Thermal Radiation from an Analytic Hydrodynamic Model with Hadronic and QGP Sources in Heavy-Ion Collisions

TL;DR

This work develops an analytic 1+1D hydrodynamic model with a quark–hadron transition to describe thermal photon production in heavy-ion collisions. By introducing a lattice-inspired, two-phase EOS via phase-specific constants $C_q$ and $C_h$, the authors obtain closed-form expressions for a two-component photon spectrum (QGP and hadronic) and test them against PHENIX non-prompt data in Au+Au at $\,\sqrt{s_{NN}}=200$ GeV. Fitting constraints informed by lattice QCD yield a transition temperature $T_{tr}$ around 156 MeV and centrality-dependent initial temperatures $T_0$, with hadronic contributions necessary to describe central data and absent in more peripheral collisions. The model also validates the hadronic channel against PHOBOS $dN/d\eta$, suggesting the framework provides a coherent analytic baseline linking photons and hadrons. Overall, the paper offers a transparent, analytic benchmark for thermal radiation in heavy-ion collisions and lays the groundwork for future 1+3D, viscous, and more microscopic refinements that can address remaining questions like the direct photon puzzle.

Abstract

In high-energy heavy-ion collisions, a nearly perfect fluid is formed, known as the strongly coupled quark-gluon plasma (QGP). After a short thermalization period, the evolution of this medium can be described by the equations of relativistic hydrodynamics. As the system expands and cools, the QGP undergoes a transition into hadronic matter, marking the onset of quark confinement. Direct photons offer insights into an essential stage of evolution, spanning from the onset of thermalization to the suppression of thermal photon production, which occurs within the hadronic phase. This paper builds upon and extends a previously published solution of relativistic hydrodynamics, incorporating an equation of state that falls within the same class as that predicted by lattice QCD. Based on this solution, a completely analytic model is constructed to describe thermal photon production, accounting for the quark-hadron transition. The model is tested against PHENIX measurements of non-prompt direct photon spectra in Au+Au collisions at $\sqrt{s_{NN}} = 200$ GeV. Good agreement is observed between the model predictions and the experimental data, enabling the investigation of the centrality dependence of the initial temperature. These results provide a benchmark for future theoretical and experimental studies of thermal radiation in heavy-ion collisions.

Figures (8)

• Figure 1: The fit of equation \ref{['eq:total-spectrum']} to the non-prompt direct photon spectrum measured by the PHENIX collaboration in $Au+Au$ collisions at $\sqrt{s_{\rm NN}} =200$ GeV for the 0–20% centrality class. The measured data points are indicated by green markers. The blue dot-dashed curve depicts the hadronic component, as defined by eq. \ref{['eq:hadronic-component']}. The red dashed curve corresponds to the yield of QGP, whose analytical expression is provided by eq. \ref{['eq:quark-component']}. The sum of these two contributions yields the total spectrum, represented by the solid black curve. The error bars denote the statistical errors of the experimental data, whereas the boxes indicate the systematic uncertainties of the same. The yellow band represents the systematic uncertainty of the model fit, quantified based on the systematic uncertainties propagated from the fitted model parameters.
• Figure 2: The fit of equation \ref{['eq:total-spectrum']} to the non-prompt direct photon spectrum measured by the PHENIX collaboration in $Au+Au$ collisions at $\sqrt{s_{\rm NN}} =200$ GeV for the 20–40% centrality class. The curves, error bars, and uncertainty boxes presented in this figure follow the same notation scheme as those used in Fig. \ref{['fig:fig1']}.
• Figure 3: The fit of equation \ref{['eq:total-spectrum']} to the non-prompt direct photon spectrum measured by the PHENIX collaboration in $Au+Au$ collisions at $\sqrt{s_{\rm NN}}=200$ GeV for the 40–60% centrality class.The curves, error bars, and uncertainty boxes presented in this figure follow the same notation scheme as those used in Fig. \ref{['fig:fig1']}.
• Figure 4: The fit of equation \ref{['eq:total-spectrum']} to the non-prompt direct photon spectrum measured by the PHENIX collaboration in $Au+Au$ collisions at $\sqrt{s_{\rm NN}}=200$ GeV for the 60–93% centrality class. The curves, error bars, and uncertainty boxes presented in this figure follow the same notation scheme as those used in Fig. \ref{['fig:fig1']}.
• Figure 5: Extracted initial temperatures as a function of centrality, obtained from comparisons between the experimental data and my analytic model with (cyan) and without (red) the inclusion of the hadronic component, shown here as qualitatively indicative results.