Thermal evolution of massive compact objects with dense quark cores

Abstract

We examine the thermal evolution of a sequence of compact objects containing low-mass hadronic and high-mass quark-hadronic stars constructed from a microscopically motivated equation of state. The dependence of the cooling tracks in the temperature versus age plane is studied on the variations of the gaplessness parameter (the ratio of the pairing gap for red-green quarks to the electron chemical potential) and the magnitude of blue quark gap. The pairing in the red-green channel is modeled assuming an inhomogeneous superconducting phase to avoid tachionic instabilities and anomalies in the specific heat; the blue colored condensate is modeled as a Bardeen-Cooper-Schrieffer (BCS)-type color superconductor. We find that massive stars containing quark matter cool faster in the neutrino-cooling era if one of the colors (blue) is unpaired and/or the remaining colors (red-green) are paired in a inhomogeneous gapless superconducting state. The cooling curves show significant variations along the sequence, as the mass (or the central density) of the models is varied. This feature provides a handle for fine-tuning the models to fit the data on the surface temperatures of same-age neutron stars. In the late-time photon cooling era we observe inversion in the temperature arrangement of models, i.e., stars experiencing fast neutrino cooling are asymptotically hotter than their slowly cooling counterparts.Comment: v1: 10 pages, 3 figures; v2: 11 pages 5 figures, matches published versio

Rapid cooling of Cassiopeia A as a phase transition in dense QCD

“…Furthermore, we choose to work with a pairing gap Δ b = 100 keV, which leads to blue quarks not affecting the cooling dynamics or the fits to Cas A data; i.e., they only play a passive role. The effect of lower values of this gap on the cooling is discussed elsewhere (Hess & Sedrakian 2011). …”

“…Note that b β = rg β /2 owing to the different numbers of colors involved. Several studies used similar parameterizations (Grigorian et al 2005;Hess & Sedrakian 2011). Furthermore, we choose to work with a pairing gap Δ b = 100 keV, which leads to blue quarks not affecting the cooling dynamics or the fits to Cas A data; i.e., they only play a passive role.…”

“…For the inhomogeneous redgreen condensate, the critical temperature changes with δμ (Hess & Sedrakian 2011)…”

“…Our cooling model is described in Hess & Sedrakian (2011), where the details of the microscopic input and the method of solution can be found. Here we describe the extension of this model, which allows us to account for the phase transition between the phases in a phenomenological manner.…”

“…Models that predict quark matter in such massive compact stars in color-superconducting states have been studied extensively (Alford et al 2005a;Klähn et al 2007;Ippolito et al 2008;Knippel & Sedrakian 2009;Kurkela et al 2010;Bonanno & Sedrakian 2012). Color superconductivity is important; otherwise, the unpaired quarks cool a star by neutrino emission rapidly to temperatures well below those observed in Cas A (Page et al 2000;Alford et al 2005b;Anglani et al 2006;Grigorian et al 2005;Hess & Sedrakian 2011).…”