Low-mass X-ray binaries from black-hole retaining globular clusters

Recent studies suggest that globular clusters (GCs) may retain a substantial population of stellar-mass black holes (BHs), in contrast to the long-held belief of a few to zero BHs. We model the population of BH low-mass X-ray binaries (BH-LMXBs), an ideal observable proxy for elusive single BHs, produced from a representative group of Milky Way GCs with variable BH populations. We simulate the formation of BH-binaries in GCs through exchange interactions between binary and single stars in the company of tens to hundreds of BHs. Additionally, we consider the impact of the BH population on the rate of compact binaries undergoing gravitational wave driven mergers. The characteristics of the BH-LMXB population and binary properties are sensitive to the GCs structural parameters as well as its unobservable BH population. We find that GCs retaining $\sim 1000$ BHs produce a galactic population of $\sim 150$ ejected BH-LMXBs whereas GCs retaining only $\sim20$ BHs produce zero ejected BH-LMXBs. Moreover, we explore the possibility that some of the presently known BH-LMXBs might have originated in GCs and identify five candidate systems.Comment: 27 pages, 18 figures, 7 tables, submitted to MNRA

Testing the no-hair theorem with GW150914

We analyze gravitational-wave data from the first LIGO detection of a binary black-hole merger (GW150914) in search of the ringdown of the remnant black hole. Using observations beginning at the peak of the signal, we find evidence of the fundamental quasinormal mode and at least one overtone, both associated with the dominant angular mode ($\ell=m=2$), with $3.6\sigma$ confidence. A ringdown model including overtones allows us to measure the final mass and spin magnitude of the remnant exclusively from postinspiral data, obtaining an estimate in agreement with the values inferred from the full signal. The mass and spin values we measure from the ringdown agree with those obtained using solely the fundamental mode at a later time, but have smaller uncertainties. Agreement between the postinspiral measurements of mass and spin and those using the full waveform supports the hypothesis that the GW150914 merger produced a Kerr black hole, as predicted by general relativity, and provides a test of the no-hair theorem at the ${\sim}10\%$ level. An independent measurement of the frequency of the first overtone yields agreement with the no-hair hypothesis at the ${\sim 20}\%$ level. As the detector sensitivity improves and the detected population of black hole mergers grows, we can expect that using overtones will provide even stronger tests.Comment: v2: journal versio

Probing the Nature of Black Holes with Gravitational Waves

In this thesis, I present a number of studies intended to improve our understanding of black holes using gravitational waves. Although black holes are relatively well understood from a theory perspective, many questions remain about the nature of the black holes in our Universe. According to general relativity, astrophysical black holes are fully described by just their mass and spin. Yet, relying on electromagnetic-based observatories alone, we still know very little about the distribution of black hole masses or spins. Moreover, as merging black holes are invisible to these electromagnetic observatories, we cannot rely on them to provide us with information about the binary black hole merger rate or binary black hole formation channels. However, by observing gravitational wave signals from these inherently dark binaries, we will soon have some answers to these questions. Indeed, the Laser Interferometer Gravitational-Wave Observatory (LIGO) has already revealed a great deal of new information about binary black holes; giving us an early glimpse into their mass and spin distributions and placing the first constraints on the binary black hole merger rate. This thesis contributes to the goal of probing the nature of black holes with gravitational waves. Binary black holes can form as an isolated binary in the galactic field or through dynamical encounters in high-density environments. Dynamical formation can significantly alter the binary parameters, which then become imprinted on the gravitational waveform. By simulating varying black hole populations in high-density globular clusters, we identify a population of highly eccentric binary black hole mergers that are characteristic of dynamical formation. Although these systems would circularize by the time they are visible in LIGO's frequency band, the future Laser Interferometer Space Antenna (LISA) is capable of distinguishing this population of eccentric mergers from the circular mergers expected of isolated field-formed binaries. As these dynamically formed binaries depend on the size of the underlying black hole population in globular clusters, we can utilize the dynamically formed merger rate to infer globular cluster black hole populations -- allowing us to reveal information about binary black hole birth environments. In order to properly estimate the parameters of binary black holes from detected gravitational wave signals, such as their masses and spins, high-accuracy waveforms are a needed. The highest accuracy waveforms are those produced by numerical relativity simulations, which solve the full Einstein equations. Using the Spectral Einstein Code (SpEC), we expand the reach of numerical relativity to simulate binary black holes with nearly extremal spins, i.e., black holes with spins near the maximal value χ = 1. These waveforms are used to calibrate existing waveform approximants used in LIGO data analyses. This ensures that the systematic errors in these approximants are small enough that if highly-spinning systems are observed, the spins are recovered without bias. Although rapidly spinning binaries have remained elusive thus far, these waveforms ensure that the highest-spin systems can be detected in the quest to uncover the spin distribution of black holes. The end state of a binary black hole merger is a newly born, single black hole that rings down like a struck bell, sending its last few ripples of gravitational waves out into the spacetime. Embedded in this 'ringdown' signal are a multitude of specific frequencies. Einstein's theory of general relativity precisely predicts the ringdown frequencies of a black hole with a given mass and spin. The statement that a black hole is entirely described by just these two parameters is known as the no-hair theorem. For black holes that obey the laws of general relativity (and consequently, the no-hair theorem), these frequencies serve as a fingerprint for the black hole. However, if the objects we observe are not Einstein's black holes, but instead something more exotic, the frequencies will not have this property and this would be a spectacular surprise. A minimum of two tones are required for this test, each with an associated frequency and damping time that depend only on the mass and spin. The conventional no-hair test relies on the so-called 'fundamental' tones of a black hole. A test relying on the fundamental modes is not expected to be feasible for another ~10-15 years, after detector sensitivity has improved significantly. However, by analyzing the ringdown of high-accuracy numerical relativity waveforms, we show that modes beyond the fundamental, known as 'overtones', are detectable in current detectors. The overtones are short-lived, but this is countered by the fact that they can initially be much stronger than the fundamental mode. By measuring two tones in the ringdown of GW150914 we perform a first test of the no-hair theorem. While the current constraints are rather loose, this first test serves as a proof of principle. This is just one example of the powerful tests that can be employed with overtones using present day detectors and the even more precise tests that can be accomplished with LISA in the future.</p

Black hole ringdown: the importance of overtones

It is possible to infer the mass and spin of the remnant black hole from binary black hole mergers by comparing the ringdown gravitational wave signal to results from studies of perturbed Kerr spacetimes. Typically these studies are based on the fundamental quasinormal mode of the dominant $\ell=m=2$ harmonic. By modeling the ringdown of accurate numerical relativity simulations, we find that the fundamental mode alone is insufficient to recover the true underlying mass and spin, unless the analysis is started very late in the ringdown. Including higher overtones associated with this $\ell=m=2$ harmonic resolves this issue, and provides an unbiased estimate of the true remnant parameters. Further, including overtones allows for the modeling of the ringdown signal for all times beyond the peak strain amplitude, indicating that the linear quasinormal regime starts much sooner than previously expected. A model for the ringdown beginning at the peak strain amplitude can exploit the higher signal-to-noise ratio in detectors, reducing uncertainties in the extracted remnant quantities. Tests of the no-hair theorem should consider incorporating overtones in the analysis.Comment: 12 pages, 11 figures; v2 matches published versio

Spin and eccentricity evolution in triple systems: From the Lidov-Kozai interaction to the final merger of the inner binary

We study the spin and eccentricity evolution of black-hole (BH) binaries that are perturbed by tertiary masses and experience the Lidov-Kozai (LK) excitation. We focus on three aspects. First, we study the spin-orbit alignment of the inner binary following the approach outlined by Antonini et al. [Mon. Not. R. Astron. Soc. 480, L58 (2018)] and Liu and Lai [Astrophys. J. 863, 68 (2018)], yet allowing the spins to have random initial orientations. We confirm the existence of a dynamical attractor that drives the spin-orbit angle at the end of the LK evolution to a value given by the initial angle between the spin and the outer orbital angular momentum (instead of to a specific value of the effective spin). Second, we follow the (inner) binary’s evolution further to the merger to study the final spin-spin alignment. We generalize the effective potential theory to include orbital eccentricity, which allows us to efficiently evolve the system in the early inspiral stages. We further find that the spin-spin and spin-orbit alignments are correlated and the correlation is determined by the initial spin-orbit angle. For systems with the spin vectors initially in the orbital plane, the final spins strongly disfavor an aligned configuration and could thus lead to a greater value of the GW recoil than a uniform spin-spin alignment would predict. Lastly, we study the maximum eccentricity excitation that can be achieved during the LK process, including the effects of gravitational-wave radiation. We find that when the tertiary mass is a supermassive BH and the inner binary is massive, then even with the maximum LK excitation, the residual eccentricity is typically less than 0.1 when the binary’s orbital frequency reaches 10 Hz, and a decihertz detector would be necessary to follow such a system’s orbital evolution

Spin and eccentricity evolution in triple systems: From the Lidov-Kozai interaction to the final merger of the inner binary

We study the spin and eccentricity evolution of black-hole (BH) binaries that are perturbed by tertiary masses and experience the Lidov-Kozai (LK) excitation. We focus on three aspects. First, we study the spin-orbit alignment of the inner binary following the approach outlined by Antonini et al. [Mon. Not. R. Astron. Soc. 480, L58 (2018)] and Liu and Lai [Astrophys. J. 863, 68 (2018)], yet allowing the spins to have random initial orientations. We confirm the existence of a dynamical attractor that drives the spin-orbit angle at the end of the LK evolution to a value given by the initial angle between the spin and the outer orbital angular momentum (instead of to a specific value of the effective spin). Second, we follow the (inner) binary’s evolution further to the merger to study the final spin-spin alignment. We generalize the effective potential theory to include orbital eccentricity, which allows us to efficiently evolve the system in the early inspiral stages. We further find that the spin-spin and spin-orbit alignments are correlated and the correlation is determined by the initial spin-orbit angle. For systems with the spin vectors initially in the orbital plane, the final spins strongly disfavor an aligned configuration and could thus lead to a greater value of the GW recoil than a uniform spin-spin alignment would predict. Lastly, we study the maximum eccentricity excitation that can be achieved during the LK process, including the effects of gravitational-wave radiation. We find that when the tertiary mass is a supermassive BH and the inner binary is massive, then even with the maximum LK excitation, the residual eccentricity is typically less than 0.1 when the binary’s orbital frequency reaches 10 Hz, and a decihertz detector would be necessary to follow such a system’s orbital evolution

On choosing the start time of binary black hole ringdown

The final stage of a binary black hole merger is ringdown, in which the system is described by a Kerr black hole with quasinormal mode perturbations. It is far from straightforward to identify the time at which the ringdown begins. Yet determining this time is important for precision tests of the general theory of relativity that compare an observed signal with quasinormal mode descriptions of the ringdown, such as tests of the no-hair theorem. We present an algorithmic method to analyze the choice of ringdown start time in the observed waveform. This method is based on determining how close the strong field is to a Kerr black hole (Kerrness). Using numerical relativity simulations, we characterize the Kerrness of the strong-field region close to the black hole using a set of local, gauge-invariant geometric and algebraic conditions that measure local isometry to Kerr. We produce a map that associates each time in the gravitational waveform with a value of each of these Kerrness measures; this map is produced by following outgoing null characteristics from the strong and near-field regions to the wave zone. We perform this analysis on a numerical relativity simulation with parameters consistent with GW150914- the first gravitational wave detection. We find that the choice of ringdown start time of $3\,\mathrm{ms}$ after merger used in the GW150914 study to test general relativity corresponds to a high dimensionless perturbation amplitude of $\sim 7.5 \times 10^{-3}$ in the strong-field region. This suggests that in higher signal-to-noise detections, one would need to start analyzing the signal at a later time for studies that depend on the validity of black hole perturbation theory.Comment: 23+4 pages, 22 figure