Measuring the Hubble constant with neutron star black hole mergers

Abstract: The detection of GW170817 and the identification of its host galaxy have allowed for the first standard-siren measurement of the Hubble constant, with an uncertainty of $\sim 14\%$. As more detections of binary neutron stars with redshift measurement are made, the uncertainty will shrink. The dominating factors will be the number of joint detections and the uncertainty on the luminosity distance of each event. Neutron star black hole mergers are also promising sources for advanced LIGO and Virgo. If the black hole spin induces precession of the orbital plane, the degeneracy between luminosity distance and the orbital inclination is broken, leading to a much better distance measurement. In addition neutron star black hole sources are observable to larger distances, owing to their higher mass. Neutron star black holes could also emit electromagnetic radiation: depending on the black hole spin and on the mass ratio, the neutron star can be tidally disrupted resulting in electromagnetic emission. We quantify the distance uncertainty for a wide range of black hole mass, spin and orientations and find that the 1-$\sigma$ statistical uncertainty can be up to a factor of $\sim 10$ better than for a non-spinning binary neutron star merger with the same signal-to-noise ratio. The better distance measurement, the larger gravitational-wave detectable volume, and the potentially bright electromagnetic emission, imply that spinning black hole neutron star binaries can be the optimal standard siren sources as long as their astrophysical rate is larger than $O(10)$ Gpc$^{-3}$yr$^{-1}$, a value allowed by current astrophysical constraints.

Measuring the Hubble Constant with Neutron Star Black Hole Mergers

In the paper titled "Measuring the Hubble constant with neutron star black hole mergers," authors Salvatore Vitale and Hsin-Yu Chen present a research study focused on utilizing gravitational wave detections to measure the Hubble constant, an important parameter governing the rate of expansion of the Universe. Previous measurements of the Hubble constant using supernovae and cosmic microwave background data have been precise but contradictory, showing a disagreement at a significance level of approximately $3\sigma$. Gravitational-wave detections offer a completely independent method of measuring the Hubble constant when they are accompanied by electromagnetic counterparts.

A key aspect of measuring the Hubble constant through gravitational waves involves determining the luminosity distance with high precision, wherein neutron star-black hole (NSBH) mergers present promising candidates. NSBH mergers have advantages for distance measurements due to specific properties, such as higher mass and possible emission of electromagnetic radiation. Additionally, if the black hole in the binary system exerts significant spin leading to spin precession, it breaks the degeneracy between the luminosity distance and orbital inclination, significantly improving distance measurement precision.

The paper explores the statistical uncertainty in measuring distances related to NSBH mergers and presents simulations that demonstrate their potential. It was found that the uncertainty in luminosity distance measurement for NSBHs could be up to ten times better compared to non-spinning binary neutron star mergers with similar signal-to-noise ratios. Specifically, systems with considerable spin precession can significantly reduce the uncertainty due to characteristic modulation of the waveform's amplitude and phase.

The paper further engages in a comparative analysis between the performances of NSBHs and binary neutron star (BNS) mergers for deriving the Hubble constant. With certain parameters, NSBHs emerge as more competitive in terms of precision, especially when their merger rate exceeds $O(10)$ Gpc$^{-3}$yr$^{-1}$, which is within the range of current astrophysical constraints. Precise measurement of the Hubble constant using NSBHs relies on a balance between the achievable precision per event and the rate of detectable events in the Universe.

The implications of utilizing NSBHs for measuring the Hubble constant are notable, as they could provide more accurate constraints if their merger rate is sufficiently high. They offer the opportunity to mitigate uncertainties arising from the peculiar velocity of host galaxies relative to the Hubble flow. The research discusses potential future developments and calls for more theoretical and numerical exploration to understand the electromagnetic and neutrino emissions accompanying NSBH mergers. Those efforts could maximize the scientific yield of future NSBH detections, potentially enhancing precision cosmology efforts.

In conclusion, while direct measurement of the Hubble constant through NSBHs presents challenges, primarily due to uncertainties in their exact merger rate and associated electromagnetic properties, their utilization could complement existing methods. Improvements in waveform models and collaborations between electromagnetic facilities and gravitational-wave astrophysics could bridge existing gaps and ensure effective utilization of NSBHs as cosmic distance indicators.