The Phase Space of Low-Mass Binary Compact Objects from LIGO-Virgo-KAGRA Catalog: Hints on the Chances of Different Formation Scenarios

TL;DR

This work expands the BCO Phase Space framework to low-mass compact objects (LMCOs) and applies it to LVK GWTC-3 events plus GW230529 to link observable GW parameters to distinct formation channels. By modeling four LMCO channels—neutron stars (NS), remnants of binary neutron star mergers (remnant-BNS), primordial black holes (PBH), and low-mass astrophysical black holes (LMABH)—and projecting theoretical trajectories onto the observed phase space defined by $(M,\chi, D_L)$ with selection effects, the authors compute channel weights and assess the plausibility of each formation pathway for individual components. The results reveal strong NS-like signatures around $M\approx1.3\,M_\odot$ and low spins, remnant-BNS tendencies near $M\approx2.0\,M_\odot$ with low spins and a secondary ridge near $2.6\,M_\odot$, LMABH clustering at $M\sim2.0$–$2.2\,M_\odot$ with moderate to high fallback, and tentative PBH indications at sub-solar initial masses; however, significant degeneracies remain due to detector sensitivity and small sample size. With future detectors and additional observables (tidal deformability, eccentricity, electromagnetic counterparts) and higher redshift reach, this phase-space approach offers a powerful, scalable path to disentangle formation channels and constrain compact-object populations across cosmic history.

Abstract

Gravitational wave (GW) observations have significantly advanced our understanding of binary compact object (BCO) formation, yet directly linking these observations to specific formation scenarios remains challenging. The BCO phase space provides a robust and data-driven approach to discover the likely formation scenarios of these binaries. In this study, we expand the previously introduced binary black hole phase space technique to encompass low-mass compact objects (LMCOs), establishing a novel framework to investigate their diverse formation mechanisms. Applying this approach to selected low-mass events $(\lesssim 5 M_\odot)$ from the GWTC-3 catalog and the recently observed GW230529 event, we show for the first time the phase space demonstration of the LMCOs and find the associated probabilities for different formation scenarios including neutron star, astrophysical black hole, or primordial black hole. Our analysis includes the astrophysical modelling uncertainties in and how it causes degeneracy between different formation scenarios. In future, with improvements in GW detector sensitivity and with detection of more GW events, the LMCO phase space framework will significantly strengthen our capacity to associate more likely formation scenarios over the other, thereby refining our understanding of compact object formation for both astrophysical and primordial scenarios, and its evolution across the cosmic redshift.

Figures (5)

• Figure 1: The probabilities of seven low-mass GW events from GWTC-3 along with GW230529, evaluated based on their mass and spin posteriors. Each GW event is represented by two rows of pie charts corresponding to the primary (top row) and secondary (bottom row) components. Each pie chart is divided into four segments indicating the likelihood of different astrophysical formation channels: Neutron Star (left wedge, vertical left colorbar), Low mass Astrophysical Black Hole (right wedge, vertical right colorbar), Primordial Black Hole (top wedge, horizontal top colorbar), and Remnant of Binary Neutron Star (bottom wedge, horizontal bottom colorbar). Colors represent the relative probability weights assigned by integrating over the joint posterior distributions for mass and spin parameters against theoretical distributions for each astrophysical channel. These values are not expected to sum to unity for any individual event, as they are not normalized per event. They are normalised in the entire phase-space volume. As a result, the event-level probabilities should be interpreted within that channel-specific context. Three primary wedges are rendered in white as the object falls outside our low-mass compact-object criteria.
• Figure 2: Evolution of the normalized merger rate density ($R(z) / R_0$) as a function of redshift ($z$) for two different delay times: $t_d = 500$ Myrs ((solid red line, corresponding to NS) and $t_d = 2$ Gyrs ((dashed blue line, corresponding to NS remnants)). The merger rate peaks at lower redshift for the longer delay time, reflecting the delayed merging of binary black holes formed at higher redshifts. The difference in the shape of the curves highlights the impact of the delay time on the merger rate evolution. The shaded region indicates the redshift range accessible to the LVK detectors for the low-mass binary black hole events considered in this analysis.
• Figure 3: This 3D plot illustrates the phase space distribution of Neutron Star, Low mass ABH, Remnant of BNS and PBH, highlighting the distribution of mass, luminosity distance, and dimensionless spin. It shows the distinct regions in the phase space occupied by these compact object. The inset presents the 2D mass-spin projection, further emphasizing the unique mass-spin correlations characteristic of each channel.
• Figure 4: Three-dimensional representation of gravitational-wave events from GWTC-3, along with the newly reported GW230529 from the fourth observing run, for which at least one component’s mean mass lies below $5\,M_\odot$. The axes display the luminosity distance (in Mpc), component mass (in $M_\odot$), and dimensionless spin. Larger circles denote the heavier components, while smaller circles represent the lighter components. Error bars reflect the measurement uncertainties in distance, mass, and spin. Dashed black lines connect the two components of each binary. Shaded regions indicate the parameter spaces corresponding to different formation channels (e.g., primordial black holes, neutron stars, remnants of binary neutron star mergers, and low-mass black holes).
• Figure 5: Projection of phase space trajectories for various formation channels of low-mass compact objects. Top Left: Neutron Stars – Illustrates the probability distribution of trajectories as functions of the mean spin ($\chi_{\mathrm{mean}}$) and mean mass ($M_{\mathrm{mean}}$). Top Right: Neutron Star Merger Remnants - Depicts the probability in the same ($M_{\mathrm{mean}}$, $\chi_{\mathrm{mean}}$) space, capturing the merger outcomes. Bottom Left: Primordial Black Holes - Displays the probability distribution in the phase space defined by the mass accretion rate index ($\dot{m}$) and the initial mass ($M_{\mathrm{int}}$). In all panels, the color bar represents the probability values. Bottom Right: Black Holes under Extreme Astrophysical Conditions - Shows trajectory probabilities influenced by the fallback fraction ($f_{\mathrm{b}}$) and the canonical black hole mean mass ($M_0$).