tokens: by most of the theoretical equations of state (e.g., Özel Freire 2016 ). Therefore, it is unlikely that this system is observed at a very large inclination angle. On the other hand, assuming that binaries are randomly inclined with respect to the observer, i.e., assuming a flat distribution of , we find a median NS mass (corresponding to ) of (see the right panel of Figure 6 ). Such a value would place M13F on the highest-mass side of the known NS mass distribution (e.g., Antoniadis et al. 2016b ; Cromartie et al. 2020 ). All of this suggests that either M13F is observed at quite small inclination angles () or it hosts a massive NS. Indeed, under the assumption of a flat distribution of , there is a probability that the compact object mass is larger than , thus favoring the case of a massive NS. Finally, we further investigate the possibility of having a standard NS mass coupled with a low-inclination angle. To this aim, we used a Markov Chain Monte Carlo sampler (Foreman-Mackey et al. 2019 ) to explore the combination of NS masses and orbital inclination angles able to reproduce the observed mass function. We defined a standard Gaussian likelihood function to minimize the difference between the left and right sides of Equation ( 2 ). We assumed a uniform prior on the distribution of and also a prior on the NS mass distribution following that empirically derived by Antoniadis et al. ( 2016b ), which is roughly a double Gaussian with a main component centered at and with a dispersion of about , and a secondary component centered at and with a dispersion of about . The posterior distribution is shown in Figure 7 , and the results based on the 16th, 50th, and 84th percentiles show that M13F could host an NS with an almost standard mass of if orbiting with an inclination angle °. Figure 6. Left panel: companion mass as a function of the NS mass. The solid horizontal line marks the best-fit value of the companion mass () and the light-gray region delimited by the two horizontal dashed lines marks its estimated uncertainty. The dark-gray shaded area is the region forbidden by the binary mass function (see Equation ( 2 )), while the dotted–dashed colored lines are the curves obtained assuming different inclination angles. The vertical line represents a canonical NS mass of . Right panel: NS mass as a function of the cosine of the orbital inclination angle, for the estimated mass of the companion star: the solid curve marks the combination of values allowed by the best-fit value of the companion mass (), while the light-gray region delimited by the two dashed curves marks the combinations allowed within the uncertainty (see the legend). The rightmost panel shows, as reference, the NS mass distribution empirically derived by Antoniadis et al. ( 2016b ). Figure 7. Corner plots showing the 1D and 2D projections of the posterior probability distribution of the NS mass and inclination angle of M13F. The 1D histograms are the marginalized probability
ner_tags: O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-CelestialObject O O O O O O O B-TextGarbage O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model I-Model O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-TextGarbage O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-TextGarbage O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O