**1. Introduction**

Gamma-ray bursts (GRBs) are intense flashes of high energy electromagnetic radiation of ∼a few 100 keV with a very brief duration of 1 s to a few minutes reaching Earth isotropically from unpredictable directions. GRBs are observationally classified in two groups: short-duration hard (∼1 s, 350 keV) and long-duration soft (∼a few 10 s of seconds to ∼1 min, ∼200 keV). These two classes are assumed to have different physical origins. In general, a small amount of matter is required to be accelerated to ultra-relativistic speeds and beamed at a small solid angle to produce GRBs. After their discovery in 1973 [1], understanding the origin of GRBs has been of utmost importance to comprehend the cosmic evolution of the early universe. Given the association of GRBs with the death of massive stars and them being observable in high redshift, in principle as high as *z* ∼ 20 [2], GRBs are often considered to probe the star formation histories over cosmic time [3].

Massive stars (&10 M) enter the Wolf-Rayet (WR) phase towards the end of or after the main-sequence [4]. Depending on the spectroscopic identification of heavy elements, such as helium, nitrogen, carbon, oxygen [4,5], and their excitation states, WR stars are primarily classified in three categories: WN, WC, and WO (see Table 4 of [5]). Theoretically, WN and WC stars are believed to be progenitors of Type Ib and Ic core-collapse supernovae (SNe), respectively, given their pre-SN He-/CO- core masses and the absence of surface H and H/He [6]. However, there is no direct evidence that suggests single WR stars as Type Ib/Ic SNe progenitors. Given the WR lifetimes of a few 10<sup>5</sup> years, one would need to observe <sup>∼</sup>10<sup>4</sup> single WR stars to draw a firm connection between them and core-collapse SNe (CCSNe), in a timescale of a few 10s of years. This considerably high number means these are not field stars; rather they are in clusters. Given that more than 70% of massive

**Citation:** Roy, A. Progenitors of Long-Duration Gamma-ray Bursts. *Galaxies* **2021**, *9*, 79. https://doi.org/ 10.3390/galaxies9040079

Academic Editors: Elena Moretti and Francesco Longo

Received: 16 July 2021 Accepted: 1 October 2021 Published: 19 October 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

stars are in binaries, the lower mass interacting binaries might be alternative progenitors of SN Type Ib/Ic [7].

Energetically, long-duration GRB (LGRB) and CCSNe both fall under the same category. In many long-duration GRBs (LGRB), the beaming-corrected total Gamma-ray energy is estimated to be <sup>∼</sup>10<sup>51</sup> erg. In addition, the total kinetic energy of the core collapse SN is <sup>∼</sup>10<sup>51</sup> erg, comparable to that of GRB jets. This naturally makes one consider the possibility of finding the connection between these two extreme phenomena. To confirm this hypothesis, there are three primary approaches available. Firstly, one can find the causal connection—whether both SN and GRB are coincident in space and time. Secondly, one can study photometry to obtain any overlap in the SN and GRB afterglow light curves. Finally, one can study spectroscopy to establish the SN-GRB connection.

Another class of SNe, Type I superluminous supernovae (henceforth SLSNe), is also believed to have a similar origin as LGRBs. SLSNe are characterized by luminosities 10–100 times larger than "typical" SNe [8–10], and their <sup>56</sup>Ni mass of <sup>∼</sup>20–30 M is much higher compared to 1 M for "typical" SNe ([11] and references therein). Their spectra show the absence of H and He, same as Type-Ic SN, and they are bare carbon and oxygen cores [12]. This indicates that SLSNe progenitors have gone through intense mass-loss and/or mixing of chemical elements that made their envelopes depleted of H and He. However, the nature of SLSNe progenitors is yet unknown. Although the most commonly believed theory for their progenitors, based on the observed properties of SLSNe, is the magnetar model—where the newly formed millisecond magnetar, i.e., rapidly rotating, highly magnetized neutron stars (NS), deposits continuous energy to the SN ejecta. LGRBs, on the other hand, are formed in the framework of collapsar model [13]—where the rapidly rotating stellar core of a massive star collapses into a black hole (BH). Determining the final fate of a massive star that forms a NS or a BH is a complex and poorly understood astrophysical problem. Several recent theoretical models invoke a few diagnostic parameters of the progenitors at the pre-SN or pre-collapse phase that determine the final fates [14–17]. For example, one such diagnostic parameter is the "so-called" core compactness parameter, *ξ*<sup>M</sup> [14]. We discuss these criteria later in this paper.

This paper aims to review the possible progenitors of LGRBs, find the connection between CCSNe and GRB, and dissociate progenitors of LGRB and SLSN based on several theoretical constraints on the pre-SN cores. Finally, we present a set of models of massive stars for varying mass, rotation rate and metallicity to narrow down a range of values that are favoured by the observed LGRB rate and its metallicity evolution. This paper is organized as follows: in Section 2, we discuss the existing observations that associate SNe with LGRBs; in Section 3, we present the leading models for the progenitors of SLSNe and LGRBs; in Section 4, we illustrate whether single or binary stars are more suitable candidates for LGRB progenitors; in Section 5, we describe the properties of WR stars that are required to form LGRB progenitors, and in Section 6, we summarise the salient points of this review article and pose the open questions that will be the focus of research for LGRB astrophysics in the coming years.
