Critical slowing down and bulk viscosity in binary neutron star mergers

Abstract

Hydrodynamic simulations of neutron star mergers rely on the clear separation between the strong-interaction, weak-interaction, and hydrodynamic timescales. In this effective framework, weak Urca interactions are typically the slowest microscopic processes, and therefore the Urca rate determines the bulk-viscous dissipation. This assumed hierarchy of dissipative mechanisms can be decisively altered, without invalidating hydrodynamics, if the trajectory of the matter in a neutron star merger passes through the vicinity of a possible low temperature QCD critical point. The enhanced density fluctuations lead to critical slowing down and rapid growth of transport coefficients including bulk viscosity. While this growth is regulated by finite-time effects, finite-size effects, and the breakdown of hydrodynamic scale separation, which bound the correlation length, we demonstrate that the QCD contribution to bulk viscosity can rival the electroweak contribution in realistic conditions. Thus, critical dynamics could leave observable imprints on the hydrodynamic evolution of neutron star mergers.

Figures (3)

• Figure 1: Estimated $\zeta_{\rm CSD}$ at the boundary of applicability of hydrodynamics for $\omega=1$ kHz, calculated using Eq. \ref{['eq:zetatscaling']} and an EV-HRG non-critical part of the EoS as described in the text. The correlation length $\xi$ is taken to be the upper bound as suggested by the minimum of Eq. \ref{['eq:finiteduration']} and Eq. \ref{['eq:finiteextent']}, the two constraints discussed in the text.
• Figure 2: Bulk viscosity due to critical slowing down $\zeta_{\rm CSD}$ as a function of $T_c-T$ for $\omega=1$ kHz obtained from the critical scaling given by Eqs. \ref{['eq:zetatscaling']}, \ref{['eq:xitempscaling']}. The gray band is based roughly on the neutrino-trapped calculations of Ref. Alford:2021lpp. We have chosen a CP at $\mu_{B,c}=\, 1.8 \, \text{GeV}, T_c= 50\,\text{MeV} , \, \alpha_{1}=\,\pi/2, \alpha_2=\, 0, \mu_{I}=0$, and use EV-HRG as a representative model of the on-critical part of the equation of state. Despite the power law dependence of $\zeta_{\rm CSD}$ on $\Delta T$, large enhancement of $\zeta$ can be present even at macroscopically relevant scales for $\rho w \gtrsim \mathcal{O}(1)$. The dashed horizontal segments of the curve are the regions of $T_c-T$ and $x-x_c$ where hydrodynamic description becomes invalid. As one can note, this happens only for coarse graining length scales which are orders of magnitude less than the typical fluid cell separation in neutron star merger simulations.
• Figure 3: As in Fig. \ref{['fig:dt']}, $\zeta_{\rm CSD}$ as a function of $T-T_c$, but here with a critical temperature $T_c=2$ MeV. Here the gray band representing the approximate electroweak baseline is roughly based on the neutrino-transparent calculations in Ref. Alford:2022ufz. Comparing with Fig. \ref{['fig:dt']}, one can see that a CP in the neutrino-transparent regime (e.g. $T_c=2$ MeV) has a much less distinct effect than one in the neutrino-trapped regime.