Spinning spectral sirens: Robust cosmological measurement using mass-spin correlations in the binary black hole population

Gravitational waves from compact binary mergers provide a direct measurement of luminosity distance, which, in combination with redshift information, serves as a cosmological probe. In order to statistically infer merger redshifts, the ``spectral standard siren" method relies on features, such as peaks, dips or breaks, in the compact object mass spectrum, which get redshifted in the detector-frame relative to the source-frame. However, if the source-frame location of these features evolves over cosmic time, the spectral siren measurement may be biased. Some features, such as the edges of the pair-instability supernova mass gap, may be more stable than others. We point out that binary black hole (BBH) spins, which are not redshifted in the detector-frame, provide a natural way to identify robust mass scales for spectral siren cosmology. For example, there is recent evidence for a mass scale in the BBH population that separates slowly spinning from more rapidly spinning BBH mergers, consistent with the lower edge of the pair instability gap. Applying our method to data from LIGO-Virgo-KAGRA's third transient catalog, we demonstrate how to isolate this mass scale and produce a robust ``spinning spectral siren" measurement of the Hubble constant: $H_0 = 85^{+99}_{-67}\,\rm{km}\, \rm{s}^{-1} \rm{Mpc}^{-1}$, or $H_0 =80^{+60}_{-46}\,\rm{km}\, \rm{s}^{-1} \rm{Mpc}^{-1}$ when combined with other mass features, such as the $\sim35\,M_\odot$ peak. We consider the possibility that the source-frame location of the $\sim35\,M_\odot$ peak evolves with redshift, and show that information from black hole spin can be used to mitigate the associated bias for self-calibrating spectral sirens.