Neutrino burst-generated gravitational radiation from collapsing supermassive stars

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 $5\times {10}^4{M}_{\odot }<M<5\times {10}^5{M}_{\odot }$, 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 $\sim 1$ 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 $\sim 5\times {10}^4{M}_{\odot }$ supermassive star could produce a neutrino burst-generated gravitational radiation signature detectable to redshift $z\lesssim 7$. 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 $z\lesssim 13$.

Figure 1

Illustration of anisotropic neutrino emission production by the integrated Sachs-Wolfe–like effect. Neutrinos moving toward the central core may fall into the BH or suffer an ISW-like differential blueshift-redshift effect driven by the increase of gravitational potential with time in a collapsing SMS.

Figure 2

Sky-averaged characteristic strain $h_c$ as a function of frequency from the neutrino burst-generated GWM signal accompanying the collapse of SMSs at $z=7$, with $\alpha =-0.02$ and with homologous core masses $5\times {10}^4{M}_{\odot }$ (red curve), $10^5{M}_{\odot }$ (blue curve), and $5\times {10}^5{M}_{\odot }$ (green curve), as labeled. The panels on the top and the bottom are based on the results for integrated neutrino luminosity from Shi & Fuller and Linke et al., respectively. The two black solid lines and the black dash line denote the sky-averaged noise curves for LISA, DECIGO, and Ultimate DECIGO, as labeled.

Figure 3

The vertical axes in the top and bottom panels show sky-averaged signal-to-noise ratios SNR for DECIGO with the result of Shi & Fuller and Ultimate DECIGO with the result of Linke et al. for overall neutrino burst characteristics, respectively. Here we take asymmetry parameter $\alpha =-0.02$. Each contour line denotes the final homologous core mass of a collapsing SMS, as labeled.

Figure 4

Contours of detectability redshift $z$ (as labeled) as a function of the neutrino emission asymmetry and the total energy radiated in neutrinos. These results were calculated assuming an SMS homologous core mass $M^{\mathrm{HC}}={10}^5{M}_{\odot }$ with neutrino burst time calculated with the result of Linke et al. Each contour curve shows the redshift for which $\mathrm{SNR}=5$ for Ultimate DECIGO.

Figure 5

$xyz$ and $x^{\prime }{y}^{\prime }{z}^{\prime }$ are coordinate systems of the detector and the source, respectively. The source is located at the origin and the detector is far out in the $\widehat{z}$ direction. We choose the neutrino emission distribution to be axisymmetric about the $z^{\prime }$ axis. The $x-z$ and $x^{\prime }-z^{\prime }$ planes are coplanar and differ by a rotation by angle $\xi$ about the $y$ axis.

Figure 6

Estimated gravitational wave time series from an SMS collapse with $M^{\mathrm{HC}}={10}^5{M}_{\odot }$ at $z=7$ and the neutrino emission asymmetry $\alpha =-0.02$. The detector is placed at equatorial plane $\xi =\pi /2$. The blue solid line shows the detector’s arm response to GWM signal. The green dashed line shows the time series filtered with a ${10}^{-2}–{10}^0\mathrm{Hz}$ bandpass filter to illustrate the signal seen by DECIGO.

Figure 7

Illustration of neutrino absorption by BH trapped surface formation. The solid circle is the trapped surface after the BH is formed. The dashed circle is the radius of neutrino peak production site. Neutrinos moving toward the core at the angle $\psi <{\psi }_c$ will be trapped in the BH and therefore make no contribution to the neutrino emission asymmetry $\alpha$.

Figure 8

Time evolution of the neutrino luminosity. The solid curve is taken from Shi & Fuller, which assumes that neutrinos only move radially outward. The dashed curve takes into account the neutrino luminosity loss due to the different time of flight at different emission angles.