to the extent that this determines the fraction of material falling back onto the collapsing star. In order to experience a kick, the black holes formation must be delayed somewhat, either from rotational support, or because event horizon formation occurs only after delayed fallback of mass initially ejected from the core. Fryer (1999) has performed core-collapse simulations in order to explore the critical mass for black hole formation, and their final masses. As a best working guess, we have constructed a mass relation from a quadratic fit to the limited data set found in Fryer

(1999). The mass of the black hole at formation (MBH ) is related to the 2 ZAMS mass of the progenitor (M ) by M = (M /25) 5.2M . We 0 BH 0 × have also chosen a simple criterion for whether a black hole will receive an asymmetric neutrino kick during collapse; namely, all objects below 40 M (referring to the ZAMS mass) experience a random kick. Above this limit, objects collapse directly to a black hole, with no kick. We explore the effect of ignoring black hole kicks in the next section. As a last step, the results of the code are normalised to the supernova rate of the Milky Way, 0.01 yr−1. Here, the code produces some arbitrarily large number of complete evolutionary sequences, including a large number of supernova events. Scaling all these events to the Milky Way SNR allows us to generate event rates out of data not previously ordered in time. This effectively simulates a constant star-formation rate, where the population of

159 merger candidates has reached a dynamic equilibrium.

4.4 Results

Tables 4.1 and 4.2 summarize the investigation. For each IMF, six simula- tions (generating 106 binary systems each) were run, varying two parame- ters: Kmax, the upper limit of the imparted kick speed (acting on a 1.4 M NS), and σ, the dispersion in the Maxwellian distribution of the kick speed. Maximum kick values were chosen at 500 km s−1(for σ = 90 km s−1and σ = 190 km s−1), and 1000 km s−1(for σ = 450 km s−1). The inclusion of the 90 km s−1kick intensity is based upon recent observational work on the velocity distribution of pulsars by Pfahl et al. (2002), which suggests a bi- modal kick distribution centered around 100 and 500 km s−1. Further ∼ ∼ discussions concerning this bi-modality can be found in Arzoumanian et al. (2002); Cordes & Chernoff (1998); Fryer et al. (1998). This range has been touched on in previous work (Grishchuk et al., 2000), but we have looked at it specifically as a new observationally-motivated choice in kick magnitude.

The following columns show the R6 rate of BH-BH , BH-NS , NS-NS and

BH-PSR pairs generated in the sample. R6 is a rate of 1 event per Myr per Milky Way galaxy, found by scaling event rates to the estimated local supernova rate of 0.01 yr−1. One must take into account that not all stars (and hence not all supernovae) occur in binaries; hence a binarity fraction must be assumed, and we take that value to be 0.5 throughout (i. e. roughly two-thirds of supernovae occur in a binary system). The alternating columns show the R6 of such pairs expected to coalesce through emission of gravita- tional radiation in less than the Hubble time (here, taken as 10 Gyr). Table 4.1 details the formation and merger rates when black holes and neutron

160 stars are given kicks as described above. Table 4.2 gives the relevant rates when black holes are not allowed to have asymmetric kicks of any kind (even if below 40 M ). Figure 4.1 show examples of the generated data sets. Here, the separa- tions of the BH-BH and BH-NS systems after the second supernova (i. e., stellar evolution has ended) are plotted against the post-mortem orbital eccentricity. Dots represent systems stable against orbital decay, whilst tri- angles represent those systems which will undergo coalescence in less than a Hubble time. Figure 4.2 shows the distribution of masses in surviving BH-BH binaries, irrespective of whether the system is unstable to orbital decay.. A clear bifurcation in mass is seen, with the vast majority at around

5–6 M , and another, smaller concentration at roughly 35 M . The low end is comprised of black holes with 20–40 M ZAMS progenitors, which lose much of their mass through a supernova (and hence experience a natal kick). The higher mass group are from more massive progenitors, and collapsed to a black hole without a supernova or the resulting kick. The histogram in figure 4.3 shows the ”chirp” mass distribution for all BH-BH systems that eventually merge from gravitational radiation. As the wave amplitude 5/6 scales like Mchirp, this plot, coupled with the sensitivity of the LIGO detec- tor, allows us to estimate a detection rate for BH-BH binaries. By way of comparison, two 1.4 M objects produce a chirp mass of 1.22 M . As can be seen from column 8 in tables 4.1 and 4.2, most NS-NS pairs that remain intact coalesce in τ < 1/H0, irrespective of IMF and kick strength. This is perhaps not surprising, since NS-NS systems must gen- erally be tightly bound to remain intact through the second supernova. For NS-NS systems, we estimate the Galactic merger rate to range from 0.04–8 ∼ Myr−1, with a strong dependence on the severity of the natal kick. Given

161 a likely LIGO I detection radius of 20 Mpc for such systems, this would ∼ imply a conservative detection rate of 0.01–3 10−3yr−1 (Phinney, 1991; × Kalogera & Lorimer, 2000), with a likely mean rate of 10−3 yr−1. These ∼ estimates are an order of magnitude lower than those stated in Grishchuk et al. (2000). A more unexpected result was the relative frequency of BH-NS pairs relative to bound NS systems. While far fewer BH-NS systems are formed, their mass allows them to weather two supernovae more frequently than two neutron stars. From an estimate of the BH-NS formation rate, we can say something about the expected frequency of BH-PSR systems. For purposes of discussion, we divide these systems into three categories, based on for- mation mechanism. The first type results from the standard scenario: a massive black hole forms first, with a regular short-lived pulsar at a later epoch. The second possibility is that the black hole progenitor transfers a substantial amount of matter on to the neutron star progenitor early in the evolution of the system. This results in the neutron star forming first, and allows the black hole progenitor to continue to spill matter through its Roche lobe on to the slowing pulsar, thereby recycling it. The last possi- bility is that the system from scenario two is disrupted by the black hole formation, resulting in a (possibly recycled) pulsar and single black hole. This channel is not relevant for our purposes, as it ceases to be a potential

LIGO source. The R6 rates for the remaining formation channels are shown in tables 4.1 and 4.2. The BH-NS column covers all formation channels for a BH-NS system, whereas the BH–PSR2 column considers only that sub- set of BH-NS systems where a recycled pulsar is formed first, via channel two, as described above. Surprisingly, of the systems that go on to form a BH-NS pair, around 40% experience the reversal described in case two

162 above, where the initially more massive star forms a compact object last. Only 0.5% of the BH-BH progenitor systems experience a similar reversal. In the first case, an ordinary, short-lived ( 106 yr) pulsar is created. In ∼ the latter, a fast, long-lived ( 109 yr) millisecond pulsar should often be ∼ the result. It is likely that type II BH-PSR systems with recycled pulsars would be observable as radio objects. The small predicted formation rate of such objects, however, is consistent with having not yet been seen among known pulsars. However, their formation rate, while 30–60 times smaller than that of “type 1” BH-NS systems, should mean that they are consider- ably more common than black holes with normal pulsar companions, being longer-lived. Also, we note that the formation rate of “type 2” BH-PSR sys- tems is more severely affected by kick intensity, as strong kicks may widen the system enough to prevent mass transfer on to the neutron star, leaving an ordinary BH-PSR system. We conclude that the galactic scale height for such systems should be substantially smaller than that of ordinary BH- NS and BH-PSR systems. Further details of the BH-PSR systems (including a prediction of orbital distributions) will be deferred to a future work (Sipior & Sigurdsson, in prep). Note finally that the chirp mass of a typical coa- lescing BH-PSR system is roughly twice as large as a NS-NS binary. As dL 5/6 scales with Mchirp, this implies at least a five-fold increase in search volume.

Adjusting the estimated R6 rates for this implies that BH-NS coalescence should be seen with substantially greater frequency than NS-NS binaries at all kick intensities, with a conservative maximum of 7 10−3 LIGO I de- × tections per year for low kick strengths. A more likely “best bet” rate is on the order of 2–3 10−3 yr−1, with a mix of high (σ = 450 km s−1) and low × (σ = 90 km s−1) kick velocities, with 60% of kicks drawn from the former, the balance from the latter (as suggested by Arzoumanian et al., 2002; Pfahl

163 et al., 2002). BH-BH systems are shown here to be far more common than either NS- NS or BH-NS hybrids. Only a small fraction of these will merge in a Hubble time, as the larger mass permits the system to remain bound at higher separations. As well, the greater mass of BH-BH systems implies a more gradual response to an increasing kick parameter. Indeed, the R6 rate for bound BH-BH system formation remains high (more than thirty per Myr in the Milky Way), even when kicks are permitted to reach 103 km s−1on a 1.4 M object. Figure 4.3 shows the distribution of chirp masses for all BH-BH systems that coalesce in less than 10 Gyr. As can be seen, there is a concentration of chirp masses around 4 M , implying a twentyfive-fold in- crease in search volume. Allowing for this, we anticipate a LIGO I detection rate of 0.3–12 10−3 yr−1, with a likely rate of 3–4 10−3 yr−1, given the × × two-component kick speed distribution described above. Figure 4.4 shows the strong correlation between the final system velocity (a function of the kick magnitude and component masses), and the time required for the sys- tem to coalesce due to emitted gravitational wave energy. A clear dynamic criterion for coalescence emerges, with slower systems rarely merging in a Hubble time. This is essentially a selection effect, as the kick speed must be of a magnitude comparable to the orbital speed of the system to have a dra- matic effect on the merger rate. Relative to the orbital speed, a weak kick will have no appreciable effect, while a strong kick will disrupt the system. So, the kick speeds that bring about more rapid mergers are necessarily tuned to the orbital speed of the system at the second supernova.

164 4.5 Discussion

We claim a “best guess” LIGO I detection rate of 3–4 10−3yr−1 for BH- × BH coalescence events, 2–3 10−3 yr−1 for BH-NS events, and 10−3 NS- × ∼ NS coalescence per year. LIGO II, with an anticipated order of magnitude increase in sensitivity, should encompass roughly 103 times the search vol- ume, with a proportional increase in event detection rates. Unless LIGO I is quite lucky, it seems unlikely that mergers from this channel will be detected until the advent of LIGO II in a few years. With LIGO II, we can antici- pate an event rate of many per year. These are essentially consistent with the most pessimistic detection rates calculated by Grishchuk et al. (2000). There are significant differences between our results and those in Portegies Zwart & Yungelson (1998), primarily regarding BH-BH coalescence, where a negligible merger rate was found. This discrepancy is likely due to our lower cutoff for black hole formation, where we adopt a value of 20 M , against the 40 M cutoff adopted by the latter. While recent models of Fryer (1999) have established a lower black hole mass cutoff, more work is needed to resolve this area of contention. LIGO-measured coalescence rates should provide a clearer resolution on this point. It is instructive to compare our results with those obtained in two recent population synthesis studies. Fryer et al. (1999) performed detailed synthesis calculations in the context of black hole-accretion driven gamma ray bursts. As a result, BH-BH binaries are not considered; however, BH-NS and NS- NS systems are. For the Salpeter IMF, and a Gaussian kick distribution peaked at 100 km s−1, FWHM of 50 km s−1(roughly corresponding to our −1 σ = 90 km s kicks), the R6 rate of BH-NS formation is identical (R6 =

16). We predict many more NS-NS (R6 of 11, as opposed to 4.2). This

165 discrepancy arises from the inclusion of hypercritical accretion in Fryer et al. scenario I for NS-NS formation. The result is that all neutron stars that pass through a common envelope phase become black holes, removing a significant channel of NS-NS pair formation. At higher kick intensities, the BH-NS formation rates remain in good agreement, whilst the NS-NS rates become more disparate. This is likely because the two high speed kick distributions are not the same, and the discrepancy affects BH-NS systems less dramatically because of the larger mass involved. Very recently, the paper of Belczynski et al. (2002) performed a simi- lar comprehensive study, considering a wide variety of kick paradigms and population synthesis models. Our anticipated LIGO I detection rates are consistently an order of magnitude lower than those reported by the au- thors for their “standard model”. Though the kick distribution chosen for this standard model is more intense than in our own work (two Maxwellian distributions, with σ = 175 km s−1and σ = 700 km s−1, with 80% of kicks drawn from the former, and the balance from the latter distribution), the mean neutron star mass is allowed to be much higher (up to 3 M , allow- ing more systems to remain bound, and shed gravitational radiation more quickly. Thus, the overall effect is to enhance the anticipated NS-NS and BH-NS merger rates. It should be noted that our calculated merger rates fall within the range of merger rates calculated by Belczynski et al. when all posited model assumptions are considered. The difference between our results and the standard model of the authors for BH-BH systems is larger, by roughly two orders of magnitude (though our results still fall within the wider range resulting from considering all the models presented). Our model assumptions are greatly discrepant at one point in particular; namely, the assumed mass function of newly-formed black holes as a function of ZAMS

166 mass. Where we take a rough interpolation between model results presented in Fryer (1999), the authors use a much more sophisticated relationship be- tween the ZAMS mass and the initial mass of the resulting black hole. This mass function tends to produce substantially more massive holes than those generated from our interpolation, and we believe this to be the principal cause of the discrepancy in merger rates for BH-BH binaries. After the neutron star/black hole mass cutoff, the second pivotal assump- tion concerns the distribution of natal kick speeds, and indeed, whether black holes can receive kicks under any circumstances. The cases of Nova Sco 1994 and XTE J1118+480 show that our natal kick assumptions are plausible. However, we suffer from a paucity of data concerning the frequency and scaling (with respect to mass) of black hole kicks. There is mounting evi- dence that neutron star kick distributions are bi-modal (Arzoumanian et al., 2002), allowing many more NS-NS systems to survive and merge after the second supernova. The greater mass of black holes means that uncertain- ties in these distributions have less effect on the coalescence of BH-NS and BH-BH systems, as can be seen in table 4.1. Coupling this fact with the “residual” merger rate one gets when black holes are not allowed natal kicks at all (cf. table 4.2), we argue that the effects of uncertainty in the natal kick models will not affect the predicted R6 rates of BH-BH and BH-NS mergers by more than factors of a few. Interestingly, the large number of BH-BH bi- naries which remain bound suggests that another merger channel; namely, a merger due to hardening resulting from external dynamical perturbations (Sigurdsson & Hernquist, 1993). We do not quantify this effect here, but note that the extent and duration of a star-formation episode could have a notable effect on the rate at which such interactions occur. Black holes experience natal kicks only when formation of the event hori-

167 zon is delayed, from fallback material and/or initial spin support. Therefore it is reasonable to posit a correlation between natal kicks and a high ini- tial spin for the nascent black hole. In a BH-BH system, the first hole is gradually spun down by interaction with the stellar wind of its companion, and will likely be a slow rotator even if it began with maximal spin. The second hole will not experience this, and should retain its high spin. We therefore predict that, for BH systems that experience natal kicks, LIGO will see a slow rotating primary, with a (generally less massive) black hole companion with near maximal spin. If the components do not experience natal kicks, we would anticipate low spins all around, with the coalescence rate primarily determined by the wind mass loss rate and the boundary cri- terion for black hole formation. This spin signature is a directly testable hypothesis—LIGO II should provide a large array of high-quality sources to verify this prediction, and allow for careful testing of gravitational wave phenomenology. A similar spin correlation may be found in BH-PSR systems, with the two categories described above having different anticipated signatures. The type I systems (black hole first, followed by standard pulsar) should have two slow rotators, as no pulsar recycling is possible. Type II systems (neu- tron star forms first, is spun up by black hole progenitor, black hole forms) should have at least one rapid rotator, and possibly two, if the black hole is spun up during its formation, as above. These spin correlations may be demonstrated with high-S/N data from LIGO II. More will be said about the spin signatures of BH-PSR systems in an upcoming paper (Sipior & Sig- urdsson, in prep), in addition to a study of the orbital parameters of such systems, and the ratio of BH-PSR to NS-PSR systems, which is relevant for new tests of General Relativity, should these systems be detected.

168 Table 4.1. Summary of source properties

−1 α σ (km s ) BH-BH τ < τh BH-NS τ < τh NS-NS τ < τh BH-PSR2 τ < τh

-2.0 90 80 1.6 26 8.2 11 8.4 0.62 0.44 -2.0 190 68 0.59 5.9 2.5 1.7 1.5 0.11 0.09 -2.0 450 62 0.11 0.38 0.2 0.09 0.06 0.0 0.0 -2.35 90 48 1.2 16 5.5 11 7.9 0.47 0.37 -2.35 190 41 0.55 4.0 1.7 1.6 1.3 0.07 0.07 -2.35 450 35 0.04 0.2 0.09 0.07 0.05 0.0 0.0

Note. — R6 formation and merger rates for BH-BH , BH-NS , NS-NS and BH- PSR systems. α is the index of the IMF power-law, σ provides the dispersion of the Maxwellian distribution of kick speeds, and the kick cutoff gives the maximum permitted kick speed (acting on a 1.4 M neutron star). Black hole kicks are permitted below a ZAMS mass of 40 M , and are scaled to the compact object mass. The BH-PSR column refers to a subset of the BH-NS systems, where the pulsar is recycled by mass transfer from the black hole progenitor star. The mass transfer should in many cases spin-up the pulsar to millisecond-order periods.

Model uncertainties, especially involving the details of black hole forma- tion, still dominate the estimates of coalescence rates to be seen by LIGO. Nonetheless, it is becoming clear that BH-BH mergers form a significant channel, comparable to the rates anticipated for NS-NS systems. While LIGO I detection rates appear too small to catch any merger events from this channel, we may still be lucky enough (at the level of a few percent) to serendipitously catch events from this channel (especially given incremental upgrades in the sensitivity of LIGO I throughout its operational lifetime). LIGO II should easily see a large number of these events every year.

169 Table 4.2. Summary of source properties

−1 α σ (km s ) BH-BH τ < τh BH-NS τ < τh NS-NS τ < τh BH-PSR2 τ < τh

-2.0 90 250 0.81 31 9.0 10 7.8 0.63 0.53 -2.0 190 240 0.62 12 5.5 1.8 1.5 0.08 0.06 -2.0 450 240 0.77 2.0 1.1 0.04 0.03 0.0 0.0 -2.35 90 170 0.55 21 6.5 11 8.1 0.55 0.47 -2.35 190 170 0.71 7.8 3.4 1.7 1.4 0.07 0.07 -2.35 450 170 0.32 1.4 0.83 0.04 0.04 0.0 0.0

Note. — R6 formation and merger rates. Identical to table 4.1, save that black hole kicks are not permitted under any circumstances. This clearly elevates the number of BH-BH and BH-NS systems seen. Interestingly, the application of natal kicks increases the fractional merger rate in BH-BH systems, though the large number of BH-BH systems which remain bound when kicks are not present means that the number of merging systems is still comparable, especially for the most energetic kick parameters.

170 Figure 4.1 A plot of the semi-major axis versus eccentricity for all BH- BH (left) and BH-NS (right) systems generated in a single run of 106 bi- naries. Triangles designate systems which will coalesce in less than 10 Gyr, whilst circles are systems stable against gravitational coalescence. For the BH-BH systems, a clear distinction between merging and stable binaries is evident. The bulk of those BH-NS binaries which remain bound after the second supernova also merge within a Hubble time. The IMF index used is α = 2.35, the Salpeter IMF. The dispersion in the Maxwellian kick applied −1 at each supernova is σ = 90 km s , with the kick maximum Kmax = 500 −1 km s . All kick speeds apply to a 1.4 M neutron star; the actual ∆v is found by scaling the kick linearly with the compact object mass.

171 Figure 4.2 Two histograms displaying mass distributions for BH-BH pairs that remain bound after the second supernova. The parameters of the run shown are an IMF parameter α = 2.35, kick parameters σ = 90 km s−1and −1 Kmax = 500 km s . The left histogram shows that black hole masses clump in two locations; one around 5 M , and the other at 35 M . We associate the lower-mass BHs with 20–40 M ZAMS progenitors, which lose much of their mass through a supernova (and hence experience a natal kick). The high-mass set came from more massive progenitors, and collapsed to a black hole without a supernova or the resulting kick.

172 Figure 4.3 Shows the distribution of chirp masses for all BH-BH systems that 5/6 will eventually merge. The gravitational wave amplitude scales as Mchirp, so this parallels the distribution of signal strengths one could expect from a BH-BH population.

173 Figure 4.4 A plot of merger time versus the final velocity of the BH-BH bi- naries (left), and BH-NS binaries (right). The natal kick parameters were −1 −1 −1 σ = 90 km s , Kmax = 500 km s (upper panels), and σ = 190 km s , −1 Kmax = 500 km s (lower panels). Of the systems that remained bound af- ter the second supernova, there is a clear correlation between increasing sys- tem speed and a shortening of the gravitational radiation merger timescale, from kick-induced high eccentricity orbits, with enhanced GW radiation at periastron passage.

174 Acknowledgments: Both authors would like to profusely thank Onno Pols and Joshua Bloom for access to the code base that we built upon here. Steinn Sigurdsson would like to acknowledge the support of the Center for Gravitational Wave Physics, and the hospitality of the Aspen Center for Physics. The Center for Gravitational Wave Physics is supported by the NSF under co-operative agreement PHY 01-14375. Michael Sipior is sup- ported in part by NASA through grant GO01152 A,B from the Smithsonian Astrophysical Observatory. He would like to acknowledge travel support kindly provided by the Zaccheus Daniel Foundation.

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186 Michael Shawn Sipior

Refereed Publications

Feigelson, E. D., Ho, L., Sipior, M. S., Ptak, A. 2002, “Chandra Survey • of Nearby Galaxies with Low-Luminosity Active Nuclei”, in prepara- tion

Sipior, M. S., Sigurdsson, S., 2002, “Nova Sco and coalescing low mass • black hole binaries as LIGO sources”, ApJ, accepted

Ciardullo, R., Bond, H. E., Sipior, M. S., Fullton, L. K., Zhang, C.-Y., • Schaefer, K. G. 1999, “Hubble Space Telescope Survey for Resolved Companions of Planetary Nebula Nuclei”, A. J., 118, 488

Andersson, N., Kokkotas, K. D., Laguna, P., Papadopoulos, P., Si- • pior, M. S. 1999, “Construction of initial data for perturbations of relativistic stars”, Phys. Rev. D, 60, 124004

Presentations

Sipior, M. S., Eracleous, M., Sigurdsson, S. “ ’Till never do us part: • an XRBs fatal dance, from X-rays to gravitational waves”, American Astronomical Society 199th Meeting, January 2002, Washington, D. C. (oral)

Sipior, M. S., Feigelson, E., Ho, L., Ptak, A., Garmire, G. “X-ray • properties of low-luminosity AGN in nearby galaxies”, New Visions of the X-Ray Universe in the XMM-Newton and Chandra Era, November 2001, Noordwijk, the Netherlands (poster)

Sipior, M. S., Eracleous, M. “Simulating X-ray emission from starburst • galaxies”, HEAD 2000, November 2000, Honolulu, Hawaii (poster)