Thermodynamic and hydrodynamic characteristics of interacting system formed in relativistic heavy ion collisions

To study the energy-dependent characteristics of thermodynamic and hydrodynamic parameters, based on the framework of a multi-source thermal model, we analyze the soft transverse momentum ($p_T$) spectra of the charged particles (${\pi }^{-}$, ${\pi }^{+}$, $K^{-}$, $K^{+}$, $\bar{p}$, and p) produced in gold–gold (Au–Au) collisions at the center-of-mass energies $\sqrt{s_{NN}}=7.7$, 11.5, 14.5, 19.6, 27, 39, 62.4, and 200$$GeV from the STAR Collaboration and in lead–lead (Pb–Pb) collisions at $\sqrt{s_{NN}}=2.76$ and 5.02$$TeV from the ALICE Collaboration. In the rest framework of emission source, the probability density function obeyed by meson momenta satisfies the Bose–Einstein distribution, and that obeyed by baryon momenta satisfies the Fermi–Dirac distribution. To simulate the $p_T$ of the charged particles, the kinetic freeze-out temperature T and transverse expansion velocity ${\beta }_T$ of emission source are introduced into the relativistic ideal gas model. Our results, based on the Monte Carlo method for numerical calculation, show a good agreement with the experimental data. The excitation functions of thermodynamic parameter T and hydrodynamic parameter ${\beta }_T$ are then obtained from the analyses, which shows an increasing tendency from 7.7$$GeV to 5.02$$TeV in collisions with different centralities.