The impact of the crust equation of state on the analysis of GW170817

The detection of GW170817, the first neutron star-neutron star merger observed by Advanced LIGO and Virgo, and its following analyses represent the first contributions of gravitational wave (GW) data to understanding dense matter. Parameterizing the high density section of the equation of state (EOS) of both neutron stars through spectral decomposition, and imposing a lower limit on the maximum mass value, led to an estimate of the stars' radii of $R_1 = 11.9_{- 1.4}^{+ 1.4}$ km and $R_2 = 11.9_{- 1.4}^{+ 1.4}$ km. These values do not, however, take into account any uncertainty owed to the choice of the crust low-density EOS, which was fixed to reproduce the SLy EOS model. We here re-analyze GW170817 data and establish that different crust models do not strongly impact the mass or tidal deformability of a neutron star: it is impossible to distinguish between low-density models with GW analysis. However, the crust does have an effect on the inferred radius. We predict the systematic error due to this effect using neutron star structure equations, and compare the prediction to results from full parameter estimation runs. For GW170817, this systematic error affects the radius estimate by 0.3 km, approximately $3\%$ of the NS radii.