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Comparability of Gubser flow gradients to p+Pb hydrodynamic simulations

Determine whether the flow gradient magnitudes and profiles in the Gubser flow solution to conformal hydrodynamics are comparable to the flow gradients present in hydrodynamic simulations of proton–lead (p+Pb) collisions, such as those performed using Israel–Stewart hydrodynamics for p+Pb at the LHC.

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Background

The paper introduces two exact solutions of conformal hydrodynamics extending Gubser flow to include nontrivial rapidity dependence via a temporal shift. The viscous, shifted solution (Solution II) is used to paper how freeze out criteria—constant temperature versus constant Knudsen number—shape the freeze out hypersurface when strong transverse and longitudinal flows are present.

When comparing their findings to prior hydrodynamic simulations of p+Pb collisions, the authors note larger discrepancies between freeze out criteria in their analytic solution than reported earlier. They list possible reasons: differences in hydrodynamic frameworks (Navier–Stokes versus Israel–Stewart), the treatment of the shear viscosity to entropy ratio, and an unresolved issue about whether the flow gradients in the Gubser solution are comparable to those in the p+Pb simulations. Resolving this comparability is important for interpreting the origin of differences in freeze out surfaces across models.

References

In this regard, however, we emphasize several key differences between our exact solution and the calculations performed in : (i), Gubser's solution (and thus our Solution II) assumes Navier-Stokes hydrodynamics, for which the shear correction $\pi{\mu\nu}$ is directly proportional to the shear tensor $\sigma{\mu\nu}$, whereas employed Israel-Stewart hydrodynamics , in which $\pi{\mu\nu}$ evolves according to a relaxation equation; (ii), did not use a constant $\tilde\eta/s$ as assumed here; and (iii), it is unclear whether the Gubser solution's flow gradients are really comparable to those present in the p+Pb simulation shown in .

— Exploring freeze out and flow using exact solutions of conformal hydrodynamics (2402.03568 - Bradley et al., 5 Feb 2024) in Section 4 (Flow and Freeze out), footnote