Viscous photons in relativistic heavy ion collisions

Theoretical studies of the production of real thermal photons in relativistic heavy ion collisions at the Relativistic Heavy Ion Collider (RHIC) are performed. The space-time evolution of the colliding system is modelled using music, a 3+1D relativistic hydrodynamic simulation, using both its ideal and viscous versions. The inclusive spectrum and its azimuthal angular anisotropy are studied separately, and the relative contributions of the different photon sources are highlighted. It is shown that the photon $v_2$ coefficient is especially sensitive to the details of the microscopic dynamics like the equation of state, the ratio of shear viscosity over entropy density, $\eta /s$, and to the morphology of the initial state.

Figure 1

(a) The evolution of temperature in a fixed cell, as a function of time. Results for ideal and viscous hydrodynamics (with $\eta /s=1/4\pi$) are shown. (b) A closer view of the early time temperature evolution.

Figure 2

The Compton and quark-antiquark annihilation contributions to photon production.

Figure 3

A comparison of the equilibrium photon rate from the processes shown in Fig. 2 (dashed lines) with that obtained tallying all channels contributing at leading order in ${\alpha }_s$ (full lines), for $N_f=3$. The lower set of curves are for $T=250$ MeV, and the upper ones are for $T=350$ MeV.

Figure 4

(a) The time evolution of different components of the local ${\pi }^{\mu \nu }$ tensor, divided by $\eta$. (b) The time evolution of the diagonal elements of ${\pi }^{ij}$ (scaled by $\eta$), and also that of the trace of the viscous tensor. The calculations are done for a fluid cell at $x=y=$ 2.5 fm, and $z=0$, and the impact parameter is $b=4.47$ fm.

Figure 5

The fraction of ${\eta }_s\approx 0$ fluid cells with a certain value of $\delta f/f_0$, for different values of the photon momentum in the nucleus-nucleus center of mass frame: 2 GeV (a), and 3 GeV (b). The range of temperature $T>250$ MeV corresponds to $\tau -{\tau }_0\lesssim$ 2 fm/$c$.

Figure 6

(a) The photon yield originating from the phase with parton degrees of freedom only. The contribution from ideal hydro is shown (solid curve), together with the result of using a time evolution associated with viscous hydrodynamics (dotted line), and using a viscous time evolution and corrected microscopic distribution functions (dash-dotted line). (b) The photon yield originating from the hadronic gas only. The meaning of the different curves is the same as that in (a).

Figure 7

The net thermal photon yield, from QGP and HG sources. The ideal spectrum (i.e., using an ideal hydrodynamics background), and the viscous spectrum (using a viscous hydrodynamics background and corrected microscopic distribution functions) are shown as a solid and dotted line, respectively.

Figure 8

(a) The thermal photon elliptic flow, considering only the photons originating from the QGP. As in previous figures, the results of using ideal hydrodynamics (solid line), viscous hydrodynamics with equilibrium rates (dotted line), and viscous hydrodynamics with $\delta f$ corrections (dash-dotted line) are shown separately. (b) The thermal photon elliptic flow, considering only the photons originating from the HG. The lines have the same meaning as those in (a).

Figure 9

The net thermal photon elliptic flow. The curves have the same meaning as in Fig. 7.

Figure 10

The thermal photon yield, showing the effect of FICs. (a) shows the contribution from the QGP, (b) that of the HG. Note that the curve labeled “FIC” also includes all viscous corrections (time evolution and $\delta f$)

Figure 11

The thermal photon $v_2$, showing the effect of FICs. (a) shows the contribution from the QGP, and (b) that of the HG. Note that the curve labeled “FIC” also includes all viscous corrections (time evolution and $\delta f$).

Figure 12

The net thermal photon yield (a) and $v_2$ (b), showing the effect of FICs. Note that the curve labeled “FIC” also includes all viscous corrections (time evolution and $\delta f$).