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ABSTRACT We assess the possibility of detecting both eccentricity and gas effects (migration and accretion) in the gravitational wave (GW) signal from LISA massive black hole binaries at redshift $z=1$. Gas induces a phase correction to the GW signal with an effective amplitude ($$C_{\rm g}$$) and a semimajor axis dependence (assumed to follow a power-law with slope $$n_{\rm g}$$). We use a complete model of the LISA response and employ a gas-corrected post-Newtonian inspiral-only waveform model TaylorF2Ecc. By using the Fisher formalism and Bayesian inference, we constrain $$C_{\rm g}$$ together with the initial eccentricity $$e_0$$, the total redshifted mass $$M_z$$, the primary-to-secondary mass ratio q, the dimensionless spins $$\chi _{1,2}$$ of both component BHs, and the time of coalescence $$t_c$$. We find that simultaneously constraining $$C_{\rm g}$$ and $$e_0$$ leads to worse constraints on both parameters with respect to when considered individually. For a standard thin viscous accretion disc around $$M_z=10^5~{\rm M}_{\odot }$$, $q=8$, $$\chi _{1,2}=0.9$$, and $$t_c=4$$ years MBHB, we can confidently measure (with a relative error of $$\lt 50$$ per cent) an Eddington ratio $${\rm f}_{\rm Edd}\sim 0.1$$ for a circular binary and $${\rm f}_{\rm Edd}\sim 1$$ for an eccentric system assuming $$\mathcal {O}(10)$$ stronger gas torque near-merger than at the currently explored much-wider binary separations. The minimum measurable eccentricity is $$e_0\gtrsim 10^{-2.75}$$ in vacuum and $$e_0\gtrsim 10^{-2}$$ in gas. A weak environmental perturbation ($${\rm f}_{\rm Edd}\lesssim 1$$) to a circular binary can be mimicked by an orbital eccentricity during inspiral, implying that an electromagnetic counterpart would be required to confirm the presence of an accretion disc. 

Extreme Mass Ratio Inspirals (EMRIs) are one of the key sources for future space-based gravitational wave interferometers. Measurements of EMRI gravitational waves are expected to determine the characteristics of their sources with sub-percent precision. However, their waveform generation is challenging due to the long duration of the signal and the high harmonic content. Here, we present the first ready-to-use Schwarzschild eccentric EMRI waveform implementation in the frequency domain for use with either graphics processing units (GPUs) or central processing units (CPUs). We present the overall waveform implementation and test the accuracy and performance of the frequency domain waveforms against the time domain implementation. On GPUs, the frequency domain waveform takes in median 0.044 s to generate and is twice as fast to compute as its time domain counterpart when considering massive black hole masses $\ge 2\times 10^6{\text{M}}_{\odot }$and initial eccentricitiese₀> 0.2. On CPUs, the median waveform evaluation time is 5 s, and it is five times faster in the frequency domain than in the time domain. Using a sparser frequency array can further speed up the waveform generation, reaching up to 0.3 s. This enables us to perform, for the first time, EMRI parameter inference with fully relativistic waveforms on CPUs. Future EMRI models, which encompass wider source characteristics (particularly black hole spin and generic orbit geometries), will require significantly more harmonics. Frequency domain models will be essential analysis tools for these astrophysically realistic and important signals. 

ABSTRACT We derive a Fisher matrix for the parameters characterizing a population of gravitational-wave events. This provides a guide to the precision with which population parameters can be estimated with multiple observations, which becomes increasingly accurate as the number of events and the signal-to-noise ratio of the sampled events increase. The formalism takes into account individual event measurement uncertainties and selection effects, and can be applied to arbitrary population models. We illustrate the framework with two examples: an analytical calculation of the Fisher matrix for the mean and variance of a Gaussian model describing a population affected by selection effects, and an estimation of the precision with which the slope of a power-law distribution of supermassive black hole masses can be measured using extreme-mass-ratio inspiral observations. We compare the Fisher predictions to results from Monte Carlo analyses, finding very good agreement. 

Standard sirens have been the central paradigm in gravitational-wave cosmology so far. From the gravitational wave signature of compact star binaries, it is possible to measure the luminosity distance of the source directly, and if additional information on the source redshift is provided, a measurement of the cosmological expansion can be performed. This review article discusses several methodologies that have been proposed to use gravitational waves for cosmological studies. Methods that use only gravitational-wave signals and methods that use gravitational waves in conjunction with additional observations such as electromagnetic counterparts and galaxy catalogs will be discussed. The review also discusses the most recent results on gravitational-wave cosmology, starting from the binary neutron star merger GW170817 and its electromagnetic counterpart and finishing with the population of binary black holes, observed with the third Gravitational-wave Transient Catalog GWTC–3. 

ABSTRACT The search for gravitational waves using Pulsar Timing Arrays (PTAs) is a computationally expensive complex analysis that involves source-specific noise studies. As more pulsars are added to the arrays, this stage of PTA analysis will become increasingly challenging. Therefore, optimizing the number of included pulsars is crucial to reduce the computational burden of data analysis. Here, we present a suite of methods to rank pulsars for use within the scope of PTA analysis. First, we use the maximization of the signal-to-noise ratio as a proxy to select pulsars. With this method, we target the detection of stochastic and continuous gravitational wave signals. Next, we present a ranking that minimizes the coupling between spatial correlation signatures, namely monopolar, dipolar, and Hellings & Downs correlations. Finally, we also explore how to combine these two methods. We test these approaches against mock data using frequentist and Bayesian hypothesis testing. For equal-noise pulsars, we find that an optimal selection leads to an increase in the log-Bayes factor two times steeper than a random selection for the hypothesis test of a gravitational wave background versus a common uncorrelated red noise process. For the same test but for a realistic European PTA (EPTA) data set, a subset of 25 pulsars selected out of 40 can provide a log-likelihood ratio that is 89 % of the total, implying that an optimally selected subset of pulsars can yield results comparable to those obtained from the whole array. We expect these selection methods to play a crucial role in future PTA data combinations. 

Abstract Using ground-based gravitational-wave detectors, we probe the mass function of intermediate-mass black holes (IMBHs) wherein we also include BHs in the upper mass gap at ∼60–130 M ⊙ . Employing the projected sensitivity of the upcoming LIGO and Virgo fourth observing run (O4), we perform Bayesian analysis on quasi-circular nonprecessing, spinning IMBH binaries (IMBHBs) with total masses 50–500 M ⊙ , 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 2 σ , the mass of the heavier component of IMBHBs can be constrained with an uncertainty of ∼10%–40% at a signal-to-noise ratio of 20. Focusing on the stellar-mass gap with new tabulations of the 12 C( α , γ ) 16 O reaction rate and its uncertainties, we evolve massive helium core stars using MESA to establish the lower and upper edges of the mass gap as ≃ 59 − 13 + 34 M ⊙ and ≃ 139 − 14 + 30 M ⊙ respectively, where the error bars give the mass range that follows from the ±3 σ uncertainty in the 12 C( α , γ ) 16 O nuclear reaction rate. We find that high resolution of the tabulated reaction rate and fine temporal resolution are necessary to resolve the peak of the BH mass spectrum. 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. Finally, we reanalyze GW190521 with a state-of-the-art aligned-spin waveform model, finding that the primary mass lies in the mass gap with 90% credibility. 

Abstract We outline the “dark siren” galaxy catalog method for cosmological inference using gravitational wave (GW) standard sirens, clarifying some common misconceptions in the implementation of this method. When a confident transient electromagnetic counterpart to a GW event is unavailable, the identification of a unique host galaxy is in general challenging. Instead, as originally proposed by Schutz, one can consult a galaxy catalog and implement a dark siren statistical approach incorporating all potential host galaxies within the localization volume. Trott & Huterer recently claimed that this approach results in a biased estimate of the Hubble constant, H 0 , when implemented on mock data, even if optimistic assumptions are made. We demonstrate explicitly that, as previously shown by multiple independent groups, the dark siren statistical method leads to an unbiased posterior when the method is applied to the data correctly. We highlight common sources of error possible to make in the generation of mock data and implementation of the statistical framework, including the mismodeling of selection effects and inconsistent implementations of the Bayesian framework, which can lead to a spurious bias.