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    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.

  2. 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, amore »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.« less
    Free, publicly-accessible full text available November 23, 2023
  3. 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 ) 16more »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.« less
  4. Abstract The Laser Interferometer Space Antenna (LISA) has the potential to reveal wonders about the fundamental theory of nature at play in the extreme gravity regime, where the gravitational interaction is both strong and dynamical. In this white paper, the Fundamental Physics Working Group of the LISA Consortium summarizes the current topics in fundamental physics where LISA observations of gravitational waves can be expected to provide key input. We provide the briefest of reviews to then delineate avenues for future research directions and to discuss connections between this working group, other working groups and the consortium work package teams. These connections must be developed for LISA to live up to its science potential in these areas.
    Free, publicly-accessible full text available December 1, 2023