Potential biases and prospects for the Hubble constant estimation via electromagnetic and gravitational-wave joint analyses

GW170817 is an outstanding event as it paved the way for multi-messenger astrophysics. It is a binary neutron stars merger, that saw the detection of gravitational waves (GW) and the detection of a gamma ray burst (GRB), with the following afterglow emission. Such events are interesting also from a cosmological point of view, as we can derive an Hubble constant H0 measurement (the current expansion rate of the Universe), independently from any cosmic distance ladder. In this work we estimate H0 using the broad band afterglow emission and the relativistic jet centroid motion from the very-large-baseline interferometry (VLBI) and HST images of GW170817. Compared to previous attempts, we join these two messengers with the GW in a simultaneous bayesian fit. We focus on two potential biases: the unknown jet structure and the possible presence of a late time flux excess. Wefind H0 = 70.1+4.6−4.4 km/s/Mpc, with a viewing angle of 20 deg and a distance of 43 Mpc fitting the complete data set. This H0 measure is about 3 times more precise than a GW-only estimation. If we do not include the centroid motion in the analysis, we get H0 = 96+13−10 km/s/Mpc, with a viewing angle of 50 deg and a distance of 31 Mpc. The high viewing angle is preferred because of the possible precence of a late time excess in the afterglow flux. We show that the afterglow alone, in the case of GW170817, is not enough to give a reliable estimation of H0, so attention should be taken in these possible biases that are included when using the electromagnetic domain in the H0 estimation, especially in the future, when more neutron star mergers events will be detected.