Improved constraints on modified gravity with eccentric gravitational waves

Recent gravitational wave observations have allowed stringent new constraints on modifications to general relativity (GR) in the extreme gravity regime. Although these observations were consistent with compact binaries with no orbital eccentricity, gravitational waves emitted in mildly eccentric binaries may be observed once detectors reach their design sensitivity. In this paper, we study the effect of eccentricity in gravitational wave constraints of modified gravity, focusing on Jordan-Brans-Dicke-Fierz theory as an example. Using the stationary phase approximation and the postcircular approximation (an expansion in small eccentricity), we first construct an analytical expression for frequency-domain gravitational waveforms produced by inspiraling compact binaries with small eccentricity in this theory. We then calculate the overlap between our approximate analytical waveforms and an eccentric numerical model (TaylorT4) to determine the regime of validity (in eccentricity) of the former. With this at hand, we carry out a Fisher analysis to determine the accuracy to which Jordan-Brans-Dicke-Fierz theory could be constrained given future eccentric detections consistent with general relativity. We find that the constraint on the theory initially deteriorates (due to covariances between the eccentricity and the Brans-Dicke coupling parameter), but then it begins to recover, once the eccentricity is larger than approximately 0.03. We also find that third-generation ground-based detectors and space-based detectors could allow for constraints that are up to an order of magnitude more stringent than current Solar System bounds. Our results suggest that waveforms in modified gravity for systems with moderate eccentricity should be developed to maximize the theoretical physics that can be extracted in the future

Topics in Gravitational Wave Physics: Black-Hole Spectroscopy, Neutron Star Dynamical Tides, and Numerical Relativity

In this thesis, we explore various topics in gravitational wave physics, including black hole spectroscopy, dynamical tides of neutron stars, numerical relativity, and modified theories of gravity. In our study of black hole spectroscopy, we develop a novel framework for identifying quasinormal modes in ringdown signals. We apply this method to numerical-relativity waveforms of binary black hole systems and find second-order and retrograde quasinormal modes in the ringdown regime. We also apply this method to GW150915, resulting in new insights into the existence of the first overtone. On the other hand, we explore how the excitation of quasinormal modes encodes information about binaries’ parameters. Focusing on superkick configurations, we find universal dependence of the mode amplitudes and phases on the binary’s configurations. Tidal effects have significant imprints on gravitational waves emitted during the final stage of the coalescence of binaries involving neutron stars. We examine how dynamical tides can be significant when neutron stars’ characteristic oscillations become resonant with orbital motion, and we investigate their impact on measuring neutron-star parameters with gravitational waves. Specifically, we conduct systematic studies on the tidal excitation of fundamental and Rossby modes of spinning neutron stars and find that their effects may be significant and detectable in the era of third-generation gravitational-wave detectors, which in turn could lead to more stringent constraints on the properties of neutron stars. Regarding numerical relativity, we implement a fully relativistic three-dimensional Cauchy-characteristic matching algorithm to establish a more accurate boundary condition for numerical-relativity simulations. We justify the correctness of the algorithm by nonlinearly propagating gravitational-wave pluses and find that the new boundary condition does reduce spurious numerical reflection at outer boundaries and improves the accuracy of the generated waveforms. The second part focuses on the initial data of binary black holes for numerical simulations. We extend the superposed harmonic initial data, which breaks down for high-spin black holes, to higher spins by introducing a new spatial coordinate system: superposed modified harmonic. We find that the new initial data preserves a nice property of the superposed harmonic system: the suppression of junk radiation. Furthermore, we find that the volume-weighted constraint violations for the new initial data converge with numerical resolution during the junk stage, which means there are fewer high-frequency components at outer spacetime regions. Finally, we investigate the features of gravitational waves within theories beyond general relativity, focusing on two specific aspects. First, we present a numerical-relativity simulation of a black hole-neutron star merger in scalar-tensor gravity with binary parameters consistent with the gravitational wave event GW200115. We consider the Damour-Esposito-Farèse extension to Brans-Dicke theory and find that the scalar-tensor system evolves faster than its general-relativity counterpart due to dipole radiation, merging a full gravitational-wave cycle before the GR counterpart. We also compare the numerical waveforms with post-Newtonian theory and find good agreement during the inspiral. Second, we propose a new approach, based on numerical-relativity waveforms, for reconstructing the late-time near-horizon geometry of merging binary black holes and computing gravitational-wave echoes from exotic compact objects. We use a physically-motivated way to impose boundary conditions near the horizon and apply the Boltzmann reflectivity to compute the quasinormal modes of non-rotating ECOs, as well as gravitational-wave echoes. Additionally, we investigate the detectability of these echoes in current and future detectors and prospects for parameter estimation.</p

Revisiting the tidal excitation of Rossby modes in coalescing binary systems

Rossby modes (r-modes) of rotating neutron stars can be excited by the gravitomagnetic forces in coalescing binary systems. The previous study by Flanagan and Racine [Phys. Rev. D 75, 044001 (2007)] showed that this kind of dynamical tide (DT) can induce phase shifts of 0.1 rad on gravitational waveforms, which is detectable by third-generation (3G) detectors. In this paper, we study the impact of this DT on measuring neutron-star parameters in the era of 3G detectors. We incorporate two universal relations among neutron star properties predicted by different equations of state: (i) the well-known I-Love relation between momentum of inertia and (f-mode) tidal Love number, and (ii) a relation between the r-mode overlap and tidal Love number, which is newly explored in this paper. We find that r-mode DT will provide rich information about slowly rotating neutron stars with frequency ranging from 10 to 100 Hz. For a binary neutron star system (with a signal-to-noise ratio around 1500 in the Cosmic Explorer), the spin frequency of each individual neutron star can be constrained to 6% (fractional error) in the best-case scenario. The degeneracy between the Love numbers of individual neutron stars is dramatically reduced: each individual Love number can be constrained to around 20% in the best case, while the fractional error for both symmetric and anti-symmetric Love numbers are reduced by factors of around 300. Furthermore, DT also allows us to measure the spin inclination angles of the neutron stars, to 0.09 rad in the best case, and thus place constraints on NS natal kicks and supernova explosion models. Besides parameter estimation, we have also developed a semi-analytic method that accurately describes detailed features of the binary evolution that arise due to the DT

Excitation of f-modes during mergers of spinning binary neutron star

Tidal effects have important imprints on gravitational waves (GWs) emitted during the final stage of the coalescence of binaries that involve neutron stars (NSs). Dynamical tides can be significant when NS oscillations become resonant with orbital motion; understanding this process is important for accurately modeling GW emission from these binaries and for extracting NS information from GW data. In this paper, we use semianalytic methods to carry out a systematic study on the tidal excitation of fundamental modes (f-modes) of spinning NSs in coalescencing binaries, focusing on the case when the NS spin is antialigned with the orbital angular momentum—where the tidal resonance is most likely to take place. We first expand NS oscillations into stellar eigenmodes, and then obtain a Hamiltonian that governs the tidally coupled orbit-mode evolution. (Our treatment is at Newtonian order, including a gravitational radiation reaction at quadrupole order.) We then find a new approximation that can lead to analytic expressions of tidal excitations to a high accuracy, and are valid in all regimes of the binary evolution: adiabatic, resonant, and postresonance. Using the method of osculating orbits, we obtain semianalytic approximations to the orbital evolution and GW emission; their agreements with numerical results give us confidence in our understanding of the system’s dynamics. In particular, we recover both the averaged postresonance evolution, which differs from the preresonance point-particle orbit by shifts in orbital energy and angular momentum, as well as instantaneous perturbations driven by the tidal motion. Finally, we use the Fisher matrix technique to study the effect of dynamical tides on parameter estimation. We find that, for a system with component masses of (1.4,1.4) M_⊙ at 100 Mpc, the constraints on the effective Love number of the (2,2) mode at Newtonian order can be improved by a factor of 3 ∼ 4 if spin frequency is as high as 500 Hz. The relative errors are 0.7 ∼ 0.8 in the Cosmic Explorer, and they might be further improved by post-Newtonian effects. The constraints on the f-mode frequency and the spin frequency are improved by factors of 5 ∼ 6 and 19 ∼ 27, respectively. In the Cosmic Explorer case, the relative errors are 0.2 ∼ 0.4 and 0.7 ∼ 1.0, respectively. Hence, the dynamical tides may potentially provide an additional channel to study the physics of NSs. The method presented in this paper is generic and not restricted to f-mode; it can also be applied to other types of tides

Using rational filters to uncover the first ringdown overtone in GW150914

There have been debates in the literature about the existence of the first overtone in the ringdown of GW150914. We develop a novel Bayesian framework to reanalyze the data of this event, by incorporating a new technique, the "rational filter" that can clean particular modes from the ringdown signal. We examine the existence of the first overtone in GW150914 from multiple novel perspectives. First, we confirm that the estimates of the remnant black hole mass and spin are more consistent with those obtained from the full IMR signal when including the first overtone at an early stage of the ringdown (right after the inferred signal peak); such improvement fades away at later times. Second, we formulate a new way to compare the ringdown models with and without the first overtone by calculating the Bayes factor at different times during the ringdown. We obtain a Bayes factor of 600 at the time when the signal amplitude reaches its peak. The Bayes factor decreases sharply when moving away from the peak time and eventually oscillates around a small value when the overtone signal is expected to have decayed. Third, we clean the fundamental mode from the ringdown of GW150914 and estimate the amplitudes of the modes using the filtered data with MCMC. The inferred amplitude of the fundamental mode is ~0 whereas the amplitude of the first overtone remains almost unchanged, implying that the filtered data is consistent with a first-overtone-only template. Similarly, if we remove the first overtone from the GW150914 data, the filtered data are consistent with a fundamental-mode-only template. Finally, after removing the fundamental mode, we use MCMC to infer the remnant black hole mass and spin from the first overtone alone. We find the posteriors are still informative and consistent with those inferred from the fundamental mode

Free-floating planets from core accretion theory: microlensing predictions

We calculate the microlensing event rate and typical time-scales for the free-floating planet (FFP) population that is predicted by the core accretion theory of planet formation. The event rate is found to be ~$1.8\times 10^{-3}$ of that for the stellar population. While the stellar microlensing event time-scale peaks at around 20 days, the median time-scale for FFP events (~0.1 day) is much shorter. Our values for the event rate and the median time-scale are significantly smaller than those required to explain the \cite{Sum+11} result, by factors of ~13 and ~16, respectively. The inclusion of planets at wide separations does not change the results significantly. This discrepancy may be too significant for standard versions of both the core accretion theory and the gravitational instability model to explain satisfactorily. Therefore, either a modification to the planet formation theory is required, or other explanations to the excess of short-time-scale microlensing events are needed. Our predictions can be tested by ongoing microlensing experiment such as KMTNet, and by future satellite missions such as WFIRST and Euclid.Comment: 6 pages, 5 figures, MNRAS in pres

Black hole spectroscopy by mode cleaning

We formulate a Bayesian framework to analyze ringdown gravitational waves from colliding binary black holes and test the no-hair theorem. The idea hinges on mode cleaning -- revealing subdominant oscillation modes by removing dominant ones using newly proposed ${\it rational~filters}$. By incorporating the filter into Bayesian inference, we construct a likelihood function that depends only on the mass and spin of the remnant black hole (no dependence on mode amplitudes and phases) and implement an efficient pipeline to constrain the remnant mass and spin without Markov chain Monte Carlo (MCMC). We test ringdown models by cleaning combinations of different modes and evaluating the consistency between the residual data and pure noise. The model evidence and Bayes factor are used to demonstrate the presence of a particular mode and to infer the mode starting time. In addition, we design a hybrid approach to estimate the remnant black hole properties exclusively from a single mode using MCMC after mode cleaning. We apply the framework to GW150914 and demonstrate more definitive evidence of the first overtone by cleaning the fundamental mode. This new framework provides a powerful tool for black hole spectroscopy in future gravitational-wave events

Excitation of f-modes during mergers of spinning binary neutron star

Tidal effects have important imprints on gravitational waves (GWs) emitted during the final stage of the coalescence of binaries that involve neutron stars (NSs). Dynamical tides can be significant when NS oscillations become resonant with orbital motion; understanding this process is important for accurately modeling GW emission from these binaries, and for extracting NS information from GW data. In this paper, we carry out a systematic study on the tidal excitation of fundamental modes of spinning NSs in coalescencing binaries, focusing on the case when the NS spin is anti-aligned with the orbital angular momentum-where the tidal resonance is most likely to take place. We first expand NS oscillations into stellar eigen-modes, and then obtain a Hamiltonian that governs the tidally coupled orbit-mode evolution. We next find a new approximation that can lead to analytic expressions of tidal excitations to a high accuracy, and are valid in all regimes of the binary evolution: adiabatic, resonant, and post-resonance. Using the method of osculating orbits, we obtain semi-analytic approximations to the orbital evolution and GW emission; their agreements with numerical results give us confidence in on our understanding of the system's dynamics. In particular, we recover both the averaged post-resonance evolution, which differs from the pre-resonance point-particle orbit by shifts in orbital energy and angular momentum, as well as instantaneous perturbations driven by the tidal motion. Finally, we use the Fisher matrix technique to study the effect of dynamical tides on parameter estimation. We find that the dynamical tides may potentially provide an additional channel to study the physics of NSs. The method presented in this paper is generic and not restricted to f mode; it can also be applied to other types of tide