  Quark matter may appear due to a hadronic-quark transition in the core of a
hybrid star. Quarkyonic matter is an approach in which both quarks and nucleons
appear as quasi-particles in a crossover transition, and provides an explicit
realization of early ideas concerning quark matter (e.g., the MIT bag model).
This description has recently been employed by McLerran and Reddy to model
chargeless (pure neutron) matter with an approach that has the virtue that the
speed of sound rises quickly at a neutron-quark transition so as to satisfy
observational constraints on the neutron star maximum mass ($\gtrsim2M_\odot$)
and the radius of a $1.4M_\odot$ star ($R_{1.4}\lesssim 13.5$ km). Traditional
models involving first-order transitions result in softer pressure-energy
density relations that have difficulty satisfying these constraints except with
very narrow choices of parameters. We propose a variation of quarkyonic matter
involving protons and leptons whose energy can be explicitly minimized to
achieve both chemical and beta equilibrium, which cannot be done in the
chargeless formulation. Quarkyonic stellar models are able to satisfy observed
mass and radius constraints with a wide range of model parameters, avoiding the
obligatory fine-tuning of conventional hybrid star models, including requiring
the transition density to be very close to the nuclear saturation density. Our
formulation fits experimental and theoretical properties of the nuclear
symmetry energy and pure neutron matter, and contains as few as three free
parameters. This makes it an ideal tool for the study of high-density matter
that is an efficient alternative to piecewise polytrope or spectral
decomposition methods.
