Electromagnetic radiation as a probe of the initial state and of viscous dynamics in relativistic nuclear collisions

The penetrating nature of electromagnetic signals makes them suitable probes to explore the properties of the strongly interacting medium created in relativistic nuclear collisions. We examine the effects of the initial conditions and shear relaxation time on the spectra and flow coefficients of electromagnetic probes, using an event-by-event 3+1-dimensional viscous hydrodynamic simulation (music).

Figure 1

Event averaged shear-stress tensor for $b_{\pi }=5,10,20$ in the local rest frame of the fluid cell located at $x=\mathrm{y}=2.\overline{6}7$ fm, $z=0$ fm. Results with $b_{\pi }=5$ are in red, $b_{\pi }=10$ in dark green and $b_{\pi }=20$ in light green. Different types of lines are used for various components of ${\pi }^{\mu \nu }$. The full line is reserved for ${\pi }^{xx}$, dashed line for ${\pi }^{yy}$, dotted line for ${\pi }^{zz}$ and dash-dotted line is used for ${\pi }^{xy}$.

Figure 2

Pion transverse momentum spectra (left panel) and charged hadron differential elliptic flow (right panel) as a function of transverse momentum, for different values of shear relaxation time. Here, and in all subsequent figures of this paper, the colored bands represent the statistical uncertainty associated with 200 hydrodynamical events.

Figure 3

Transverse momentum spectra (left panel) and differential elliptic flow (right panel) of thermal photons as a function of transverse momentum, for different values of shear relaxation time.

Figure 4

Differential elliptic flow of thermal photons emitted by the QGP (left panel) and emitted by the hadronic medium (HM) (right panel) as a function of transverse momentum, for different values of shear relaxation time.

Figure 5

Differential elliptic flow of thermal dileptons for $M=m_{\rho }$ (left panel) and $M=1.5\mathrm{GeV}$ (right panel) as a function of transverse momentum, for different values of shear relaxation time.

Figure 6

Influence of ${\tau }_{\pi }$ on higher flow harmonics of thermal dileptons at $M=m_{\rho }:v_3\left(p_T\right)$ is in the left panel, and $v_4\left(p_T\right)$ is in the right panel.

Figure 7

Differential elliptic flow of dileptons emitted by the QGP (left panel) and emitted by the hadronic medium (right panel) as a function of the dilepton invariant mass, for different values of shear relaxation time. The effect of the viscous correction to the QGP rate is presented in the left panel, whereas that of the HM rate is small and hence only results using the rate including the viscous correction is presented in the right panel.

Figure 8

Dilepton yield (left panel) and elliptic flow (right panel) as a function of invariant mass, for different values of shear relaxation time.

Figure 9

Shear-stress tensor for $c=0,1/2,1$ in the local rest frame of the fluid cell located at $x=\mathrm{y}=2.\overline{6}7$ fm, $z=0$ fm, averaged over all events. Results with $c=0$ are displayed in red, $c=1/2$ in gray, and $c=1$ in yellow.

Figure 10

Pion transverse momentum spectra (left panel) and charged hadron differential elliptic flow (right panel) as a function of transverse momentum, for different values of the initial shear-stress tensor.

Figure 11

Transverse momentum spectra (left panel) and differential elliptic flow (right panel) of thermal photons as a function of transverse momentum, for different values of initial ${\pi }^{\mu \nu }$.

Figure 12

Thermal photon elliptic flow with and without viscous corrections ($\delta R$) to the emission rates.

Figure 13

Dilepton yield (left panel) and elliptic flow (right panel) as a function of invariant mass, for different values of initial ${\pi }^{\mu \nu }$.

Figure 14

Differential elliptic flow of dileptons emitted by the QGP (left panel) and emitted by the hadronic medium (HM) (see right panel) as a function of the dilepton invariant mass, for different values of initial shear stress tensor. Only the QGP dileptons are calculated with and without viscous correction $\delta R$ to the rate, while the HM dileptons are calculated with the viscous correction.