# The speed of sound in hadronic matter

Castorina P, Cleymans J, Miller DE, Satz H (2010)

EUROPEAN PHYSICAL JOURNAL C 66(1-2): 207-213.

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We calculate the speed of sound c (s) in an ideal gas of resonances, whose mass spectrum is assumed to have the Hagedorn form rho(m)similar to m (-a) exp {bm}, which leads to singular behavior at the critical temperature T (c) =1/b. With a=4 the pressure and the energy density remain finite at T (c) , 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 T (c) resonance effects dominate, which causes c (s) to vanish as (T (c) -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 T (c) , the actual critical behavior in these models is no longer present.

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### Cite this

Castorina P, Cleymans J, Miller DE, Satz H. The speed of sound in hadronic matter.

*EUROPEAN PHYSICAL JOURNAL C*. 2010;66(1-2):207-213.Castorina, P., Cleymans, J., Miller, D. E., & Satz, H. (2010). The speed of sound in hadronic matter.

*EUROPEAN PHYSICAL JOURNAL C*,*66*(1-2), 207-213.Castorina, P., Cleymans, J., Miller, D. E., and Satz, H. (2010). The speed of sound in hadronic matter.

*EUROPEAN PHYSICAL JOURNAL C*66, 207-213.Castorina, P., et al., 2010. The speed of sound in hadronic matter.

*EUROPEAN PHYSICAL JOURNAL C*, 66(1-2), p 207-213.P. Castorina, et al., “The speed of sound in hadronic matter”,

*EUROPEAN PHYSICAL JOURNAL C*, vol. 66, 2010, pp. 207-213.Castorina, P., Cleymans, J., Miller, D.E., Satz, H.: The speed of sound in hadronic matter. EUROPEAN PHYSICAL JOURNAL C. 66, 207-213 (2010).

Castorina, P., Cleymans, J., Miller, D. E., and Satz, Helmut. “The speed of sound in hadronic matter”.

*EUROPEAN PHYSICAL JOURNAL C*66.1-2 (2010): 207-213.
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arXiv 0906.2289

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