Cooling of quark stars from perturbative QCD

TL;DR

This work assesses the thermal evolution of quark stars using a perturbative QCD equation of state with running coupling and strange-quark mass, applied to both bare stars and stars with a hadronic crust. Bare quark stars cool too quickly to match observed luminosities, whereas introducing a crust slows cooling and yields better agreement, though substantial equation-of-state uncertainties remain, particularly at early times. The study highlights the crust's role as a thermal insulator and examines sensitivity to the renormalization scale, finding that the cooling band narrows for bare stars after about one year while remaining broad for crusted configurations. Comparing with MIT bag-model predictions further clarifies how crust presence and EoS choice influence interpretations of thermal data and motivates future work on color-superconducting phases and refined microphysics.

Abstract

We investigate the thermal evolution of quark stars with and without a hadronic crust using an equation of state derived from perturbative QCD that incorporates the running of the strong coupling and the strange quark mass. Our analysis reveals that bare quark stars cool too rapidly to match the luminosity data, including those of the coldest observed isolated neutron stars, even when the uncertainty from the renormalization scale is taken into account. In contrast, configurations featuring a hadronic crust exhibit slower cooling and improved agreement with observational data. We also observe that the cooling band for bare quark stars narrows significantly after $t \sim 1$ year, whereas the configurations with a crust exhibit a larger uncertainty throughout their time evolution.

Figures (9)

• Figure 1: Pressure (left panel) and energy density (right panel), each scaled by their respective Fermi values, shown as functions of the strange quark chemical potential $\mu$. Bands represent the renormalization-scale dependence in the range between $\bar{\Lambda} = 2\mu$ and $\bar{\Lambda} = 4\mu$.
• Figure 2: Equation of state $P(\epsilon)$ for a quark star with a nuclear crust. The low-density sector is described by a BPS equation of state, whereas the high-density sector is built from cold and dense pQCD.
• Figure 3: The main (left) panel shows the full mass-radius diagram computed from the pQCD EoS. Gray curves correspond to configurations without a crust, whereas blue curves include a nuclear crust. The right-hand panels provide zoom views isolating the impact of the crust for the cases $\bar{\Lambda}=2\mu$ (top) and $\bar{\Lambda}=4\mu$ (bottom).
• Figure 4: Redshifted photon luminosity $L_{\infty}$ as a function of stellar age for a quark star with $M=1.4\ M_{\odot}$. Observed data points correspond to measured thermal emission from isolated neutron stars (see main text for details).
• Figure 5: Radial temperature profiles of a $1.4\ M_{\odot}$ bare quark star during the early thermal evolution, computed for different stellar ages $t$, using pQCD EoS with $\bar{\Lambda}=2\mu$ (left) and $\bar{\Lambda}=4\mu$ (right). Each curve is labeled by its corresponding age in years, from $t=0$ (initial condition) to $t=1$ yr.