Density dependent strong coupling constant of QCD derived from compact star data

Abstract

The present work is an endeavour to connect the properties of tiny nearly massless objects with those of some of the most massive ones, the compact stars. Since 1996 there is major influx of X-ray and $\gamma$ ray data from binary stars, one or both of which are compact objects that are difficult to explain as neutron stars since they contain a mass M in too small a radius R . The suggestion has been put forward that these are strange quark stars (SS) explainable in a simple model with chiral symmetry restoration (CSR) for the quarks and the M, R and other properties like QPOs (quasi periodic oscillations) in their X-ray power spectrum. It would be nice if this astrophysical data could shed some light on fundamental properties of quarks obeying QCD. One can relate the strong coupling constant of QCD, $\alpha_s$ to the quark mass through the Dyson-Schwinger gap equation using the real time formalism of Dolan and Jackiw. This enables us to obtain the density dependence of $\alpha_s$ from the simple CSR referred to above. This way fundamental physics, difficult to extract from other models like for example lattice QCD, can be constrained from present-day compact star data and may be put back to modelling the dense quark phase of early universe.Comment: 7 pages, 4 figure