Azimuthally sensitive femtoscopy in event-by-event hydrodynamics

I analyze the pion femtoscopy correlations in noncentral Au-Au and Pb-Pb collisions. The azimuthally sensitive Hanbury-Brown-Twiss (HBT) method is used to extract the interferometry radii depending on the azimuthal angle with respect to the second- and third-order event plane. The results are in semiquantitative agreement with the STAR collaboration data on the HBT radii with respect to the second-order reaction plane, with the preliminary PHENIX collaboration data on the HBT radii with respect to the third-order reaction plane in Au-Au collisions at 200 GeV, and with the preliminary ALICE collaboration data for the HBT radii with respect to the second-order event plane for Pb-Pb collisions at $2.76$ TeV.

Figure 1

Contours of constant entropy density of the fireball in the transverse plane ($s=2$, 4, 8, 16 fm${}^{-3},...$). The consecutive panels (a)–(e) show the fireball at different fluid evolution times ${\tau }_0=0.6$ fm/$c$, $\tau -{\tau }_0=2$, 4, 6, and 8 fm/$c$. The initial distribution corresponds to the optical Glauber model density at the impact parameter $b=0$, with additional triangularity ${\varepsilon }_3=0.12$.

Figure 2

Third-order Fourier coefficient of the azimuthal oscillations of the HBT radii with respect to third-order event plane as function of the transverse momentum for smooth initial conditions [Eq. (2)], $R_{o,3}^2/R_{o,0}^2$ (a), $R_{s,3}^2/R_{s,0}^2$ (b), $R_{os,3}^2/R_{s,0}^2$ (c).

Figure 3

HBT radii (zeroth-order Fourier coefficients) with respect to second-order event plane for Au-Au collisions at 200 GeV for different centralities, $R_{o,0}^2$ (a), $R_{s,0}^2$ (b), and $R_{l,0}^2$ (c). STAR collaboration data [17] are denoted by full symbols, circles for $0.15$ GeV$<k_{\perp }<0.25$ GeV, stars for $0.25$ GeV$<k_{\perp }<0.35$ GeV, and triangles for $0.35$ GeV$<k_{\perp }<0.65$ GeV. Results of event-by-event hydrodynamic calculations are shown with open symbols connected with lines.

Figure 4

Second-order Fourier coefficients of the oscillations of the HBT radii with respect to the second-order event plane for Au-Au collisions at 200 GeV for different centralities, $R_{o,2}^2/R_{s,0}^2$ (a), $R_{s,2}^2/R_{s,0}^2$ (b), $R_{os,2}^2/R_{s,0}^2$ (c). STAR collaboration data [17] are compared to results of hydrodynamic calculations, same symbols as in Fig. 3.

Figure 5

The HBT radii $R_o$ (a), $R_s$ (b), and $R_l$ (c) for Au-Au collisions at 200 GeV; the squares denote the STAR collaboration data [8]. The hydrodynamic model results for event-by-event fluctuating emission sources [Eq. (4)], for the averaged emission source [Eq. (9)], and for the zeroth-order radii from the azimuthally sensitive HBT analysis are represented by the dashed-dotted, solid, and dashed lines respectively.

Figure 6

The third-order Fourier coefficients of the oscillations of the HBT radii with respect to third-order event plane for Au-Au collisions at 200 GeV for centrality 0–20% as function of the transverse mass. (a) $R_{o,3}^2/R_{o,0}^2$, preliminary PHENIX data [23] (circles) are compared to hydrodynamic calculations (triangles connected with lines). (b) $R_{s,3}^2/R_{s,0}^2$, preliminary PHENIX data (triangles) are compared to hydrodynamic calculations (squares connected with lines).

Figure 7

Same as Fig. 6 but for centrality 20–60%.

Figure 8

The third-order Fourier coefficients of the oscillations of the HBT radius $R_{os,3}^2/R_{s,0}^2$ with respect to third-order event plane for Au-Au collisions at 200 GeV. Hydrodynamic simulation results for centrality 0–20% and 20–60% are denoted with squares and triangles respectively.

Figure 9

HBT radii (zeroth-order Fourier coefficients) with respect to the second-order event plane for Pb-Pb collisions at $2.76$ TeV for different centralities, $R_{o,0}^2$ (a), $R_{s,0}^2$ (b), and $R_{l,0}^2$ (c). Preliminary ALICE collaboration data [20] are denoted by full symbols, circles for $0.2$ GeV$<k_{\perp }<0.3$ GeV, squares for $0.3$ GeV$<k_{\perp }<0.4$ GeV, triangles for $0.4$ GeV$<k_{\perp }<0.5$ GeV, and diamonds for $0.5$ GeV$<k_{\perp }<0.7$ GeV. Results of event-by-event hydrodynamic calculations are shown with open symbols connected with lines.

Figure 10

The second-order Fourier coefficients of the oscillations of the HBT radii with respect to second-order event plane for Pb-Pb collisions at $2.76$ TeV for different centralities, $R_{o,2}^2/R_{s,0}^2$ (a), $R_{s,2}^2/R_{s,0}^2$ ((b), and $R_{os,2}^2/R_{s,0}^2$ ((c). Preliminary ALICE collaboration data [20] are compared to results of hydrodynamic calculations, same symbols as in Fig. 9.

Figure 11

The third-order Fourier coefficients of the oscillations of the HBT radii with respect to third-order event plane for Pb-Pb collisions at $2.76$ TeV for different centralities, $R_{o,3}^2/R_{s,0}^2$ (a), $R_{s,3}^2/R_{s,0}^2$ (b), and $R_{os,3}^2/R_{s,0}^2$ (c). Results of hydrodynamic calculations are denoted with the same symbols as in Fig. 9.