The stiffness of the hadronic equation of state has been extracted from the production rate of $K^{+}$ mesons in heavy-ion collisions around $1A\mathrm{GeV}$ incident energy. The data are best described with a compression modulus $K$ around 200 MeV, a value which is usually called “soft.” This is concluded from a detailed comparison of the results of transport theories with the experimental data using two different procedures: (i) the energy dependence of the ratio of $K^{+}$ from $\mathrm{Au}+\mathrm{Au}$ and $\mathrm{C}+\mathrm{C}$ collisions and (ii) the centrality dependence of the $K^{+}$ multiplicities. It is demonstrated that input quantities of these transport theories which are not precisely known, such as the kaon-nucleon potential, the $\Delta N\to N{K}^{+}\Lambda$ cross section, or the lifetime of the $\Delta$ in matter, do not modify this conclusion.

• Received 5 July 2005

DOI:https://doi.org/10.1103/PhysRevLett.96.012302