Spectra and elliptic flow of light hadrons in an expanding fire-cylinder model for the RHIC Beam Energy Scan

We investigate the transverse momentum spectra ($p_T$) and elliptic flow ($v_2$) of ${\pi }^{\pm }$, $K^{\pm }$, $p$, and $\bar{p}$ produced in peripheral Au+Au collisions at $\sqrt{s_{\mathrm{N}\mathrm{N}}}=7.7$, 11.5, 19.6, 27, and 39 GeV in the Beam Energy Scan (BES) Program at the Relativistic Heavy Ion Collider (RHIC). The analysis is carried out within an expanding elliptic fire-cylinder model that incorporates longitudinal expansion and anisotropic transverse flow. Particle production at kinetic freeze-out is obtained using a local equilibrium distribution function with a blast-wave-like fluid velocity profile derived from the expansion dynamics of the elliptic fire-cylinder. The model parameters governing the collective expansion are first constrained by fitting the midrapidity $p_T$ spectra of ${\pi }^{\pm }$ and are then applied, without further adjustment, to $K^{\pm }$, $p$, and $\bar{p}$. The model provides a consistent description of the $p_T$ spectra and reproduces the qualitative behavior of the elliptic flow for all considered particle species.