Neutron stars with crossover to color superconducting quark matter

We follow the idea that the QCD phase diagram may be described by a crossover from a hadron resonance gas to perturbative QCD using the switch function ansatz of Albright, Kapusta and Young [1]. While the switch function could be calibrated at vanishing baryon chemical potential with data from lattice QCD simulations, it has been suggested recently by Kapusta and Welle [2] that in the zero temperature limit, the switch function parameter $\mu_0$ could be constrained by neutron star phenomenology, in particular by massive pulsars like PSR J0740+6620 with a mass exceeding $2~M_\odot$. In this work we demonstrate that this procedure to constrain the QCD phase diagram does crucially depend on the fact that cold dense quark matter is very likely in a color superconducting state.