Measuring the Hubble constant with kilonovae using the Expanding Photosphere Method

While gravitational wave (GW) standard sirens from neutron star (NS) mergers have been proposed to offer good measurements of the Hubble constant, we show in this paper how a variation of the expanding photosphere method (EPM) or spectral-fitting expanding atmosphere method, applied to the kilonovae (KNe) associated with the mergers, can provide an independent distance measurement to individual mergers that is potentially accurate to within a few percent. There are four reasons why the KN-EPM overcomes the major uncertainties commonly associated with this method in supernovae: 1) the early continuum is very well-reproduced by a blackbody spectrum, 2) the dilution effect from electron scattering opacity is likely negligible, 3) the explosion times are exactly known due to the GW detection, and 4) the ejecta geometry is, at least in some cases, highly spherical and can be constrained from line-shape analysis. We provide an analysis of the early VLT/X-shooter spectra AT2017gfo showing how the luminosity distance can be determined, and find a luminosity distance of $D_L = 44.5\pm0.8$ Mpc in agreement with, but more precise than, previous methods. We investigate the dominant systematic uncertainties, but our simple framework, which assumes a blackbody photosphere, does not account for the full time-dependent three-dimensional radiative transfer effects, so this distance should be treated as preliminary. The luminosity distance corresponds to an estimated Hubble constant of $H_0 = 67.0\pm 3.6$ km s$^{-1}$ Mpc$^{-1}$, where the dominant uncertainty is due to the modelling of the host peculiar velocity. We also estimate the expected constraints on $H_0$ from future KN-EPM-analysis with the upcoming O4 and O5 runs of the LIGO collaboration GW-detectors, where five to ten similar KNe would yield 1\% precision cosmological constraints.