Vol.0 (20xx) No.0, 000–000

11institutetext: Department of Physics, Technion, Haifa, 3200003, Israel;
<EMAIL_ADDRESS>
Received 20xx month day; accepted 20xx month day

# Review: The role of jets in exploding supernovae and in shaping their
remnants

Noam Soker 11

###### Abstract

I review studies of core collapse supernovae (CCSNe) and similar transient
events that attribute major roles to jets in powering most CCSNe and in
shaping their ejecta. I start with reviewing the jittering jets explosion
mechanism that I take to power most CCSN explosions. Neutrino heating does
play a role in boosting the jets. I compare the morphologies of some CCSN
remnants to planetary nebulae to conclude that jets and instabilities are
behind the shaping of their ejecta. I then discuss CCSNe that are descendants
of rapidly rotating collapsing cores that result in fixed-axis jets (with
small jittering) that shape bipolar ejecta. A large fraction of the bipolar
CCSNe are superluminous supernovae (SLSNe). I conclude that modelling of SLSNe
lightcurves and bumps in the lightcurves must include jets, even when
considering energetic magnetars and/or ejecta interaction with the
circumstellar matter (CSM). I connect the properties of bipolar CCSNe to
common envelope jets supernovae (CEJSNe) where an old neutron star or a black
hole spirals-in inside the envelope and then inside the core of a red
supergiant. I discuss how jets can shape the pre-explosion CSM, as in
supernova 1987A, and can power pre-explosion outbursts (precursors) in binary
systems progenitors of CCSNe and CEJSNe. Binary interaction facilitate also
the launching of post-explosion jets.

###### keywords:

(stars:) supernovae: general; supernova remnants; Interstellar Medium (ISM),
Nebulae; stars: jets; binaries: general.

##  1 Introduction

In this review I summarize many, but not all, of the studies in the last
decade that attribute major roles to jets in core collapse supernovae (CCSNe)
and related energetic stellar transients, in particular common envelope jets
supernovae (CEJSNe). I concentrate on studies that adopt the view that jets
explode most, or even all, CCSNe.

CEJSNe are defined as jet-powered energetic transient events where an old
neutron star (NS) or an old black hole (BH) accrete mass from the envelope and
then from the core of a red supergiant (RSG) star and launch energetic jets
(section 4). I consider the role of jets in powering and in shaping events
that are true CCSNe (sections 2 and 3), CEJSNe, which during the first weeks
of the event might be classified as CCSNe (section 4), pre-explosion shaping
of the CSM in CCSNe and type Ia supernovae (SNe Ia; section 5), pre-explosion
outbursts (section 6), and post-explosion powering (section 7).

The different sections reveal the very large parameter space that jets
introduce. The parameter space includes regular CCSNe, as well as rare
combinations of parameters that can explain peculiar transients.

In this review I do not discuss high-energy processes inside the jets (gamma
rays, cosmic ray acceleration, neutrino production, r-process nucleosynthesis)
as each one of these processes requires a separate review. These processes
might definitely take place in many of the systems with energetic jets that I
review.

Because the different sections review different scenarios and different
processes, although in all of them jets play the major roles, this review has
no summary of the results, but rather a summary of some open questions
(section 8). Instead, each section has its own short summary that together
with Table 1 serve as the summary of the review.

Phase |  Compact object |  System |  Source of mass |  Source of A.M. |  Fraction |  Event |  §
---|---|---|---|---|---|---|---
Pre-Explosion |  MS |  Binary |  RSG/WR |  Orbital |  Small |  ILOT (LRN) |  5,6
Pre-Explosion |  NS/BH |  Binary |  RSG/WR |  Orbital |  Small |  CEJSN-impostor |  5, 6
Pre-Explosion |  2(NS/BH/MS) |  Triple |  RSG/WR |  Orbital: triple +inner binary |  Very Small |  CEJSN-impostor (or ILOT for MSs) |  5, 6
Explosion |  New NS |  S/B/T |  core |  Core Convection (jittering jets) |  Most CCSNe |  CCSN |  2
Explosion |  New NS |  B/T |  core |  Core rotation |  Small |  CCSN: SNe/SLSNe |  3, 7.3
Explosion |  New BH |  S/B/T |  Core + envelope |  Envelope Convection (jittering jets) |  Small |  CCSN: SLSNe +peculiar CCSNe |  2
Explosion |  New BH |  B/T |  Core + Envelope |  Core + Envelope rotation |  Medium |  CCSN: SLSNe + peculiar CCSNe |  3, 7.3
Explosion |  Old NS/BH |  B/T |  Core in a CEE |  Orbital |  Small |  CEJSN (including FBOTs) |  4
Post-Explosion |  New NS/BH |  S/B/T |  Fallback Ejecta |  Pre- Explosion rotation |  Small |  Extended lightcurve and/or bumps |  7
Post-Explosion |  New NS/BH |  Binary |  MS Companion |  Orbital |  Very small |  Extended lightcurve and/or bumps |  7
Post-Explosion |  Old NS/BH |  Binary |  Ejecta |  Orbital |  Very small |  Small extra energy |  4, 7
Table 1: The main type of jet-driven events (seventh column) and the phase of
the jet activity (first column) that I review in the different sections (last
column). In the second column I list the compact object that accretes mass. In
the third column I list the required type of interacting system. Note that
single-star (S) processes can take place also in binary (B) systems and in
triple (T) systems, and that binary processes might take place in triple-star
systems as well. The fourth and fifth columns list the source of the accreted
mass and its angular momentum with respect to the accreting object,
respectively. The sixth column lists the fraction of such systems relative to
the total number of CCSNe. Abbreviation. A.M.: angular momentum; BH: black
hole; CCSNe: core collapse supernovae; CEE: common envelope evolution; CEJSN:
common envelope jets supernova; FBOT: Fast blue optical transient; ILOT:
intermediate luminosity optical transient (other names include red nova and
luminous red nova, LRN); MS: Main sequence; NS: neutron star; RSG: red
supergiant; S/B/T: single/binary/triple; SLSNe: superluminous supernovae; WR:
Wolf–Rayet.

In Table 1 I list the main jet-activity phases (first column) and transient
types (next to last column). The table does not cover all possibilities. In
the second column I list the compact object that accretes mass and launches
the jets, a main sequence star (MS), a NS or a BH. In the third column I
indicate whether the system might be a single star (S), a binary system (T),
or a triple system (T). In the forth and fifth columns I indicate the main
mass and angular momentum sources of the accreted mass, respectively. In the
sixth column I list my crude estimate of the fraction of these events and
phases. I elaborate on each of these in the respective section that I list in
the last column. The rich spectrum of processes and properties of jets
explains not only regular CCSNe but also peculiar CCSNe and similar
transients.

$\bigstar$ Summary of section 1. There is a rich spectrum of processes by
which jets can influence the properties of CCSNe and CEJSNe, including their
pre-explosion, explosion, and post explosion shaping and light curves, e.g.,
bumps in the light curve (Table 1).

##  2 The jittering jets explosion mechanism

###  2.1 The definition of the mechanism

In the jittering jets explosion mechanism jets that the newly born NS (or BH)
launches in varying directions in a stochastic manner explode the star (Soker
2010; Papish & Soker 2011; for some later studies see, e.g., Papish & Soker
2014b; Gilkis & Soker 2015; Quataert et al. 2019; Soker 2019a, 2020b; Antoni &
Quataert 2022; Shishkin & Soker 2022; Soker 2022a, d). The NS launches these
jets as it accretes mass via an accretion disk (or belt) with stochastic
angular momentum variations. The source of these angular momentum variations
is the pre-collapse stochastic convection motion in the core. The
perturbations are amplified by instabilities above the newly born NS. I
schematically present the mechanism in Fig. 1 (from Gilkis & Soker 2015) and
turn now to further discuss its properties (section 2.2).

Figure 1: A schematic presentation of the jittering jets explosion mechanism
(From Gilkis & Soker 2015). The two-sided arrow on the upper left of each
panel represents a length of $\simeq 500{~{}\rm km}$. The four panels span an
evolution time of several seconds. (a) The pre-collapse inner core just before
collapse. The convective vortices in the silicon-burning shell (shown) and/or
the oxygen-burning shell (not shown) of the pre-collapse core are the seeds of
stochastic angular momentum fluctuations. (b) In-falling gas onto the newly
born NS passes through the stalled shock and the spiral modes of the standing
accretion shock instability (SASI) amplify the seed angular momentum
perturbations. (c) The stochastic angular momentum variations of the accreted
mass leads to the formation of an intermittent accretion disk/belt around the
NS that launches jittering jets. (d) The jittering jets are shocked and
inflate hot bubbles that explode the core and then star. The entire jet-
activity phase lasts for one to few seconds, and there might $\approx{\rm
few}-30$ jet-launching episodes.

###  2.2 The stochastic angular momentum source

The jittering jets explosion mechanism is an alternative to the much older
delayed neutrino explosion mechanism that Bethe & Wilson (1985) suggested four
decades ago to explain CCSNe. Hundreds of papers studied the neutrino-driven
mechanism over the years (e.g., Heger et al. 2003; Janka 2012; Nordhaus et al.
2012; Couch & Ott 2013; Bruenn et al. 2016; Janka et al. 2016; O’Connor &
Couch 2018; Müller et al. 2019; Burrows & Vartanyan 2021; Fujibayashi et al.
2021; Boccioli et al. 2022; Nakamura, Takiwaki, & Kotake 2022). Despite the
very sophisticated three-dimensional (3D) hydrodynamical simulations of the
delayed neutrino mechanism it still encounters some problems (which I will not
elaborate on in this study; see, e.g., Kushnir 2015; Papish, Nordhaus, & Soker
2015). One of the main limitations of the delayed neutrino mechanism is that
even when the explosion energy is scaled to observed CCSNe this mechanism is
limited to explosion energies (mainly the kinetic energy of the ejecta) of
$E_{\rm exp}<3\times 10^{51}{~{}\rm erg}$ (e.g., Fryer 2006; Fryer et al.
2012; Papish, Nordhaus, & Soker 2015; Ertl et al. 2016; Sukhbold et al. 2016;
Gogilashvili et al. 2021).

The fundamental ingredients and outcomes of the jittering jets explosion
mechanism are as follows.

  1. 1.

Source of angular momentum. The source of angular momentum is the stochastic
convective motion in the precollapse core (e.g., Gilkis & Soker 2014, 2016;
Shishkin & Soker 2021) or envelope (e.g., Quataert et al. 2019). These seed
perturbations are amplified by instabilities behind the stalled shock inside a
radius of $r\simeq 100{~{}\rm km}$ (Soker 2019a, c), mainly by the spiral
standing accretion shock instability (spiral SASI, e.g., Andresen et al. 2019;
Walk et al. 2020; Nagakura et al. 2021; Shibagaki et al. 2021, for some
simulations of the spiral SASI). The large stochastic angular momentum
fluctuations of the mass that the newly born NS accretes allow the formation
of intermittent accretion disks that launch the jittering jets (e.g., Papish &
Soker 2011; Gilkis & Soker 2014, 2015; Quataert et al. 2019; accretion belts
are also possible, Schreier & Soker 2016).

  2. 2.

The crucial role of magnetic fields. Magnetic fields are essential ingredients
in the launching of the jets, and must be included in future numerical
simulations of the jittering jets explosion mechanism (e.g., Soker 2018b,
2019a, 2020b).

  3. 3.

Coupling to neutrino heating. Although neutrino heating does not play the main
role in powering CCSNe according to the jittering jets explosion mechanism,
neutrino heating boosts the energy of the jittering jets (Soker 2022d).

  4. 4.

No failed CCSNe. As core and envelope convection zones exist in all CCSN
progenitors (e.g., Shishkin & Soker 2021; Antoni & Quataert 2022; Shishkin &
Soker 2022), according to the jittering jets explosion mechanism there are no
failed CCSNe (e.g., Soker 2017b). The observational finding by Byrne & Fraser
(2022) of no failed CCSNe indirectly supports the jittering jets explosion
mechanism.

  5. 5.

Feedback mechanism. The jittering jets explosion mechanism operates through a
negative feedback mechanism (see review by Soker 2016b). In the negative jet
feedback mechanism the jets regulate their power by their effect on the mass
accretion rate onto the compact object that launches the jets. Specifically,
if the mass accretion rate increases so is the power of the jets. However, the
interaction of the jets with the ambient gas, which is the reservoir of the
accreted mass, expel and inflate the ambient gas. This in turn reduces the
mass accretion rate, and hence the jets’ power, closing the negative feedback
cycle. As long as there is no explosion, falling material feeds the accretion
disk that launches the jets. Because there is no hundred percent conversion
efficiency of jets’ energy to unbind the ejecta, i.e., the ejecta expands at
velocities much above the binding energy, this explains why typical CCSN
explosion energy is about several times the ejecta binding energy.

  6. 6.

Typical properties of the jittering jets. During an explosion by jittering
jets there might $\approx{\rm few}-30$ jet-launching episodes. Some
characteristic values for most, but not all, CCSNe are as follows (Papish &
Soker 2014a). Jets are launched with velocities of $\simeq 10^{5}{~{}\rm
km}{~{}\rm s}^{-1}$ (neutrino observations limit the jets in most cases to be
non-relativistic, e.g. Guetta et al. 2020). In total the jets carry an energy
of $\simeq 10^{51}{~{}\rm erg}$. The explosion time might be $\simeq 1-{\rm
few}{~{}\rm s}$. Each individual jet-launching episode carries a mass of
$\approx 10^{-3}M_{\odot}$ and lasts for a time period of $\simeq
0.01-0.1\sec$. Each accretion disk of an episode has a mass of $\approx
10^{-2}M_{\odot}$. During the entire jet-driven explosion process the newly
born NS accretes a mass of $\approx 0.1M_{\odot}$ through intermittent
accretion disks. From one episode to the next the jets might change axis
direction by a very large angle. The number of episodes and the changes in
jets’ directions depend on the properties of the convection motion, the
binding energy of the ejecta, and the precollapse core rotation.

  7. 7.

Smooth connection to superluminous supernovae (SLSNe). When the precollapse
core rotation is fast enough to allow a stable accretion disk to form there
will be only one axis (with small jittering around this axis) along which the
NS launches jets. The jets will be inefficient in removing core and envelope
mass from the equatorial plane. As a result of that the NS accretes more mass,
and might become a BH. Therefore, not only that according to the jittering
jets explosion mechanism (more generally, according to the jet feedback
explosion mechanism) there are no failed CCSNe, but rather the formation of a
BH implies a very energetic CCSN (e.g., Gilkis et al. 2016). The outcomes are
luminous CCSNe (LSNe) or superluminous CCSNe (SLSNe) that have bipolar
morphologies. I study these CCSNe in section 3. Not only the jet-driven
explosion mechanism connects regular CCSNe to LSNe and SLSNe, but it also
connects the fixed-axis (with small jittering) jets model to CEJSNe that I
discuss in section 4.

  8. 8.

Signatures of jets in supernova remnants (SNRs). Many SNRs possess signatures
of jets, as is the expectation in the jittering jets explosion mechanism.
These features include ‘Ears’ that carry a small fraction of the total
explosion energy and SNRs with point-symmetry morphologies. I devote section
2.3 to review these signatures.

  9. 9.

Natal kick of the neutron star. Bear & Soker (2018a) adopted the tug-boat
mechanism where a massive clump that the explosion process ejects from the
core gravitationally pulls and accelerates the NS (e.g., Nordhaus et al. 2010;
Wongwathanarat et al. 2013; Janka 2017; different explanations to natal kick
velocity exist, e.g., Yao et al. 2021 and Xu et al. 2022 for recent studies).
Bear & Soker (2018a) list two processes to explain why in the jittering jets
explosion mechanism the natal kick velocity avoids small angles to the jets’
axis. ($i$) The jets prevent the formation of dense clumps along their
propagation direction; ($ii$) Dense clumps supply the gas to the accretion
disk that launches the jets and therefore concentrate in a plane perpendicular
to the jets. One or more of the dense clumps are ejected and pull the NS. In
Fig. 2 I present the cumulative distribution function ${\rm W}_{\alpha}$ of
the projected angles between the NS natal kick direction and the jets’-axis,
and compare with the expectation of random distribution and a distribution of
perpendicular angles only (from Soker 2022a). Clearly the kick velocity avoids
small angles to the jets’ axis.

Figure 2: The cumulative distribution function ${\rm W}_{\alpha}$ of projected
angles between the NS natal kick direction and the jets’-axis for 13 SNRs
(from Soker 2022a). The lower blue line represents the cumulative distribution
function where in all SNRs the three-dimensional NS kick velocity is
perpendicular to the jets’ axis. The straight orange line represents the
random cumulative distribution function.

The above properties distinguish the jittering jets explosion mechanism from
other jet-driven explosion mechanisms (e.g., LeBlanc & Wilson 1970; Khokhlov
et al. 1999; Aloy et al. 2000; MacFadyen, Woosley, & Heger 2001; Burrows et
al. 2007; Barkov & Komissarov 2008; Wheeler, Maund, & Couch 2008; Maeda et al.
2012; López-Cámara et al. 2013; Bromberg & Tchekhovskoy 2016; Nishimura et al.
2017; Sobacchi et al. 2017; Grimmett et al. 2021; Gottlieb et al. 2022a, c;
Perley et al. 2022; Ghodla et al. 2022). In particular, these mechanisms
assume a rapidly rotating precollapse core, something that is not required in
the jittering jets explosion mechanism.

Gottlieb et al. (2022a) conduct magnetohydrodynamic simulations of a
collapsing core onto a central rapidly rotating BH of $4M_{\odot}$. Their
study is relevant to points 1-4 and 7 above. Gottlieb et al. (2022a) find that
jet launching requires both rapid rotation and strong magnetic fields. In
cases of too low angular momentum only weak jets are formed or not at all. In
the jittering jets explosion mechanism most CCSNe have a central NS and
therefore the accretion process is different than that onto a rapidly rotating
BH. In addition, neutrino heating, which Gottlieb et al. (2022a) do not
include in their simulations, boosts the jets (Soker 2022d). Therefore I
expect that a NS can launch jets event in cases of angular momentum that is
somewhat below the minimum to form a thin accretion disk, i.e., it forms an
accretion belt (Schreier & Soker 2016)). The formation of a BH in the
jittering jets explosion mechanism requires rapidly rotating pre-collapse core
(point 7 above), and therefore it is along the results of Gottlieb et al.
(2022a). I expect strong jets (although not necessarily that break out to give
a gamma ray burst).

Another possible effect is the formation of double-peak lightcurves in cases
where strong jets transport some of the newly synthesised 56Ni to the outer
regions of the ejecta (Orellana & Bersten 2022). (Orellana & Bersten 2022)
demonstrate how the jet-delivered 56Ni in the outer regions of the ejecta can
power the first peak, before the inner 56Ni powers the second (regular) peak
in of lightcurve. It is not clear whether individual jets of the jittering
jets are sufficiently strong to explain this effect, or whether only stronger
jets that also explode bipolar CCSNe can power this process.

Before closing this subsection I point out that at present the absence of
self-consistent magnetohydrodynamical simulations that show that the jittering
jets explosion mechanism actually works is still a drawback of the model.
Future simulations that will require huge computer resources are still needed
to establish this explosion mechanism.

$\bigstar$ Summary of section 2.2. The development of the jittering jets
explosion mechanism brought the call to change paradigm from neutrino-driven
explosions to jet-driven explosions of all CCSNe (e.g., Papish, Nordhaus, &
Soker 2015; Bear et al. 2017). (Izzo et al. 2019 and Piran et al. 2019 adopted
this earlier call but with a weaker emphasize of the jets’ major role.) In the
present review I strengthen this call.

###  2.3 Signatures of jittering jets in SNRs

####  2.3.1 Large scale structures

Many CCSN remnants possess morphological features that are imprints of jets
(e.g., Bear et al. 2017; Grichener & Soker 2017; Yu & Fang 2018; Lu et al.
2021; Soker 2022a). One of the clearest example is the north-east jet of
Cassiopeia A (e.g., Grefenstette et al. 2017). Some examples of other claims
for signatures of jets in SNRs include Vela SNR (e.g., García et al. 2017;
Sapienza et al. 2021) and IC 443 (e.g., Greco et al. 2018). I note that the
jets’ axis that Sapienza et al. (2021) and García et al. (2017) identify in
the Vela SNR is not the one that Grichener & Soker (2017) take to be the jets’
axis. However, according to the jittering jets explosion mechanism there are
many more than one jets’ axis, and the question is how many of these reveal
themselves in the SNR.

I concentrate here on similarities of SNR morphologies with morphologies of
planetary nebulae (PNe; for a review on the shaping of PNe see, e.g., De Marco
2009). This approach allows the usage of morphologies of PNe that are thought
to result from jets to argue for jets in CCSNe (e.g., Bear & Soker 2017; Bear
et al. 2017; Akashi, Bear, & Soker 2018; Bear & Soker 2018b; Soker 2022a).
Although other models exists for the formation of ears that do not include
jets I here adopt the view that ears are shaped by jets and present arguments
to support this. The other model include the simulations of Blondin,
Lundqvist, & Chevalier (1996) of a spherical CCSN ejecta that runs into a CSM
with a density gradient, and a spherical explosion into a CSM with a dense
ring (e.g., Chiotellis, Boumis, & Spetsieri 2021; Ustamujic et al. 2021). In
the later model the ears are actually a ring protruding from the main ejecta,
rather than two opposite polar ears.

In Fig. 3 I compare some SNRs to some PNe. I present four SNRs with the marks
of the ‘Ears’. Ears are two opposite protrusions from the main part of the SNR
of from the PN main shell that are smaller than the main nebula and with a
cross section that decreases monotonically from the base of an ear at the
shell to its far end (e.g., Akashi & Soker 2021a; small departures from this
definition are possible.) The upper two rows of Fig. 3 present three PNe, two
of which show jets. The region where a jet breaks out from the main shell has
a shape that I term ‘jet opening’, which in most cases obeys the definition of
an ear. Grichener & Soker (2017) argue that the ears in the four SNRs in the
two lower rows, as well as other SNRs that they study, are actually jet
openings. Namely, they were shaped by jets (also Bear et al. 2017). They
further estimate that about third of all CCSN remnants (CCSNRs) have clear
ears.

Figure 3: Comparing some signatures of jets in planetary nebulae (PNe) and
CCSNe with emphasize on ‘Ears’, which in some cases can be identified as jet
opening as I mark in the upper rows. Upper row: Images of the PN Fleming 1
from Boffin et al. (2012). Second row: Left two panels are images of PN NGC
3918 from Corradi et al. (1999), and the third panel from left is an HST image
of NGC 3918 (ESA/Hubble and NASA; not to scale with the left images). Right
panel is a Webb’s MIRI image in the mid-infrared (NASA, ESA, CSA, and STScI).
The two lower rows are of SNRs with marks from Grichener & Soker (2017) that
define and emphasize the ears. These marks were used to estimate the energy of
the jets that inflated the ears. Third row left: An X-ray image taken from the
Chandra gallery (based on Hwang et al. 2004). Red, blue and green represent Si
He$\alpha$ (1.78-2.0 keV), Fe K (6.52-6.95 keV), and 4.2-6.4 keV continuum,
respectively. Third row right: ACIS/Chandra image of SNR 3C58 in the energy
bands $0.5-1.0{~{}\rm keV}$ (red), $1.0-1.5{~{}\rm keV}$ (green), and
$1.5-10{~{}\rm keV}$ (blue), based on Slane et al (2004); Lower row left: An
H$\alpha$ image of the SNR Semeis 147 taken from Gvaramadze (2006) who
reproduced an image from Drew et al. (2005). Lower row right: Composite image
of the SNR W44 taken from the Chandra gallery. The cyan represents X-ray
(based on Shelton et al 2004), while the red, blue and green represent infra-
red (based on NASA/JPL-Caltech). The three beige thick lines schematically
define the S-shape of this SNR that hint at jet precession.

Fig. 4 that I take from Bear et al. (2017) emphasises the barrel shape, i.e.,
a hollow cylinder with convex-shaped surface. The three PNe in that figure
have clear indications that jets shaped the barrel-shaped main nebula. Bear et
al. (2017) suggest that this was the case in the SNR RCW 103 as well. Akashi,
Bear, & Soker (2018) simulated this shaping by jets.

Figure 4: Comparing some signatures of jets in the CCSN remnant (CCSNR) RCW
103 and three PNe emphasizing two opposite arcs that are the projection of an
axially-symmetric barrel-shaped nebula. This figure is from Bear et al.
(2017). The composite image of SNR RCW 103 is of X-ray (colors according to
energy bands: low=red, medium=green, highest=blue) together with an optical
image from the Digitized Sky Survey (image from the Chandra website; based on
Rea et al. 2016). The proposed original directions of the, already dead, jets
in the CCSNR RCW 103 are marked by yellow thick arrows. The three PNe are A 63
(image from Mitchell et al. 2007), NGC 40 (images from Meaburn et al. 1996),
and NGC 3918 (images from Corradi et al. 1999; images are rotated).

According to the jittering jets feedback mechanism the jets collide with the
core, explode the core, and by that explode the entire star. The explosion
from that time on is actually similar to that expected in the delayed neutrino
mechanism. The negative feedback cycle implies that when the entire core is
ejected the high-mass-accretion rate onto the newly born NS ceases, although
late fallback with low-mass-accretion rate might continue (see section 7).
However, at the time of core explosion there is mass that already flows
towards the newly born NS. As a result of that one or two jet-launching
episodes might occur after core explosion. These jets expand to large
distances before they encounter the already diluted ejecta. Therefore, these
last jets might penetrate into the ejecta and even go out from the main
ejecta. As such, these jets might leave imprints on the ejecta, such as ears
and hollowed barrel-shaped SNR.

From an energetic point of view, the two jets of each jet-launching episode
carry only a few per cents to few tens of per cents of the explosion energy
(point 6 in section 2.2). Therefore, the energy that inflate the ears has that
typical value. Grichener & Soker (2017) built a simple geometrical scheme (for
that purpose are the marks on the lower panels in Fig. 3) to estimate the
energy of the two jets (combined) that inflated the ears relative to that of
the CCSN explosion, $\epsilon_{\rm ears}$. Bear et al. (2017) present these
fractional energies against the explosion energy. They also added to that
graph the relative jets’ energy in six SLSNe that Piran et al. (2019) study. I
present their graph in Fig. 5. Bear et al. (2017) finding that the energy of
the jets that inflated the ears is only a small fraction of the explosion
energy is compatible with the expectation of the jittering jets explosion
mechanism. In section 3 I discuss jets that have a constant axis and therefore
shape the ejecta to become bipolar, namely with two very large inflated
bubbles rather than ears.

Figure 5: The energy to inflate the ears in 11 CCSNRs and the jets’ energy in
6 SLSNe relative to the explosion energy, $\epsilon_{\rm ears}$ (blue dots)
and $\epsilon_{\rm SN,jets}$ (red crosses), respectively, as function of the
explosion energy $E_{\rm SN}$. The black horizontal lines connect dots for the
same SNR of the minimum and maximum values of the explosion energy. The
vertical dotted pink line connects the two options for the western ear of
N49B. The red crosses are for the ratio $\epsilon_{\rm SN,jets}\equiv E_{\rm
SN,jets}/E_{\rm SN}$, where the values of $E_{\rm SN,jets}$ and $E_{\rm SN}$
are taken from Table 1 of Piran et al. (2019). The graph is from Bear et al.
(2017) who give all details.

$\bigstar$ Summary of section 2.3.1. About third of all CCSNRs have ears.
Comparison to PNe (Figs. 3 and 4) suggests that the ears were shaped by jets.
These jets most likely played a significant role in the explosion process. The
energy to inflate the ears is $\simeq 1-10\%$ of the explosion energy (Fig.
5), compatible with the expectation of the jittering jets explosion mechanism.

####  2.3.2 Clumps and filaments

CCSNR structures are inhomogeneous, e.g., in having filaments, arcs, clumps,
and as discussed above some have ears. In many cases different elements are
concentrated in different zones. Examples of CCSNRs with filaments and clumps
include Cassiopeia A (e.g., images by Grefenstette et al. 2017; Lee et al.
2017) SNR G$292.0+1.8$ (e.g., Park et al. 2002, 2007), Vela (e.g., Aschenbach
et al. 1995; García et al. 2017), and SNR W49B (e.g., Lopez et al. 2013; Sano
et al. 2021). The case of SNR W49B is interesting. González-Casanova et al.
(2014) performed hydrodynamical simulations and argued that a jet-driven CCSN
explosion can explain the distribution of metals, like silicon and iron, in
SNR W49B. The jets’ axis they propose (also Miceli et al. 2008; Lopez et al.
2011, 2013) and the jets’ axis that Bear & Soker (2017) suggest to explain the
morphology SNR W49B are perpendicular to each other. Future studies should
settled this disagreement.

According to the delayed neutrino explosion mechanism instabilities that
develop during the explosion process alone form clumps and filaments in the
inner ejecta (e.g., Janka et al. 2017; Wongwathanarat et al. 2017; Gabler et
al. 2021; Sandoval et al. 2021; Larsson et al. 2021). According to the
jittering jets explosion mechanism the shaping is due both to instabilities
and to jets (e.g., Soker 2022a).

This dispute between the two explosion mechanism supporters is best
demonstrated in SN 1987A that has a clumpy and filamentary ejecta as recent
observations show (e.g., Fransson et al. 2015, 2016; Larsson et al. 2016;
Abellán et al. 2017; Matsuura et al. 2017). Kjær et al. (2010) argued for
shaping by instabilities alone. However, Soker (2017b) and later Abellán et
al. (2017) found that neutrino driven explosion simulations (e.g.,
Wongwathanarat et al. 2015) do not fit all observations of SN 1987A. Bear &
Soker (2018b) studied some morphological features of SN 1987A (Abellán et al.
2017) alongside morphologies of some other CCSNRs and of PNe. They
strengthened earlier claims that jittering jets likely played a crucial role
in the explosion and shaping of SN 1987A. Bear & Soker (2018b) noted that the
structure of the ejecta of SN 1987A from Abellán et al. (2017) rule-out the
old claim of Wang et al. (2002) for two opposite non-jittering jets that
exploded SN 1987a. More recently, Ono et al. (2020) and Orlando et al. (2020)
performed 3D hydrodynamical simulations of evolution of SN 1987A and concluded
that jet-driven explosion with the jets’ axis in the plane of the inner CSM
ring best reproduce the explosion morphology and element distribution. Bear &
Soker (2018b) took the jets’ axis to be at an angle to the plane of the inner
ring. This disagreement on the jets’ axis should be settled by further
exploration of SN 1987A.

The dispute exists also in the analysis of SNR Cassiopeia A, for which
Wongwathanarat et al. (2015), Orlando et al. (2021) and Orlando et al. (2022)
argued that the neutrino-driven explosion mechanism can account for the
distribution of some metals, while in Soker (2017b) I argued that jets seem to
have played a crucial role is the shaping of Cassiopeia A during its
explosion. Orlando et al. (2016) already argued that instabilities alone
cannot account for all morphological features of Cassiopeia A.

Most recently I (Soker 2022a) analyzed the structure of SNR 0540-69.3 from the
observations of Park et al. (2010) and Larsson et al. (2021). Although Larsson
et al. (2021) argued that instabilities alone can account for the ejecta
structure, I argued for jittering jets (in addition to instabilities). I
identified a point-symmetric morphology in the VLT/MUSE velocity map in a
plane along the line of sight (perpendicular to the plane of the sky), as I
show in the upper two rows of Fig. 6 that are based on the results of Larsson
et al. (2021). Comparing the four pairs of two opposite clumps that the images
in Fig. 6 show to point-symmetric PNe, three of which I present in the lower
row of Fig. 6, brought me to propose that two or four pairs of jittering jets
shaped the inner ejecta of SNR 0540-69.3. In Soker (2022a) I further argued
that both jets and instabilities mix elements in the ejecta of CCSNe.

Figure 6: Upper two rows: Two-dimensional velocity maps of SNR 0540-69.3 taken
from figure 4 of Larsson et al. (2021). $v_{\rm z}$ is the velocity along the
line of sight, while $v_{\rm slit}$ is the velocity along the slit (see their
paper for details). In Soker (2022a) I added the same four lines, P1 to P4, on
all panels to mark four pairs of opposite clumps that together form a point-
symmetric morphology (A-D; B-E; C-F; Gn-Gs). In the lower-left panel I added
the marks to clumps Gn and Gs, while clumps A to F are from Larsson et al.
(2021). The pulsar is at $v_{\rm slit}=0$ in these panels. Lower row: Three
PNe, PN He2-138 (PN G320.1-09.6), PN M1-37 (PN G002.6-03.4) and IC 4846 (PN
G027.6-09.6), that have point-symmetric morphologies that Sahai & Trauger
(1998), Sahai (2000) and Sahai, Morris, & Villar (2011), respectively,
attribute to jets. The three lines on the M1-37 image are from the original
image of Sahai (2000). For more details see Soker (2022a).

Figs 3 and 6 show that jets change directions in PNe. Here I concentrate on
the jittering of jets in CCSNe that is caused by the convective motion of the
precollapse core. There are other effects than can change the jets’ axis not
only in CCSNe, but also in a variety of systems from binary systems, like
progenitors of PNe, and up to jets of active galactic nuclei. In binary
systems the gravitational force of the companion can cause the disk to
precess. However, I would like to comment on an effect where the jets have
feedback on the angular momentum. If the interaction of the jets with the
ambient medium causes mater to fall towards the accretion disk this material
will have a velocity with a small angle to the original jets’ axis. As a
result of that the angular momentum of this gas is at a large angle to the
angular momentum of the accretion disk that launches the jets. As this falling
gas feeds the accretion disk it changes its angular momentum axis, hence the
jets’ axis. In cooling flow clusters of galaxies active galactic nucleus jets
might cause dense clumps to feed the accretion disk around the supermassive BH
(Soker 2018a). I termed this jittering jets by negative angular momentum
feedback (Soker 2021b). Gottlieb et al. (2022c) conduct 3D magneto-
hydrodynamical simulation of a CCSN and find that bound gas from the two jet-
inflated cocoons feeds the accretion disk and tilts it somewhat. This lead to
jets with relatively small jittering that they term wobbling jets.

$\bigstar$ Summary of section 2.3.2. Both jets and instabilities shape clumps
and filaments in the ejecta of CCSNe. Instabilities alone cannot account for
some properties, like point-symmetric morphologies and some elements
distributions. In most cases jets jitter by moderate to large angles between
different jet-launching episodes.

##  3 Bipolar core collapse supernovae

###  3.1 Super-luminous supernovae (SLSNe)

Two sources feed angular momentum to the mass that the NS accretes, the
precollapse core rotation (point 7 in section 2.2) and the angular momentum
fluctuations of the precollapse core convection that are amplified by
instabilities (point 1 of section 2.2). When the precollapse specific angular
momentum is large enough to allow the formation of a stable accretion disk
around the newly born NS the jittering is relatively small and occurs around a
fix axis along the precollapse angular momentum of the core. This is the
fixed-axis jets explosion process. Because all jets share more or less the
same axis they very efficiently expel gas from the polar directions
surroundings, but not from the equatorial plane surroundings. The outcome is a
bipolar explosion, i.e., the morphology is of two opposite large bubbles
(rather than ears) with a waist between them.

Because of the low efficiency in mass ejection the total energy that the jets
carry is much larger than the binding energy of the ejected gas. Therefore,
the fixed-axis jets explosion process leads to a super-energetic CCSN. If even
a small fraction of the kinetic energy is channelled to radiation the outcome
is a LSNe or a SLSN. The prediction of the jittering jets explosion mechanism,
or more generally the jet-feedback explosion mechanism, is that most SLSNe and
a large fraction of LSNe are bipolar. I adopt here the definition (e.g., Gomez
et al. 2022) that SLSNe have peak r-band magnitude of $M_{\rm r}<-20$, and
LSNe have peak r-band magnitude of $M_{\rm r}=-19$ to $-20$.

The accretion of equatorial mass can lead to the formation of a BH. Therefore,
according to the jittering jets explosion mechanism the formation of BHs in
CCSNe comes along with super-energetic CCSNe, rather than with failed CCSNe
(e.g., Gilkis et al. 2016; Soker 2017b).

Chugai et al. (2005) suggested a bipolar nickel ejecta, i.e., two opposite
jets of ${}^{56}Ni$, inside a spherical hydrogen-rich envelope for the type
IIP SN 2004dj. They estimated the nickel mass to be $\approx 0.02M_{\odot}$.
Utrobin & Chugai (2019) suggested a similar model for the type IIP SN 2016X
but with a nickel mass of $\approx 0.03M_{\odot}$. They took the explosion to
be bipolar, but not to the degree of shaping the spherical hydrogen shell.
These CCSNe are not LSNe/SLSNe. Because of the spherical envelope such a
scenario might also take place with large jittering and pre-collapse core with
moderate rotation velocity. Namely, the nickel bipolar structure is the last
jet-launching episode, but a relatively massive one, in the jittering jets
explosion mechanism.

Hungerford, Fryer, & Warren (2003) conducted 3D hydrodynamical simulation of
jet-driven explosion and studied the effects of such asymmetrical explosions
on mixing and gamma ray line emission. Hungerford, Fryer, & Rockefeller (2005)
studied these effects in case of a “single-lobe” CCSN explosion as the delayed
neutrino mechanism predicts in some case, and Wollaeger et al. (2017) examined
the influence of single-lobe explosion on the emission from UV to IR. In that
respect I note that two opposite jets must not always be equal, and even
jittering jets can be unequal. The two opposite lobes of the SNR W50 that the
jets from SS 433 inflate are highly unequal (e.g., Dubner et al. 1998), and so
are the two unequal opposite lobes of the proto-planetary nebula OH 231.8+4.2
that were most likely shaped by jets (e.g., Bujarrabal et al. 2002).

As with some other (but not all) issues, the jittering jets explosion
mechanism and the delayed neutrino explosion mechanism depart also on their
explanation of SLSNe. The jittering jets explosion mechanism attribute most of
the energy of SLSNe to powering by jets, even when there are other processes,
like ejecta-CSM collision (section 7) and a magnetar, which I discuss next.

Most fittings of SLSNe lightcurves that assume the delayed neutrino explosion
mechanism require extra energy sources because this mechanism cannot explain
CCSN explosion energies of $E_{\rm SN}\ga 2\times 10^{51}{~{}\rm erg}-3\times
10^{51}{~{}\rm erg}$ (e.g., Gogilashvili et al. 2021; section 2.2). The most
popular extra energy source in these modellings is a rapidly rotating
magnetized NS, i.e., a magnetar (e.g., Maeda et al. 2007; Greiner et al. 2015;
Metzger et al. 2015; Yu et al. 2017; Margutti et al. 2018; Suzuki & Maeda
2021; for possible SLSN energy sources see, e.g., Wang, Wang, & Dai 2019).

The formation of a magnetar is also the expectation in the jittering jets
explosion mechanism when the precollapse core is rapidly rotating. However, in
the jittering jets explosion mechanism whenever there is an energetic magnetar
there are also energetic jets that are likely to deposit more energy to the
ejecta than the magnetar does (Soker 2016a, 2017a; Soker & Gilkis 2017a).
Following these studies Shankar et al. (2021) discuss accretion and jets’
launching by a magnetar in broad-lined Type Ic CCSNe.

Indeed, studies that do not include jets encounter problems in a large
fraction of the SLSNe they try to fit. Nicholl et al. (2017) fit lightcurves
of 38 SLSNe with magnetars. Soker & Gilkis (2017a) find that in about half of
these fittings the CCSN explosion energy, before any magnetar powering, must
be $E_{\rm SN}>2\times 10^{51}{~{}\rm erg}$. Because this is a larger energy
than what the delayed neutrino mechanism can account for Soker & Gilkis
(2017a) conclude that jets exploded these SLSNe. The recent
magnetohydrodynamic simulations by Reichert et al. (2022) further support the
claim of Soker & Gilkis (2017a) that jets explode SLSNe.

In yet another study (Soker 2022e) I examine the modelling of the lightcurves
of 40 LSNe by Gomez et al. (2022). For their fitting Gomez et al. (2022)
consider in addition to the explosion energy itself the contribution by a
magnetar and by helium burning. I find that in 10 LSNe that Gomez et al.
(2022) fit the total energy of these two extra energy sources is larger than
the ejecta kinetic energy that they fit. In 8 LSNe the total energy of the
delayed neutrino explosion mechanism and these two extra sources combined is
smaller than the fitted kinetic energy. Instead, I propose in that paper that
jets play an important role in powering the explosion and lightcurve of LSNe,
as I claim for SLSNe, and actually for most CCSNe.

In a recent paper Kangas et al. (2022) analyze 14 hydrogen-rich SLSNe and try
to fit their lightcurves with either a magnetar or with an ejecta-CSM
collision. In half of the SLSNe that they fit by magnetar powering the initial
energy of the magnetar is very large (spin period $P_{\rm mag}\leq
0.002{~{}\rm s}$) such that the final mass accretion onto the NS was most
likely through an accretion disk that launched more energetic jets even (Soker
2017a). In half of the cases that they fit with ejecta-CSM collision the
kinetic energy and radiation combined carry more energy than what the delayed
neutrino explosion mechanism can supply (section 2.2), again requiring jets to
explode these SLSNe. I claim that jets played a dominant role in the explosion
of all these hydrogen-rich SLSNe.

The same arguments hold for the fitting by Chen et al. (2022) of the
lightcurves of 70 hydrogen-poor SLSNe. They fit by either a magnetar model or
an ejecta-CSM interaction + 56Ni. I find that about $33\%$ of their magnetar
fittings have $P_{\rm mag}\leq 0.002{~{}\rm s}$. As I argued above (Soker
2017a) such a rapidly rotating magnetars are likely to be spun-up during the
last phase of their formation by an accretion disk/belt that launches jets. I
argue that even the slower magnetars in their fitting most likely launched
jets at explosion. From the 70 lightcurves that Chen et al. (2022) fit 14 do
much better with ejecta-CSM powering of the lightcurve than with magnetars. In
7 out of these 14 SLSNe the kinetic energy of the ejecta is much larger than
what the delayed neutrino explosion mechanism can supply, e.g., $E_{\rm
kin}\simeq 2.5\times 10^{52}{~{}\rm erg}$ and $E_{\rm kin}\simeq 2\times
10^{52}{~{}\rm erg}$ for ZTF18aaisyyp and ZTF18aajqcue, respectively. Clearly
if these models are correct jets exploded these SLSNe. Again, I argue that
jets exploded all these SLSNe.

In a recent study Eiger et al. (2021) find no correlations between the
properties of CCSN SNRs and the magnetar and pulsar they host. I argue that
their findings are compatible with my claim that jets supply most of the
explosion energy and the kinetic energy of the ejecta rather than the
magnetars they host.

Most CCSNe are not bipolar. Lazzati et al. (2012) showed in their two-
dimensional hydrodynamical simulations of relativistic jets that only in cases
of weak bipolar jets the outcome is dynamically indistinguishable from regular
CCSNe. I expect in those cases to have jittering jets rather than fixed-axis
jets. Barnes et al. (2018) conduct two-dimensional relativistic hydrodynamics
simulations and argue that relativistic jets can explain broad-lined SNe Ic.
Shankar et al. (2021) reach similar conclusions with two-dimensional
relativistic hydrodynamics simulations. However, in a recent study Eisenberg,
Gottlieb, & Nakar (2022) find that collimated jets do not produce outflows
that are consistent with observations of CCSNe. Instead, they argue, in gamma
ray bursts there are narrow jets that produce the gamma emission, and a much
wider outflow that explodes the star, including a wide cocoon (e.g., Pais,
Piran, & Nakar 2022). Wang et al. (2022) continue this idea and discuss jets
with large opening angles of about tens of degrees to power the CCSN that
accompanied the gamma ray burst GRB 171205A. Indeed, the general jet feedback
mechanism (in CCSNe, in clusters of galaxies, and in binary stars) operate
most efficiently with wide jets or with precessing/jittering jets (for review
see Soker 2016b). I expect that in most bipolar CCSNe the exploding jets are
not relativistic.

For comparison, I comment on the NS activity at birth of most CCSNe, which are
not bipolar. Beniamini et al. (2019) estimate that a fraction of
$0.4^{+0.6}_{-0.3}$ of NSs are born as magnetars. Most of these have long spin
periods, $P_{s}\approx 0.01-0.1{~{}\rm s}$, and their energy does not dominate
nor the explosion nor the lightcurve. Gofman & Soker (2020) estimate the spin
period of the NS remnants of CCSNe with explosion energies of
$10^{50}-10^{51}{~{}\rm erg}$, which are the majority of CCSNe, to be in the
range of $P_{s}\approx 0.01-0.1{~{}\rm s}$. We expect many of them to have
medium to strong magnetic fields as magnetic fields are required for jet-
launching. Namely, the NS with strong magnetic fields are born as magnetar,
but with low energy because of their relatively slow rotation. In this regard
the jittering jets explosion mechanism is compatible with the finding of
Beniamini et al. (2019).

$\bigstar$ Summary of section 3.1. Jets must play an important role in
powering the explosion and lightcurves of LSNe and SLSNe, most likely the
dominant role. Modelling of SLSN lightcurves must include jets, even when they
consider an energetic magnetar. In most cases the jets have a fixed-axis or a
small jittering around a fixed axis. The fixed axis results from a rapid
precollapse core rotation. A close binary companion (a main sequence star, an
NS, or a BH) might spin-up the core to the required rapid rotation.

###  3.2 The role of the viewing angle

In CCSNe with bipolar ejecta, i.e., a morphology of two polar lobes with an
equatorial waist between them, the viewing angle influences the observed
lightcurve.

Kaplan & Soker (2020b) built simple bipolar CCSN ejecta models and examined
the basic structure of the lightcurve for an observer in and near the
equatorial plane. They built the ejecta from an equatorial ejecta and faster
polar jet-inflated ejecta. At early times the polar lobes are optically thick,
and because of their faster polar velocity the polar photosphere grows faster
than the photosphere near the equatorial plane. The outcome is a CCSN that is
more luminous than a similar spherical explosion. The jets supply the extra
energy to inflate and accelerate the polar lobes and to the extra radiation.
As the polar ejecta expands faster, its optical depth decreases faster and at
later times the polar photosphere decreases faster than the equatorial
photosphere, and eventually the equatorial ejecta hides the polar photosphere
from an observer near the equatorial plane. This leads to a rapid luminosity
decline, and even an abrupt decline in the lightcurve.

Kaplan & Soker (2020b) could fit with their toy model the abrupt decline in
the light curve of SN 2018don. In Fig. 7 I present their fitting to the light
curve of SN 2018don. In a recent study Akashi, Michaelis, & Soker (2022) show
with three dimensional hydrodynamical simulations that bipolar explosions can
indeed explain such lightcurves. I suggest (Soker 2022e) that bipolar
explosion might explain the lightcurve of the stripped-envelope SLSN SN
2020wnt that has a ‘knee’, because the bipolar explosion can account also for
that (for observations see Tinyanont et al. 2021; Gutiérrez et al. 2022;
Tinyanont et al. 2022). I will return to LSNe and SLSNe in section 7 where I
discuss post-explosion jets.

Figure 7: Fitting the lightcurve of a LSNe with bipolar ejecta (figure from
Kaplan & Soker 2020b). The green and the red points are the lightcurves of SN
2018don in the g-band and r-band, respectively, from Lunnan et al. (2020). The
blue line is the lightcurve from a toy model by Kaplan & Soker (2020b) where
more details can be found.

Consider fast blue optical transients (FBOTs), and in particular AT2018cow-
like FBOTs that are bright transients (e.g., Margutti et al. 2019) that have
only few days rise time to peak emission (e.g., Prentice et al. 2018; Perley
et al. 2019). They display hydrogen lines (e.g., Margutti et al. 2019), and
show high velocities of $\ga 0.1c$ and a total kinetic energy of $\simeq
10^{51}-10^{52}{~{}\rm erg}$ (e.g., Coppejans et al. 2020).

Soker et al. (2019) and Soker (2022c) suggest that AT2018cow-like FBOTs are
classes of CEJSNe and CEJSN-impostors, respectively (section 4), for which the
viewing angle play a crucial role. Metzger (2022) suggests a version of the
CEJSN scenario of Soker et al. (2019) where the core-NS/BH merger takes place
$>100{~{}\rm yr}$ post CEE. In the CEJSN scenario for FBOTs the fast outflow
is accounted for by a fast polar outflow and an observer away from the
equatorial plane. The same holds for the bipolar CCSN explosion model that
Gottlieb, Tchekhovskoy, & Margutti (2022b) propose for AT2018cow-like FBOTs.
In their model the jets interact with the stellar envelope. Kashiyama &
Quataert (2015) propose a model where the progenitor collapses to form a BH
that accretes mass via an accretion disk that power the FBOT by a disk wind.
Similarly, Tsuna, Kashiyama, & Shigeyama (2021) proposed a CCSN with a bipolar
outflow from a BH accretion disk to account for the fast-rising transient
AT2018lqh (Ofek et al. 2021). All these models, whether CEJSNe or CCSNe, are
bipolar (see also Guarini, Tamborra, & Margutti 2022), and viewing angle is
important. FBOTs are likely observed away from the equatorial plane.

$\bigstar$ Summary of section 3.2. Viewing angle influences the lightcurves of
bipolar explosions. Bipolar explosions that we observe from the equatorial
plane might explain some puzzling features in some CCSN lightcurves. FBOTs are
a class of bipolar explosions of CCSNe and/or CEJSNe, that are likely observed
along or close to the polar axis.

##  4 Common envelope jets supernovae (CEJSNe)

A CEJSN is a transient event with typical time scales like CCSNe or longer and
with energies like those of CCSNe or larger that is powered by jets that a NS
or a BH (NS/BH) launch as they accrete mass from the envelope and then core of
a RSG (e.g, Soker et al. 2019; Grichener & Soker 2019a; Schrøder et al. 2020;
Grichener & Soker 2021; for studies of NS/BH merger with the RSG core that do
not emphasize jets see, e.g., Fryer & Woosley 1998 and Chevalier 2012). They
therefore might mimic (peculiar) CCSNe. In cases where the NS/BH does not
enter the core, i.e., it enters and then exits the RSG envelope or it removes
the entire envelope in a common envelope evolution (CEE) and avoids entering
the core, the event is a CEJSN-impostor (e.g., Gilkis, Soker, & Kashi 2019;
López-Cámara et al. 2019, 2020; Grichener, Cohen, & Soker 2021). However, in
this review I will use CEJSN to refer to CEJSN impostors as well as CEJSNe.
Some CEJSNe involve triple-star interaction (e.g., Soker 2021a, b; Akashi &
Soker 2021b). I schematically present the main phases of the CEJSN evolution
in Fig. 8.

Figure 8: A schematic drawing (not to scale) of the main CEJSN evolutionary
phases. Abbreviation. MS: main sequence; NS/BH: a neutron star or a black
hole. RSG: red super giant; SN: supernova.

Numerical simulations show that the jets regulate their power because they
remove mass from their vicinity and reduce the density, hence the accretion
rate and the jets’ power (e.g., López-Cámara et al. 2019; Grichener, Cohen, &
Soker 2021; Schreier et al. 2021; Hillel, Schreier, & Soker 2022). This is the
jet feedback mechanism in a CEE (e.g., Soker 2016b). Even jets from a main
sequence star might efficiently expel mass from the giant envelope (e.g.,
Shiber et al. 2019), and more so the energetic jets that a NS/BH launches
(Schreier et al. 2021; Hillel, Schreier, & Soker 2022). This efficient mass
removal might increases the CEE efficiency parameter to values of $\alpha_{\rm
CE}>1$ as some scenarios demand (e.g. Fragos et al. 2019; Zevin et al. 2021;
García et al. 2021).

Two key processes allow energetic CEJSNe. (1) An efficient cooling of the mass
that the NS/BH accretes by neutrino emission when the accretion rate is
sufficiently high, $\dot{M}_{\rm acc}\ga 10^{-3}M_{\odot}{~{}\rm yr}^{-1}$
(Houck & Chevalier 1991; Chevalier 1993, 2012). (2) A density gradient in the
RSG envelope and the RSG core that implies that the accreted mass has a
specific angular momentum that forms an accretion disk around the NS/BH (e.g.,
Armitage & Livio 2000; Papish, Nordhaus, & Soker 2015; Soker & Gilkis 2018).

CEJSNe might account for some enigmatic transients that at first are
classified as CCSNe, e.g. the unusual gamma-ray burst GRB 101225A for which
Thöne et al. (2011) suggested the merger of a NS with a helium star. Soker &
Gilkis (2018) proposed a CEJSN event to explain the puzzling iPTF14hls
transient (Arcavi et al. 2017) and similar transients, e.g., SN 2020faa (Yang
et al. 2021). I will return to iPTF14hls in section 7.2.2. FBOTs (section 3.2)
and in particular AT2018cow-like FBOTs might be CEJSNe (Soker et al. 2019;
Metzger 2022) or CEJSN-impostors (Soker 2022c). Schrøder et al. (2020)
proposed that the transients SN1979c and SN1998s were CEJSN events. Dong et
al. (2021) proposed the CEJSN scenario for the luminous radio transient VT
J121001+495647.

CEJSN events and CCSNe share the same main powering mechanism that is the
launching of jets by a NS/BH, an old NS/BH companion in CEJSN events and a
newly born NS/BH in CCSNe. Therefore, it is not surprising that CEJSNe might
mimic CCSNe. Some CEJSNe might be more energetic and/or have a slower
declining lightcurves than typical CCSNe. Because of the binary interaction
CEJSN events cover a more extended range of explosion properties (e.g., see
table 1 of Soker et al. 2019).

Triple-star CEJSNe add to the rich variety of properties, e.g., a tight binary
system of a NS and a main sequence star enters the envelope of a RSG and merge
inside the RSG envelope (Soker 2021a), or a tight binary system of two NS/BHs
that enters the RSG envelope and ends in one of several CEJSN channels (table
1 of Soker 2021b), like a NS-NS merger inside the envelope (Akashi & Soker
2021b).

In their population synthesis study Schrøder et al. (2020) estimate that the
rate CEJSN events where a NS/BH enters the core of an RGB star is $\approx
0.5\%$ of the rate of CCSNe. About half the cases are with a NS star companion
and about half with a BH companion. The CEJSN-impostor events, where the NS/BH
does not enter the core, amount to $\approx 2\%$ of the rate of CCSNe.

$\bigstar$ Summary of section 4. Jets that a NS/BH launches power CEJSNe, much
as I argue for CCSNe. The main differences are that in CEJSNe the NS/BH are
old and the source of the accreted mass is the envelope and then the core
inside which the NS/BH orbits, i.e., a CEE. Because of the similar powering
mechanism CEJSNe mimic CCSNe and in particular bipolar CCSNe, but have some
other properties, like they might last longer and contain more energy. The
rate of CEJSNe is only few per cent of the CCSN rate. Some CEJSN-impostors
might end as a close NS/BH-NS/BH binary system that much later suffers merger
due to gravitational wave emission. In other words, many of the gravitational
wave sources that evolved through a CEE have experienced a CEJSN-impostor
event.

##  5 Shaping the CSM

###  5.1 Core collapse supernovae

I start with the three rings of SN 1987A that I present in Fig. 9. The ejecta
of SN 1987A has been strongly colliding with the inner ring for about 23 years
(e.g., Fransson et al. 2013; Frank et al. 2016; Larsson et al. 2019; see
McCray & Fransson 2016 for a review). The rings were ejected $\approx
20,000{~{}\rm yr}$ before explosion (e.g., Panagia et al. 1996; McCray &
Fransson 2016).

Figure 9: Comparing the morphology of the three CSM rings of SN 1987A to the
morphologies of two planetary nebulae. The right column are zoomed-in images
of the left column images, but do not have the same orientation. Details of
the images that are not of concern to this study can be found in the sources
of the images. Credits: SN 1987a: Left: Burrows et al. (1995); Right: X-ray:
NASA/CXC/SAO/PSU/K, Frank et al. (2016); Optical: NASA/STScI; Millimeter:
ESO/NAOJ/NRAO/ALMA. MyCn 18: Left: O’Connor et al. (2000); Right: Sahai et al.
(1999). The Necklace nebula (IPHASX J194359.5+170901): Left: Corradi et al.
(2011). Right: NASA/ESA/the Hubble Heritage Team (STScI/AURA).

Although there are scenarios for the formation of the three rings of SN 1987A
that involve no jets (e.g., Soker 1999; Tanaka & Washimi 2002; Sugerman et al.
2005; Morris & Podsiadlowski 2009), I attribute their shaping to jets (Soker
2002). The supporting argument comes from the morphological similarities to
those of some PNe. In Fig. 9 I present these similarities with two PNe. Note
that these jets are likely to be wide, like jets from post-asymptotic giant
branch binary systems (e.g., Bollen et al. 2022; for review emphasizing wide
jets see Soker 2016b).

The PN MyCN 18 and SN 1987A share a bipolar structure of pairs of opposite
outer rings, one pair in SN 1987A and several pairs in MyCn 18. The deep image
of MyCn 18 reveals broken jets at large distances from the bipolar structure
and along its symmetry axis. Most likely several jet-launching episodes shaped
the several rings of MyCn 18 as a result of the interaction of the jets with a
CSM. This supports a scenario where pairs of jets shaped the pair of outer
rings of SN 1987A, as Akashi & Soker (2016) demonstrate in their three-
dimensional hydrodynamical simulations.

The Necklace PN and SN 1987A share the structure of a clumpy equatorial ring.
Again, the Necklace PN was shaped by jets as the image shows. This suggests
that jets shaped also the inner ring of SN 1987A, as Akashi et al. (2015) show
with three-dimensional hydrodynamical simulations. I do not argue that
necessarily only jet compressed the equatorial outflow that formed the ring.
Equatorial mass ejection during a CEE phase might added mass to the ring.

The star that launches the jets in the scenario I discuss here is a main
sequence companion that entered a CEE with the RSG (then) progenitor of SN
1987A. Before it entered the envelope the companion accreted mass from the RSG
envelope via an accretion disk that launched the jets. As it spiralled-in
towards the envelope and inside it, the companion spun-up the progenitor of SN
1987a (e.g., Chevalier & Soker 1989) and diverted its evolution towards a blue
giant (e.g., Podsiadlowski, Joss, & Rappaport 1990). The companion did not
survive the CEE.

There are other CSM morphologies into which CCSN explosions might occur, e.g.,
a bipolar CSM around a WR star (e.g., Meyer 2021). Therefore, in principle a
bipolar CCSNR might result from either jets during the explosion or a bipolar
CSM, or both.

$\bigstar$ Summary of section 5.1. I suggest that the three CSM rings of SN
1987A were ejected by a binary system that entered a CEE $\approx
20,000{~{}\rm yr}$ before explosion, and that a main sequence companion to the
progenitor of SN 1987A launched jets that shaped the rings. The interaction of
the jets with the CSM gave rise to a transient event, an intermediate
luminosity optical transient (ILOT).

###  5.2 Shaping ears in type Ia supernovae

This section is the only one in this review where I refer to type Ia
supernovae (SNe Ia). Jets do not power SNe Ia and so I refer only to the
shaping. As well, I will not get into the question of which SN Ia scenarios
allow ears (for that see table 1 in Soker 2019b).

Many SNRs of SNe Ia (SNRs Ia) have the structure of two opposite ears. In Fig.
10 I present three SNRs Ia with ears alongside three PNe with small ears; some
PNe with large ears are in Figs. 3 and 4. Tsebrenko & Soker (2015a) and
Chiotellis, Boumis, & Spetsieri (2021) give more examples of SNRs Ia with
ears.

Figure 10: Comparing ‘ears’ in three SNRs Ia with ears of three PNe. Each
yellow arrow points at an ear. See NGC 40 and NGC 3918 in fig. 4 for PNe with
larger ears and NGC 3132 in Fig 3 for asymmetrical ears (I marked the ears
there ‘jet opening’ to indicate that we identify the jets in some of these
PNe). I adopt the view that these and similar SNRs Ia are SNIPs (for SNe
inside PNe). Credits: G1.9+0.3: Borkowski et al. (2014); Kepler: Reynolds et
al. (2007); G299.2-2.9: Park et al. (2007) (for SNR images see also the
Chandra homepage); IC 418: NASA/ESA and The Hubble Heritage Team (STScI/AURA);
NGC 7139: KPNO/NOIRLab/NSF/AURA/Gert Gottschalk and Sibylle Froehlich/Adam
Block; NGC 2022: ESA/Hubble and NASA, R. Wade.

I will follow Tsebrenko & Soker (2015a) and take the view that jets shape ears
in SNRs Ia. Tsebrenko & Soker (2013b) simulated the shaping of ears by either
a spherical SN Ia exploding into a CSM with ears, or by jets in the SN Ia
explosion itself that expand into a spherical CSM. The SN Ia explosion
simulations by Perets et al. (2019), where a CO white dwarf tidally destroys a
HeCO white dwarf, yield faster bipolar outflow that might shape ears. Their
study show that some SN Ia explosion scenarios might shape jets. However, I
will take the view that SNe Ia are more or less spherical (beside maybe some
clumps) and that the ears result from the CSM that the progenitor of the SN Ia
blew hundreds of thousands or years to thousands or years before explosion.
The CSM is actually a proto-PN (Cikota et al. 2017), a PN, or a remnant of a
PN, and these are SNe Ia inside PNe, which are termed SNIPs (Tsebrenko & Soker
2015a). I crudely estimated that about half of SNe Ia are SNIPs (Soker 2022b).

It is important to emphasize that here I argue that the jets where launched
during the formation phase of the PN that preceded the SN Ia explosion. The SN
Ia itself has a large-scale spherical structure. It explodes into a CSM with
ears, a prot-PN, a PN, or an old PN.

In the model I adopt here the ears are along the symmetry axis of the SNR.
Some models for ear formation take them to be projections of an equatorial
ring/torus. Chiotellis, Boumis, & Spetsieri (2021) simulate the formation of
ears in SNIPs, but they take the ears to be in the equatorial plane and do not
include jets (see also Chiotellis, Boumis, & Spetsieri 2020). Burkey et al.
(2013) also take the ears of the Kepler SNR to be in the equatorial plane. I
note that Sun & Chen (2019) find that the ears in the Kepler SNR consist
mainly of Si-rich and S-rich ejecta, thus, they argue, favoring shaping by
jets that are related to the explosion, rather than ears from a preceding
planetary nebula. This requires further study.

In the Kepler SNR (e.g., Kasuga et al. 2021) and in the SNR G1.9+0.3 (e.g.,
Borkowski et al. 2017) the ejecta interacts with a CSM. Tsebrenko & Soker
(2015b) simulates the formation of the complicated ears SNR G1.9+0.3 by adding
clumps to the ears in the PN. In the SNR G299.2-2.9 the ears are less
symmetric, with a clear elongation only in one side. Post et al. (2014)
consider the possibility that G299.2-2.9 interacts with a CSM, but also argues
that it is unlikely to be a SNIP because of only one-sided ear. However, I
note that some PNe do have very unequal ears. A good example is the Webb’s
MIRI image of NGC 3132 that I present in the right-most panel in the second
row of Fig. 3 (for an analysis of this image see De Marco et al. 2022) .

$\bigstar$ Summary of section 5.2. Some SNRs Ia have ears that I take to
indicate shaping by jets. Although in principle the jets might be part of the
explosion process, I consider more likely the explosion of a large-scale
spherical SN Ia inside a CSM that is a PN (SNIP). The ears result from the
shaping of the PN by jets.

##  6 Jet-driven pre-explosion outbursts

This section deals with pre-explosion jets in binary systems where a companion
to the progenitor of the CCSN (or the CEJSN) launches the jets as it accretes
mass from the progenitor.

Observations show that some CCSNe and some other transients experience
outbursts years to days before explosion. These are termed precursors (e.g.,
Tsuna, Takei, & Shigeyama 2022 for a recent lightcurve calculations).
Prominent is the class of SN 2009ip-like (2009ip-like; e.g., Smith et al.
2010; Smith, Mauerhan, & Prieto 2014; Fraser et al. 2013; Mauerhan et al.
2013; Pastorello et al. 2013; Graham et al. 2014; Smith et al. 2022)
transients that have precursors, fast rising and declining lightcurves and
bumps during the decline phase. Some other members of this group are SN 2010mc
(e.g., Ofek et al. 2013; Smith, Mauerhan, & Prieto 2014), LSQ13zm (Tartaglia
et al. 2016), SN 2013gc (Reguitti et al. 2019), SN 2015bh (e.g., Elias-Rosa et
al. 2016; Thöne et al. 2017), AT 2016jbu (e.g., Bose et al. 2017; Kilpatrick
et al. 2018; Brennan et al. 2022a), SN 2016bdu (e.g., Pastorello et al. 2018),
and SN 2019zrk (Fransson et al. 2022; Strotjohann et al. 2021). In their study
of SN 2019zrk Fransson et al. (2022) point out that 2009ip-like transients
might emit a substantial fraction of the radiation in the UV and in X-rays as
in SN 2009ip (Margutti et al. 2014). All these properties are not easy to
explain by CCSNe, unless some other ingredients are added.

It is not clear what fraction of 2009ip-like transients are true CCSNe (e.g.,
Smith, Mauerhan, & Prieto 2014) and what fraction are CEJSNe (e.g., Gilkis,
Soker, & Kashi 2019; Schrøder et al. 2020). My view is that this group of
transients bridges in its properties and powering CCSNe and CEJSNe. In other
words, some of them might be true CCSNe and some might be CEJSNe, but in all
of them jets play major roles before, during, and after the explosion, and the
ejecta has a highly non-spherical morphology, most likely bipolar.

The quest for an explanation to the pre-explosion outbursts encounters some
challenges. Quataert & Shiode (2012) and Shiode & Quataert (2014) suggested
that waves that the vigorous convection motion in the core, from the phase of
core carbon burning until core collapse, can excite waves that propagate to
the envelope. Soker & Gilkis (201b7) proposed that the vigorous convection can
set a magnetic activity where magnetic flux tubes that buoy to the envelope
deposit energy to the envelope. The dissipation of the wave energy and/or
magnetic energy in the envelope heats the envelope and inflates it (e.g.,
Fuller 2017; Fuller & Ro 2018; Wu & Fuller 2021).

However, models that are based on only wave energy (or magnetic energy)
encounter two problems. The first one is that waves cause mainly envelope
inflation rather than mass ejection (e.g., Mcley & Soker 2014; Ouchi & Maeda
2019; Wu & Fuller 2022), and cannot explain dense CSM, e.g., as Fransson et
al. (2022) mention for SN 2019zrk. The three-dimensional simulations by Tsang,
Kasen, & Bildsten (2022) yield somewhat more ejected mass, but cannot solve
the problem. The second challenge, as mentioned for example by Fransson et al.
(2022), is that there are observations of fast, velocities of $\simeq
10^{4}{~{}\rm km}{~{}\rm s}^{-1}$, outflows in pre-explosion outbursts, like
in SN 2009ip (e.g., Pastorello et al. 2013).

The similarity of some pre-explosion outbursts to the outbursts of ILOTs,
e.g., as Smith et al. (2010) and Soker & Kashi (2013) discussed for SN 2009ip
and Brennan et al. (2022b) discussed for AT 2016jbu, suggests that jets power
these outbursts much as they power ILOTs (other names include gap objects,
luminous red novae and intermediate luminosity red transients). Namely, the
main energy source of mass ejection during pre-explosion outbursts is
accretion onto a compact companion that launches jets. The companion can be a
main sequence star, a WR star, or a NS/BH. Some ILOTs must be powered by jets
because of their bipolar morphology, e.g., Nova 1670 (CK Vulpeculae; Kamiński
et al. 2021), and I take the view that most ILOTs are powered by jets (e.g.,
Soker 2020a).

Indeed, jets can solve the two problems that models that are based on wave
energy only encounter (for a more detailed discussion see Soker 2022f). Mcley
& Soker (2014) already found that the energy that waves are likely to deposit
to the RSG envelope before explosion mainly causes envelope expansion, but not
much mass ejection. Their conclusion was that a mass-accreting companion
powers the outbursts by launching jets. The waves inflate the envelope that in
turn transfers mass to the more compact companion via an accretion disk that
launches energetic jets. Danieli & Soker (2019) studied this process in cases
where the companion is a NS.

Jets can also account for high velocities of a fraction of the pre-explosion
ejecta. Hydrodynamical simulations showed that even jets from main sequence or
WR companions that expand at velocities of $v_{\rm jet}\approx
2000-3000{~{}\rm km}{~{}\rm s}^{-1}$ can accelerate gas to velocities of $\ga
10,000{~{}\rm km}{~{}\rm s}^{-1}$ when they interact with the CSM. Tsebrenko &
Soker (2013a) showed this process with parameters that fit the expected pre-
explosion of SN 2009ip and Akashi & Kashi (2020) obtained such high velocities
when they applied parameters that fit the Great Eruption of Eta Carinae, which
is an energetic ILOT event. The observations of high pre-explosion velocities
is not a problem at all for cases with a NS/BH companion because NS/BHs launch
very fast and energetic jets (e.g., Gilkis, Soker, & Kashi 2019).

$\bigstar$ Summary of section 6. Although the energy that core-excited waves
(and possible magnetic flux tubes that buoy out) carry to the envelope might
cause some CCSN progenitors to expand and lose some mass before explosion,
energetic pre-explosion outbursts (precursors) require jets for their
powering. A more compact companion that accretes mass from the inflated
envelope of the CCSN progenitor launches these jets.

##  7 Post-explosion jet-powering

###  7.1 Post-explosion jets

A NS/BH launches post-explosion jets if it accretes mass through an accretion
disk after explosion (I do not consider jets from a pulsar). Several processes
can lead to post-explosion accretion in CCSNe.

Many studies refer to post-explosion accretion of fallback gas (e.g, Chevalier
1995; Della Valle et al. 2006; Moriya et al. 2010; Akashi & Soker 2022;
Pellegrino et al. 2022), including in bipolar jet-driven CCSNe (e.g., Tominaga
2009), and in relation to gamma ray bursts (e.g., Lin et al. 2020). Dexter &
Kasen (2013) conduct a thorough study of fallback accretion in CCSNe and
discuss up to months-long post-explosion jets that power SLSNe. The processes
that they discuss are relevant to this review, and I will not review these
processes that cause late fallback mass accretion. I also note that Metzger et
al. (2015) study the detail powering by a magnetar and briefly mention that a
BH accreting fallback gas has the same effects on the lightcurve. As I already
mentioned in this review and in earlier papers, my view is that energetic
magnetars must be accompanied by jets that most likely supply more energy to
the explosion. Therefore, jets and magnetar powering are not two alternatives.
Rather both jets and magnetar operate or jets alone, but not an energetic
magnetar alone.

There are other processes that might lead to post-explosion jets in CCSNe,
including the accretion of CCSN ejecta gas by a pre-existing NS/BH (e.g.,
Fryer, Rueda, & Ruffini 2014; Becerra et al. 2015, 2019; Akashi & Soker 2020)
and the feeding of the newly born NS/BH by a close main sequence star that the
explosion causes its envelope to inflate (e.g., Ogata, Hirai, & Hijikawa 2021;
Hober, Bear, & Soker 2022), or even a direct collision of the NS with the main
sequence star (Hirai & Podsiadlowski 2022). In a recent study Becerra et al.
(2022) find in their simulations of a CCSN with a close NS that both NSs, the
old and the newly-born NS, accrete mass within several minutes after the
explosion. They, however, do not simulate jets. I expect both NSs to launch
jets (e.g., Akashi & Soker 2020).

In CEJSNe the post-explosion accretion is more likely even due to the large
angular momentum in the system. This leads to fixed-axis jets that might leave
equatorial gas bound after the explosion, much as in CCSNe that have rapid
pre-explosion rotation and collapse to form a BH (section 3.1).

$\bigstar$ Summary of section 7.1. There are several ways to feed a NS/BH
through an accretion disk after an explosion. It might be a newly born NS/NH
in CCSNe or an old NS/BH in CEJSNe and in rare CCSNe. This feeding requires a
large value of specific angular momentum in the system, most likely by a
binary system. Either one star survives or both stars do. The same binary
system can trigger also pre-explosion jets. Therefore, many explosions that
have late jet-powering might also have precursors.

###  7.2 Jet-powered bumps

In this section I argue that some (but not all) bumps in the lightcurves of
CCSNe and CEJSNe are powered by jets. As such, studies cannot ignore the role
of jets when building models for bumps and the powering by jets should be
compared with the powering by other energy sources. This is true in particular
for what I term sharp-bumps, which are defined as relatively luminous and
short bumps.

Many studies refer to magnetar (e.g., Chugai & Utrobin 2022) and/or ejecta-CSM
interaction powering of bumps (e.g., Hosseinzadeh et al. 2022 for a recent
study). Metzger, Beniamini, & Giannios (2018) do mention fallback accretion by
a magnetar that can change the smooth magnetar power.

####  7.2.1 The toy model

The collision of a CCSN ejecta with a close CSM channels kinetic energy to
thermal energy and then radiation, and as a result of that can delay the
lightcurve decline and/or power bumps in the lightcurve (e.g., Li et al. 2020;
Fiore et al. 2021; Sollerman et al. 2021; Chen et al. 2022; Zenati et al. 2022
for some examples from the last three years). This holds also for 2009ip-like
transients (e.g., Brennan et al. 2022a; Fransson et al. 2022). Gangopadhyay et
al. (2020) discuss ejecta-CSM interaction in the peculiar Type IIn SN 2012ab
and mention that the explosion has a jet-structured outflow. This CCSN seems
to have clear indications for a jet-driven explosion. I will consider the
possibility that some (but definitely not all) bumps in the lightcurves of
CCSNe and CEJSNe are powered by late jets. Alternatively to ejecta-CSM
interaction Moriya et al. (2022) suggest that magnetar can power bumps. My
view (section 3.1) is that any energetic magnetar is accompanied by even more
energetic jets.

We do not have yet a model to derive the properties of the jets for a given
bump because of the large volume of the parameter space and because the jet-
ejecta interaction, which does not have a spherical symmetry, is very
complicated. Parameters include the duration of the jet-activity phase, the
velocity of the jets, their mass outflow rate, their opening angle, and the
morphology of the CSM, which I expect to be non-spherical. Nonetheless, using
simple toy models we have derived some plausible set of parameters in two
specific cases (sections 7.2.2 and 7.2.3).

Kaplan & Soker (2020a) built a toy model that gives the timescale and extra
luminosity of a jet-driven bump in the lightcurve. The toy model cannot give
the details of the extra light curve. The model takes the jet-ejecta
interaction to be short and treats it like a ‘mini-explosion’ inside the
ejecta, as Fig. 11 schematically shows. There are two opposite mini-explosions
for the two opposite jets. The interaction of a jet with the ejecta shocks the
jet material and the ejecta. The shocked regions together make the ‘cocoon’.
The input parameters of the toy model are the explosion energy and mass of the
ejecta, the energy of the jets, the initial mass in the cocoons, the half
opening angle of the jet, the opacity, the location of the jet-ejecta
interaction relative to the photosphere, and the time of the jet-ejecta
interaction.

Figure 11: A Schematic illustration (not to scale) of the interaction of the
two opposite jets with the SN ejecta–the ‘mini-explosions’ (from Kaplan &
Soker 2020a).

####  7.2.2 The sharp bump in the lightcurve of iPTF14hls

There are several late peaks in the lightcurve of iPTF14hls (Arcavi et al.
2017; Sollerman et al. 2019), which is an enigmatic transient for its high
luminosity, fast outflow, slow decay, and bumps in the lightcurve. Theoretical
scenarios to explain iPTF14hls include powering by a magnetar (e.g., Arcavi et
al. 2017; Dessart 2018; Woosley 2018), a pair instability supernova (e.g.,
Woosley 2018; Vigna-Gómez et al. 2019; Wang et al. 2022), an interaction of
the ejecta with a CSM (e.g., Andrews & Smith 2017; Milisavljevic & Margutti
2018), fallback accretion (e.g., Arcavi et al. 2017; Wang et al. 2018; Liu et
al. 2019), a CEJSN event (e.g., Soker & Gilkis 2018; Yalinewich & Matzner
2019), models based on late accretion onto a BH (e.g., Chugai 2018) or a NS
(e.g.,e.g., Liu et al. 2019), a jittering jets explosion model that forms a
black hole (Quataert et al. 2019), and wind-driven models (Moriya, Mazzali, &
Pian 2020; Uno & Maeda 2020). In some of these scenarios jets play the major
powering role (e.g., Chugai 2018; Soker & Gilkis 2018; Liu et al. 2019;
Quataert et al. 2019).

Kaplan & Soker (2020a) focused on one bump in the lightcurve of iPTF14hls, the
third peak according to the definition of Wang et al. (2018). Wang et al.
(2018) attributed the powering of the bumps to intermittent accretion of
fallback material with a total mass of $\approx 0.2M_{\odot}$. However, they
could not fit the third peak because it is bright and short, i.e., a sharp
bump. They suggested that the third peak is due to a magnetic activity of the
NS.

The third peak has a duration of 30 days and a total extra radiated energy of
$E_{\rm rad,b}\simeq 10^{49}{~{}\rm erg}$. Kaplan & Soker (2020a) found that
they could fit the properties of the third peak with their toy model for jets
that together have a kinetic energy of $E_{\rm jets}=0.016E_{\rm SN}$ and for
an initial mass in the two cocoons of $M_{\rm cocoons}=0.027M_{\rm SN}$, where
$E_{\rm SN}$ and $M_{\rm SN}$ are the explosion energy and the ejecta mass,
respectively. The last number implies that the initial half-opening angle of
the cocoon (see Fig. 11) is $\alpha_{c}=13.2^{\circ}$ . The jet-ejecta
interaction time is $t_{\rm j,0}=309~{}{\rm d}$. About third of the energy of
the jets ends in radiation for these parameters, $E_{\rm rad,b}\simeq
0.3E_{\rm jets}$. This is a high efficiency relative to an ejecta-CSM
interaction (section 7.2.3). Kaplan & Soker (2020a) took the ‘mini-explosion’
location (the place where the jet deposit the energy in the ejecta) to be at
half the photosphere radius and the half opening angle of the jets to be
$\alpha_{j}=5^{\circ}$.

To explain the radiated energy Kaplan & Soker (2020a) found that the energy in
the two jets combined is $E_{\rm jets}=3.5\times 10^{49}{~{}\rm erg}$. If the
jets carry $\simeq 10\%$ of the accretion energy and have an initial velocity
of $v_{j}\simeq 10^{5}{~{}\rm km}{~{}\rm s}^{-1}$, they found that the central
object should accrete a mass of $M_{\rm acc,3}\simeq 0.0035M_{\odot}$ in this
jet-launching episode.

In principle jets can account for the other peaks in the light curve of
iPTF14hls, but for that we should use longer-lasting jets with varying mass
loss rates, rather than a short jet-launching episode.

I do not claim that the above set of jets’ parameters is unique, but rather
that it is possible to explain some bumps with jets much better than with
ejecta-CSM interaction. Definitely there is also the ejecta-CSM interaction
that powers the lightcurve in iPTF14hls and many other CCSNe and CEJSNe, but
jets can better explain sharp bumps, as I also demonstrate next.

####  7.2.3 The sharp bump in the lightcurve of SN 2019zrk

In a recent study (Soker 2022f) I used the toy model of Kaplan & Soker (2020a)
(section 7.2.1) to explain the sharp bump in the light curve of SN 2019zrk.
This peak starts at $t\simeq 95~{}{\rm days}$ (measured from the rise of the
main peak), has its maximum luminosity at $t_{\rm bump}\simeq 110~{}{\rm
days}$, declines on a similar time to its rise time, and has a total extra
radiation of $E_{\rm rad,b}\simeq 1.8\times 10^{48}{~{}\rm erg}$ (Fransson et
al. 2022).

Fransson et al. (2022) argued that this bump is powered by ejecta-CSM
interaction. However, I argued (Soker 2022f) that this explanation encounters
severe problems. I noted that the spectra during the bump ($t=109~{}{\rm
days}$) is very similar to that before the bump ($t=83~{}{\rm days}$). This
implies that the powering mechanism of the bump should affect both the ejecta
photosphere and the H$\alpha$ emitting gas. However, the ejecta-CSM
interaction takes place at a much larger radius than the photosphere radius at
these late times. Therefore, only a small fraction of the energy that the
ejecta-CSM collision process emits will reach the photosphere, $f_{\rm
ph}\simeq 0.006$. It is unlikely that the ejecta-CSM interaction has
sufficient energy to explain this bump. I would expect the ejecta-CSM
collision to change the spectrum as it should not have the same spectrum as
the photosphere. These arguments of efficiency and spectrum should be examined
in any claim that an ejecta-CSM collision powers bumps.

In applying the toy model (Soker 2022f) I took the bump’s timescale to be its
rise time, $t_{\rm toy,b}=15{~{}\rm d}$, and for its luminosity $L_{\rm
toy,b}=E_{\rm rad,b}/t_{\rm toy,b}$. I took the ‘mini-explosion’ to take place
at a radius of 0.1 times the ejecta outer radius because the photosphere has
already moved deep into the ejecta. For the same reason I took the fraction of
the ejecta mass that the two jets interact with to be only $0.02$, $M_{\rm
cocoons}=0.02M_{\rm SN}$. The jets-ejecta interaction time is $t_{\rm
j,0}=100~{}{\rm days}$. For the ejecta mass I took $M_{\rm SN}=10M_{\odot}$,
and assumed that the front of the ejecta moves at a faster velocity than the
observed velocity after ejecta-CSM collision of $v_{\rm ex}\simeq 1.6\times
10^{4}{~{}\rm km}{~{}\rm s}^{-1}$ (Fransson et al. 2022), such that the
explosion energy itself is $E_{\rm SN}=0.3M_{\rm SN}(2\times 10^{4}{~{}\rm
km}{~{}\rm s}^{-1})^{2}=2.4\times 10^{52}{~{}\rm erg}$. I took the other
parameters as in Kaplan & Soker (2020a).

I found that I can account for the timescale and luminosity of the sharp bump
of SN 2019ark if the two jets carry a total energy of $E_{\rm 2j}\simeq
0.0012E_{\rm SN}=3\times 10^{49}{~{}\rm erg}$. About $6\%$ of the this energy
ends in the extra radiation of the bump.

Again, this set of the toy model parameters is not unique, but demonstrates
the possibility that jets power some bumps.

$\bigstar$ Summary of section 7.2. The main conclusion from this entire
section is that jets can account for many sharp bumps (but not all) in the
lightcurves of CCSNe and other transients, for some of which other powering
models encounter problems. Any modelling of bumps should compare jet-powering
with ejecta-CSM interaction and magnetar powering.

###  7.3 Long-duration post-explosion jets

As I commented in section 7.1 jets can power the light curve of CCSNe in
combination or not with ejecta-CSM interaction and/or an energetic magnetar.
In sections 7.2.2 and 7.2.3 I demonstrated the formation of bumps by short-
duration (impulsive) post-explosion jet-launching episodes. I here consider
long-duration jets, i.e., jets that the NS/BH launches starting at or
immediately after explosion to days to months after explosion. These jets can
power LSNe and SLSNe. For that I open by presenting in Fig. 12 a figure from
Gomez et al. (2022). In Soker (2022e) I added to this figure SN 2020wnt and a
red line that I will explain below.

Figure 12: A figure from Gomez et al. (2022) of CCSNe-I in the plane of peak
r-band absolute magnitude versus luminosity rise time with additions of SN
2020wnt and the red line from Soker (2022e). The inset lists the different
CCSN classes.

There are six SLSNe to the far right of the distribution on Fig. 12, and one
LSN to the far right, SN 2018don. In section 3.2 I discussed the possibility
that strong jets exploded SN 2018don and shaped its ejecta to a bipolar
morphology (Kaplan & Soker 2020b), and that we observe this LSN from near its
equatorial plane. Lunnan et al. (2020) consider SN 2018don to be a SLSN and
not a LSN because extinction implies that its true luminosity is much higher.
If this is the case SN 2018don moves higher in Fig. 12 and it becomes a SLSN
that is not off to the right. I also mentioned in section 3.2 that SN 2020wnt
might also be a bipolar SLSN that we observed from near its equatorial plane
(Soker 2022e).

I now discuss the possibility that long-duration jets power the LSNe and SLSNe
with the longest rise time, as I derived in a recent study (Soker 2022e, where
I give more details). In that study I used a toy model that is a modification
of the toy model of Kaplan & Soker (2020a) that I mentioned in section 7.2.1.
To derive the simplest relation between the rise time and luminosity in this
toy model I made several simple modifications and adopted simple assumptions
as follows. (1) I assumed that the longest rise time of LSNe an SLSNe for a
given luminosity (peak r-band magnitude) is determined by a long jet-activity
phase. The interaction process starts early and ends at $t_{\rm j,f}$. (2) I
kept the explosion energy and ejecta mass as in the scaling of Kaplan & Soker
(2020a), i.e., $E_{\rm SN}=2\times 10^{52}{~{}\rm erg}$ and $M_{\rm
SN}=10M_{\odot}$, respectively. (3) I changed the opacity to $\kappa_{\rm
c}=0.1{~{}\rm cm}^{2}{~{}\rm g}^{-1}$, as a typical value that Gomez et al.
(2022) list. (4) I assumed that the jets are active for a long time so that
the energy the two jets deposit increases with time according to $E_{\rm
2j}(t)=({t_{\rm j,f}}/{100{~{}\rm d}}){\epsilon_{E,0}}E_{\rm SN}$. (5) I
assumed that the location of the mini-explosion, namely the radius where the
jets deposit their energy inside the ejecta, increases linearly with time and
is given by $R_{\rm ME}=({t_{\rm j,f}}/{100{~{}\rm d}})\beta_{0}R_{\rm ej}$,
where $R_{\rm ej}$ is the radius of the outer ejecta. (6) I kept as in the
scaled equation of Kaplan & Soker (2020a) the values of the mass in one cocoon
relative to the ejecta mass $\epsilon_{V}\equiv M_{\rm 1,cocoon}/M_{\rm SN}$
and the half opening angle of each jet $\alpha_{j}=5^{\circ}$.

Using the above modifications and assumptions in the toy model of Kaplan &
Soker (2020a) I obtained (Soker 2022e) a relation between the luminosity and
rise time of the longest LSNe and SLSNe

$\displaystyle\begin{aligned} &L_{\rm c}\simeq 1.6\times
10^{44}\left(\frac{\epsilon_{V}}{0.067}\right)^{-1}\left(\frac{\epsilon_{E,0}}{1}\right)\left(\frac{\sin{\alpha_{\rm
j}}}{0.087}\right)\\\
&\times\left(\frac{\beta_{0}}{0.5}\right)\left(\frac{M_{\rm
SN}}{10M_{\odot}}\right)^{-3/2}\left(\frac{E_{\rm SN}}{2\times 10^{51}{~{}\rm
erg}}\right)^{3/2}\\\ &\times\left(\frac{\kappa_{\rm c}}{0.1{~{}\rm
cm}^{2}{~{}\rm g}^{-1}}\right)^{-1}\left(\frac{t_{\rm j,f}}{100{~{}\rm
d}}\right)^{3}{~{}\rm erg}{~{}\rm s}^{-1}.\end{aligned}$ (1)

I took the rise time to be the end time of the activity phase of the powerful
jets, i.e., $t_{\rm rise}\simeq t_{\rm j,f}$, although the rise time might be
somewhat longer than $t_{\rm j,f}$ because of photon diffusion time. The red
line in Fig. 12 is equation (1) for $L_{\rm c}$ as expressed in r-band
magnitude $M_{\rm r}=4.64-2.5\log(L_{\rm c}/L_{\odot})$.

The red line in Fig. 12 is not unique. It rather represents a trend in cases
where long-duration jets power the longest LSNe and SLSNe. This relation is
not unique because of the very large parameter space of jet-ejecta
interaction, as I mentioned already in this review. The toy model reflects
this large parameter space, but does not include all parameters. For example,
the power of the jets is unlikely to be constant as I assumed above. The trend
that this relation (equation 1) demonstrates is that for massive ejecta of
$M_{\rm SN}\ga 10M_{\odot}$ the peak luminosity rapidly increases with the
duration of the jet activity, $L_{c}\propto t^{\xi}_{\rm j,f}$ with $\xi\simeq
3$. The massive ejecta might account also for the long-duration fallback
accretion that feeds the accretion disk that launches the jets.

Jets might explain also the powering of LSNe and SLSNe that are to the left of
the red line. For example, the jet activity phase might be shorter. It is also
possible that the powering of these CCSNe is only by jets launched at the
explosion time itself. As well, for a given jet-activity duration the peak
luminosity can be much higher if the ejecta mass is smaller and/or the jets
are more energetic ($\epsilon_{E,0}$ is larger). In addition, the viewing
angle plays a significant role in determining the light curve (e.g., Akashi,
Michaelis, & Soker 2022).

$\bigstar$ Summary of section 7.3. Long lasting jets might account for the
general right boundary of most CCSNe-I (hydrogen deficient CCSNe) in the plane
of the peak r-band magnitude versus rise time. Namely, for the LSNe and SLSNe
with the longest rise time (beside those to the far right). In some cases
strong jets at explosion form bipolar ejecta that with a correct viewing angle
might account for some peculiar CCSNe. I do not claim that magnetars and/or
ejecta-CSM interaction do not add to the powering of these LSNe and SLSNe. My
claim is rather that we must include jets when we use magnetar powering, and
should consider jets alongside ejecta-CSM interaction.

##  8 Open questions

I list some of the key open questions.

  * •

Can the pre-collapse core convection zones supply sufficient amount of angular
momentum fluctuations to lead to the formation of intermittent accretion disk
or belt around the newly born NS? Can such stochastic intermittent accretion
disks/belts launch sufficiently energetic jittering jets to explode the star?
I presented arguments in this review for positive answers to both questions,
but there is a need for high-resolution magnetohydrodynamical simulations to
confirm my claim.

  * •

What is the exact relation and mutual influence of powering by jets and of
neutrino heating?

  * •

What determines whether the CCSN remnant is a NS or a BH? My view is that pre-
collapse rapid core rotation implies inefficient jet feedback mechanism that
in turn leads to the formation of a BH. Again, this requires confirmation by
high-resolution magnetohydrodynamical simulations.

  * •

Are there failed CCSNe? My view as I presented here is that there are no
failed supernovae. Even when the remnant is a BH there is a bright explosion
driven by energetic jets. Further observational and theoretical studies are
needed.

  * •

What is the relative role of jets, magnetars, and ejecta-CSM interaction in
powering SLSNe? I presented here arguments for that jets supply most of the
energy in most cases, but in many cases the two other processes also play
roles.

  * •

What are the roles of jets that a companion launches before explosion in
shaping the CSM, and how does the binary interaction influence the explosion
(like stripping the envelope of the progenitor and/or spinning-up its core)?

  * •

What is the role of jets that a companion launches in powering pre-explosion
outbursts?

  * •

What is the relation of the triggering mechanism of pre-explosion outbursts to
the explosion mechanism? I argued that strong convective motion in the pre-
collapse core are behind these two mechanisms.

  * •

How can we observationally distinguish between peculiar CCSNe and CEJSNe?

## Acknowledgements

I thank Paz Beniamini, Nikolai Chugai, Fabio De Colle, Chris Fryer, Ore
Gottlieb, Diego López-Cámara, Keiichi Maeda, Salvatore Orlando, Yu Wang,
Yossef Zenati, and an anonymous referee for helpful comments. This research
was supported by a grant from the Israel Science Foundation (769/20).

## References

  * Abellán et al. (2017) Abellán, F. J., Indebetouw, R., Marcaide, J. M., et al. 2017, ApJ, 842, L24
  * Akashi et al. (2015) Akashi M., Sabach E., Yogev O., Soker N., 2015, MNRAS, 453, 2115. doi:10.1093/mnras/stv1666
  * Akashi & Soker (2016) Akashi M., Soker N., 2016, MNRAS, 462, 206. doi:10.1093/mnras/stw1683
  * Akashi, Bear, & Soker (2018) Akashi M., Bear E., Soker N., 2018, MNRAS, 475, 4794. doi:10.1093/mnras/sty029
  * Akashi, Michaelis, & Soker (2022) Akashi M., Michaelis A., Soker N., 2022, arXiv, arXiv:2208.13222
  * Akashi & Soker (2020) Akashi M., Soker N., 2020, ApJ, 901, 53. doi:10.3847/1538-4357/abad35
  * Akashi & Soker (2021a) Akashi M., Soker N., 2021a, ApJ, 913, 91. doi:10.3847/1538-4357/abf7bb
  * Akashi & Soker (2021b) Akashi M., Soker N., 2021b, ApJ, 923, 55. doi:10.3847/1538-4357/ac2d2b
  * Akashi & Soker (2022) Akashi M., Soker N., 2022, ApJ, 930, 59. doi:10.3847/1538-4357/ac6102
  * Akashi & Kashi (2020) Akashi M., Kashi A., 2020, MNRAS, 494, 3186. doi:10.1093/mnras/staa1014
  * Aloy et al. (2000) Aloy M. A., Muller E., Ibanez J. M., Marti, J. M., & MacFadyen A. 2000, ApJ, 531, L119
  * Andresen et al. (2019) Andresen H., Müller E., Janka H.-T., Summa A., Gill K., Zanolin M., 2019, MNRAS, 486, 2238. doi:10.1093/mnras/stz990
  * Andrews & Smith (2017) Andrews J. E., Smith N., 2018, MNRAS, 477, 74
  * Antoni & Quataert (2022) Antoni A., Quataert E., 2022, MNRAS, 511, 176. doi:10.1093/mnras/stab3776
  * Arcavi et al. (2017) Arcavi, I., Howell, D. A., Kasen, D., et al. 2017, Nature, 551, 210
  * Armitage & Livio (2000) Armitage, P. J., & Livio, M. 2000, ApJ, 532, 540
  * Aschenbach et al. (1995) Aschenbach, B., Egger, R., & Trümper, J. 1995, Nature, 373, 587
  * Barkov & Komissarov (2008) Barkov M. V., Komissarov S. S., 2008, MNRAS, 385, L28. doi:10.1111/j.1745-3933.2008.00427.x
  * Barnes et al. (2018) Barnes J., Duffell P. C., Liu Y., Modjaz M., Bianco F. B., Kasen D., MacFadyen A. I., 2018, ApJ, 860, 38. doi:10.3847/1538-4357/aabf84
  * Bear et al. (2017) Bear, E., Grichener, A., & Soker, N. 2017, MNRAS, 472, 1770
  * Bear & Soker (2017) Bear E., Soker N., 2017, MNRAS, 468, 140. doi:10.1093/mnras/stx431
  * Bear & Soker (2018a) Bear, E. & Soker, N. 2018a, ApJ, 855, 82. doi:10.3847/1538-4357/aaad07
  * Bear & Soker (2018b) Bear E., Soker N., 2018b, MNRAS, 478, 682. doi:10.1093/mnras/sty1053
  * Becerra et al. (2015) Becerra L., Cipolletta F., Fryer C. L., Rueda J. A., Ruffini R., 2015, ApJ, 812, 100. doi:10.1088/0004-637X/812/2/100
  * Becerra et al. (2019) Becerra L., Ellinger C. L., Fryer C. L., Rueda J. A., Ruffini R., 2019, ApJ, 871, 14. doi:10.3847/1538-4357/aaf6b3
  * Becerra et al. (2022) Becerra L. M., Moradi R., Rueda J. A., Ruffini R., Wang Y., 2022, arXiv, arXiv:2208.03069
  * Beniamini et al. (2019) Beniamini P., Hotokezaka K., van der Horst A., Kouveliotou C., 2019, MNRAS, 487, 1426. doi:10.1093/mnras/stz1391
  * Bethe & Wilson (1985) Bethe, H. A., & Wilson, J. R. 1985, ApJ, 295, 14
  * Blondin, Lundqvist, & Chevalier (1996) Blondin J. M., Lundqvist P., Chevalier R. A., 1996, ApJ, 472, 257. doi:10.1086/178060
  * Boccioli et al. (2022) Boccioli L., Mathews G. J., Suh I.-S., O’Connor E. P., 2022, ApJ, 926, 147. doi:10.3847/1538-4357/ac4603
  * Boffin et al. (2012) Boffin H. M. J., Miszalski B., Rauch T., Jones D., Corradi R. L. M., Napiwotzki R., Day-Jones A. C., et al., 2012, Sci, 338, 773. doi:10.1126/science.1225386
  * Bollen et al. (2022) Bollen D., Kamath D., Van Winckel H., De Marco O., Verhamme O., Kluska J., Wardle M., 2022, arXiv, arXiv:2208.08752
  * Borkowski et al. (2017) Borkowski K. J., Gwynne P., Reynolds S. P., Green D. A., Hwang U., Petre R., Willett R., 2017, ApJL, 837, L7. doi:10.3847/2041-8213/aa618c
  * Borkowski et al. (2014) Borkowski K. J., Reynolds S. P., Green D. A., Hwang U., Petre R., Krishnamurthy K., Willett R., 2014, ApJL, 790, L18. doi:10.1088/2041-8205/790/2/L18
  * Bose et al. (2017) Bose S., Monard L. A. G., Seidel M. K., Dong S., Hsiao E., Shappee B. J., Bond H. E., et al., 2017, ATel, 9937
  * Brennan et al. (2022a) Brennan S. J., Fraser M., Johansson J., Pastorello A., Kotak R., Stevance H. F., Chen T.-W., et al., 2022a, MNRAS, 513, 5642. doi:10.1093/mnras/stac1243
  * Brennan et al. (2022b) Brennan S. J., Fraser M., Johansson J., Pastorello A., Kotak R., Stevance H. F., Chen T.-W., et al., 2022b, MNRAS, 513, 5666. doi:10.1093/mnras/stac1228
  * Bruenn et al. (2016) Bruenn, S. W., Lentz, E. J., Hix, W. R., et al. 2016, ApJ, 818, 123
  * Bromberg & Tchekhovskoy (2016) Bromberg, O., & Tchekhovskoy, A. 2016, MNRAS, 456, 1739
  * Bujarrabal et al. (2002) Bujarrabal V., Alcolea J., Sánchez Contreras C., Sahai R., 2002, A&A, 389, 271. doi:10.1051/0004-6361:20020455
  * Burkey et al. (2013) Burkey M. T., Reynolds S. P., Borkowski K. J., Blondin J. M., 2013, ApJ, 764, 63. doi:10.1088/0004-637X/764/1/63
  * Burrows et al. (2007) Burrows A., Dessart L., Livne E., Ott C. D., Murphy J., 2007, ApJ, 664, 416. doi:10.1086/519161
  * Burrows et al. (1995) Burrows C. J., Krist J., Hester J. J., Sahai R., Trauger J. T., Stapelfeldt K. R., Gallagher J. S., et al., 1995, ApJ, 452, 680. doi:10.1086/176339
  * Burrows & Vartanyan (2021) Burrows, A. & Vartanyan, D. 2021, Nature, 589, 29. doi:10.1038/s41586-020-03059-w
  * Byrne & Fraser (2022) Byrne R., Fraser M., 2022, MNRAS, 514, 1188. doi:10.1093/mnras/stac1308
  * Chen et al. (2022) Chen Z. H., Yan L., Kangas T., Lunnan R., Sollerman J., Schulze S., Perley D. A., et al., 2022, arXiv, arXiv:2202.02060
  * Chevalier (1993) Chevalier, R. A. 1993, ApJ, 411, L33
  * Chevalier (1995) Chevalier R. A., 1995, PhR, 256, 95. doi:10.1016/0370-1573(94)00103-A
  * Chevalier (2012) Chevalier R. A., 2012, ApJL, 752, L2. doi:10.1088/2041-8205/752/1/L2
  * Chevalier & Soker (1989) Chevalier R. A., Soker N., 1989, ApJ, 341, 867. doi:10.1086/167545
  * Chiotellis, Boumis, & Spetsieri (2020) Chiotellis A., Boumis P., Spetsieri Z. T., 2020, Galax, 8, 38. doi:10.3390/galaxies8020038
  * Chiotellis, Boumis, & Spetsieri (2021) Chiotellis A., Boumis P., Spetsieri Z. T., 2021, MNRAS, 502, 176. doi:10.1093/mnras/staa3573
  * Chugai (2018) Chugai, N. N. 2018, Astronomy Letters, 44, 370
  * Chugai et al. (2005) Chugai N. N., Fabrika S. N., Sholukhova O. N., Goranskij V. P., Abolmasov P. K., Vlasyuk V. V., 2005, AstL, 31, 792. doi:10.1134/1.2138766
  * Chugai & Utrobin (2022) Chugai N. N., Utrobin V. P., 2022, MNRAS, 512, L71. doi:10.1093/mnrasl/slab131
  * Cikota et al. (2017) Cikota A., Patat F., Cikota S., Spyromilio J., Rau G., 2017, MNRAS, 471, 2111. doi:10.1093/mnras/stx1734
  * Coppejans et al. (2020) Coppejans D. L., Margutti R., Terreran G., Nayana A. J., Coughlin E. R., Laskar T., Alexander K. D., et al., 2020, ApJL, 895, L23. doi:10.3847/2041-8213/ab8cc7
  * Corradi et al. (1999) Corradi R. L. M., Perinotto M., Villaver E., Mampaso A., Gonçalves D. R., 1999, ApJ, 523, 721. doi:10.1086/307768
  * Corradi et al. (2011) Corradi R. L. M., Sabin L., Miszalski B., Rodríguez-Gil P., Santander-García M., Jones D., Drew J. E., et al., 2011, MNRAS, 410, 1349. doi:10.1111/j.1365-2966.2010.17523.x
  * Couch & Ott (2013) Couch, S. M., & Ott, C. D. 2013, ApJ, 778, L7
  * Danieli & Soker (2019) Danieli B., Soker N., 2019, MNRAS, 482, 2277. doi:10.1093/mnras/sty2892
  * Della Valle et al. (2006) Della Valle M., Chincarini G., Panagia N., Tagliaferri G., Malesani D., Testa V., Fugazza D., et al., 2006, Natur, 444, 1050. doi:10.1038/nature05374
  * De Marco (2009) De Marco O., 2009, PASP, 121, 316. doi:10.1086/597765
  * De Marco et al. (2022) De Marco O., Akashi M, Akras S., Alcolea J., Aleman I., Amram P., Balick B., De Beck E. Blackman E. G., et al., 2022, submitted
  * Dessart (2018) Dessart, L. 2018, A&A, 610, L10
  * Dexter & Kasen (2013) Dexter J., Kasen D., 2013, ApJ, 772, 30. doi:10.1088/0004-637X/772/1/30
  * Dong et al. (2021) Dong D. Z., Hallinan G., Nakar E., Ho A. Y. Q., Hughes A. K., Hotokezaka K., Myers S. T., et al., 2021, Sci, 373, 1125. doi:10.1126/science.abg6037
  * Drew et al. (2005) Drew, J. E., Greimel, R., Irwin, M. J., et al. 2005, MNRAS, 362, 753
  * Dubner et al. (1998) Dubner G. M., Holdaway M., Goss W. M., Mirabel I. F., 1998, AJ, 116, 1842. doi:10.1086/300537
  * Eiger et al. (2021) Eiger L., Lopez L., Auchettl K., Holland-Ashford T., Ramirez-Ruiz E., 2021, AAS
  * Eisenberg, Gottlieb, & Nakar (2022) Eisenberg M., Gottlieb O., Nakar E., 2022, arXiv, arXiv:2201.08432
  * Elias-Rosa et al. (2016) Elias-Rosa N., Pastorello A., Benetti S., Cappellaro E., Taubenberger S., Terreran G., Fraser M., et al., 2016, MNRAS, 463, 3894. doi:10.1093/mnras/stw2253
  * Ertl et al. (2016) Ertl T., Janka H.-T., Woosley S. E., Sukhbold T., Ugliano M., 2016, ApJ, 818, 124. doi:10.3847/0004-637X/818/2/124
  * Fiore et al. (2021) Fiore A., Chen T.-W., Jerkstrand A., Benetti S., Ciolfi R., Inserra C., Cappellaro E., et al., 2021, MNRAS, 502, 2120. doi:10.1093/mnras/staa4035
  * Fragos et al. (2019) Fragos, T., Andrews, J. J., Ramirez-Ruiz, E., Meynet, G., Kalogera, V., Taam, R. E., & Zezas, A., 2019, ApJ, 883, L45. doi:10.3847/2041-8213/ab40d1
  * Frank et al. (2016) Frank K. A., Zhekov S. A., Park S., McCray R., Dwek E., Burrows D. N., 2016, ApJ, 829, 40. doi:10.3847/0004-637X/829/1/40
  * Fransson et al. (2015) Fransson, C., Larsson, J., Migotto, K., et al. 2015, ApJ, 806, L19
  * Fransson et al. (2013) Fransson C., Larsson J., Spyromilio J., Chevalier R., Gröningsson P., Jerkstrand A., Leibundgut B., et al., 2013, ApJ, 768, 88. doi:10.1088/0004-637X/768/1/88
  * Fransson et al. (2016) Fransson, C., Larsson, J., Spyromilio, J., Leibundgut, B., McCray, R., and Jerkstrand, A, 2016, ApJ, 821, L5
  * Fransson et al. (2022) Fransson C., Sollerman J., Strotjohann N. L., Yang S., Schulze S., Barbarino C., Kool E. C., et al., 2022, arXiv, arXiv:2206.06497
  * Fraser et al. (2013) Fraser M., Inserra C., Jerkstrand A., Kotak R., Pignata G., Benetti S., Botticella M.-T., et al., 2013, MNRAS, 433, 1312. doi:10.1093/mnras/stt813
  * Fryer (2006) Fryer, C. L. 2006, New A Rev., 50, 492
  * Fryer et al. (2012) Fryer C. L., Belczynski K., Wiktorowicz G., Dominik M., Kalogera V., Holz D. E., 2012, ApJ, 749, 91. doi:10.1088/0004-637X/749/1/91
  * Fryer, Rueda, & Ruffini (2014) Fryer C. L., Rueda J. A., Ruffini R., 2014, ApJL, 793, L36. doi:10.1088/2041-8205/793/2/L36
  * Fryer & Woosley (1998) Fryer, C. L., & Woosley, S. E. 1998, ApJ, 502, L9
  * Fujibayashi et al. (2021) Fujibayashi S., Takahashi K., Sekiguchi Y., Shibata M., 2021, ApJ, 919, 80. doi:10.3847/1538-4357/ac10cb
  * Fuller (2017) Fuller J., 2017, MNRAS, 470, 1642. doi:10.1093/mnras/stx1314
  * Fuller & Ro (2018) Fuller J., Ro S., 2018, MNRAS, 476, 1853. doi:10.1093/mnras/sty369
  * Gabler et al. (2021) Gabler, M., Wongwathanarat, A., & Janka, H.-T. 2021, MNRAS, 502, 3264. doi:10.1093/mnras/stab116
  * Gangopadhyay et al. (2020) Gangopadhyay A., Turatto M., Benetti S., Misra K., Kumar B., Cappellaro E., Pastorello A., et al., 2020, MNRAS, 499, 129. doi:10.1093/mnras/staa2606
  * García et al. (2021) García, F., Simaz Bunzel, A., Chaty, S., Porter, E., & Chassande-Mottin, E. 2021, A&A, 649, A114. doi:10.1051/0004-6361/202038357
  * García et al. (2017) García, F., Suárez, A. E., Miceli, M., Bocchino, F., Combi, J. A., Orlando, S. and Sasaki, M. 2017, A&A, 604, L5
  * Ghodla et al. (2022) Ghodla S., Eldridge J. J., Stanway E. R., Stevance H. F., 2022, arXiv, arXiv:2208.03999
  * Gilkis & Soker (2014) Gilkis, A., & Soker, N. 2014, MNRAS, 439, 4011
  * Gilkis & Soker (2015) Gilkis A., Soker N., 2015, ApJ, 806, 28. doi:10.1088/0004-637X/806/1/28
  * Gilkis & Soker (2016) Gilkis A., Soker N., 2016, ApJ, 827, 40. doi:10.3847/0004-637X/827/1/40
  * Gilkis, Soker, & Kashi (2019) Gilkis A., Soker N., Kashi A., 2019, MNRAS, 482, 4233. doi:10.1093/mnras/sty3008
  * Gilkis et al. (2016) Gilkis, A., Soker, N., & Papish, O. 2016, ApJ, 826, 178. doi:10.3847/0004-637X/826/2/178
  * Gofman & Soker (2020) Gofman R. A., Soker N., 2020, MNRAS, 494, 5902. doi:10.1093/mnras/staa1197
  * Gogilashvili et al. (2021) Gogilashvili, M., Murphy, J. W., & Mabanta, Q. 2021, MNRAS, 500, 5393. doi:10.1093/mnras/staa3546
  * Gomez et al. (2022) Gomez S., Berger E., Nicholl M., Blanchard P. K., Hosseinzadeh G., 2022, arXiv, arXiv:2204.08486
  * González-Casanova et al. (2014) González-Casanova D. F., De Colle F., Ramirez-Ruiz E., Lopez L. A., 2014, ApJL, 781, L26. doi:10.1088/2041-8205/781/2/L26
  * Gottlieb et al. (2022a) Gottlieb O., Lalakos A., Bromberg O., Liska M., Tchekhovskoy A., 2022a, MNRAS, 510, 4962. doi:10.1093/mnras/stab3784
  * Gottlieb, Tchekhovskoy, & Margutti (2022b) Gottlieb O., Tchekhovskoy A., Margutti R., 2022b, MNRAS, 513, 3810. doi:10.1093/mnras/stac910
  * Gottlieb et al. (2022c) Gottlieb O., Liska M., Tchekhovskoy A., Bromberg O., Lalakos A., Giannios D., Mösta P., 2022c, ApJL, 933, L9. doi:10.3847/2041-8213/ac7530
  * Graham et al. (2014) Graham M. L., Sand D. J., Valenti S., Howell D. A., Parrent J., Halford M., Zaritsky D., et al., 2014, ApJ, 787, 163. doi:10.1088/0004-637X/787/2/163
  * Greco et al. (2018) Greco E., Miceli M., Orlando S., Peres G., Troja E., Bocchino F., 2018, A&A, 615, A157. doi:10.1051/0004-6361/201832733
  * Grefenstette et al. (2017) Grefenstette B. W., Fryer C. L., Harrison F. A., Boggs S. E., DeLaney T., Laming J. M., Reynolds S. P., et al., 2017, ApJ, 834, 19. doi:10.3847/1538-4357/834/1/19
  * Greiner et al. (2015) Greiner J., Mazzali P. A., Kann D. A., Krühler T., Pian E., Prentice S., Olivares E. F., et al., 2015, Natur, 523, 189. doi:10.1038/nature14579
  * Grichener, Cohen, & Soker (2021) Grichener A., Cohen C., Soker N., 2021, ApJ, 922, 61. doi:10.3847/1538-4357/ac23dd
  * Grichener & Soker (2017) Grichener, A., & Soker, N. 2017, MNRAS, 468, 1226
  * Grichener & Soker (2019a) Grichener, A. & Soker, N. 2019, ApJ, 878, 24. doi:10.3847/1538-4357/ab1d5d
  * Grichener & Soker (2021) Grichener A., Soker N., 2021, MNRAS, 507, 1651. doi:10.1093/mnras/stab2233
  * Grimmett et al. (2021) Grimmett J. J., Müller B., Heger A., Banerjee P., Obergaulinger M., 2021, MNRAS, 501, 2764. doi:10.1093/mnras/staa3819
  * Guarini, Tamborra, & Margutti (2022) Guarini E., Tamborra I., Margutti R., 2022, ApJ, 935, 157. doi:10.3847/1538-4357/ac7fa0
  * Guetta et al. (2020) Guetta D., Rahin R., Bartos I., Della Valle M., 2020, MNRAS, 492, 843. doi:10.1093/mnras/stz3245
  * Gutiérrez et al. (2022) Gutiérrez C. P., Pastorello A., Bersten M. Benetti S. Orellana M., Fiore A., Karamenhmetoglu E., Kravtsov T., et al., 2022, arXiv:2206.01662
  * Gvaramadze (2006) Gvaramadze, V. V. 2006, A&A, 454, 239
  * Heger et al. (2003) Heger A., Fryer C. L., Woosley S. E., Langer N., Hartmann D. H., 2003, ApJ, 591, 288. doi:10.1086/375341
  * Hillel, Schreier, & Soker (2022) Hillel S., Schreier R., Soker N., 2022, MNRAS, 514, 3212. doi:10.1093/mnras/stac1341
  * Hirai & Podsiadlowski (2022) Hirai R., Podsiadlowski P., 2022, arXiv, arXiv:2208.00915
  * Hober, Bear, & Soker (2022) Hober O., Bear E., Soker N., 2022, MNRAS, 516, 1846. doi:10.1093/mnras/stac2373
  * Hosseinzadeh et al. (2022) Hosseinzadeh G., Berger E., Metzger B. D., Gomez S., Nicholl M., Blanchard P., 2022, ApJ, 933, 14. doi:10.3847/1538-4357/ac67dd
  * Houck & Chevalier (1991) Houck, J. C., & Chevalier, R. A. 1991, ApJ, 376, 234
  * Hungerford, Fryer, & Rockefeller (2005) Hungerford A. L., Fryer C. L., Rockefeller G., 2005, ApJ, 635, 487. doi:10.1086/497323
  * Hungerford, Fryer, & Warren (2003) Hungerford A. L., Fryer C. L., Warren M. S., 2003, ApJ, 594, 390. doi:10.1086/376776
  * Hwang et al. (2004) Hwang, U., Laming, J. M., Badenes, C., et al. 2004, ApJ, 615, L117
  * Izzo et al. (2019) Izzo L., de Ugarte Postigo A., Maeda K., Thöne C. C., Kann D. A., Della Valle M., Sagues Carracedo A., et al., 2019, Natur, 565, 324. doi:10.1038/s41586-018-0826-3
  * Janka (2012) Janka, H.-T. 2012, Annual Review of Nuclear and Particle Science, 62, 407. doi:10.1146/annurev-nucl-102711-094901
  * Janka (2017) Janka, H.-T. 2017, ApJ, 837, 84
  * Janka et al. (2017) Janka, H.-T., Gabler, M., & Wongwathanarat, A. 2017, Supernova 1987A:30 years later - Cosmic Rays and Nuclei from Supernovae and their Aftermaths, 331, 148
  * Janka et al. (2016) Janka, H.-T., Melson, T., & Summa, A. 2016, Annual Review of Nuclear and Particle Science, 66, 341. doi:10.1146/annurev-nucl-102115-044747
  * Kamiński et al. (2021) Kamiński T., Steffen W., Bujarrabal V., Tylenda R., Menten K. M., Hajduk M., 2021, A&A, 646, A1. doi:10.1051/0004-6361/202039634
  * Kangas et al. (2022) Kangas T., Yan L., Schulze S., Fransson C., Sollerman J., Lunnan R., Omand C. M. B., et al., 2022, arXiv, arXiv:2207.12059
  * Kaplan & Soker (2020a) Kaplan N., Soker N., 2020a, MNRAS, 492, 3013. doi:10.1093/mnras/staa020
  * Kaplan & Soker (2020b) Kaplan N., Soker N., 2020b, MNRAS, 494, 5909. doi:10.1093/mnras/staa1201
  * Kashiyama & Quataert (2015) Kashiyama K., Quataert E., 2015, MNRAS, 451, 2656. doi:10.1093/mnras/stv1164
  * Kasuga et al. (2021) Kasuga T., Vink J., Katsuda S., Uchida H., Bamba A., Sato T., Hughes J. P., 2021, ApJ, 915, 42. doi:10.3847/1538-4357/abff4f
  * Khokhlov et al. (1999) Khokhlov, A. M., Höflich, P. A., Oran, E. S., et al. 1999, ApJ, 524, L107
  * Kilpatrick et al. (2018) Kilpatrick C. D., Foley R. J., Drout M. R., Pan Y.-C., Panther F. H., Coulter D. A., Filippenko A. V., et al., 2018, MNRAS, 473, 4805. doi:10.1093/mnras/stx2675
  * Kjær et al. (2010) Kjær, K., Leibundgut, B., Fransson, C., Jerkstrand, A., & Spyromilio, J. 2010, A&A, 517, A51
  * Kushnir (2015) Kushnir D., 2015, arXiv, arXiv:1506.02655
  * Larsson et al. (2019) Larsson J., Fransson C., Alp D., Challis P., Chevalier R. A., France K., Kirshner R. P., et al., 2019, ApJ, 886, 147. doi:10.3847/1538-4357/ab4ff2
  * Larsson et al. (2016) Larsson, J., Fransson, C., Spyromilio, J., et al. 2016, ApJ, 833, 147
  * Larsson et al. (2021) Larsson J., Sollerman J., Lyman J. D., Spyromilio J., Tenhu L., Fransson C., Lundqvist P., 2021, ApJ, 922, 265. doi:10.3847/1538-4357/ac2a41
  * Lazzati et al. (2012) Lazzati D., Morsony B. J., Blackwell C. H., Begelman M. C., 2012, ApJ, 750, 68. doi:10.1088/0004-637X/750/1/68
  * LeBlanc & Wilson (1970) LeBlanc J. M., Wilson J. R., 1970, ApJ, 161, 541. doi:10.1086/150558
  * Lee et al. (2017) Lee, Y.-H., Koo, B.-C., Moon, D.-S., Burton, M. G., Lee, J.-J., 2017, ApJ, 837, 118. doi:10.3847/1538-4357/aa60c0
  * Li et al. (2020) Li L., Wang S.-Q., Liu L.-D., Wang X.-G., Liang E.-W., Dai Z.-G., 2020, ApJ, 891, 98. doi:10.3847/1538-4357/ab718d
  * Lin et al. (2020) Lin J., Lu R.-J., Lin D.-B., Wang X.-G., 2020, ApJ, 895, 46. doi:10.3847/1538-4357/ab88a7
  * Liu et al. (2019) Liu T., Song C.-Y., Yi T., Gu W.-M., Wang X.-F., 2019, JHEAp, 22, 5
  * Lopez et al. (2011) Lopez L. A., Ramirez-Ruiz E., Huppenkothen D., Badenes C., Pooley D. A., 2011, ApJ, 732, 114. doi:10.1088/0004-637X/732/2/114
  * Lopez et al. (2013) Lopez, L. A., Ramirez-Ruiz, E., Castro, D., & Pearson, S. 2013, ApJ, 764, 50
  * López-Cámara et al. (2019) López-Cámara, D., De Colle, F., & Moreno Méndez, E. 2019, MNRAS, 482, 3646
  * López-Cámara et al. (2020) López-Cámara, D., Moreno Méndez, E., & De Colle, F. 2020, MNRAS, 497, 2057
  * López-Cámara et al. (2013) López-Cámara, D., Morsony, B. J., Begelman, M. C., & Lazzati, D. 2013, ApJ, 767, 19
  * Lu et al. (2021) Lu C.-Y., Yan J.-W., Wen L., Fang J., 2021, RAA, 21, 033. doi:10.1088/1674-4527/21/2/33
  * Lunnan et al. (2020) Lunnan R., Yan L., Perley D. A., Schulze S., Taggart K., Gal-Yam A., Fremling C., et al., 2020, ApJ, 901, 61. doi:10.3847/1538-4357/abaeec
  * MacFadyen, Woosley, & Heger (2001) MacFadyen A. I., Woosley S. E., Heger A., 2001, ApJ, 550, 410. doi:10.1086/319698
  * Maeda et al. (2012) Maeda, K., Moriya, T., Kawabata, K., et al. 2012, Mem. Soc. Astron. Italiana, 83, 264
  * Maeda et al. (2007) Maeda K., Tanaka M., Nomoto K., Tominaga N., Kawabata K., Mazzali P. A., Umeda H., et al., 2007, ApJ, 666, 1069. doi:10.1086/520054
  * Margutti et al. (2018) Margutti R., Chornock R., Metzger B. D., Coppejans D. L., Guidorzi C., Migliori G., Milisavljevic D., et al., 2018, ApJ, 864, 45. doi:10.3847/1538-4357/aad2df
  * Margutti et al. (2019) Margutti R., Metzger B. D., Chornock R., Vurm I., Roth N., Grefenstette B. W., Savchenko V., et al., 2019, ApJ, 872, 18. doi:10.3847/1538-4357/aafa01
  * Margutti et al. (2014) Margutti R., Milisavljevic D., Soderberg A. M., Chornock R., Zauderer B. A., Murase K., Guidorzi C., et al., 2014, ApJ, 780, 21. doi:10.1088/0004-637X/780/1/21
  * Matsuura et al. (2017) Matsuura, M., Indebetouw, R., Woosley, S., et al. 2017, MNRAS, 469, 3347
  * Mauerhan et al. (2013) Mauerhan J. C., Smith N., Filippenko A. V., Blanchard K. B., Blanchard P. K., Casper C. F. E., Cenko S. B., et al., 2013, MNRAS, 430, 1801. doi:10.1093/mnras/stt009
  * McCray & Fransson (2016) McCray R., Fransson C., 2016, ARA&A, 54, 19. doi:10.1146/annurev-astro-082615-105405
  * Mcley & Soker (2014) Mcley L., Soker N., 2014, MNRAS, 445, 2492. doi:10.1093/mnras/stu1952
  * Meaburn et al. (1996) Meaburn J., Lopez J. A., Bryce M., Mellema G., 1996, A&A, 307, 579
  * Metzger (2022) Metzger B. D., 2022, ApJ, 932, 84. doi:10.3847/1538-4357/ac6d59
  * Metzger, Beniamini, & Giannios (2018) Metzger B. D., Beniamini P., Giannios D., 2018, ApJ, 857, 95. doi:10.3847/1538-4357/aab70c
  * Metzger et al. (2015) Metzger B. D., Margalit B., Kasen D., Quataert E., 2015, MNRAS, 454, 3311. doi:10.1093/mnras/stv2224
  * Meyer (2021) Meyer D. M.-A., 2021, MNRAS, 507, 4697. doi:10.1093/mnras/stab2426
  * Miceli et al. (2008) Miceli M., Decourchelle A., Ballet J., Bocchino F., Hughes J., Hwang U., Petre R., 2008, AdSpR, 41, 390. doi:10.1016/j.asr.2007.01.030
  * Milisavljevic & Margutti (2018) Milisavljevic, D., & Margutti, R. 2018, Space Sci. Rev., 214, 68
  * Mitchell et al. (2007) Mitchell D. L., Pollacco D., O’Brien T. J., Bryce M., López J. A., Meaburn J., Vaytet N. M. H., 2007, MNRAS, 374, 1404. doi:10.1111/j.1365-2966.2006.11251.x
  * Moriya, Mazzali, & Pian (2020) Moriya T. J., Mazzali P. A., Pian E., 2020, MNRAS, 491, 1384. doi:10.1093/mnras/stz3122
  * Moriya et al. (2022) Moriya T. J., Murase K., Kashiyama K., Blinnikov S. I., 2022, MNRAS, 513, 6210. doi:10.1093/mnras/stac1352
  * Moriya et al. (2010) Moriya T., Tominaga N., Tanaka M., Nomoto K., Sauer D. N., Mazzali P. A., Maeda K., et al., 2010, ApJ, 719, 1445. doi:10.1088/0004-637X/719/2/1445
  * Morris & Podsiadlowski (2009) Morris T., Podsiadlowski P., 2009, MNRAS, 399, 515. doi:10.1111/j.1365-2966.2009.15114.x
  * Müller et al. (2019) Müller, B., Tauris, T. M., Heger, A., et al. 2019, MNRAS, 484, 3307
  * Nagakura et al. (2021) Nagakura H., Burrows A., Vartanyan D., Radice D., 2021, MNRAS, 500, 696. doi:10.1093/mnras/staa2691
  * Nakamura, Takiwaki, & Kotake (2022) Nakamura K., Takiwaki T., Kotake K., 2022, MNRAS, 514, 3941. doi:10.1093/mnras/stac1586
  * Nicholl et al. (2017) Nicholl, M., Guillochon, J., & Berger, E. 2017, ApJ, 850, 55
  * Nishimura et al. (2017) Nishimura, N., Sawai, H., Takiwaki, T., Yamada, S., & Thielemann, F.-K. 2017, ApJ, 836, L21
  * Nordhaus et al. (2012) Nordhaus J., Brandt T. D., Burrows A., Almgren A., 2012, MNRAS, 423, 1805. doi:10.1111/j.1365-2966.2012.21002.x
  * Nordhaus et al. (2010) Nordhaus, J., Brandt, T. D., Burrows, A., Livne, E., & Ott, C. D. 2010, Phys. Rev. D, 82, 103016
  * O’Connor & Couch (2018) O’Connor E. P., Couch S. M., 2018, ApJ, 865, 81. doi:10.3847/1538-4357/aadcf7
  * O’Connor et al. (2000) O’Connor J. A., Redman M. P., Holloway A. J., Bryce M., López J. A., Meaburn J., 2000, ApJ, 531, 336. doi:10.1086/308452
  * Ofek et al. (2021) Ofek E. O., Adams S. M., Waxman E., Sharon A., Kushnir D., Horesh A., Ho A., et al., 2021, ApJ, 922, 247. doi:10.3847/1538-4357/ac24fc
  * Ofek et al. (2013) Ofek E. O., Sullivan M., Cenko S. B., Kasliwal M. M., Gal-Yam A., Kulkarni S. R., Arcavi I., et al., 2013, Natur, 494, 65. doi:10.1038/nature11877
  * Ogata, Hirai, & Hijikawa (2021) Ogata M., Hirai R., Hijikawa K., 2021, MNRAS, 505, 2485. doi:10.1093/mnras/stab1439
  * Ono et al. (2020) Ono M., Nagataki S., Ferrand G., Takahashi K., Umeda H., Yoshida T., Orlando S., et al., 2020, ApJ, 888, 111. doi:10.3847/1538-4357/ab5dba
  * Orellana & Bersten (2022) Orellana M., Bersten M., 2022, arXiv, arXiv:2209.03923
  * Orlando et al. (2016) Orlando, S., Miceli, M., Pumo, M. L., & Bocchino, F. 2016, ApJ, 822, 22
  * Orlando et al. (2020) Orlando S., Ono M., Nagataki S., Miceli M., Umeda H., Ferrand G., Bocchino F., et al., 2020, A&A, 636, A22. doi:10.1051/0004-6361/201936718
  * Orlando et al. (2022) Orlando S., Wongwathanarat A., Janka H.-T., Miceli M., Nagataki S., Ono M., Bocchino F., et al., 2022, arXiv, arXiv:2202.01643
  * Orlando et al. (2021) Orlando, S., Wongwathanarat, A., Janka, H.-T., Miceli, M., Ono, M., Nagataki, S., Bocchino, F., & Peres, G. 2021, A&A, 645, A66. doi:10.1051/0004-6361/202039335
  * Ouchi & Maeda (2019) Ouchi R., Maeda K., 2019, ApJ, 877, 92. doi:10.3847/1538-4357/ab1a37
  * Pais, Piran, & Nakar (2022) Pais M., Piran T., Nakar E., 2022, arXiv, arXiv:2208.14459
  * Panagia et al. (1996) Panagia N., Scuderi S., Gilmozzi R., Challis P. M., Garnavich P. M., Kirshner R. P., 1996, ApJL, 459, L17. doi:10.1086/309930
  * Papish, Nordhaus, & Soker (2015) Papish O., Nordhaus J., Soker N., 2015, MNRAS, 448, 2362. doi:10.1093/mnras/stv131
  * Papish & Soker (2011) Papish O., Soker N., 2011, MNRAS, 416, 1697. doi:10.1111/j.1365-2966.2011.18671.x
  * Papish & Soker (2014a) Papish O., Soker N., 2014a, MNRAS, 438, 1027. doi:10.1093/mnras/stt2199
  * Papish & Soker (2014b) Papish, O., & Soker, N. 2014b, MNRAS, 443, 664
  * Park et al. (2010) Park, S., Hughes, J. P., Slane, P. O., Mori, K., & Burrows D. N. 2010, ApJ, 710, 948. doi:10.1088/0004-637X/710/2/948
  * Park et al. (2002) Park, S., Roming, P. W. A., Hughes, J. P., Slane, P. O., Burrows, D. N., Garmire, G. P. and Nousek, J. A.. 2002, ApJ, 564, L39
  * Park et al. (2007) Park S., Slane P. O., Hughes J. P., Mori K., Burrows D. N., Garmire G. P., 2007, ApJ, 665, 1173. doi:10.1086/520105
  * Pastorello et al. (2013) Pastorello A., Cappellaro E., Inserra C., Smartt S. J., Pignata G., Benetti S., Valenti S., et al., 2013, ApJ, 767, 1. doi:10.1088/0004-637X/767/1/1
  * Pastorello et al. (2018) Pastorello A., Kochanek C. S., Fraser M., Dong S., Elias-Rosa N., Filippenko A. V., Benetti S., et al., 2018, MNRAS, 474, 197. doi:10.1093/mnras/stx2668
  * Pellegrino et al. (2022) Pellegrino C., Howell D. A., Terreran G., Arcavi I., Bostroem K. A., Brown P. J., Burke J., et al., 2022, arXiv, arXiv:2205.07894
  * Perets et al. (2019) Perets H. B., Zenati Y., Toonen S., Bobrick A., 2019, arXiv, arXiv:1910.07532
  * Perley et al. (2019) Perley D. A., Mazzali P. A., Yan L., Cenko S. B., Gezari S., Taggart K., Blagorodnova N., et al., 2019, MNRAS, 484, 1031. doi:10.1093/mnras/sty3420
  * Perley et al. (2022) Perley D. A., Sollerman J., Schulze S., Yao Y., Fremling C., Gal-Yam A., Ho A. Y. Q., et al., 2022, ApJ, 927, 180. doi:10.3847/1538-4357/ac478e
  * Piran et al. (2019) Piran T., Nakar E., Mazzali P., Pian E., 2019, ApJL, 871, L25. doi:10.3847/2041-8213/aaffce
  * Podsiadlowski, Joss, & Rappaport (1990) Podsiadlowski P., Joss P. C., Rappaport S., 1990, A&A, 227, L9
  * Post et al. (2014) Post S., Park S., Badenes C., Burrows D. N., Hughes J. P., Lee J.-J., Mori K., et al., 2014, ApJL, 792, L20. doi:10.1088/2041-8205/792/1/L20
  * Prentice et al. (2018) Prentice S. J., Maguire K., Smartt S. J., Magee M. R., Schady P., Sim S., Chen T.-W., et al., 2018, ApJL, 865, L3. doi:10.3847/2041-8213/aadd90
  * Quataert et al. (2019) Quataert, E., Lecoanet, D., & Coughlin, E. R. 2019, MNRAS, 485, L83. doi:10.1093/mnrasl/slz031
  * Quataert & Shiode (2012) Quataert E., Shiode J., 2012, MNRAS, 423, L92. doi:10.1111/j.1745-3933.2012.01264.x
  * Reguitti et al. (2019) Reguitti A., Pastorello A., Pignata G., Benetti S., Cappellaro E., Turatto M., Agliozzo C., et al., 2019, MNRAS, 482, 2750. doi:10.1093/mnras/sty2870
  * Reichert et al. (2022) Reichert M., Obergaulinger M., Aloy M.-A., Gabler M., Arcones A., Thielemann F.-K., 2022, arXiv, arXiv:2206.11914
  * Reynolds et al. (2007) Reynolds S. P., Borkowski K. J., Hwang U., Hughes J. P., Badenes C., Laming J. M., Blondin J. M., 2007, ApJL, 668, L135. doi:10.1086/522830
  * Sahai (2000) Sahai R., 2000, ApJL, 537, L43. doi:10.1086/312748
  * Sahai et al. (1999) Sahai R., Dayal A., Watson A. M., Trauger J. T., Stapelfeldt K. R., Burrows C. J., Gallagher J. S., et al., 1999, AJ, 118, 468. doi:10.1086/300939
  * Sahai, Morris, & Villar (2011) Sahai R., Morris M. R., Villar G. G., 2011, AJ, 141, 134. doi:10.1088/0004-6256/141/4/134
  * Sahai & Trauger (1998) Sahai R., Trauger J. T., 1998, AJ, 116, 1357. doi:10.1086/300504
  * Sandoval et al. (2021) Sandoval M. A., Hix W. R., Messer O. E. B., Lentz E. J., Harris J. A., 2021, ApJ, 921, 113. doi:10.3847/1538-4357/ac1d49
  * Sano et al. (2021) Sano H., Yoshiike S., Yamane Y., Hayashi K., Enokiya R., Tokuda K., Tachihara K., et al., 2021, ApJ, 919, 123. doi:10.3847/1538-4357/ac0dba
  * Sapienza et al. (2021) Sapienza V., Miceli M., Peres G., Bocchino F., Orlando S., Greco E., Combi J. A., et al., 2021, A&A, 649, A56. doi:10.1051/0004-6361/202140412
  * Schreier et al. (2021) Schreier R., Hillel S., Shiber S., Soker N., 2021, MNRAS, 508, 2386. doi:10.1093/mnras/stab2687
  * Schreier & Soker (2016) Schreier R., Soker N., 2016, RAA, 16, 70. doi:10.1088/1674-4527/16/5/070
  * Schrøder et al. (2020) Schrøder S. L., MacLeod M., Loeb A., Vigna-Gómez A., Mandel I., 2020, ApJ, 892, 13. doi:10.3847/1538-4357/ab7014
  * Shankar et al. (2021) Shankar S., Mösta P., Barnes J., Duffell P. C., Kasen D., 2021, MNRAS, 508, 5390. doi:10.1093/mnras/stab2964
  * Shelton et al (2004) Shelton, R., & Kuntz, K., & Petre, R. 2004, ApJ, 611, 906
  * Shibagaki et al. (2021) Shibagaki S., Kuroda T., Kotake K., Takiwaki T., 2021, MNRAS, 502, 3066. doi:10.1093/mnras/stab228
  * Shiber et al. (2019) Shiber, S., Iaconi, R., De Marco, O., & Soker, N. 2019, MNRAS, 488, 5615. doi:10.1093/mnras/stz2013
  * Shiode & Quataert (2014) Shiode J. H., Quataert E., 2014, ApJ, 780, 96. doi:10.1088/0004-637X/780/1/96
  * Shishkin & Soker (2021) Shishkin D., Soker N., 2021, MNRAS, 508, L43. doi:10.1093/mnrasl/slab105
  * Shishkin & Soker (2022) Shishkin D., Soker N., 2022, MNRAS, 513, 4224. doi:10.1093/mnras/stac1075
  * Rea et al. (2016) Rea, N., Borghese, A., Esposito, P., Coti Zelati, F., Bachetti, M., Israel, G. L. and De Luca, A. 2016, ApJ, 828, L13
  * Slane et al (2004) Slane, P., & Helfand, D., & Swaluw, E., & Murray, S. 2004, ApJ, 616, 403
  * Smith et al. (2022) Smith N., Andrews J. E., Filippenko A. V., Fox O. D., Mauerhan J. C., Van Dyk S. D., 2022, MNRAS, 515, 71. doi:10.1093/mnras/stac1669
  * Smith, Mauerhan, & Prieto (2014) Smith N., Mauerhan J. C., Prieto J. L., 2014, MNRAS, 438, 1191. doi:10.1093/mnras/stt2269
  * Smith et al. (2010) Smith N., Miller A., Li W., Filippenko A. V., Silverman J. M., Howard A. W., Nugent P., et al., 2010, AJ, 139, 1451. doi:10.1088/0004-6256/139/4/1451
  * Sobacchi et al. (2017) Sobacchi, E., Granot, J., Bromberg, O., & Sormani, M. C. 2017, MNRAS, 472, 616
  * Soker (1999) Soker N., 1999, MNRAS, 303, 611. doi:10.1046/j.1365-8711.1999.02268.x
  * Soker (2002) Soker N., 2002, ApJ, 577, 839. doi:10.1086/342227
  * Soker (2010) Soker N., 2010, MNRAS, 401, 2793. doi:10.1111/j.1365-2966.2009.15862.x
  * Soker (2016a) Soker N., 2016a, NewA, 47, 88. doi:10.1016/j.newast.2016.02.009
  * Soker (2016b) Soker, N. 2016b, New A Rev., 75, 1. doi:10.1016/j.newar.2016.08.002
  * Soker (2017a) Soker N., 2017a, ApJL, 839, L6. doi:10.3847/2041-8213/aa6a10
  * Soker (2017b) Soker, N. 2017b, Research in Astronomy and Astrophysics, 17, 113. doi:10.1088/1674-4527/17/11/113
  * Soker (2018a) Soker N., 2018a, RNAAS, 2, 48. doi:10.3847/2515-5172/aab9b5
  * Soker (2018b) Soker N., 2018b, arXiv:1805.03447
  * Soker (2019a) Soker N., 2019a, RAA, 19, 095. doi:10.1088/1674-4527/19/7/95
  * Soker (2019b) Soker N., 2019b, NewAR, 87, 101535. doi:10.1016/j.newar.2020.101535
  * Soker (2019c) Soker N., 2019c, arXiv, arXiv:1907.13312
  * Soker (2020a) Soker N., 2020a, ApJ, 893, 20. doi:10.3847/1538-4357/ab7dbb
  * Soker (2020b) Soker N., 2020b, RAA, 20, 024. doi:10.1088/1674-4527/20/2/24
  * Soker (2021a) Soker, N. 2021a, MNRAS, 504, 5967. doi:10.1093/mnras/stab1275
  * Soker (2021b) Soker N., 2021b, MNRAS, 506, 2445. doi:10.1093/mnras/stab1860
  * Soker (2021b) Soker N., 2021b, arXiv:2111.11906
  * Soker (2022a) Soker N., 2022a, RAA, 22, 035019. doi:10.1088/1674-4527/ac49e6
  * Soker (2022b) Soker N., 2022b, RAA, 22, 035025. doi:10.1088/1674-4527/ac4d25
  * Soker (2022c) Soker N., 2022c, RAA, 22, 055010. doi:10.1088/1674-4527/ac5b40
  * Soker (2022d) Soker N., 2022, RAA, 22, 095007. doi:10.1088/1674-4527/ac7cbc
  * Soker (2022e) Soker N., 2022, ApJ, 935, 108. doi:10.3847/1538-4357/ac822d
  * Soker (2022f) Soker N., 2022f, arXiv, arXiv:2207.02753
  * Soker & Gilkis (2017a) Soker N., Gilkis A., 2017a, ApJ, 851, 95. doi:10.3847/1538-4357/aa9c83
  * Soker & Gilkis (201b7) Soker N., Gilkis A., 2017b, MNRAS, 464, 3249. doi:10.1093/mnras/stw2546
  * Soker & Gilkis (2018) Soker N., Gilkis A., 2018, MNRAS, 475, 1198. doi:10.1093/mnras/stx3287
  * Soker et al. (2019) Soker, N., Grichener, A., & Gilkis, A. 2019, MNRAS, 484, 4972
  * Soker & Kashi (2013) Soker N., Kashi A., 2013, ApJL, 764, L6. doi:10.1088/2041-8205/764/1/L6
  * Sollerman et al. (2019) Sollerman, J., Taddia, F., Arcavi, I., et al. 2019, A&A, 621, A30