Physical Models for the Astrophysical Population of Black Holes

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Introduction

Gravitational-wave observations of binary black holes have revealed unexpected structures in the black hole mass distribution. Previous studies employ physically motivated phenomenological models and infer the parameters that control the features of the mass distribution that are allowed in their model, associating the constraints on those parameters with their physical motivations a posteriori. In this work, we take an alternative approach in which we introduce a model parameterizing the underlying stellar and core-collapse physics and obtaining the remnant black hole distribution as a derived by-product. In doing so, we constrain the stellar physics necessary to explain the astrophysical distribution of black hole properties under a given model.

Problem: The distribution of BH masses from gravitational-wave observations exhibits a bump around ~35 solar masses.
 
Goal: To understand the physical processes that lead to this bump and to constrain the underlying astrophysical parameters.
 
Methodology: The authors introduce a model that parameterizes the mapping between progenitor mass and remnant BH mass, accounting for mass-dependent mass loss. This approach allows them to infer constraints on stellar physics and the core-collapse process.
 

Key Findings

  • The current data are consistent with no redshift evolution in the core-remnant mass relationship.
  • The data provide weak constraints on the change of these parameters.
  • The PPISN process, previously proposed as an explanation for the observed excess of black holes at ~35 M, is unlikely to be the primary driver of the bump.
  • The model prefers a steeper merger rate history than the star formation rate, but it is consistent with short delay times between binary formation and merger.
  • The data are consistent with little to no scatter around the progenitor remnant mass mapping.

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Model Details

  • Progenitor Mass Function (IMF): The model assumes a broken power-law IMF for compact object progenitors.
  • Mapping from Progenitor Mass to Remnant Mass (M₁-MBH): The model utilizes a piecewise linear-quadratic mapping, with the transition point (Mtr) and the maximum remnant mass (MBHmax) being free parameters.
  • Scatter in the Mapping: A lognormal distribution is used to introduce scatter around the M₁-MBH mapping.
  • Redshift Evolution: The parameters Mtr and MBHmax are allowed to evolve with redshift.
  • Second-Generation (2G) BHs: A power-law tail is included to model the contribution of 2G BHs.
  • Pairing Function: A power-law pairing function with slope β is used to model the distribution of total mass.
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