Dynamics and Gravitational Wave Signature of Collapsar Formation

We perform $3+1$ general relativistic simulations of rotating core collapse in the context of the collapsar model for long gamma-ray bursts. We employ a realistic progenitor, rotation based on results of stellar evolution calculations, and a simplified equation of state. Our simulations track self-consistently collapse, bounce, the postbounce phase, black hole formation, and the subsequent early hyperaccretion phase. We extract gravitational waves from the spacetime curvature and identify a unique gravitational wave signature associated with the early phase of collapsar formation.

Figure 1

Progenitor model u75. Left ordinate: Radial density distribution. Right ordinate: Angular velocity (red dash-dotted curve) and specific angular momentum (blue solid curve) as a function of cylindrical radius $\varpi$ as given by our rotation law, reproducing features seen in the rotating progenitors of 4. Vertical lines mark the enclosed mass.

Figure 2

Top: Maximum density ${\rho }_{\max }$ and central ADM lapse function ${\alpha }_{\min }$ as a function of postbounce time in all models. After horizon formation, the region interior to it is excluded from min or max finding. Bottom: BH mass and dimensionless spin $a^{\star }$ as a function of postbounce time. All models follow the same accretion history once a BH forms and settles down. The data shown in this figure are from the LR runs since these were carried out longest after BH formation.

Figure 3

Snapshots of the meridional density distribution with superposed velocity vectors in model u75rot1 taken at various times. The top left panel (note its special spatial range) shows a snapshot from 10 ms after bounce. The top right and bottom left panels show the point of PNS instability and the time at which the AH first appears, respectively. The bottom right panel, generated with a separate color range, shows the hyperaccreting BH at $\sim 15\mathrm{ms}$ after its formation. All colormaps have density isocontours superposed at densities (from outer to inner) of $\rho =(0.1,0.25,0.5,0.75,1.0,2.5,5.0)\times {10}^{10}\mathrm{g}{\mathrm{cm}}^{-3}$.

Figure 4

Top: GW signals $h_{+,e}$ emitted by the rotating models as seen by an equatorial observer and rescaled by distance $D$. The inset plot shows the strong burst associated with BH formation and ringdown. The full waveforms are available from http://www.stellarcollapse.org/gwcatalog. Bottom: Spectrogram of the GW signal emitted by the most rapidly spinning model u75rot2.