The Speed of Sound in Hadronic Matter

We calculate the speed of sound cs in an ideal gas of resonances, whose mass spectrum is assumed to have the Hagedorn form ρ(m)~m-aexp {bm}, which leads to singular behavior at the critical temperature Tc = 1/b. With a = 4 the pressure and the energy density remain finite at Tc, while the specific heat diverges there. As a function of the temperature, the corresponding speed of sound initially increases similarly to that of an ideal pion gas, until near Tc resonance effects dominate, which causes cs to vanish as (Tc-T)1/4. In order to compare this result to the physical resonance gas models, we introduce an upper cut-off M in the resonance mass integration. Although the truncated form still decreases somewhat in the region around Tc, the actual critical behavior in these models is no longer present.