Based on the recently solidified notion that the jittering jets explosion mechanism JJEM is the primary explosion mechanism of corecollapse supernovae CCSNe I estimate some typical properties of the jittering jets. From the imprints of jittering jets in the outskirts of some CCSN remnants I estimate the halfopening angles of jittering jets that shape CCSN remnants to be 110 degrees. I also estimate that intermittent accretion disks around the newly born neutron star NS can launch jets after they live for only several times their orbital period around the NS. To operate the JJEM requires the intermittent accretion disks that launch the jets to amplify the magnetic fields in a dynamo and the magnetic fields to reconnect to release their energy rapidly. I estimate the width of magnetic field reconnection zones to be 0.005r0.1km near the surface of the NS. This width requires a numerical resolution several times smaller than the resolution of present CCSN simulations. I argue therefore that existing simulations of the CCSN explosion mechanism are still far from correctly simulating CCSN explosions.
['Astrophysics - High Energy Astrophysical Phenomena']
Learning from corecollapse supernova remnants on the explosion mechanism
{'Learning from core-collapse supernova remnants on the explosion mechanism': 'Noam Soker 1  \n1 Department of Physics, Technion, Haifa, 3200003, Israel; soker@physics.technion.ac.il  \n(Dated: September 2024)', 'ABSTRACT': 'Based on the recently solidified notion that the jittering jets explosion mechanism (JJEM) is the primary explosion mechanism of core-collapse supernovae (CCSNe), I estimate some typical properties of the jittering jets. From the imprints of jittering jets in the outskirts of some CCSN remnants, I estimate the half-opening angles of jittering jets that shape CCSN remnants to be α j /similarequal 1 · -10 · . I also estimate that intermittent accretion disks around the newly born neutron star (NS) can launch jets after they live for only several times their orbital period around the NS. To operate, the JJEM requires the intermittent accretion disks that launch the jets to amplify the magnetic fields in a dynamo and the magnetic fields to reconnect to release their energy rapidly. I estimate the width of magnetic field reconnection zones to be D rec ≈ 0 . 005 r ≈ 0 . 1 km near the surface of the NS. This width requires a numerical resolution several times smaller than the resolution of present CCSN simulations. I argue, therefore, that existing simulations of the CCSN explosion mechanism are still far from correctly simulating CCSN explosions.  \nKeywords: supernovae: general - stars: jets - ISM: supernova remnants - stars: massive', '1. INTRODUCTION': "Two competing theoretical explosion mechanisms of massive stars utilize the gravitational energy the collapsing core releases as it forms a new neutron star (NS) to power core-collapse supernovae (CCSNe). In the delayed-neutrino explosion mechanism, neutrinos mediate the gravitational energy to explode the star (e.g., Bethe & Wilson 1985; Heger et al. 2003; Nordhaus et al. 2010, 2012; Janka 2012; Burrows 2013; Muller et al. 2019, 2024; Fujibayashi et al. 2021; Fryer et al. 2022; Boccioli et al. 2022, 2023; Boccioli & Roberti 2024; Nakamura et al. 2022, 2024; Olejak et al. 2022; Burrows et al. 2023; Andresen et al. 2024; Burrows et al. 2024b; Janka & Kresse 2024; Muller 2024; van Baal et al. 2024; Wang & Burrows 2024; Laplace et al. 2024). The magnetorotational explosion mechanism, where a pair of energetic opposite jets with a fixed axis explode the star, requires a rapidly rotating pre-collapse core (for recent studies see, e.g., Shibagaki et al. 2024; Zha et al. 2024a); therefore, it can power only a very small fraction of CCSNe. Despite being powered by jets, I take the magnetorotational explosion mechanism part of the neutrino-driven mechanism because it attributes most CCSNe, those with  \nno pre-collapse rapidly rotating cores, to the delayedneutrino explosion mechanism.  \nIn the jittering jets explosion mechanism (JJEM), jets that the newly born NS launches mediate the gravitational energy and explode the star in all CCSNe (e.g., Soker 2010; Papish & Soker 2011, 2014a; Gilkis & Soker 2014, 2016; Soker 2020, 2022a,b, 2023a; Shishkin & Soker 2021, 2022, 2023; Wang et al. 2024). Neutrino heating plays a role in the JJEM in boosting the effect of jets, but it does not play the primary role (Soker 2022c).  \nThe morphological signatures left by pairs of jets in many CCSN remnants (CCSNRs) are compatible with the JJEM, which considers such jets part of the explosion mechanism. Such signatures include opposite pairs of ears, nozzles, clumps, and filaments in CCSNRs, (e.g., Grichener & Soker 2017 who estimated the energies of the pairs of jets in several CCSNRs). The similarities of jet-shaped morphological features in CCSNRs with jet-shaped morphologies in planetary nebulae (e.g., Bear et al. 2017; Bear & Soker 2017, 2018; Soker 2022b, 2024a; Bear et al. 2024) and in cooling flow clusters (Soker 2024b) solidify the claim for CCSNR shaping by energetic jets. The claim for shaping by energetic jets that are part of the pairs of jets that explode progenitors  \nof the CCSNRs is particularly strong on CCSNRs that possess point-symmetric morphology (Soker & Shishkin 2024). A point-symmetric morphology has two or more pairs of opposite structural features (ears, clumps, filaments, nozzles) that do not share the same symmetry axis. The present list of point-symmetric CCSNRs and the studies that attributed their morphologies to jittering jets are: SNR 0540-69.3 (Soker 2022a), the Vela CCSNR (Soker 2023b; Soker & Shishkin 2024), CTB 1 (Bear & Soker 2023), N63A (Soker 2024c), SN 1987A (Soker 2024d,e), G321.3-3.9 (Soker 2024b; Shishkin & Soker 2024), G107.7-5.1 (Soker 2024b), Cassiopeia A (Bear & Soker 2024), the Cygnus Loop (Shishkin et al. 2024), and Puppis A (Bear et al. 2024).  \nBased on this list of point-symmetric CCSNRs and other CCSNRs with signatures of one pair of jets, I consider the JJEM to be CCSNe's primary or even sole explosion mechanism. This implies that the newly born NS manages to launch jets within several seconds from the formation of the proto-NS and the bounce of the shock that the proto-NS forms as the collapse stops due to nuclear forces. I use this implication to deduce some properties of the jet-launching process from young NSs (Section 2). I then show (Section 3) that to simulate the relevant processes for the JJEM, three-dimensional (3D) magneto-hydrodynamical (MHD) numerical codes must have very high spatial resolution beyond the reach of most present computers available to the community. I summarize this short study and conclude that the community is far from simulating the correct CCSN explosion process.", '2.1. Previously derived JJEM parameters': 'According to the JJEM, the basic explosion process starts when the newly born NS (and later the black hole if the NS collapses into a black hole) accretes mass with stochastic angular momentum from the collapsing core via intermittent accretion disks. The stochastic angular momentum results from instabilities above the NS, including the spiral standing accretion shock instability (e.g., Buellet et al. 2023 for a recent study of this instability), that amplify angular momentum seed fluctuations in the collapsing core material. The seed fluctuations come from the convective motion in the pre-collapse core (e.g., Papish & Soker 2014a; Gilkis & Soker 2014, 2016; Shishkin & Soker 2023; Wang et al. 2024), and, in some cases, possibly from the envelope (e.g., Quataert et al. 2019; Antoni & Quataert 2022, 2023). In cases of a rapid precollapse core rotation, the stochastic angular momentum variations are around this rotation axis (e.g., Soker  \n2023a). Namely, it is not entirely stochastic at a whole solid angle.  \nEarlier studies have derived some of the basic properties of the JJEM, which I summarize in Table 1. The first 11 properties are in a table from an earlier paper (Soker 2024e). In this study, I added the last three rows (12-14). Table 1 presents the range of typical values of the JJEM and the justifications for these values. The values the table lists are for iron CCSNe, not electroncapture CCSNe. In electron-capture CCSNe, the primary explosion phase (jet-launching period) might be much longer, up to several minutes to even a few hours rather than seconds (Wang et al. 2024).', '2.2. Half-opening angle of the jets': "The ears on the outskirts of many CCSNRs (e.g., Grichener & Soker 2017; Bear et al. 2017; see Section 1) show that the shaping jets could penetrate the ejecta. For that, the momentum per unit area of the jets cannot be much smaller than the average of the CCSN ejecta and might be even larger. The typical momentum of a jet that carries a mass of m 1j = 0 . 5 m 2j , by values from Table 1, is  \np 1j = m 1j v 1j /similarequal 5 -100 M /circledot km s -1 . (1)  \nThe radial momentum of a typical CCSN is  \np ej , r = M ej v ej ≈ 3 × 10 4 M /circledot km s -1 , (2)  \nfor a typical ejecta mass of M ej /similarequal 8 M /circledot and ejecta velocity of v ej /similarequal 4000 km s -1 , such that the kinetic (explosion) energy is E k /similarequal 1 . 3 × 10 51 erg. The value of p ej , r can vary greatly from one CCSN to another. I use equation (2) only to scale the next equation. For the momentum of the jets per unit area to be as large as that of the ejecta or more, the half-opening angle of the jets should be  \nα j /lessorsimilar 2 ( p 1j p ej , r ) 1 / 2 = 3 . 6 · ( p 1j 10 -3 p ej , r ) 1 / 2 . (3)  \nConsidering the extensive range in the possible jet and ejecta momenta values, I take the half-opening angle's demand to be α j /lessorsimilar 1 · -10 · .  \nIn an earlier paper (Soker 2022c), I suggested the collimation of the jets by the pressure of the ambient gas close to the NS, below the gain region, because the pressure in that region is much larger than in the gain region (e.g., Janka 2001). Further out, the material that the jet shocks, the so-called cocoon, maintains the collimation of the jet or might even compress it somewhat (Soker 2022c). Here, I quantify the collimation and find that these collimation processes should be efficient in bringing the opening angle of the jets to be small.  \nTable 1. Typical parameters of jittering jets in iron-core CCSNe  \nNotes: The first 11 properties are from an earlier table (Soker 2024e); the last three rows are quantities I estimate in this study. # The values in the table are for CCSNe of collapsing iron-rich core. Jets of electron capture supernovae are less energetic, and the explosion might last for minutes to a few hours (Wang et al. 2024).  \n& Izzo et al. (2019) reported the possible indication for jets at /similarequal 10 5 km s -1 in SN 2017iuk associated with GRB 171205A. Guetta et al. (2020) claim that most CCSNe have no signatures of relativistic jets, supporting the non-relativistic jet velocity. References: [B+25]: Bear et al. (2024); [BGS17]: Bear et al. (2017); [GiSo15]: Gilkis & Soker (2015);[GrSo17]: Grichener & Soker (2017); [Li04]: Livio (2004); [Ni18]: Nisini et al. (2018); [PaSo11]: Papish & Soker (2011); [PaSo14a]: Papish & Soker (2014a); [PaSo14b]: Papish & Soker (2014b); [ShSo14]: Shishkin & Soker (2021); [So24e]: Soker (2024e); [So24f]: Soker (2024f).  \nClumps are also observed in point-symmetric CCSNRs. Clumps can be the tip of jets. Another possibility is that jet-inflated bubbles in the core compress clumps, as Papish & Soker (2014a) have shown, and the clumps penetrate the ejecta and imprint the morphology. Similarities with cooling flow clusters support this process of forming clumps in some, but not all, cases (Soker 2024b).", '2.3. Minimum time for jet launching': 'Bear et al. (2024) proposed a new mechanism to impart a natal kick velocity to the NS, the kick by early asymmetrical pair (kick-BEAP) mechanism. In the kickBEAP mechanism, the NS launches a pair (or two)  \nof two opposite jets where one is much more powerful. The momentum asymmetry between the two jets is significant enough to impart a large velocity to the NS (Bear et al. 2024). The kick-BEAP operates within t b /lessorsimilar 0 . 2 s after shock bounce when the accretion of core material onto the NS is very high. At that early phase, the radius of the hot NS is much larger than its final radius, R ( < 0 . 2 s) /similarequal 40 km (e.g., Raynaud et al. 2020) instead of R Ns /similarequal 12 km; it is a proto-NS.  \nThe jets of the kick-BEAP mechanism are launched from a radius of /similarequal 40 km. The orbital period at this radius, for a mass of still M /similarequal 1 . 2 M /circledot , is τ Kep /similarequal 0 . 004 s. The high-mass accretion rate lasts for /similarequal 0 . 2 s (e.g.,  \nMuller et al. 2017; Burrows et al. 2024a), and a jetlaunching episode for a shorter time; Bear et al. (2024) scale with a jet launching period of ∆ t 1 = 0 . 05 s. But the accretion disk starts to launch jets before it ceases to exist. Namely when its age is < 0 . 05 s /similarequal 10 τ Kep .  \nThe conclusion from this discussion, namely, under the assumption of the kick-BEAP mechanism in the frame of the JJEM, is that an accretion disk can launch jets even if it exists for only a short time, as brief as /lessorsimilar 10 τ Kep , namely, for only several times the orbital period at the jet-launching radius. This time is shorter than the relaxation time of the accretion disk, which implies unequal opposite jets (Soker 2024c).', '2.4. The rotational energy of the accreted material': "In the JJEM, there are jet-launching episodes with varying angular momentum directions. This implies that the orbital velocity of an accretion disk that launches jets is inclined to the orbital velocity of the accretion disk from the previous jet-launching episode. One effect is the amplification of magnetic fields. The differential rotation within an accretion disk amplifies the azimuthal magnetic field. The accretion disk of the next jet-launching episode is not in the same plane, i.e., it is inclined to that plane. Therefore, it stretches the magnetic field lines in its orbital motion direction, which is inclined to the previous one. This further amplifies the magnetic fields in the stochasticω (S ω ) effect that I suggested in an earlier paper (Soker 2020). Here, I consider the possible dynamic implications of the inclined consecutive accretion disks.  \nThe orbital velocity near the surface of the NS during the explosion process when the NS is not yet settled to its final radius is v Kep /similarequal 10 5 km s -1 . This is about the typical jets' velocity in the JJEM, v j /similarequal v Kep (Table 1). The two jets in each jet-launching episode carry a fraction η 2j /similarequal 0 . 1 of the mass in the accretion disk so that a fraction of 1 -η 2j is accreted. The jets carry angular momentum, and the accreted mass settles onto the NS with lower rotational velocity than in the accretion disk. As with young stellar objects that rotate at tens of percent of the break-up velocity (e.g., Huang et al. 2010), I take here the rotational velocity of the accreted mass to be v rot = δ K v Kep , with δ rot /similarequal 0 . 3 -0 . 5. Since v j /similarequal v Kep , I take v rot = δ j v j , with δ j /similarequal 0 . 3 -0 . 5. The ratio of the rotational energy of the accreted mass in an episode to the energy of the jets of that episode is then  \nE rot E 2j /similarequal 1 . 4 ( δ j 0 . 4 ) 2 ( 1 -η j 9 η j ) . (4)  \nThe kinetic energy of the accreted mass is about equal to the kinetic energy of the pair of jets from the same jet-launching episode.  \nThe implication of the relation E rot /similarequal E 2j is as follows. Because the next accretion phase will have a different angular momentum, the velocity in the new accretion disk will not be parallel to that in the previous one that has just been accreted. There will be a large friction in the boundary between the accreted material of the two accretion episodes. A large fraction of the kinetic energy will be dissipated, much more than in an accretion flow with a fixed angular momentum axis. The dissipated kinetic rotational energy ends in heat, high pressure that accelerates material out, and magnetic fields. Any heat carried by neutrinos will not affect the launching of the jets. On the other hand, the hot gas can accelerate material outwards before it cools, adding energy directly to the outflow, namely, jets. A fraction of the dissipated energy ends in magnetic fields, which play a crucial role in jet launching.  \nFuture magnetohydrodynamic simulations of the CCSN explosion process should include this friction between accreted material from consecutive jet-launching episodes. This demands a high, but not very high, numerical resolution. The zone between consecutive accretion episodes behaves like a boundary layer where the velocity has a large gradient. A boundary layer in fixedaxis accretion disks can boost mass ejection if shocks occur within it (e.g., Soker & Regev 2003). The width of the boundary layer is of the order of the disk's halfthickness. Allowing for a disk half-thickness of /similarequal 0 . 1 r and demanding resolving the boundary layer by at least four cells requires the numerical resolution near the NS to have a cell size of ∆ /lessorsimilar 0 . 025 r . This is about the resolution of present simulations of CCSNe, as I discuss in Section 3, where I also show that magnetic processes require even finer resolution.", '3. THE REQUIRED NUMERICAL RESOLUTION': "The conversion of the gravitational energy of the collapsing stellar core to the kinetic energy of the jets that explode the star involves intermediate energy forms of rotational energy of the accretion disk (or of a sub-Keplerian accretion flow through a belt; Schreier & Soker 2016) and magnetic energy. Magnetic energy is crucial in the JJEM (Soker 2018, 2019a,b, 2020). However, as I show next, accurate simulations of jittering jets demand numerical resolutions beyond those in present three-dimensional hydrodynamical and magnetohydrodynamical simulations.  \nThe sheared velocity of the accreted gas, particularly differential rotation in the intermittent accretion disks, and the convection amplify the magnetic energy, i.e., the dynamo process. The rapid release of magnetic energy requires rapid reconnection of magnetic field lines.  \nI turn to estimate the necessary resolution that allows for the correct simulation of the rapid reconnection. If reconnection occurs on a too large scale, then the dynamo is inefficient, and reconnection is not as violent as required.  \nConsider a reconnection process where two magnetic flux tubes with opposite field lines approach each other. Let λ tube be the typical size of a magnetic flux tube. After reconnection, the material is ejected to opposite sides at the Alfven velocity v A , while the two magnetic flux tubes approach each other at a velocity of v rec ≈ 0 . 1 v A (e.g., Parker 1979). The width of the reconnection zone is very small  \nD rec ≈ λ tube v rec v A ≈ 0 . 1 λ tube . (5)  \nFor a violent magnetic reconnection event, the reconnection should occur on a time scale τ rec that is shorter than the material's escape time from the considered radius, /similarequal r/v Kep . I crudely demand, therefore,  \nτ rec ≈ λ tube 0 . 1 v a /lessorsimilar r v Kep . (6)  \nTo resolve the reconnection process, the size of the grid cells should resolve the two halves of the reconnection zone, each half of an approaching flux tube (of opposite field lines). Namely, ∆ < 0 . 5 D rec . With equations (5) and (6), the constraint on the grid cells becomes  \n∆ /lessorsimilar 0 . 05 λ tube /lessorsimilar 0 . 005 ( v a v Kep ) r. (7)  \nIn a powerful magnetic activity v a /similarequal v Kep , the Alfven speed will not be larger than the rotation speed. Considering then this ratio of v a /v Kep and that the reconnection zone should be resolved by more than two cells, better at least four cells, I conclude that for simulating the JJEM, the grid cells should be ∆ /lessorsimilar 0 . 002 r .  \nIn the recent magnetohydrodynamical simulations of CCSNe that Varma et al. (2023), Powell & Muller (2024), and Zha et al. (2024b), conducted, the numbers of grid cells in the three coordinates were ( N r , N θ , N φ ) = (550 , 128 , 256), corresponding to an angular resolution of 1 . 4 · , or ∆ θ,φ = 0 . 0245 r . They have near the NS ∆ r /similarequal 0 . 015 r in the radial direction. This resolution is several times, and up to an order of magnitude, too coarse for the demand of the JJEM. Raynaud et al. (2020) performed magnetohydrodynamic simulations of magnetar formation. They have high resolution but simulated only the inner /similarequal 40 km, namely, the proto-NS but not its surroundings. With the grid of ( N r , N θ , N φ ) = (257 , 512 , 1024), the resolution of ∆ θ,φ = 0 . 006 r is almost as required for simulating the JJEM, but not yet as needed.  \nThe main finding of this discussion is that the present three-dimensional magnetohydrodynamical simulations do not yet have the resolution and ingredients to simulate the JJEM.", '4. DISCUSSION AND SUMMARY': 'Last year, studies of the JJEM analyzed in depth the point-symmetrical morphologies of about ten CCSNRs (see list in Section 1). The main conclusion of the indepth analysis is that jittering jets shaped all these CCSNRs, and the shaping jets were part of the tens of jets that exploded the star (e.g., Soker & Shishkin 2024). The conclusion of jet-shaping of CCSNRs is based in part on carefully studying many morphological similarities between CCSNRs and jet-shaped planetary nebulae and hot gas in clusters of galaxies where pairs of jets shape pairs of bubbles, clumps, rims, and nozzles (e.g., Soker 2024b; Bear et al. 2024; see a talk from 2024: https://www.youtube.com/watch?v=hJYc6EfgxJU).  \nAlthough the tool of identifying the morphological imprints of jets is not familiar in the CCSN community, it is standard in analyzing structures of planetary nebulae and hot gas in clusters of galaxies, making the claim for jet-shaped CCSNRs robust. The analysis of these point-symmetrical CCSNRs motivated the present paper.  \nBased on the solidification of the JJEM in 2024 and the understanding that jets shape many CCSNRs, I estimated more parameters of the JJEM (rows 12-14 in Table 1). I estimated the typical half opening of the shaping jittering jets to be α j /similarequal 1 · -10 · . Namely, these are not wide jets. I also estimated that an accretion disk around the newly born NS can launch jets even when its lifetime is only several times the orbital period in the radius where it launches the jets. Table 1 lists the estimated parameters of the JJEM.  \nWhile studies of the JJEM in 2024 focused on point-symmetrical morphologies of CCSNRs, studies of the competing delayed-neutrino explosion mechanism have focused on three-dimensional simulations to revive the stalled shock (e.g., Burrows et al. 2024a; Janka & Kresse 2024; Muller 2024; Muller et al. 2024; Nakamura et al. 2024; van Baal et al. 2024; Wang & Burrows 2024). As far as I know, when I wrote this paper, none of the studies of the delayedneutrino explosion mechanism suggested any explanation for point-symmetrical CCSNRs. Some researchers in private communications mentioned shaping by postexplosion jets and/or interaction with the interstellar medium or the circumstellar material. However, in a detailed analysis of several CCSNRs, Soker & Shishkin (2024) find that these mechanisms encounter severe dif-fi  \nlties. Post-explosion jets and ambient gas cannot explain the point-symmetrical structures of some heavy elements that come from the deep core of the CCSN progenitor (e.g., O, Ne, Mg, Si, S, Fe) and as observed in some CCSNRs, and nor the point-symmetrical structures in the inner zones of some CCSNRs.  \nThe strongest argument against the JJEM made by supporters of the delayed neutrino explosion mechanism is that their simulations do not obtain jittering jets. In this study, I dismissed this argument. In Section 3, I argued that the numerical resolution in magnetohydro-  \ndynamical simulations appropriate to the JJEM should be much higher than in current simulations. Specifically, the typical size of grid cells in radius r should be ∆ /lessorsimilar 0 . 002 r . Current CCSN simulations have grid cells larger by /greaterorsimilar 3 -5 times from this constraint. I conclude that the simulations of the CCSN explosion mechanism are still a long way from simulating the correct CCSN explosion mechanism.', 'ACKNOWLEDGEMENTS': 'A grant from the Pazy Foundation supported this research.', 'REFERENCES': '- -. 2018, arXiv e-prints, arXiv:1805.03447,\n- doi: 10.48550/arXiv.1805.03447\n- -. 2019a, arXiv e-prints, arXiv:1907.13312,  \ndoi: 10.48550/arXiv.1907.13312  \n- -. 2019b, Research in Astronomy and Astrophysics, 19, 095, doi: 10.1088/1674-4527/19/7/95\n- -. 2020, Research in Astronomy and Astrophysics, 20, 024, doi: 10.1088/1674-4527/20/2/24\n- -. 2022a, Research in Astronomy and Astrophysics, 22, 035019, doi: 10.1088/1674-4527/ac49e6\n- -. 2022b, Research in Astronomy and Astrophysics, 22, 122003, doi: 10.1088/1674-4527/ac9782\n- -. 2022c, Research in Astronomy and Astrophysics, 22, 095007, doi: 10.1088/1674-4527/ac7cbc\n- -. 2023a, Research in Astronomy and Astrophysics, 23, 095020, doi: 10.1088/1674-4527/ace9b3\n- -. 2023b, Research in Astronomy and Astrophysics, 23, 115017, doi: 10.1088/1674-4527/acf446\n- -. 2024a, Galaxies, 12, 29, doi: 10.3390/galaxies12030029\n- -. 2024b, The Open Journal of Astrophysics, 7, 49, doi: 10.33232/001c.120279\n- -. 2024c, The Open Journal of Astrophysics, 7, 12, doi: 10.21105/astro.2311.03286\n- -. 2024d, NewA, 107, 102154,\n- doi: 10.1016/j.newast.2023.102154\n- -. 2024e, Research in Astronomy and Astrophysics, 24, 075006, doi: 10.1088/1674-4527/ad4fc2\n- -. 2024f, The Open Journal of Astrophysics, 7, 12,  \ndoi: 10.21105/astro.2311.03286  \n- Soker, N., & Regev, O. 2003, A&A, 406, 603,\n- doi: 10.1051/0004-6361:20030809\n- Soker, N., & Shishkin, D. 2024, arXiv e-prints, arXiv:2409.02626, doi: 10.48550/arXiv.2409.02626\n- van Baal, B. F. A., Jerkstrand, A., Wongwathanarat, A., & Janka, H.-T. 2024, MNRAS,  \ndoi: 10.1093/mnras/stae1603  \n- Varma, V., Muller, B., & Schneider, F. R. N. 2023, MNRAS, 518, 3622, doi: 10.1093/mnras/stac3247\n- Wang, N. Y. N., Shishkin, D., & Soker, N. 2024, arXiv e-prints, arXiv:2401.06652,  \ndoi: 10.48550/arXiv.2401.06652  \nWang, T., & Burrows, A. 2024, ApJ, 969, 74,  \ndoi: 10.3847/1538-4357/ad5009  \nZha, S., Muller, B., & Powell, J. 2024a, arXiv e-prints,  \narXiv:2403.02072, doi: 10.48550/arXiv.2403.02072  \n- -. 2024b, ApJ, 969, 141, doi: 10.3847/1538-4357/ad4ae7'}