Multispectral Sirens: Gravitational-wave Cosmology with (Multi-) Subpopulations of Binary Black Holes

Abstract The cosmic expansion rate can be directly measured with gravitational-wave (GW) data of the compact binary mergers by jointly constraining the mass function of the population and the cosmological model via the so-called spectral sirens. Such a method relies on the features in the mass functions, which may originate from some individual subpopulations and hence become blurred/indistinct due to the superposition of different subpopulations. In this work, we propose a novel approach to constrain the cosmic expansion rate with subpopulations of GW events, named multispectral sirens. The advantage of the multispectral sirens compared to the traditional spectral sirens is demonstrated by the simulation with the mock data. The application of this approach to the GWTC-3 data yields <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>73.3</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>25.6</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>29.9</mml:mn> </mml:mrow> </mml:msubsup> <mml:mspace width="0.25em"/> <mml:msup> <mml:mrow> <mml:mi>Mpc</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mspace width="0.25em"/> <mml:mi>km</mml:mi> <mml:mspace width="0.25em"/> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">s</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math> (median and symmetric 68.3% credible interval), which is about 19% tighter than the result inferred with the traditional spectral sirens utilizing a powerlaw+peak mass function. The incorporation of the bright standard siren GW170817 with a uniform prior in [10, 200] (log-uniform prior in [20,140]) Mpc −1 km s −1 gives <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>71.1</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>7.5</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>15.0</mml:mn> </mml:mrow> </mml:msubsup> <mml:mspace width="0.25em"/> <mml:mo stretchy="false">(</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>70.3</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>7.1</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>12.9</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo stretchy="false">)</mml:mo> <mml:mspace width="0.50em"/> <mml:msup> <mml:mrow> <mml:mi>Mpc</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mspace width="0.50em"/> <mml:mi>km</mml:mi> <mml:mspace width="0.50em"/> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">s</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math> (68.3% confidence level), corresponding to an improvement of ∼26% (23%) with respect to the measurement from sole GW170817.