A General-relativistic Determination of the Threshold Mass to Prompt Collapse in Binary Neutron Star Mergers

Abstract

We study the lifetimes of the remnant produced by the merger of two neutron stars and revisit the determination of the threshold mass to prompt collapse, M th . Using a fully general-relativistic numerical approach and a novel method for a rigorous determination of M th , we show that a nonlinear universal relation exists between the threshold mass and the maximum compactness. For the temperature-dependent equations of state considered here, our results improve a similar linear relation found recently with methods that are less accurate but yield quantitatively similar results. Furthermore, exploiting the information from GW170817, we use the universal relation to set lower limits on the stellar radii for any mass.

Constructing binary neutron star initial data with high spins, high compactnesses, and high mass ratios

“…The elliptic equations (13), (14), (15) and (16) together with the algebraic equation (17) are the main equations that we have to solve in order to construct initial data. We do so using the SGRID program [22,[34][35][36], which uses pseudospectral methods to accurately compute spatial derivatives.…”

“…The elliptic equations (13), (14), (15), and (16) above have to be solved incorporating the boundary conditions lim r→∞ ψ = 1, lim r→∞ B i = 0, lim r→∞ αψ = 1 (23) at spatial infinity, and…”

“…In order to construct initial data we have to solve the elliptic equations (13), (14), (15), and (16). This is done using SGRID's pseudospectral method as in [34][35][36] where we use Chebychev expansions and introduce grid points at the Chebychev extrema.…”

“…Since we solve Eqs. (13), (14), (15), and (16) on 38 computational domains we need interdomain boundary conditions that connect them. In principle, these interdomain boundary conditions are very simple.…”

“…Collisions of such massive stars might be almost indistinguishable from the merger of small black holes (BH), since the amount of the ejected material and consequently the brightness of the kilonova typically decrease for high compactnesses and larger total masses [13]. Additional simulations are needed to further improve estimates of the prompt collapse threshold [14,15], i.e., the mass at which the colliding neutron stars immediately form a black hole. Such threshold mass estimates will become particularly important once the increasing number of GW triggers will no longer allow expensive EM follow-up campaigns for all potential GW candidates and thus observational overhead needs to be reduced.…”