Neutrino burst-generated gravitational radiation from collapsing supermassive stars

Abstract

We estimate the gravitational radiation signature of the electron/positron annihilation-driven neutrino burst accompanying the asymmetric collapse of an initially hydrostatic, radiation-dominated supermassive object suffering the Feynman-Chandrasekhar instability. An object with a mass $5\ifmmode\times\else\texttimes\fi{}{10}^{4}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}<\phantom{\rule{0ex}{0ex}}M<5\ifmmode\times\else\texttimes\fi{}{10}^{5}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$, with primordial metallicity, is an optimal case with respect to the fraction of its rest mass emitted in neutrinos as it collapses to a black hole: lower initial mass objects will be subject to scattering-induced neutrino trapping and consequently lower efficiency in this mode of gravitational radiation generation, while higher masses will not get hot enough to radiate significant neutrino energy before producing a black hole. The optimal case collapse will radiate several percent of the star's rest mass in neutrinos and, with an assumed small asymmetry in temperature at peak neutrino production, produces a characteristic linear memory gravitational wave burst signature. The time scale for this signature, depending on redshift, is $\ensuremath{\sim}1\text{ }\text{ }$ to 10 s, optimal for proposed gravitational wave observatories like DECIGO. Using the response of that detector, and requiring a signal-to-noise ratio $\mathrm{SNR}>5$, we estimate that collapse of a $\ensuremath{\sim}5\ifmmode\times\else\texttimes\fi{}{10}^{4}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ supermassive star could produce a neutrino burst-generated gravitational radiation signature detectable to redshift $z\ensuremath{\lesssim}7$. With the envisioned ultimate DECIGO design sensitivity, we estimate that the linear memory signal from these events could be detectable with $\mathrm{SNR}>5$ to $z\ensuremath{\lesssim}13$.