  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.
