Hierarchical analysis of gravitational-wave measurements of binary black hole spin-orbit misalignments

Binary black holes may form both through isolated binary evolution and through dynamical interactions in dense stellar environments. The formation channel leaves an imprint on the alignment between the black hole spins and the orbital angular momentum. Gravitational waves from these systems directly encode information about the spin--orbit misalignment angles, allowing them to be (weakly) constrained. Identifying sub-populations of spinning binary black holes will inform us about compact binary formation and evolution. We simulate a mixed population of binary black holes with spin--orbit misalignments modelled under a range of assumptions. We then develop a hierarchical analysis and apply it to mock gravitational-wave observations of these populations. Assuming a population with dimensionless spin magnitudes of $\chi = 0.7$, we show that tens of observations will make it possible to distinguish the presence of subpopulations of coalescing binary black holes based on their spin orientations. With $100$ observations it will be possible to infer the relative fraction of coalescing binary black holes with isotropic spin directions (corresponding to dynamical formation in our models) with a fractional uncertainty of $\sim 40\%$. Meanwhile, only $\sim 5$ observations are sufficient to distinguish between extreme models---all binary black holes either having exactly aligned spins or isotropic spin directions.Comment: 12 pages, 9 figures. Updated to match version published in MNRAS as 10.1093/mnras/stx176

Gravitational wave energy spectrum of a parabolic encounter

We derive an analytic expression for the energy spectrum of gravitational waves from a parabolic Keplerian binary by taking the limit of the Peters and Matthews spectrum for eccentric orbits. This demonstrates that the location of the peak of the energy spectrum depends primarily on the orbital periapse rather than the eccentricity. We compare this weak-field result to strong-field calculations and find it is reasonably accurate (~10%) provided that the azimuthal and radial orbital frequencies do not differ by more than ~10%. For equatorial orbits in the Kerr spacetime, this corresponds to periapse radii of rp > 20M. These results can be used to model radiation bursts from compact objects on highly eccentric orbits about massive black holes in the local Universe, which could be detected by LISA.Comment: 5 pages, 3 figures. Minor changes to match published version; figure 1 corrected; references adde

Parameter estimation on compact binary coalescences with abruptly terminating gravitational waveforms

Gravitational-wave astronomy seeks to extract information about astrophysical systems from the gravitational-wave signals they emit. For coalescing compact-binary sources this requires accurate model templates for the inspiral and, potentially, the subsequent merger and ringdown. Models with frequency-domain waveforms that terminate abruptly in the sensitive band of the detector are often used for parameter-estimation studies. We show that the abrupt waveform termination contains significant information that affects parameter-estimation accuracy. If the sharp cutoff is not physically motivated, this extra information can lead to misleadingly good accuracy claims. We also show that using waveforms with a cutoff as templates to recover complete signals can lead to biases in parameter estimates. We evaluate when the information content in the cutoff is likely to be important in both cases. We also point out that the standard Fisher matrix formalism, frequently employed for approximately predicting parameter-estimation accuracy, cannot properly incorporate an abrupt cutoff that is present in both signals and templates; this observation explains some previously unexpected results found in the literature. These effects emphasize the importance of using complete waveforms with accurate merger and ringdown phases for parameter estimation.Comment: Very minor changes to match published versio

Inference on gravitational waves from coalescences of stellar-mass compact objects and intermediate-mass black holes

Gravitational waves from coalescences of neutron stars or stellar-mass black holes into intermediate-mass black holes (IMBHs) of $\gtrsim 100$ solar masses represent one of the exciting possible sources for advanced gravitational-wave detectors. These sources can provide definitive evidence for the existence of IMBHs, probe globular-cluster dynamics, and potentially serve as tests of general relativity. We analyse the accuracy with which we can measure the masses and spins of the IMBH and its companion in intermediate-mass ratio coalescences. We find that we can identify an IMBH with a mass above $100 ~ M_\odot$ with $95\%$ confidence provided the massive body exceeds $130 ~ M_\odot$. For source masses above $\sim200 ~ M_\odot$, the best measured parameter is the frequency of the quasi-normal ringdown. Consequently, the total mass is measured better than the chirp mass for massive binaries, but the total mass is still partly degenerate with spin, which cannot be accurately measured. Low-frequency detector sensitivity is particularly important for massive sources, since sensitivity to the inspiral phase is critical for measuring the mass of the stellar-mass companion. We show that we can accurately infer source parameters for cosmologically redshifted signals by applying appropriate corrections. We investigate the impact of uncertainty in the model gravitational waveforms and conclude that our main results are likely robust to systematics.Comment: 9 pages, 11 figure

Forward Modeling of Double Neutron Stars: Insights from Highly-Offset Short Gamma-Ray Bursts

We present a detailed analysis of two well-localized, highly offset short gamma-ray bursts---GRB~070809 and GRB~090515---investigating the kinematic evolution of their progenitors from compact object formation until merger. Calibrating to observations of their most probable host galaxies, we construct semi-analytic galactic models that account for star formation history and galaxy growth over time. We pair detailed kinematic evolution with compact binary population modeling to infer viable post-supernova velocities and inspiral times. By populating binary tracers according to the star formation history of the host and kinematically evolving their post-supernova trajectories through the time-dependent galactic potential, we find that systems matching the observed offsets of the bursts require post-supernova systemic velocities of hundreds of kilometers per second. Marginalizing over uncertainties in the stellar mass--halo mass relation, we find that the second-born neutron star in the GRB~070809 and GRB~090515 progenitor systems received a natal kick of $\gtrsim 200~\mathrm{km\,s}^{-1}$ at the 78\% and 91\% credible levels, respectively. Applying our analysis to the full catalog of localized short gamma-ray bursts will provide unique constraints on their progenitors and help unravel the selection effects inherent to observing transients that are highly offset with respect to their hosts.Comment: 18 pages, 7 figures, 1 table. ApJ, in pres

Evolutionary Origins of Binary Neutron Star Mergers: Effects of Common Envelope Efficiency and Metallicity

The formation histories of compact binary mergers, especially stellar-mass binary-black hole mergers, have recently come under increased scrutiny and revision. In this paper we revisit the question of the dominant formation channel and efficiency of forming binary neutron-star mergers. We use the stellar and binary evolution code MESA and implement an up-to-date and detailed method for common envelope and mass transfer. We preform simulations for donor masses between 8-20 solar masses with a neutron star companion of 1.4 and 2.0 solar masses, at two metallicities, using varying common envelope efficiencies, and two prescriptions for electron-capture supernovae. In contrast to the case of binary-black hole mergers, for a neutron star companion of 1.4 solar masses, all binary neutron star mergers are formed following a common envelope phase, while for a neutron star mass of 2.0 solar masses we identify a small subset of mergers following only stable mass transfer if the neutron star receives a large natal kick. Regardless of neutron star companion mass, we find that large supernova natal kicks are favored in the formation of binary neutron star mergers, and find more mergers at subsolar metallicity compared to solar.Comment: accepted to Ap

Rapid determination of LISA sensitivity to extreme mass ratio inspirals with machine learning

Gravitational wave observations of the inspiral of stellar-mass compact objects into massive black holes (MBHs), extreme mass ratio inspirals (EMRIs), enable precision measurements of parameters such as the MBH mass and spin. The Laser Interferometer Space Antenna is expected to detect sufficient EMRIs to probe the underlying source population, testing theories of the formation and evolution of MBHs and their environments. Population studies are subject to selection effects that vary across the EMRI parameter space, which bias inference results if unaccounted for. This bias can be corrected, but evaluating the detectability of many EMRI signals is computationally expensive. We mitigate this cost by (i) constructing a rapid and accurate neural network interpolator capable of predicting the signal-to-noise ratio of an EMRI from its parameters, and (ii) further accelerating detectability estimation with a neural network that learns the selection function, leveraging our first neural network for data generation. The resulting framework rapidly estimates the selection function, enabling a full treatment of EMRI detectability in population inference analyses. We apply our method to an astrophysically motivated EMRI population model, demonstrating the potential selection biases and subsequently correcting for them. Accounting for selection effects, we predict that LISA will measure the MBH mass function slope to a precision of 8.8%, the CO mass function slope to a precision of 4.6%, the width of the MBH spin magnitude distribution to a precision of 10% and the event rate to a precision of 12% with EMRIs at redshifts below z=6.Comment: 12 pages, 4 figure

Localization of Compact Binary Sources with Second Generation Gravitational-wave Interferometer Networks

GW170817 began gravitational-wave multimessenger astronomy. However, GW170817 will not be representative of detections in the coming years -- typical gravitational-wave sources will be closer the detection horizon, have larger localization regions, and (when present) will have correspondingly weaker electromagnetic emission. In its design state, the gravitational-wave detector network in the mid-2020s will consist of up to five similar-sensitivity second-generation interferometers. The instantaneous sky-coverage by the full network is nearly isotropic, in contrast to the configuration during the first \change{three} observing runs. Along with the coverage of the sky, there are also commensurate increases in the average horizon for a given binary mass. We present a realistic set of localizations for binary neutron stars and neutron star--black hole binaries, incorporating intra-network duty cycles and selection effects on the astrophysical distributions. Based on the assumption of an $80\%$ duty cycle, and that two instruments observe a signal above the detection threshold, we anticipate a median of $28$ sq.\ deg.\ for binary neutron stars, and $50$--$120$ sq.\ deg.\ for neutron star--black hole (depending on the population assumed). These distributions have a wide spread, and the best localizations, even for networks with fewer instruments, will have localizations of $1$--$10$ sq.\ deg.\ range. The full five instrument network reduces localization regions to a few tens of degrees at worst.Comment: 20 pages, 8 figures, 3 tables, accepted in Ap