[Paper Review] Numerical Simulations of the Random Angular Momentum in Convection: Implications for Supergiant Collapse to Form Black Holes

Andrea Antoni, Eliot Quataert|arXiv (Cornell University)|Jul 19, 2021

Gamma-ray bursts and supernovaePhysics and Astronomy67 references54 citations

TL;DR

This study uses 3D hydrodynamical simulations in the Athena++ framework to show that random convective motions in non-rotating red supergiant (RSG) envelopes can generate sufficient specific angular momentum to form rotationally-supported accretion flows during black hole (BH) formation, even with zero net angular momentum. The key result is that such flows can power long-duration transients, with BH spin reaching ∼0.5 when most of the hydrogen envelope accretes, despite the progenitor being non-rotating.

ABSTRACT

During the core collapse of massive stars that do not undergo a canonical energetic explosion, some of the hydrogen envelope of a red supergiant (RSG) progenitor may infall onto the newborn black hole (BH). Within the Athena++ framework, we perform three-dimensional, hydrodynamical simulations of idealized models of supergiant convection and collapse in order to assess whether the infall of the convective envelope can give rise to rotationally-supported material, even if the star has zero angular momentum overall. Our dimensionless, polytropic models are applicable to the optically-thick hydrogen envelope of non-rotating RSGs and cover a factor of 20 in stellar radius. At all radii, the specific angular momentum due to random convective flows implies associated circularization radii of 10 - 1500 times the innermost stable circular orbit of the BH. During collapse, the angular momentum vector of the convective flows is approximately conserved and is slowly varying on the timescale relevant to forming disks at small radii. Our results indicate that otherwise failed explosions of RSGs lead to the formation of rotationally-supported flows that are capable of driving outflows to large radii and powering observable transients. When the BH is able to accrete most of the hydrogen envelope, the final BH spin parameter is $\sim$ 0.5, even though the star is non-rotating. For fractional accretion of the envelope, the spin parameter is generally lower and never exceeds 0.8. We discuss the implications of our results for transients produced by RSG collapse to a black hole.

Motivation & Objective

• To investigate whether random convective motions in non-rotating red supergiant (RSG) envelopes can generate sufficient angular momentum to form rotationally-supported accretion flows during black hole (BH) formation.
• To determine if such flows can power observable transients in failed supernovae (FSN), despite the star having zero net angular momentum.
• To quantify the resulting BH spin and accretion dynamics when the hydrogen envelope is partially or fully accreted.
• To assess the implications for long-duration transients, including ultra-long gamma-ray bursts and energetic Type II supernovae.

Proposed method

• Performs three-dimensional, idealized, polytropic hydrodynamical simulations using the Athena++ code to model the convective envelope and collapse of a non-rotating RSG.
• Uses dimensionless, axisymmetric models covering a 20-fold range in stellar radius to isolate the role of convective angular momentum.
• Tracks the evolution of specific angular momentum (jrand) from convective flows and compares it to the innermost stable circular orbit (ISCO) angular momentum (jISCO).
• Simulates the collapse phase to examine whether jrand remains coherent down to small radii, enabling circularization and rotational support.
• Analyzes accretion dynamics, including mass accretion rates, circularization radii, and final BH spin parameters.
• Compares results across different accretion fractions to determine spin evolution and transient potential.

Experimental results

Research questions

• RQ1 Can random convective motions in a non-rotating RSG envelope generate sufficient angular momentum to form rotationally-supported accretion flows during BH formation?
• RQ2 What is the resulting black hole spin parameter when the entire hydrogen envelope accretes, despite zero net angular momentum in the progenitor?
• RQ3 How do the circularization radii of convectively generated angular momentum compare to the ISCO of the BH?
• RQ4 To what extent can rotational support drive outflows and power long-duration transients in failed supernovae?

Key findings

• Random convective flows in the RSG envelope generate specific angular momentum (jrand) that is 10–1500 times larger than jISCO, the Keplerian angular momentum at the ISCO, across all radii.
• The angular momentum vector of convective flows is approximately conserved during collapse and varies slowly on the timescale relevant for disk formation at small radii.
• Even with zero net angular momentum, the accretion of most of the hydrogen envelope leads to a final BH spin parameter of ∼0.5.
• For partial envelope accretion, the BH spin is generally lower and never exceeds 0.8, indicating a robust upper limit on spin from convective angular momentum.
• The coherent nature of jacc down to circularization radii enables the formation of rotationally-supported flows capable of driving outflows to large radii.
• The results suggest that failed supernovae of RSGs can power month- to year-long transients with luminosities up to ∼10^40 erg s⁻¹, potentially explaining ultra-long gamma-ray transients and energetic Type II supernovae.