Kinetic theory and the speed of sound in dense matter

Abstract

We discuss a constraint on the speed of sound, $c_s^2$, derived from relativistic kinetic theory and show how it can be expressed in terms of the average sound speed, $\langle c_s^2 \rangle$. This reformulation highlights the interplay between instantaneous and integrated stiffness of the equation of state and allows the kinetic-theory bound to be visualized as a restriction in the $c_s^2$-$\langle c_s^2 \rangle $ plane.

Figures (1)

• Figure 1: Probability density function (PDF) of the EOS in the $c_s^2-\langle c_s^2 \rangle$ space. The black, solid line shows the averaged EOS obtained by averaging the pressure for given energy density. The arrows on the black line indicate the direction of increasing density. The blue, dotted ellipse shows the $d_c=0.2$ threshold Annala:2023cwx, red, dash-dotted line shows $\beta=0$Marczenko:2023txe, and green, dash-doubly-dotted line marks $\gamma = 1.75$Annala:2019puf threshold. The gray band shows the pQCD constraint. The dashed vertical and horizontal lines mark $c_s^2 = \langle c_s^2 \rangle = 1/3$. The region above the purple, dashed line is not admissible by the kinetic theory (see text for details).