Constraints on gamma-ray burst inner engines in a Blandford–Znajek framework

Abstract

Under the assumption that a Gamma-ray Burst (GRB) is ultimately produced by a Blandford-Znajek (BZ) jet from a highly spinning black hole (BH), we put limits on the magnetic field and BH mass needed to power observed long and short GRBs. For BHs in the range of 2 − 10M (for long GRBs) and 0.5 − 4M (for short GRBs), we find magnetic fields in the range of 5x10 14 B 10 17 G are needed to power the observed GRBs. Under the simple assumption of flux conservation, we estimate the magnetic fields of the progenitor systems for both long and short GRBs, finding that single massive star progenitors require fields ∼ 10 6 G and NS merger systems require fields ∼ 10 15 G. We also discuss the implications and consequences of high magnetic fields in GRB BH-disk systems, in terms of MRI field growth and magnetically arrested disks. Finally, we examine the conditions under which the progenitor systems can retain enough angular momentum to create BHs spinning rapidly enough to power BZ jets.

The evolution of gamma-ray burst jet opening angle through cosmic time

“…Given equation 7 (or 9) above, we can ask whether the jet opening angle dependence on L j , ρ, and/or R might lead to cosmological evolution of this quantity. We have already shown (Lloyd-Ronning et al 2019a) that the gamma-ray emitted luminosity L γ (∝ L j ) is not correlated with redshift. Average density, however, is expected to evolve as both the IMF and metallicity evolve throughout cosmic time.…”

“…These include: 1) enough mass and angular momentum in the system to sustain an accretion disk and launch a jet, 2) no hydrogen envelope; this is based on both theory (the requirement that the jet is able to breakout from the system's envelope) and observations of Type Ic supernova associated with lGRBs, and 3) significant magnetic flux (along with angular momentum) to launch a jet (assuming a magnetically launched jet as in the Blandford-Znajek framework (Blandford & Znajek 1977). See, e.g., Barkov & Komissarov (2008); Komissarov & Barkov (2009); Barkov & Komissarov (2010); Lloyd-Ronning et al (2019a) for a consideration of these conditions for lGRB systems). We discuss these requirements briefly and generally in the context of several of lGRB progenitor systems.…”

Radio Loud vs. Radio Quiet Gamma-ray Bursts: the Role of Binary Progenitors

“…The jet power depends strongly on the spin of the black hole, the magnetic flux, and the mass of the black hole, although we note the complicated interplay between all three of these variables (for example, as discussed in the previous section, the angular momentum of the system will affect how much mass initially collapses into the black hole vs forming a centrifugally supported disk). We can simplistically write down, under the assumption of flux conservation, the magnetic flux in terms of magnetic field strength B and mass of the black hole 4 , which leads us to the following expression for the observed jet luminosity (Lloyd-Ronning et al 2019a):…”

“…The conditions required to produce an lGRB from a collapsing star (MacFadyen & Woosley 1999;Yoon & Langer 2005;Hirschi et al 2005;Yoon et al 2006;Woosley & Heger 2006), and indeed the jet launching mechanism itself (e.g. Barkov & Komissarov (2008); Komissarov & Barkov (2009); Lloyd-Ronning et al (2019a); King & Pringle (2021)), are still open questions. It is an ongoing pursuit to determine and understand which stars make gamma-ray bursts, and why.…”

The Consequences of Gamma-ray Burst Jet Opening Angle Evolution on the Inferred Star Formation Rate

“…We obtained this value by assuming roughly 0.1% of stars result in a supernova -of these supernovae, only about ∼ 15% (Smith et al 2011) are of Type Ib/c, the type associated with long gamma-ray bursts. Of this subset of Type Ib/c supernovae, only about 10% (Chapman et al 2007;Kanaan & de Freitas Pacheco 2013) successfully launch a GRB jet (due to conditions such as sufficient angular momentum and magnetic flux to launch a jet powerful enough to pierce through the progenitor envelope; a discussion of some of these issues can be found in Lloyd-Ronning et al (2019a)). This normalization is a big uncertainty, of course, and there is room for a range of values given our current state of knowledge.…”