Towards asteroseismology of core-collapse supernovae with gravitational wave observations – II. Inclusion of space–time perturbations

Abstract

Improvements in ground-based, advanced gravitational wave (GW) detectors may allow in the near future to observe the GW signal of a nearby core-collapse supernova. For the most common type of progenitors, likely with slowly rotating cores, the dominant GW emission mechanisms are the post-bounce oscillations of the proto-neutron star (PNS) before the explosion. We present a new procedure to compute the eigenmodes of the system formed by the PNS and the stalled accretion shock in general relativity including spacetime perturbations. The new method improves on previous results by accounting for perturbations of both the lapse function and the conformal factor. We apply our analysis to two numerical core-collapse simulations and show that our improved method is able to obtain eigenfrequencies that accurately match the features observed in the GW signal and to predict the qualitative behaviour of quasi-radial oscillations. Our analysis is possible thanks to a newly developed algorithm to classify the computed eigenmodes in different classes (f-, p-, and g-modes), improving previous results which suffered from misclassification issues. We find that most of the GW energy is stored in the lowest order eigenmodes, in particular in the 2 g 1 mode and in the 2 f mode. Our results also suggest that a low-frequency component of the GW signal attributed in previous works to the characteristic frequency of the Standing Accretion Shock Instability, should be identified as the fundamental quadrupolar f-mode. We also develop a formalism to estimate the contribution of quasi-radial (l = 0) modes to the quadrupolar component of the GW emission in the case of a deformed background, with application to rapidly rotating cores. This work provides further support for asteroseismology of core-collapse supernovae and the inference of PNS properties based on GW observations.

Multimessenger asteroseismology of core-collapse supernovae

“…That branch of modes has increasing frequency with increasing n. To the left of the minimum of n(f ) are gmodes, which have decreasing frequency with increasing n (see eg. [22,24]). We are unable to determine whether the best-fit perturbative mode function in Fig.…”

“…To characterize the modes, we followed a strategy of mode function matching, rather than mode frequency matching as in [22][23][24]. We believe this is a more robust approach that is less susceptible to mode misidentification, especially given the approximations employed in both simulations and perturbative schemes.…”

“…They claimed an improved coincidence between their perturbative mode frequencies and certain emission features in the GW spectrograms from simulations. The Cowling approximation was then relaxed even further in [24], where the conformal factor of the spatial metric was allowed to vary as well, leaving only the shift vector fixed.…”

Consistent perturbative modeling of pseudo-Newtonian core-collapse supernova simulations

“…Once the perturbative mode spectrum is obtained, a matching procedure is necessary to determine which modes are actually active in the simulation. A mode frequency matching procedure has been used frequently [5][6][7], whereby the evolution of perturbative mode frequencies are overlaid on simulation gravitational wave spectrograms, and then matching is judged by frequency coincidence over time.…”

“…Frequency mismatches between simulations and perturbative calculations can arise due to the use of different equations of motion in the simulations versus those used in the perturbative calculation. For example, in [5,7] the general relativistic hydrodynamic equations were used in the perturbative calculation, with either no metric perturbations [5] or a subset of possible metric perturbations [7]. Their simulations correspondingly use general relativistic hydrodynamics and a spatially-conformally flat metric approximation for spacetime.…”