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The interior of neutron stars contains matter at the highest densitiesrealized in our Universe. Interestingly, theoretical studies of dense matter,in combination with the existence of two solar mass neutron stars, indicatethat the speed of sound $c_s$ has to increase to values well above theconformal limit ($c_s^2\sim 1/3$) before decreasing again at higher densities.The decrease could be explained by either a strong first-order phase transitionor a cross-over transition from hadronic to quark matter. The latter scenarioleads to a pronounced peak in the speed of sound reaching values above theconformal limit, naturally explaining the inferred behavior. In this work, weuse the Nuclear-Physics Multi-Messenger Astrophysics framework \textsc{NMMA} tocompare predictions of the quarkyonic matter model with astrophysicalobservations of neutron stars, with the goal of constraining model parameters.Assuming quarkyonic matter to be realized within neutron stars, we find thatthere can be a significant amount of quarks inside the core of neutron starswith masses in the two solar mass range, amounting to up to $\sim 0.13M_\odot$,contributing $\sim 5.9\%$ of the total mass. Furthermore, for the quarkyonicmatter model investigated here, the radius of a $1.4M_\odot$ neutron star wouldbe $13.44^{+1.69}_{-1.54} (13.54^{+1.02}_{-1.04})$ km, at $95\%$ credibility,without (with) the inclusion of AT2017gfo.

Probing Quarkyonic Matter in Neutron Stars with the Bayesian Nuclear-Physics Multi-Messenger Astrophysics Framework