Influence of temperature-dependent shear viscosity on elliptic flow at backward and forward rapidities in ultrarelativistic heavy-ion collisions

We explore the influence of a temperature-dependent shear viscosity over entropy density ratio ${\eta }_s/s$ on the azimuthal anisotropies $v_2$ and $v_4$ of hadrons at various rapidities. We find that in $\mathrm{Au}+\mathrm{Au}$ collisions at full Relativistic Heavy Ion Collider energy, $\sqrt{s_{\mathrm{NN}}}=200\mathrm{GeV}$, the flow anisotropies are dominated by hadronic viscosity at all rapidities, whereas in $\mathrm{Pb}+\mathrm{Pb}$ collisions at the Large Hadron Collider energy, $\sqrt{s_{\mathrm{NN}}}=2760\mathrm{GeV}$, the flow coefficients are affected by the viscosity in both the plasma and hadronic phases at midrapidity, but the further away from midrapidity, the more dominant the hadronic viscosity becomes. We find that the centrality and rapidity dependence of the elliptic and quadrangular flows can help to distinguish different parametrizations of $({\eta }_s/s)\left(T\right)$. We also find that at midrapidity the flow harmonics are almost independent of the decoupling criterion, but they show some sensitivity to the criterion at backward and forward rapidities.

Figure 1

Different parametrizations of ${\eta }_s/s$ as a function of temperature. The LH-LQ line has been shifted downward and the HH-HQ upward for better visibility.

Figure 2

The charged particle pseudorapidity distribution $d{N}_{\mathrm{ch}}/d{\eta }_{\mathrm{ch}}$. Experimental data are from the PHOBOS Collaboration [63].

Figure 3

Transverse momentum spectra of positive pions at the RHIC. Experimental data are from the PHENIX Collaboration [64].

Figure 4

Transverse momentum spectra of positive kaons at the RHIC. Experimental data are from the PHENIX Collaboration [64].

Figure 5

Transverse momentum spectra of protons at the RHIC. Experimental data for protons (upper) and antiprotons (lower) are from the PHENIX Collaboration [64].

Figure 6

Charged hadron $v_2\left(p_T\right)$ at the RHIC. Experimental data are from the STAR Collaboration [66].

Figure 7

Charged hadron $v_2\left({\eta }_{\mathrm{ch}}\right)$ at the RHIC. Experimental data are from the PHOBOS [67] and STAR [68] Collaborations.

Figure 8

Charged hadron $v_4\left(p_T\right)$ at the RHIC. Experimental data are from the STAR Collaboration [68].

Figure 9

Charged hadron $v_4\left({\eta }_{\mathrm{ch}}\right)$ at the RHIC. Experimental data are from the STAR Collaboration [68].

Figure 10

The charged particle pseudorapidity distribution $d{N}_{\mathrm{ch}}/d{\eta }_{\mathrm{ch}}$ at the LHC. Experimental data are from the ALICE Collaboration [72].

Figure 11

Transverse momentum spectra of positive pions at the LHC. Experimental data are from the ALICE Collaboration [73].

Figure 12

Transverse momentum spectra of positive kaons at the LHC. Experimental data are from the ALICE Collaboration [73].

Figure 13

Transverse momentum spectra of protons at ALICE. Experimental data for protons and antiprotons are from the ALICE Collaboration [73].

Figure 14

Charged hadron $v_2\left(p_T\right)$ at the LHC. Experimental data are from the ALICE Collaboration [75].

Figure 15

Charged hadron $v_2\left({\eta }_{\mathrm{ch}}\right)$ at the LHC.

Figure 16

Charged hadron $v_4\left(p_T\right)$ at the LHC.

Figure 17

Charged hadron $v_4\left({\eta }_{\mathrm{ch}}\right)$ at the LHC.

Figure 18

Parametrizations of $({\eta }_s/s)\left(T\right)$ rescaled to lead to similar charged hadron $v_2\left(p_T\right)$ in central collisions at the RHIC (top) and the LHC (bottom).

Figure 19

Charged hadron $v_2\left(p_T\right)$ at the RHIC. Experimental data are from the STAR Collaboration [66].

Figure 20

Charged hadron $v_2\left({\eta }_{\mathrm{ch}}\right)$ at the RHIC. Experimental data are from the PHOBOS [67] and STAR [68] Collaborations.

Figure 21

Charged hadron $v_4\left(p_T\right)$ at the RHIC. Experimental data are from the STAR Collaboration [68].

Figure 22

Charged hadron $v_2\left(p_T\right)$ at the LHC. Experimental data are from the ALICE Collaboration [75].

Figure 23

Charged hadron $v_2\left({\eta }_{\mathrm{ch}}\right)$ at the LHC.

Figure 24

Charged hadron $v_4\left(p_T\right)$ at the LHC.

Figure 25

The charged particle pseudorapidity distribution $d{N}_{\mathrm{ch}}/d{\eta }_{\mathrm{ch}}$ at the RHIC obtained by using two different freeze-out criteria. Experimental data are from the PHOBOS Collaboration [63].

Figure 26

The charged particle pseudorapidity distribution $d{N}_{\mathrm{ch}}/d{\eta }_{\mathrm{ch}}$ at the LHC obtained by using two different freeze-out criteria. Experimental data are from the ALICE Collaboration [72].

Figure 27

Charged hadron $v_2\left(p_T\right)$ at the RHIC obtained by using two different freeze-out criteria. Experimental data are from the STAR Collaboration [66].

Figure 28

Charged hadron $v_2\left(p_T\right)$ at the LHC obtained by using two different freeze-out criteria. Experimental data are from the ALICE Collaboration [75].

Figure 29

Charged hadron $v_2\left({\eta }_{\mathrm{ch}}\right)$ at the RHIC obtained by using two different freeze-out criteria. Experimental data are from the STAR Collaboration [66].

Figure 30

Charged hadron $v_2\left({\eta }_{\mathrm{ch}}\right)$ at the LHC obtained by using two different freeze-out criteria. Experimental data are from the ALICE Collaboration [75].