Projecting the likely importance of weak-interaction-driven bulk viscosity in neutron star mergers

Abstract

In this work, we estimate how much bulk viscosity driven by Urca processes is likely to affect the gravitational wave signal of a neutron star coalescence. In the late inspiral, we show that bulk viscosity affects the binding energy at fourth post-Newtonian (PN) order. Even though this effect is enhanced by the square of the gravitational compactness, the coefficient of bulk viscosity is likely too small to lead to observable effects in the waveform during the late inspiral, when only considering the orbital motion itself. In the post-merger, however, the characteristic time-scales and spatial scales are different, potentially leading to the opposite conclusion. We post-process data from a state-of-the-art equal-mass binary neutron star merger simulation to estimate the effects of bulk viscosity (which was not included in the simulation itself). In that scenario, we find that bulk viscosity can reach high values in regions of the merger. We compute several estimates of how much it might directly affect the global dynamics of the considered merger scenario, and find that it could become significant. Even larger effects could arise in different merger scenarios or in simulations that include non-linear effects. This assessment is reinforced by a quantitative comparison with relativistic heavy-ion collisions where such effects have been explored extensively.

Beta Equilibrium under Neutron Star Merger Conditions

“…In this paper, we will study the conditions for beta equilibrium in ordinary nuclear matter (where all the baryon number is contributed by neutrons (n) and protons (p)) in the temperature range 1 MeV T 5 MeV. This regime, which arises in neutron star mergers [1][2][3][4], is cool enough so that neutrinos are not trapped, but warm enough so that there are corrections to the lowtemperature equilibrium condition. It has previously been shown [5] that in this regime the full beta equilibrium condition is…”

Conservative finite volume scheme for first-order viscous relativistic hydrodynamics

“…The BDNK algorithm presented here should be sufficiently stable and accurate to be applied to a variety of relativistic hydrodynamics problems where first-order dissipation might be relevant. Among those would be the investigation of viscous effects in the inspiral [74] and merger [5] of binary neutron star systems. The guaranteed causality of the BDNK equations would also motivate the application of this numerical scheme to simulations of heavy-ion collisions, where current MIS approaches show acausal behavior [35].…”

“…Formally, this procedure can be thought of in terms of an expansion about thermodynamic equilibrium; in equilibrium, the hydrodynamic variables { , u a , n} are constants, and all derivative corrections to T ab , J a drop out, yielding the perfect fluid conserved currents (3)(4). Near equilibrium, these derivative terms amount to small corrections, and terms at higher order (either with higher-order derivatives or products of lower-order derivative terms) make successively smaller contributions 5 . Explicitly, this approach asserts that the "true" conserved currents (from the full microphysical theory, whatever that may be) can be written in a gradient ex- 4 Entropy can increase when shocks are present, though.…”

“…Since the weak solution may not be unique, the physical one is that which satisfies the second law of thermodynamics [47]. 5 Though in most cases it is unknown if the gradient expansion converges, there are many known examples where it does not [48] [49] [50] [51]. Remarkably, in some cases even beginning with far from equilibrium and varied initial conditions, solutions still approach a similar ideal hydrodynamic evolution at late times, a phenomenon typically attributed to the existence of a universal attractor solution [52] [53].…”

“…Experimental breakthroughs in studying the QGP, in particular, have spurred significant growth in the theoretical understanding of relativistic fluids, as the Relativistic Heavy Ion Collider (RHIC) is now sufficiently sensitive to observe phenomena beyond the scope of ideal (non-dissipative) hydrodynamics [3]. Likewise, there are indications that similar phenomena may become relevant in modeling astrophysical sources for the next generation of telescopes and gravitational-wave observatories [4] [5], further motivating theoretical focus on extending relativistic hydrodynamics beyond thermodynamic equilibrium.…”