Browsing by Author "Kesden, Michael"
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Item A Unified Relativistic Treatment of Tidal Disruption Events and a New Model for Self-Intersections Involving Tidal Debris Streams for Schwarzschild Black Holes(2018-08) Servin, Juan E.; Kesden, MichaelThis dissertation concerns the astrophysical phenomena known as tidal disruption events~(TDEs), where stars are ripped apart by gravitational tides from their host galaxies' central supermassive black hole~(SBH). Stars are driven onto orbits appropriate for disruption via gravitational interactions with their stellar neighbors, and it is these interactions that determine the rate at which we may observe TDEs. Observations for such events have gained popularity in recent years, as they provide an additional avenue for probing the spacetime near non-active galactic centers. Conveniently, measurements for galactic transients are already underway, and have found, up to the publication of this dissertation, a few dozen TDE candidates. Theoretical predictions for TDEs have been conducted under both Newtonian gravity and general relativity, with numerical simulations of TDE rates and the post disruption stream evolution being common examples. Models for TDEs, however, have proven to be a greater challenge, as the phenomenon covers a wide range of length and time scales. With the recent increased interest in black holes due to gravitational-wave detection, correcting current TDE models to fall more in line with observations can only aid our understanding of these massive galactic objects. The rest of this dissertation is as follows. Our first chapter will introduce the reader to some basic history of TDEs, from their inception as a means to feed mass into galactic centers to their modern interpretations. We also provide a brief overview of Newtonian loss-cone theory~(and its role in determining the rate at which TDEs are observed) and general relativity~(which is used to correct for relativistic effects in the aforementioned loss-cone theory). The second chapter comprises a published work concerning a unified treatment of TDEs that maps Newtonian predictions to their relativistically corrected counterparts. Our third chapter presents a new model where we track the evolution of the post-disruption tidal stream and provides predictions for observations of light curves. Our fourth chapter discusses a generalization of our work in Chapter 2 from the Schwarzschild metric to the Kerr metric, and we close with some concluding remarks.Item Analyzing Tidal Circularization In Exoplanet Systems To Determine The Tidal Dissipation Efficiency Of Giant Planets(August 2023) Mahmud, Mohammad M 1986-; Penev, Kaloyan; Wu, Yunan; King, Lindsay J.; Kesden, Michael; Ishak-Boushaki, Mustapha; Anderson, PhillipA planet in the gravitational field of its parent star experiences a tidal force due to the variation of the gravitation at different points on it at different distances from the star. The planet gets distorted, being stretched by this difference of gravity. This distortion raises two bulges (called “tidal bulges”) along the star-planet joining line on two opposite sides of the planet (p). When it (p) revolves in an eccentric orbit, the tidal distortion varies since the tidal force varies with the distance from the star. The repetitive tidal distortion causes a periodic variation of the amplitude of the tidal bulges. The difference between the planet’s rotational angular speed and the system’s orbital angular speed also varies with the planet-star distance. It causes the tidal bulges to move around the planet, creating a tidal wave. The friction and viscous force within the different layers of the planet resist the motion of the tidal wave and the variation of its amplitude, resulting in the generation of heat. Ultimately, some portion of the system’s orbital energy converts into heat. The gradual loss of the system’s orbital energy reduces the orbital eccentricity and semimajor axis. A ubiquitously used term that parameterizes tidal dissipation is the modified tidal quality factor (Q′ pl). Q′ pl is inversely proportional to the tidal dissipation rate. In this project, we determined a possible range of Q′ pl of short-period gas giants. The periodically varying tide acting on different parts of the planet, sometimes coupling with other forces (like Coriolis force), generates multiple components of the tidal wave that depend on the time-dependent tidal frequency. So we prescribe an empirical model where Q′ pl may depend on the frequency to consider different possible tidal wave components. We applied our analysis to 78 exoplanet systems consisting of a single planet orbiting a single host star. We worked out an allowed range of the frequency-dependent Q′ pl for each system and combined them to find general constraints on Q′ pl. We determined the upper limit of Q′ pl by requiring that if the system starts evolution with a sufficiently high initial eccentricity, then the eccentricity simulated at the present age for which the simulated orbital period matches the measured value of the orbital period, should be lower than the envelope observed in the ‘eccentricity vs. semimajor axis to planetary radius scatter plot’ of a collection of exoplanet systems. We determined the lower limit of the same parameter by requiring that it should not be lower than the measured orbital eccentricity at the present age. We find that the value of log10 Q′ pl for HJs is 5.0 ± 0.5 for the range of tidal period from 0.8 to 7 days. We do not see any clear sign of frequency dependence of Q′ pl within the mentioned uncertainties.Item Binary Black-Hole Spin Precession: Dynamical Evolution and Gravitational-Wave Parameter Estimation(2019-12) Zhao, Xinyu; Kesden, MichaelEinstein’s general relativity predicts the existence of black holes. A binary black hole is a system of two black holes orbiting each other. During the inspiral of a binary black hole, the separation between the two black holes shrinks slowly and gravitational waves are emitted until the merger, at which time the gravitational waves peak. We use analytic solutions for generic spin precession at second post-Newtonian(2PN) order to derive Fourier series for the total and orbital angular momenta. On the precession timescale, the angle between the total and orbital angular momenta oscillates with nutation period ⌧ , during which the orbital angular momentum L precesses about the total angular momentum J by an angle ↵. As black holes inspiral, they can pass through nutational resonances (⌦ = n!), at which the total angular momentum tilts by an angle ✓tilt, where ⌦ ⌘ ↵/⌧ is the precession frequency and ! ⌘ 2⇡/⌧ is the nutation frequency. We are the first to identify and study the nutational resonances. We derive an approximate expression for this tilt angle and show the angle is usually less than 103 radians at PN regime. We also show that both precession and nutation can modulate the frequency and amplitude of the gravitational waveforms. In the absence of radiation reaction, the amplitudes and frequencies of precession and nutation can be treated as constant parameters. Using two different approximations to calculate the gravitational-waveform modulation (frequency modulation and amplitude modulation), we calculate the Fisher matrix for waveform models that include these parameters and use this to determine how accurately these parameters can be measured.Item Circularization of Tidal Disruption Streams for Schwarzschild Black Holes and Distribution of Orbital Inclinations of Tidally Disrupted Stars for Kerr Black Holes(2021-12-01T06:00:00.000Z) Rossi, Joseph D; Kesden, Michael; Akbar, Mohammed; Ishak-Boushaki, Mustapha; King, Lindsay; Penev, Kaloyan; Anderson, PhillipTidal Disruption Events (TDEs) occur when a star approaches sufficiently close to a supermassive black hole (SMBH) such that the tidal gravitational field of the SMBH overcomes the self-gravity of the star, causing the star to rip apart. A stream of debris is formed from the star’s remnants, which proceeds to orbit about the black hole. Relativistic apsidal precession causes leading elements of the stream to collide with trailing elements, dissipating energy on the way to circularization. We explore this circularization process for Schwarzschild, or spherically symmetric, SMBHs, finding that the process is likely to take longer than was first expected, and uncovering two distinct regimes of circularization. We then show work on how TDE rates depend on orbital inclination for Kerr, or axisymmetric SMBHs.Item Connecting Stellar-Binary Evolution with Binary Black-Hole Spin Precession(2021-04-28) Steinle, Nathan A; Kesden, MichaelStellar-mass binary black-holes (BBHs) can form in one of two main ways: either the black holes (BHs) form first from single stars and then form a binary through dynamical interactions in a dense cluster, or the BHs form together from the kindred evolution of isolated binary stars. Distinguishing between these two formation channels with BBH sources observed via gravitational-wave (GW) detection is a new and promising field of research. Although the masses of the BBH are easier parameters to constrain, the spin orientations are more useful for determining the BBH’s origin: isotropically distributed spin directions are expected in the dynamical channel, whereas spin directions depend on the particular astrophysical evolution in the isolated channel. This has consequences for the resultant spin precession of the BBHs, since it implies that BBHs from the dynamical channel are expected to exhibit generic spin precession features, while those from the isolated channel are expected to have mostly aligned spins and hence suppressed spin precession. However, if BHs receive natal kicks when their stellar progenitors undergo core collapse, or if binary stars generally form with misalignments, then BBH spins may not be aligned in the isolated channel, and spin precession would be present. Motivated by this, we present a simplified model of binary stellar evolution to identify regions of the parameter space that produce BBHs with large spins misaligned with their orbital angular momentum. The masses and spins of these BBHs are determined by the complicated interplay of phenomena such as tides, winds, accretion, common-envelope evolution (CEE), supernova (SN) natal kicks, and stellar core-envelope spin coupling. In Scenario A [B] of our model, stable mass transfer (SMT) occurs after Roche-lobe overflow (RLOF) of the more [less] massive star, while CEE follows RLOF of the less [more] massive star. Each scenario is further divided into Pathways 1 and 2 depending on whether the core of the more massive star collapses before or after RLOF of the less massive star. We parameterize the boundary in the parameter space between these two pathways with the transition mass ratio, qtrans, which depends on the initial separation, masses, and metallicity. If the stellar cores are weakly coupled to their envelopes, highly spinning BBHs can be produced if natal spins greater than 10% of the breakup value are preserved during the Wolf-Rayet (WR) stage. BBHs can alternatively acquire high spins by tidal synchronization during the WR stage in Scenario A or accretion onto the initially more massive star in Scenario B. BBH spins can become highly misaligned if the SN kicks are comparable to the orbital velocity which is more easily achieved in Pathway A1 where the SN of the more massive star precedes CEE. It was previously unclear whether such highly spinning and misaligned binaries are possible from the isolated channel. Our model of isolated BBH formation motivates our new framework for modeling the spin precession of BBHs. Various studies over previous decades have uncovered a great diversity of spin precession dynamics. We summarize these possibilities into a “taxonomy” using a multitimescale analysis in which the entire dynamics on the precession timescale tpre ∼ r 5/2/M3/2 depends only on the evolution of the total spin magnitude S = |S1 + S2| (Kesden et al., 2015; Gerosa et al., 2015). Precession is “generic” when L nutates (raises and lowers like a draw bridge) at frequency ω, due to the oscillation of S, while L precesses in a cone about the total angular momentum J, which is fixed in direction, at frequency ΩL. In the special case of “regular” precession, nutation vanishes since S is constant implying that ΩL and the angle θL subtending L and J are both constant. We present five parameters that describe the motion of the direction of L as functions of S: the precession amplitude hθLi, the precession frequency hΩLi, the nutation amplitude ∆θL, the nutation frequency ω, and the precessionfrequency variation ∆ΩL. Using BBHs with isotropically distributed spin directions, we explore the behavior of these parameters and we stress that nutation is a generic feature of BBH spin precession. High spin magnitudes allow for the largest nutations at moderate mass ratios (q ≈ 0.6). Maximally nutating systems are correlated with binaries that satisfy the condition J k L sometime during inspiral, one such binary is the “up-down” configuration. In the extreme limits of q, nutation vanishes due to the constancy of S and precession is “regular”. Lastly, we outline future avenues of research. (1) We use our new spin precession framework to study the precession and nutation of the BBHs generated from our model of isolated stellar-binary evolution. BBHs with significant misalignments from natal kicks precess unless alignment mechanisms, such as tides in Scenario A or accretion in Scenario B, realign the WR or BH spins. Although aspects of stellar-binary evolution conspire against the emergence of highly nutating systems, e.g., strong core-envelope coupling produces small BH spins implying BBHs might exhibit “regular” precession, we find that such systems are still plausible. BBHs that evolve from Scenario A can highly nutate if high BH spins are inherited from weak core-envelope coupling of the stellar progenitors, and if the initial separation is sufficiently large to avoid tidal alignment - but not too large in Pathway A1 otherwise too many binaries can be unbound by the first natal kick. High BH spin from tidal synchronization of the WR progenitor is only effective on the initially less massive star in Pathway A1 but is effective on both stars in Pathway A2, while tidal alignment suppresses the precession amplitude hθLi. In Scenario B, the initially more massive star generally evolves into a highly spinning BH, implying that ∆θL can be significant if the BH that forms from the initially less massive star inherits a high spin from weak core-envelope coupling. ∆θL is suppressed in Pathway B1 if accretion is Eddington-limited, or in Pathway B2 if a substantial amount of mass loss accompanies BH formation of the initially more massive star, due to the Kerr spin limit, resulting in a high BBH mass ratio. Stellar binaries with weak core-envelope coupling in Pathway B2 generally allow for systems with significant ∆θL. We compare these behaviors to those of BBHs with isotropic spin misalignments, as would be expected from the dynamical formation channel. (2) We compare the observational signatures of our five parameters to the signatures of other spin precession parameters in the literature, such as the effective precession parameter, χp, and the leading-order post-Newtonian spin-dependent correction to the GW phase, β, to try to elucidate the various nuances that make a genuine detection of nutation difficult.Item Constraining Tidal Quality Factor in Low-mass Eclipsing Binaries Using Tidal Synchronization(2022-12-01T06:00:00.000Z) Patel, Ruskin 1992-; Penev, Kaloyan; Goux, Warren J.; Kesden, Michael; Ishak-Boushaki, Mustapha; King, Lindsay J.; Anderson, Phillip C.Tides play a crucial role in shaping the evolution of the bodies in binary systems. With the discovery of close-in hot Jupiter systems from exoplanet missions such as Kepler and TESS, it has become imperative to understand the tidal effects, which can shed light on their formation and observed orbital properties. Various models proposed in the literature come with some inherent assumptions on the evolution of binary systems under the influence of tides. The tidal dissipation in stars or planets is generally studied empirically using an efficiency parameter, commonly known as the Tidal Quality Factor (Q∗). Throughout the literature, significant inconsistencies exist in the constraints obtained on Q∗. In this thesis, we aim to remove these inconsistencies by relaxing some of the assumptions previously made and exploring the dependencies of Q∗ on stellar and orbital properties. We perform Monte Carlo Markov Chain simulations to find tight constraints on Q∗ using the observed rotation periods of primary star in eclipsing binary systems, selected from the Kepler Catalog.Item Distinguishing Black-Hole Spin-Orbit Resonances by their Gravitational-Wave Signatures(American Physical Society, 2014-06-24) Gerosa, D.; O'Shaughnessy, R.; Kesden, Michael; Berti, E.; Sperhake, U.; 0000 0001 2678 2731 (Kesden, M); Kesden, MichaelIf binary black holes form following the successive core collapses of sufficiently massive binary stars, precessional dynamics may align their spins, S₁ and S₂, and the orbital angular momentum L into a plane in which they jointly precess about the total angular momentum J. These spin orientations are known as spin-orbit resonances since S₁, S₂, and L all precess at the same frequency to maintain their planar configuration. Two families of such spin-orbit resonances exist, differentiated by whether the components of the two spins in the orbital plane are either aligned or antialigned. The fraction of binary black holes in each family is determined by the stellar evolution of their progenitors, so if gravitational-wave detectors could measure this fraction they could provide important insights into astrophysical formation scenarios for binary black holes. In this paper, we show that even under the conservative assumption that binary black holes are observed along the direction of J (where precession-induced modulations to the gravitational waveforms are minimized), the waveforms of many members of each resonant family can be distinguished from all members of the other family in events with signal-to-noise ratios ρ ≃10, typical of those expected for the first detections with Advanced LIGO and Virgo. We hope that our preliminary findings inspire a greater appreciation of the capability of gravitational-wave detectors to constrain stellar astrophysics and stimulate further studies of the distinguishability of spin-orbit resonant families in more expanded regions of binary black-hole parameter space.Item Effective Potentials and Morphological Transitions for Binary Black Hole Spin Precession(American Physical Society, 2015-02-24) Kesden, Michael; Gerosa, D.; O'Shaughnessy, R.; Berti, E.; Sperhake, U.We derive an effective potential for binary black hole (BBH) spin precession at second post-Newtonian order. This effective potential allows us to solve the orbit-averaged spin-precession equations analytically for arbitrary mass ratios and spins. These solutions are quasiperiodic functions of time: after a fixed period, the BBH spins return to their initial relative orientations and jointly precess about the total angular momentum by a fixed angle. Using these solutions, we classify BBH spin precession into three distinct morphologies between which BBHs can transition during their inspiral. We also derive a precession-averaged evolution equation for the total angular momentum that can be integrated on the radiation-reaction time and identify a new class of spin-orbit resonances that can tilt the direction of the total angular momentum during the inspiral. Our new results will help efforts to model and interpret gravitational waves from generic BBH mergers and predict the distributions of final spins and gravitational recoils.Item Enhancing Gravitational Wave Detection Using Machine Learning and Ambient Noise Suppression(August 2023) Murali, Chinthak 1993-; Lumley, David; Williams, Nathan; King, Lindsay J.; Zhu, Hejun; Kesden, Michael; Arrowsmith, StephenIn this thesis, we present two separate deep learning pipelines for the detection and parameter estimation of astrophysical gravitational waves. In part one, we present a convolutional neural network, designed in the auto-encoder configuration that can detect and denoise gravitational waves from merging black hole binaries, orders of magnitude faster than the conventional matched-filtering based detection that is currently employed at advanced-LIGO (aLIGO) and the LVK (LIGO-VIRGO-KAGRA) network in general. The Neural-Network architecture is such that it learns from the sparse representation of data in the time-frequency domain and constructs a non-linear mapping function that maps this representation into two separate masks for signal and noise, facilitating the separation of the two, from raw data. This approach is the first of its kind to apply machine learning based gravitational wave detection/denoising from binary mergers in the 2D representation of gravitational wave data. We applied our formalism to the first gravitational wave event detected, GW150914, successfully recovering the signal at all three phases of coalescence at both aLIGO detectors. This method is further tested on the gravitational wave data from the second observing run (O2) of aLIGO, reproducing all binary black hole mergers detected in O2 at both detectors. The Neural-Net seems to have uncovered a pattern of ‘ringing’ after the ringdown phase of the coalescence, which is not a feature that is present in the conventional binary merger templates. This method can also interpolate and extrapolate between modeled templates and explore gravitational waves that are unmodeled and hence not present in the template bank of signals used in the matched-filtering detection pipelines. Faster and efficient detection schemes, such as this method, will be instrumental as ground based detectors reach their design sensitivity, likely to result in several hundreds of potential detections in a few months of observing runs. In part two, we present another deep learning based architecture using convolutional neural network to estimate the intrinsic parameter of the black holes from the observed raw gravi- tational wave data. This framework has the capability to estimate parameters of coalescing binaries, orders of magnitude faster than the conventional Bayesian analysis based param- eter inference employed at the LVK network. We also attempt to estimate the individual spin components of both black holes, which is often not possible using Bayesian inference. This machine learning based parameter inference scheme, to the best of our knowledge is the first of its kind that can make direct estimation of individual spin components of both black holes from raw detector data. In part three, we present an overview of Ambient Seismic Noise (ASN) and the importance of its mitigation in enhancing ground based gravitational wave detection. ASN is one of the biggest noise contributors below 20Hz in ground based gravitational wave detectors. Seismic Newtonian noise arising from gravity gradients created by seismic waves will become the limiting noise source at low frequencies for second generation gravitational wave detectors. Low frequency noise suppression will especially enhance gravitational wave detection from heavier coalescing astrophysical systems. In this part, we also present results from a series of seismic weight-drop experiments performed at the gravitational wave test detector site at Western Australia. This analysis would be one of many seismic experiments that can help characterize and study the detector location for better seismic isolation and noise suppression.Item Explaining LIGO's Observations via Isolated Binary Evolution with Natal Kicks(Amer Physical Soc) Wysocki, Daniel; Gerosa, Davide; O'Shaughnessy, Richard; Belczynski, Krzysztof; Gladysz, Wojciech; Berti, Emanuele; Kesden, Michael; Holz, Daniel E.; Kesden, MichaelWe compare binary evolution models with different assumptions about black-hole natal kicks to the first gravitational-wave observations performed by the LIGO detectors. Our comparisons attempt to reconcile merger rate, masses, spins, and spin-orbit misalignments of all current observations with state-of-the-art formation scenarios of binary black holes formed in isolation. We estimate that black holes (BHs) should receive natal kicks at birth of the order of sigma similar or equal to 200 (50) km/s if tidal processes do (not) realign stellar spins. Our estimate is driven by two simple factors. The natal kick dispersion sigma is bounded from above because large kicks disrupt too many binaries (reducing the merger rate below the observed value). Conversely, the natal kick distribution is bounded from below because modest kicks are needed to produce a range of spin-orbit misalignments. A distribution of misalignments increases our models' compatibility with LIGO's observations, if all BHs are likely to have natal spins. Unlike related work which adopts a concrete BH natal spin prescription, we explore a range of possible BH natal spin distributions. Within the context of our models, for all of the choices of s used here and within the context of one simple fiducial parameterized spin distribution, observations favor low BH natal spin.Item Multi-Timescale Analysis of Phase Transitions in Precessing Black-Hole Binaries(American Physical Society, 2015-09-14) Gerosa, D.; Kesden, Michael; Sperhake, U.; Berti, E.; O'Shaughnessy, R.; Kesden, MichaelThe dynamics of precessing binary black holes (BBHs) in the post-Newtonian regime has a strong timescale hierarchy: the orbital timescale is very short compared to the spin-precession timescale which, in turn, is much shorter than the radiation-reaction timescale on which the orbit is shrinking due to gravitational-wave emission. We exploit this timescale hierarchy to develop a multiscale analysis of BBH dynamics elaborating on the analysis of Kesden et al. [Phys. Rev. Lett. 114, 081103 (2015)]. We solve the spin-precession equations analytically on the precession time and then implement a quasiadiabatic approach to evolve these solutions on the longer radiation-reaction time. This procedure leads to an innovative "precession-averaged" post-Newtonian approach to studying precessing BBHs. We use our new solutions to classify BBH spin precession into three distinct morphologies, then investigate phase transitions between these morphologies as BBHs inspiral. These precession-averaged post-Newtonian inspirals can be efficiently calculated from arbitrarily large separations, thus making progress towards bridging the gap between astrophysics and numerical relativity.Item Nano-biothiol Interactions of Engineered Nanoparticles(December 2021) Zhou, Qinhan; Zheng, Jie; Kesden, Michael; Gnade, Bruce E.; Nielsen, Steven O.; Meloni, Gabriele; D'Arcy, SheenaNanomedicines have been extensively studied in the past decades at the fundamental level because they could potentially make a paradigm shift in human healthcare. Nano-bio interactions play a central role in the precise control of the benefit and hazards of nanomedicines, but current studies mainly focus on how nanoparticles are taken up by cells and interact with different receptors. There is still not enough investigation of how the physiological environment transforms engineered nanoparticles through a variety of biochemical reactions. This dissertation aims to fundamentally understand the nanoparticle-biochemical interactions and the in vivo transport of engineered nanoparticles modulated by these interactions. In Chapter 1 of this dissertation, an overall review is given on the current understanding of nanobio interactions at the molecular and chemical levels, particularly. In Chapter 2, we systematically investigated how the nanoparticle size, the thiols species, and the protein binding affect the interactions between the nanoparticles and thiols at the in vitro level. In Chapter 3, we focused on unraveling the relation between the nanoparticle-biothiol interactions in vitro and the nanoparticle-biothiol interactions in vivo. In Chapter 4, we explored the nanoparticle-biothiol interactions in the diseased mice model and illustrated the application of nanoparticle-biothiol interactions in disease diagnosis. Finally, in Chapter 5, we present the summary and outlook. These new understanding on nano-biochemical interactions at both in vitro and in vivo levels will help further advance physiology at the nanoscale as well as open new pathways to early disease diagnosis and treatment.Item Precessional Instability in Binary Black Holes with Aligned Spins(2015-10-02) Gerosa, Davide; Kesden, Michael; O'Shaughnessy, Richard; Klein, Antoine; Berti, Emanuele; Sperhake, Ulrich; Trifiro, Daniele; Kesden, MichaelBinary black holes on quasicircular orbits with spins aligned with their orbital angular momentum have been test beds for analytic and numerical relativity for decades, not least because symmetry ensures that such configurations are equilibrium solutions to the spin-precession equations. In this work, we show that these solutions can be unstable when the spin of the higher-mass black hole is aligned with the orbital angular momentum and the spin of the lower-mass black hole is antialigned. Spins in these configurations are unstable to precession to large misalignment when the binary separation r is between the values (r{ud±}= √X̅₁ ± √q̅x̅)⁴ (1-q)⁻² M where M is the total mass, q ≡ m₂/m₁ is the mass ratio, and χ₁ (χ₂) is the dimensionless spin of the more (less) massive black hole. This instability exists for a wide range of spin magnitudes and mass ratios and can occur in the strong-field regime near the merger. We describe the origin and nature of the instability using recently developed analytical techniques to characterize fully generic spin precession. This instability provides a channel to circumvent astrophysical spin alignment at large binary separations, allowing significant spin precession prior to merger affecting both gravitational-wave and electromagnetic signatures of stellar-mass and supermassive binary black holes.Item Quantum Search on Molecular Graphs and Word-representable Line Graphs(2021-12-01T06:00:00.000Z) Akrobotu, Prosper Delanyo; Akbar, Mohammad; Kesden, Michael; Dragovic, Vladimir; Ramakrishna, Viswanath; Dabkowski, MieczyslawThe work presented in this thesis broadly falls under two quantum search procedures: quantum search using a continuous-time quantum walk and quantum search using adiabatic quantum evolution. The searches are conducted on three different graphs: the molecular graph of graphene, the molecular graph of alkane, and on the line graphs of (non-)word-representable graphs. For the latter, a classical solver was also used to resolve a long-standing question. Quantum search using a continuous-time quantum walk was implemented for a marked node on the molecular graph of graphene, the hexagonal lattice. It was established that including second-nearest-neighbor coupling does not have a significant impact on the search time but does seem to improve the probability of success. This builds on the work of Foulger, Gnutzmann, and Tanner on quantum search on graphene who considered only the nearest-neighbor interactions. Quantum search using adiabatic quantum computation was implemented for (a) searching for isomers of alkanes, (b) searching for the most influential node in a network, and (c) for the decision problem of word-representable line graphs. Quadratic unconstrained binary optimization (QUBO) formulations were proposed for these problems to be embedded and solved on both quantum annealing and gate-based quantum computers such as D-Wave quantum annealers and IBM quantum computers. The dynamics of the search is described by a quantum system evolving under a slowly varying Hamiltonian. Based on the adiabatic theorem, the search evolves from the ground state of an initial Hamiltonian H0 to the ground state of a problem Hamiltonian HP . The primary objective in each case was to construct an efficient HP for the search problem. Using the QUBO results from the D-Wave 2000Q and IBM Q QASM simulators, we were able to verify and search for all isomers of alkanes with at most 9 carbon atoms and for the most influential node of undirected networks using eigenvector centrality. Finally, our formulation of the decision problem of word-representable graphs showed that the line graphs of non-word-representable graphs are not always non-word-representable. This answers a 10- year-old open problem.Item Scaffolded Training Environment for Physics Programming (STEPP)(Association for Computing Machinery, Inc, 2019-06) Kitagawa, Midori; Fishwick, Paul Anthony; Kesden, Michael; Urquhart, Mary; Guadagno, R.; Jin, Rong; Tran, Ngoc M.; Omogbehin, Erik; Prakash, Aditya; Awaraddi, Priyanka; Hale, Baily; Suura, Ken; Raj, A.; Stanfield, J.; Vo, H.; Kitagawa, Midori; Fishwick, Paul Anthony; Kesden, Michael; Urquhart, Mary; Jin, Rong; Tran, Ngoc M.; Omogbehin, Erik; Prakash, Aditya; Awaraddi, Priyanka; Hale, Baily; Suura, KenWe are a year into the development of a software tool for modeling and simulation (M&S) of 1D and 2D kinematics consistent with Newton’s laws of motion. Our goal has been to introduce modeling and computational thinking into learning high-school physics. There are two main contributions from an M&S perspective: (1) the use of conceptual modeling, and (2) the application of Finite State Machines (FSMs) to model physical behavior. Both of these techniques have been used by the M&S community to model high-level “soft systems” and discrete events. However, they have not been used to teach physics and represent ways in which M&S can improve physics education. We introduce the NSF-sponsored STEPP project along with its hypothesis and goals. We also describe the development of the three STEPP modules, the server architecture, the assessment plan, and the expected outcomes. ©2019 Association of Computing Machinery.Item Spherically Symmetric Static Solutions in General Relativity(2021-12-01T06:00:00.000Z) Solanki, Rahulkumar; King, Lindsay J.; Stefan, Mihaela C.; Akbar, Mohammad; Kesden, Michael; Ishak-Boushaki, Mustapha; Penev, KaloyanThis thesis studies spherically symmetric static solutions in general relativity. The most general form of matter in general relativity compatible with staticity and spherical symmetry is anisotropic fluid. We study all possible algorithms that can generate all solutions of the anisotropic fluid system via quadrature using all possible pairs of the four basic functions of the system as input functions. We also study sub-algorithms that generate all solutions that are regular at the center and, for this, we revisit the conditions for central regularity for both isotropic and anisotropic systems and obtain all possible sets of equivalent initial conditions for regularity by combining the Einstein equations with the previouslyknown geometric conditions of regularity. Our study provides a reformulation of an existing algorithm for the system and provides its first regularity analysis. A surprisingly simple new algorithm for the anisotropic system follows from our study that aligns itself with the regularity conditions. This concordance enables us to find solutions that satisfy all the other hard-to-achieve conditions of physical acceptability. Anisotropy has increasingly been shown to be physically relevant in recent times. We keep the well-studied isotropic system as a special case and use it as a frame of reference for measuring the success of our study of the anisotropic system. We then study the hydrostatic equilibrium of static (an)isotropic fluid spheres. From the condition of hydrostatic equilibrium, we explore maps between (an)isotropic solutions with the same density profiles and develop solution-generating techniques to find new solutions from existing ones. We compare and give physical interpretations of several equilibrium configurations in terms of fluid variables and provide several examples where the solutiongenerating theorems can be utilized to find physically acceptable anisotropic solutions. This include a new exact solution that satisfies all physically desirable conditions. Finally, we study light propagation in Kottler, i.e., Schwarzschild-(anti-)de Sitter, spacetime. The metric of this spacetime is known in canonical coordinates and, unlike its Λ = 0 version (i.e, Schwarzschild metric), this metric was not known in isotropic coordinates (in which the constant-time hypersurfaces are flat). We obtain the Kottler metric in isotropic coordinates. This further enables us to plot the refractive indices of Kottler spacetime and show that the invariance of Snell’s law in ordinary geometric optics is analogous to projective equivalence in isotropic static coordinates. We conclude with a summary and some future directions.Item Stellar Tidal Disruption Events in General Relativity(Springer/Plenum Publishers, 2019-02-12) Stone, Nicholas C.; Kesden, Michael; Cheng, Roseanne M.; van Velzen, Sjoert; 0000-0002-5987-1471 (Kesden, M); Kesden, MichaelA tidal disruption event (TDE) ensues when a star passes too close to a supermassive black hole (SMBH) in a galactic center, and is ripped apart by its tidal field. The gaseous debris produced in a TDE can power a bright electromagnetic flare as it is accreted by the SMBH; so far, several dozen TDE candidates have been observed. For SMBHs with masses above approximate to 10⁷ M⊙, the tidal disruption of solar-type stars occurs within ten gravitational radii of the SMBH, implying that general relativity (GR) is needed to describe gravity. Three promising signatures of GR in TDEs are: (1) a super-exponential cutoff in the volumetric TDE rate for SMBH masses above approximate to 10⁸ M⊙ due to direct capture of tidal debris by the event horizon, (2) delays in accretion disk formation (and a consequent alteration of the early-time light curve) caused by the effects of relativistic nodal precession on stream circularization, and (3) quasi-periodic modulation of X-ray emission due to global precession of misaligned accretion disks and the jets they launch. We review theoretical models and simulations of TDEs in Newtonian gravity, then describe how relativistic modifications give rise to these proposed observational signatures, as well as more speculative effects of GR. We conclude with a brief summary of TDE observations and the extent to which they show indications of these predicted relativistic signatures.Item Study of Intrinsic Alignment of Galaxies in Recent Galaxy Surveys(2021-12-01T06:00:00.000Z) Pedersen, Eske M; Ishak-Boushaki, Mustapha; González, Juan E.; Kesden, Michael; Penev, Kaloyan; Da Silveira Rodrigues, Fabiano; King, Lindsay J.Weak lensing is one of the most promising new probes of cosmological parameters. However, it also comes with its own series of systematics and challenges to overcome. In this dissertation we will focus on our work done to isolate the astrophysical systematic effect known as intrinsic alignment of galaxies. We first introduce the methodology and underlying theory that gave rise to the field of weak gravitational lensing, explaining how minuscule changes in the shapes of distant galaxies can be used to obtain better constraints on the matter distribution and the makeup of our entire universe. Then we introduce the idea that galaxies are not isolated objects, but rather are located inside clusters of galaxies or along gas-rich filaments of the large scale structure of the universe. This leads to a systematic effect in the form of the galaxy shapes being distorted prior to lensing, because they intrinsically align with the large scale structure around them. This effect causes either false negatives or false positives when interpreted as weak lensing distortions in observations. Intrinsic alignment of galaxies was first detected about a decade and a half ago, and since then a few different approaches have been suggested to mitigate this. Our work is focused on the idea of using the extra information like unused correlations available within modern cosmological surveys to isolate these intrinsic alignment signals. This provides us with the dual advantages of getting rid of a systematic effect but also gives the possibility of studying the intrinsic alignment itself in more detail. Our work has focused on the development of analysis tools for this separation and the subsequent application of these tools to detect of intrinsic alignment of galaxies. This is done in anticipation of the upcoming Vera Rubin Observatory’s Legacy Survey of Space and Time (LSST). The tools described in this dissertation were made specifically to be ready for this survey and were developed as extensions to the analysis tools being developed for the LSST by its Dark Energy Science Collaboration (DESC). Since LSST has not yet begun, we have applied these tools to two earlier surveys: The Kilo Degree Survey (KiDS)’s data release of approximately 450 square degrees and the Dark Energy Survey (DES)’s year one data release. In both cases we have found strong signs of intrinsic alignment using our self-calibration analysis. We also showed how we can use this method to handle both intrinsic alignment in galaxy-galaxy lensing and in cosmic shear correlations. This has strong implications for constraining the physics of galaxy evolution with LSST.Item The Averaging Problem in Cosmology and Macroscopic Gravity(2022-08-01T05:00:00.000Z) Agashe, Anish; Ishak-Boushaki, Mustapha; Gevorgyan, Vladimir; King, Lindsay; Kesden, Michael; Penev, Kaloyan; Akbar, MohammadThe dynamics of the universe are traditionally modelled by employing cosmological so- lutions to the Einstein field equations. In these solutions, the matter distribution is taken to be averaged over cosmological scales, and hence, the Einstein tensor needs to be av- eraged as well. To construct such an averaged theory of gravity, one needs a covariant averaging procedure for tensor fields. Macroscopic gravity (MG) is one such theory. It gives the macroscopic Einstein field equations (mEFEs) where the effects due to averag- ing are encapsulated in a correction term, the so-called back-reaction. This additional term accounts for the non-commutativity between the averaging operation and the calculation of Einstein tensor. In this dissertation, we analyse how to deal with inhomogeneities within macroscopic gravity. First, we model the inhomogeneities as linear perturbations around the spa- tially homogeneous Friedmann-Robertson-Lemaître-Walker (FLRW) geometry. Then, we analyse exact inhomogeneous models with plane and spherically symmetric geometries. We calculate the back-reaction in these models and analyse how it modifies observations done within them. First, we explore the application of the MG formalism to an almost-FLRW model. Namely, we find solutions to the field equations of MG taking the averaged universe to be almost- FLRW modelled using a linearly perturbed FLRW metric. We study several solutions with different functional forms of the metric perturbations including plane waves ansatzes. We find that back-reaction terms are present not only at the background level but also at perturbed level, reflecting the non-linear nature of the averaging process. To analyse how observations get modified by the back-reaction, we derive the expres- sions for distance measures in MG. We analyse two cases. In the first one, the back- reaction modifies distances only through the expansion history. In the second one, the back-reaction density parameter enters the distance formulae in such a way that, phe- nomenologically, it is degenerate with a spatial curvature. Turning to the perturbations, we derive an equation for growth of structure and analyse how back-reaction modifies the linear growth rate. Thus, the averaging effect can extend to both the expansion and the growth of structure in the universe. Then, we turn our attention to inhomogeneous models with plane and spherically sym- metric geometries. We calculate the MG correction term for such models and find that it takes the form of an anisotropic fluid with a qualitative behaviour of an effective cur- vature in the field equations. We categorise the solutions according to the source for the space-time – vacuum, dust and perfect fluid. Within these three categories, we treat, in detail, the cases of the static spherically symmetric vacuum solution (Schwarzschild exte- rior), the static spherically symmetric perfect fluid solutions (Schwarzschild interior and Tolman VII) and the non-static spherically symmetric dust solution (Lemaître-Tolman- Bondi (LTB)). This is a first step towards analysing back-reaction in inhomogeneous cos- mology with MG.Item Unified Treatment of Tidal Disruption by Schwarzschild Black Holes(2017-04-03) Servin, Juan; Kesden, Michael; 0000-0002-5987-1471 (Kesden, M); Servin, Juan; Kesden, MichaelStars on orbits with pericenters sufficiently close to the supermassive black hole at the center of their host galaxy can be ripped apart by tidal stresses. Some of the resulting stellar debris becomes more tightly bound to the hole and can potentially produce an observable flare called a t (TDE). We provide a self-consistent, unified treatment of TDEs by nonspinning (Schwarzschild) black holes, investigating several effects of general relativity including changes to the boundary in phase space that defines the loss-cone orbits on which stars are tidally disrupted or captured. TDE rates decrease rapidly at large black hole masses due to direct stellar capture, but this effect is slightly countered by the widening of the loss cone due to the stronger tidal fields in general relativity. We provide a new mapping procedure that translates between Newtonian gravity and general relativity, allowing us to better compare predictions in both gravitational theories. Partial tidal disruptions in relativity will strip more material from the star and produce more tightly bound debris than in Newtonian gravity for a stellar orbit with the same angular momentum. However, for deep encounters leading to full disruption in both theories, the stronger tidal forces in relativity imply that the star is disrupted further from the black hole and that the debris is therefore less tightly bound, leading to a smaller peak fallback accretion rate. We also examine the capture of tidal debris by the horizon and the relativistic pericenter precession of tidal debris, finding that black holes of 10⁶ solar masses and above generate tidal debris precessing by 10° or more per orbit.