Distinguishing between Black Holes and Neutron Stars within a Population of Weak Tidal Measurements

TL;DR

This work investigates whether tidal signatures in gravitational-wave CBC inspirals can distinguish NSs from BHs across a population. It combines Fisher-matrix forecasts for individual events with a hierarchical Bayesian population model that treats the NS fraction $f_{ ext{NS}}(m)$ as a function of mass. The findings indicate that single-event tides are difficult to exploit for NS/BH separation at higher masses, and even large catalogs with current detectors yield only weak constraints on $f_{ ext{NS}}(m)$; determining the NS content across masses will generally require catalogs of $>O(200)$ events, though sub-solar mass systems offer more informative constraints. Next-generation detectors like Cosmic Explorer and Einstein Telescope could enable robust population-level inferences about NS fractions, with profound implications for understanding compact-object formation and the NS equation of state.

Abstract

We study the ability of tidal signatures within the inspiral of compact binaries observed through gravitational waves (GWs) to distinguish between neutron stars (NSs) and black holes (BHs). After quantifying how hard this measurement is on a single-event basis, we investigate the ability of a large catalog of GW detections to constrain the fraction of NS in the population as a function of mass: $f_{\mathrm{NS}}(m)$. Using simulated catalogs with realistic measurement uncertainty, we find that $> O(200)$ events will be needed before we can precisely measure $f_{\mathrm{NS}}$, and catalogs of $> O(100)$ events will be needed before we can even rule out the possibility that all low-mass objects are BHs with GW data alone (i.e., without electromagnetic counterparts). Therefore, this is unlikely to occur with advanced detectors, even at design sensitivity. Nevertheless, it could be feasible with next-generation facilities like Cosmic Explorer and Einstein Telescope.

Figures (6)

• Figure 1: Tidal deformability ($\Lambda$) as a function of the gravitational mass ($m$). We show the (black) maximum-likelihood EoS from essickAstrophysicalConstraintsSymmetry2021essickDetailedExaminationAstrophysical2021a and a (red) simple power-law with $\Lambda \propto m^{-5}$.
• Figure 2: Measurement uncertainty for $\Tilde{\Lambda}$ for individual events. (top) $\rho_\mathrm{opt}$ required to achieve $\Tilde{\Lambda} = \sigma_{\Tilde{\Lambda}}$ as a function of source-frame masses for our reference EoS (Fig. \ref{['fig:ns_tides']}). (bottom) Relative uncertainty ($\Tilde{\Lambda} / \sigma_{\Tilde{\Lambda}}$) at $\rho_\mathrm{opt}=10$. The boundary between NSs and BHs ($M_\mathrm{TOV}$) is denoted by black lines.
• Figure 3: Mass distribution assumed in our analysis. (left) The compact object rate density for (black) the overall distribution, (blue) NSs, and (red) BHs. (right) The rate density for the four different binary sub-populations in the joint source-frame component mass plane; grey dashed lines denote the boundaries between sub-populations ($M_\mathrm{TOV}$).
• Figure 4: (left) Hyperposterior for $f_\text{NS}$ when it is assumed to be a constant throughout the entire NS mass range: (colors) hyperposterior averaged over catalog realizations at different catalog sizes and (grey) hyperposteriors for individual catalog realizations for $N_{\text{det}} = 190$. (right) Size of the 68% HPD credible region vs. catalog size: (grey) individual catalog realizations and (black) 68% HPD CR for the hyperposterior averaged over catalog realizations. (colored) Vertical lines denote the catalog sizes highlighted in the left panels.
• Figure 5: Hyperposteriors and credible region sizes for the two-dimensional inference with $f_\text{NS}^\mathrm{true} = 1$. Colors match Fig. \ref{['fig:mean_hpd_1d']}, and the upper-left and lower-right panels show the marginalized one-dimensional posteriors for $f_\mathrm{NS}$ in the upper ($f_\mathrm{NS}^{\mathrm{high}}$) and lower ($f_\mathrm{NS}^\mathrm{low}$) mass bins, respectively.