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GW170817 is a binary neutron star merger that exhibited a gravitational wave(GW) and a gamma-ray burst, followed by an afterglow. In this work, we estimatethe Hubble constant ($H_0$) using broad-band afterglow emission andrelativistic jet motion from the Very Long Baseline Interferometry and HubbleSpace Telescope images of GW170817. Compared to previous attempts, we combinethese messengers with GW in a simultaneous Bayesian fit. We probe the $H_0$measurement robustness depending on the data set used, the assumed jet model,the possible presence of a late time flux excess. Using the sole GW leads to a$20\%$ error ($77^{+21}_{-10}$ km/s/Mpc, medians, 16th-84th percentiles),because of the degeneracy between viewing angle ($\theta_v$) and luminositydistance ($d_L$). The latter is reduced by the inclusion in the fit of theafterglow light curve, leading to $H_0=96^{+13}_{-10}$ km/s/Mpc, a large value,caused by the fit preference for high viewing angles due to the possiblepresence of a late-time excess in the afterglow flux. Accounting for the latterby including a constant flux component at late times brings$H_0=78.5^{+7.9}_{-6.4}$ km/s/Mpc. Adding the centroid motion in the analysisefficiently breaks the $d_L-\theta_v$ degeneracy and overcome the late-timedeviations, giving $H_0 = 69.0^{+4.4}_{-4.3}$ km/s/Mpc (in agreement withPlanck and SH0ES measurements) and $\theta_v = 18.2^{+1.2}_{-1.5}$ deg. This isvalid regardless of the jet structure assumption. Our simulations show that fornext GW runs radio observations are expected to provide at most few othersimilar events.

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