We investigate the potential of ground-based gravitational-wave detectors to probe the mass function of intermediate-mass black holes (IMBHs) wherein we also include BHs in the upper mass gap $sim 60-130~M_odot$. Using the noise spectral density of t
he upcoming LIGO and Virgo fourth observing (O4) run, we perform Bayesian analysis on quasi-circular non-precessing, spinning IMBH binaries (IMBHBs) with total masses $50mbox{--} 500 M_odot$, mass ratios 1.25, 4, and 10, and (dimensionless) spins up to 0.95, and estimate the precision with which the source-frame parameters can be measured. We find that, at $2sigma$, the source-frame mass of the heavier component of the IMBHBs can be constrained with an uncertainty of $sim 10-40%$ at a signal to noise ratio of $20$. Focusing on the stellar-mass gap, we first evolve stars with massive helium cores using the open-source MESA software instrument to establish the upper and lower edges of the mass gap. We determine that the lower edge of the mass gap is $simeq$ 59$^{+34}_{-13}$ $M_{odot}$, while the upper edge is $simeq$ 139$^{+30}_{-14}$ $M_{odot}$, where the error bars indicate the mass range that follows from the $pm 3sigma$ uncertainty in the ${}^{12}text{C}(alpha, gamma) {}^{16} text{O}$ nuclear rate. We then study IMBHBs with components lying in the mass gap and show that the O4 run will be able to robustly identify most such systems. In this context, we also re-analyze the GW190521 event and show that the 90$%$ confidence interval of the primary-mass measurement lies inside the mass gap. Finally, we show that the precision achieved with the O4 run (and future O5 run) could be crucial for understanding the mass function, the formation mechanism, and evolution history of IMBHs.
The detection of gravitational waves (GWs) and an accompanying electromagnetic (E/M) counterpart have been suggested as a future probe for cosmology and theories of gravity. In this paper, we present calculations of the luminosity distance of sources
taking into account inhomogeneities in the matter distribution that are predicted in numerical simulations of structure formation. In addition, we show that inhomogeneities resulting from clustering of matter can mimic certain classes of modified gravity theories, or other effects that dampen GW amplitudes, and deviations larger than $delta u sim mathcal{O}(0.1) (99% rm{C.L.})$ to the extra friction term $ u$, from zero, would be necessary to distinguish them. For these, we assume mock GWs sources, with known redshift, based on binary population synthesis models, between redshifts $z=0$ and $z=5$. We show that future GW detectors, like Einstein Telescope or Cosmic Explorer, will be needed for strong constraints on the inhomogeneity parameters and breaking the degeneracy between modified gravity effects and matter anisotropies by measuring $ u$ at $5 %$ and $1 %$ level with $100$ and $350$ events respectively.
We introduce the use of autoregressive normalizing flows for rapid likelihood-free inference of binary black hole system parameters from gravitational-wave data with deep neural networks. A normalizing flow is an invertible mapping on a sample space
that can be used to induce a transformation from a simple probability distribution to a more complex one: if the simple distribution can be rapidly sampled and its density evaluated, then so can the complex distribution. Our first application to gravitational waves uses an autoregressive flow, conditioned on detector strain data, to map a multivariate standard normal distribution into the posterior distribution over system parameters. We train the model on artificial strain data consisting of IMRPhenomPv2 waveforms drawn from a five-parameter $(m_1, m_2, phi_0, t_c, d_L)$ prior and stationary Gaussian noise realizations with a fixed power spectral density. This gives performance comparable to current best deep-learning approaches to gravitational-wave parameter estimation. We then build a more powerful latent variable model by incorporating autoregressive flows within the variational autoencoder framework. This model has performance comparable to Markov chain Monte Carlo and, in particular, successfully models the multimodal $phi_0$ posterior. Finally, we train the autoregressive latent variable model on an expanded parameter space, including also aligned spins $(chi_{1z}, chi_{2z})$ and binary inclination $theta_{JN}$, and show that all parameters and degeneracies are well-recovered. In all cases, sampling is extremely fast, requiring less than two seconds to draw $10^4$ posterior samples.
A passing gravitational wave causes a deflection in the apparent astrometric positions of distant stars. The effect of the speed of the gravitational wave on this astrometric shift is discussed. A stochastic background of gravitational waves would re
sult in a pattern of astrometric deflections which are correlated on large angular scales. These correlations are quantified and investigated for backgrounds of gravitational waves with sub- and super-luminal group velocities. The statistical properties of the correlations are depicted in two equivalent and related ways: as correlation curves and as angular power spectra. Sub-(super-)luminal gravitational wave backgrounds have the effect of enhancing (suppressing) the power in low-order angular modes. Analytical representations of the redshift-redshift and redshift-astrometry correlations are also derived. The potential for using this effect for constraining the speed of gravity is discussed.
Gravitational wave astrophysics relies heavily on the use of matched filtering both to detect signals in noisy data from detectors, and to perform parameter estimation on those signals. Matched filtering relies upon prior knowledge of the signals exp
ected to be produced by a range of astrophysical systems, such as binary black holes. These waveform signals can be computed using numerical relativity techniques, where the Einstein field equations are solved numerically, and the signal is extracted from the simulation. Numerical relativity simulations are, however, computationally expensive, leading to the need for a surrogate model which can predict waveform signals in regions of the physical parameter space which have not been probed directly by simulation. We present a method for producing such a surrogate using Gaussian process regression which is trained directly on waveforms generated by numerical relativity. This model returns not just a single interpolated value for the waveform at a new point, but a full posterior probability distribution on the predicted value. This model is therefore an ideal component in a Bayesian analysis framework, through which the uncertainty in the interpolation can be taken into account when performing parameter estimation of signals.
Extreme mass ratio in-spirals (EMRIs) are candidate events for gravitational wave detection in the millihertz range (by detectors like LISA and eLISA). These events involve a stellar-mass black hole, or a similar compact object, descending in the gra
vitational field of a supermassive black hole, eventually merging with it. Properties of the in-spiralling trajectory away from resonance are well known and have been studied extensively, however little is known about the behaviour of these binary systems at resonance, when the radial and lateral frequencies of the orbit become commensurate. We describe the two existing models, the instantaneous frequency approach used by Gair, Bender, and Yunes, and the standard two timescales approach implemented by Flanagan and Hinderer. In both cases, the exact treatment depends on the modelling of the gravitational self-force, which is currently not available. We extend the results in Gair, Bender and Yunes to higher order in the on-resonance flux modification, and argue that the instantaneous frequency approach is also a valid treatment of the resonance problem. The non-linear differential equations which arise in treating resonances are interesting from a mathematical view point. We present our algorithm for perturbative solutions and the results to third order in the infinitesimal parameter, and discuss the scope of this approach.
A common technique for detection of gravitational-wave signals is searching for excess power in frequency-time maps of gravitational-wave detector data. In the event of a detection, model selection and parameter estimation will be performed in order
to explore the properties of the source. In this paper, we develop a Bayesian statistical method for extracting model-dependent parameters from observed gravitational-wave signals in frequency-time maps. We demonstrate the method by recovering the parameters of model gravitational-wave signals added to simulated advanced LIGO noise. We also characterize the performance of the method and discuss prospects for future work.
We demonstrate the use of automatic Bayesian inference for the analysis of LISA data sets. In particular we describe a new automatic Reversible Jump Markov Chain Monte Carlo method to evaluate the posterior probability density functions of the a prio
ri unknown number of parameters that describe the gravitational wave signals present in the data. We apply the algorithm to a simulated LISA data set containing overlapping signals from white dwarf binary systems (DWD) and to a separate data set containing a signal from an extreme mass ratio inspiral (EMRI). We demonstrate that the approach works well in both cases and can be regarded as a viable approach to tackle LISA data analysis challenges.
