Density Profiles of Collapsed Rotating Massive Stars Favor Long Gamma-Ray Bursts

Abstract

Long-duration gamma-ray bursts (lGRBs) originate in relativistic collimated outflows—jets—that drill their way out of collapsing massive stars. Accurately modeling this process requires realistic stellar profiles for the jets to propagate through and break out of. Most previous studies have used simple power laws or pre-collapse models for massive stars. However, the relevant stellar profile for lGRB models is in fact that of a star after its core has collapsed to form a compact object. To self-consistently compute such a stellar profile, we use the open-source code GR1D to simulate the core-collapse process for a suite of low-metallicity rotating massive stellar progenitors that have undergone chemically homogeneous evolution. Our models span a range of zero-age main-sequence (ZAMS) masses: M ZAMS = 13, 18, 21, 25, 35, 40, and 45M ☉. All of these models, at the onset of core-collapse, feature steep density profiles, ρ ∝ r −α , with α ≈ 2.5, which would result in jets that are inconsistent with lGRB observables. We follow the collapses of four of the seven models until they form black holes (BHs) and the other three models until they form proto-neutron stars (PNSs). We find, across all models, that the density profile outside the newly formed BH or PNS is well represented by a flatter power law with α ≈ 1.35–1.55. Such flat density profiles are conducive to the successful formation and breakout of BH-powered jets and are, in fact, required to reproduce observable properties of lGRBs. Future models of lGRBs should be initialized with shallower post-collapse stellar profiles, like those presented here, instead of the much steeper pre-collapse profiles that are typically used.

Collapsar Black Holes Are Likely Born Slowly Spinning

“…However, those shells will accelerate as they freefall and reach similar velocities. Importantly, the freefall time of those shells is 0.1 s, implying that after that time the progenitor structure is consistent with that of Halevi et al (2023). We have verified via a direct simulation that an 5 The accretion rate also increases with the BH mass,  ~~am v M ff 1…”

“…The stellar envelope undergoes solid body rotation well below the centrifugal value throughout the star, with the specific angular momentum given by 6 where r g ≡ GM/c 2 = 6.3 × 10 5 cm is the BH gravitational radius and ω 0 = 50 s −1 . We note that prior to the BH formation, Halevi et al (2023) found that the innermost (≈10 8.5 cm) stellar shells accelerate to high velocities. Since our simulations do not have self-gravity, we set the radial velocity to zero.…”

“…If indeed α = 1.5 at the onset of the BH formation is a universal value, one can derive a universal accretion rate. All mass density profiles obtained by Halevi et al (2023) roughly coincide with the initial profile used in the simulations performed by Gottlieb et al (2022b). In these models, Gottlieb et al (2022b) used a representative total stellar mass (including the BH mass) of 18.2 M e .…”

“…The accretion rate is determined by the mass density profile of the stellar envelope. Recently, Halevi et al (2023) examined the stellar density profile evolution during the PNS stage, between the onset of the core collapse and the formation of the BH. They found that all stellar evolution models, which feature steep density profiles with a power-law index of α = 2.5 at the onset of the collapse, consistently converge to a shallower density profile with α = 1.5 at the BH formation time.…”

On the Anticorrelation between Duration and Redshift in Gamma-Ray Bursts

“…Because the duration of a GRB (in the context of a black holedisk central engine) is roughly proportional to the amount of mass in the disk divided by its accretion rate 6 (i.e.,  T M M int ), longer-duration GRBs at lower redshifts imply these systems have more massive accretion disks, lower accretion rates, or both. Of course, extrapolating from the final state of the progenitor star (or stars) to the black hole-disk system that produces the GRB jet is not straightforward (Halevi et al 2022). However, we might expect general trends to hold -for example, a more extended massive star and/or one with an overall higher angular momentum reservoir may be able to produce a longer-lived jet upon collapse, leading to a longerduration GRB (see the recent arguments in Lloyd-Ronning 2022).…”