Vol.0 (20xx) No.0, 000–000

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

# Imprints of the jittering jets explosion mechanism in the morphology of the
supernova remnant SNR 0540-69.3

Noam Soker 11

###### Abstract

I identify a point-symmetric structure in recently published VLT/MUSE velocity
maps of different elements in a plane along the line of sight at the center of
the supernova remnant SNR 0540-69.3, and argue that jittering jets that
exploded this core collapse supernova shaped this point-symmetric structure.
The four pairs of two opposite clumps that compose this point symmetric
structure suggest that two to four pairs of jittering jets shaped the inner
ejecta in this plane. In addition, intensity images of several spectral lines
reveal a faint strip (the main jet-axis) that is part of this plane of
jittering jets and its similarity to morphological features in a few other
SNRs and in some planetary nebulae further suggests shaping by jets. My
interpretation implies that in addition to instabilities, jets also mix
elements in the ejecta of core collapse supernovae. Based on the point-
symmetric structure and under the assumption that jittering jets exploded this
supernova, I estimate the component of the neutron star natal kick velocity on
the plane of the sky to be $\simeq 235{~{}\rm km}{~{}\rm s}^{-1}$, and at an
angle of $\simeq 47^{\circ}$ to the direction of the main jet-axis. I analyse
this natal kick direction together with other 12 SNRs in the frame of the
jittering jets explosion mechanism.

###### keywords:

ISM: supernova remnants - stars: jets - supernovae: general - supernovae:
individual (SNR 0540-69.3)

##  1 INTROCUTION

Core collapse supernova (CCSN) remnants (SNRs) have inhomogeneous structures
of filaments, arcs, clumps, and ‘Ears’ (two opposite protrusions from the main
SNR). Examples include the SNRs Vela (images by, e.g., Aschenbach et al. 1995;
García et al. 2017), SNR G$292.0+1.8$ (e.g., Park et al. 2002, 2007), and SNR
W49B (e.g., Lopez et al. 2013; Sano et al. 2021). This holds for the inner
ejecta of CCSNe that have inhomogeneous structures of filaments, clumps, and
rings of the different heavy elements such as oxygen, silicon, sulfur, argon
and iron. According to the delayed neutrino explosion mechanism of CCSNe
instabilities that are inherently exist in this explosion mechanism cause
these filamentary structures of the inner ejecta (e.g., Janka et al. 2017;
Wongwathanarat et al. 2017; Gabler et al. 2021; Sandoval et al. 2021).
According to the jittering jets explosion mechanism of CCSNe both
instabilities and jittering jets shape the ejecta (e.g., Papish & Soker 2014a;
Papish et al. 2015a; Gilkis & Soker 2016). In the jittering jets explosion
mechanism instabilities inherently exist, in particular the spiral standing
accretion shock instability (for studies of this instability see, e.g.,
Blondin & Mezzacappa 2007; Rantsiou et al. 2011; Fernández 2015; Kazeroni et
al. 2017), because these instabilities supply the stochastic angular momentum
to form the intermittent accretion disk that launches the jittering jets
(e.g., Papish et al. 2015a; Shishkin & Soker 2021).

In some cases instabilities alone cannot account for the filamentary structure
of the ejecta and it seems that jets as well shape the ejecta. Consider the
clumpy/filamentary structure of the ejecta of SN 1987A (e.g., Fransson et al.
2015, 2016; Larsson et al. 2016; Abellán et al. 2017; Matsuura et al. 2017),
now SNR 1987A. Although there are claims that the non-symmetric explosion of
SN 1987A is due to instabilities alone (e.g., Kjær et al. 2010), recent
studies suggest that this is not the case. Abellán et al. (2017) find that
none of the neutrino driven explosion models they compare to fit all
observations of SN 1987A, a conclusion that supports a similar earlier claim
by Soker (2017). Soker (2017) compared the Fe structure of SN 1987A from
Larsson et al. (2016) with the numerical simulations by Wongwathanarat et al.
(2015) and concluded that the neutrino-driven explosion mechanism cannot
account for the structure of the Fe/Si-bright regions of SN 1987A (but this is
in dispute in the literature, e.g., Janka et al. 2017). Namely, the numerical
simulations of Wongwathanarat et al. (2015) predict several narrow Fe-rich
fingers while the observed Fe/Si-bright structure is of two large regions.
Bear & Soker (2018b) use the observations of Abellán et al. (2017) to compare
some morphological features of SN 1987A with morphological features of other
SNRs and with planetary nebulae, and further argue that jittering jets played
a crucial role in the explosion of SN 1987A. I note that the earlier claim of
Wang et al. (2002) that two opposite non-jittering jets exploded SN 1987a is
in conflict with the structure of the ejecta that Abellán et al. (2017) reveal
(see discussion by Bear & Soker 2018b).

Wongwathanarat et al. (2015) and Orlando et al. (2021) compared numerical
simulations of the neutrino-driven explosion mechanism with the structure of
SNR Cassiopeia A and argued that these simulations reproduce the morphological
distribution of some metals in SNR Cassiopeia A. On the other hand, in Soker
(2017) I examined the structure of Cassiopeia A from the observations of
Grefenstette et al. (2017) and Lee et al. (2017) and showed that the metal
distributions that Wongwathanarat et al. (2015) obtain from their numerical
simulations cannot account for the observations. I instead argued that jets
seem to have played a crucial role is the shaping of SNR Cassiopeia A during
its explosion. I note also that Orlando et al. (2016) argued for the existence
of a large-scale asymmetrical outflow in Cassiopeia A as instabilities alone
cannot account for its morphology.

Another strong indication from SNRs to the role of jets in CCSN explosions is
the presence of ears (Bear & Soker 2017; Bear et al. 2017; Grichener & Soker
2017). While the distributions of heavy metals reveal mainly the SNR inner
structures, ears reveal the role of jets in the outskirts of the ejecta. The
reason is that most likely the ears are shaped by the last jets that the newly
born neutron star (NS) has launched. This launching episode takes place after
the core has exploded and therefore the jets can propagate to large distances
(e.g., Bear et al. 2017).

In the present study I examine the newly published high-quality observations
and analysis of SNR 0540-69.3 by Larsson et al. (2021) to argue that there is
a point-symmetric structure as expected in the jittering jets explosion
mechanism (section 2). X-ray observations (e.g. Park et al. 2010) show that
SNR 0540-69.3 has a large-scale rectangle shape, but one that is highly non-
homogeneous. The $2.5-7{~{}\rm keV}$ intensity map, however, contains two
bright spots on opposite sides of the center (one to the east and one to the
west; figure 1 of Park et al. 2010). This pair might be or not part of the
point symmetric structure that I study here. However, because the two bright
spots are on the edge of the SNR and are faint, I do not explore their nature
here.

In section 3 I use my claim for jittering jets in a plane to estimate the
projected angle between the pulsar natal kick direction and the main jet-axis
of the jittering jets. I incorporate this angle with 12 other SNRs for which
the projected angles of the jets to the kick velocity exist. I use these 13
angles to strengthen an earlier claim that the natal kick velocity avoids
small angle with respect to the main jet-axis. I discuss and summarise my
study in section 4.

##  2 Imprints of jittering jets

###  2.1 The main jet-axis

The high resolution VLT/MUSE observations and high quality three-dimensional
reconstruction of the ejecta of SNR 0540-69.3 by Larsson et al. (2021) allow
the identification of a point-symmetric morphology. I first present in Fig. 1
the images as Larsson et al. (2021) do in their figure 1. On these images I
added yellow double-headed arrows along a faint strip that goes through the
center of the SNR as I mark by the black solid line in the upper left panel of
Fig. 1 (all yellow arrows on the different panels are on the same position). I
term this axis the main jet-axis, but as I discuss below in might represent a
plane along the line of sight. From comparison of such central faint strips in
planetary nebulae and in SNRs earlier studies (e.g., Bear et al. 2017; Akashi
et al. 2018) suggested that the faint strip in SNRs is the direction of two
opposite jets that cleaned the axis from most of the gas. Here, as well, I
suggest hat this central faint strip marks the direction of two opposite jets,
or even two to four such pairs of jets in a plane. Namely, as I show in
section 2.2 more likely there is a jittering plane that represents two or more
pairs of jittering jets. I also note that the double-headed arrows that mark
the faint strip do not go through the pulsar, but rather through the pulsar
wind nebula (PWN) blob. However, the pulsar is inside the faint strip as the
strip is wide, but not at its central axis.

Figure 1: My claim for a main jet-axis on the plane of the sky as I mark with
yellow double-headed arrows on the images reproduced from figure 1 of Larsson
et al. (2021). My additions are the yellow arrows, the dashed lines on the
upper left panel that are the same as the dashed black line on the third lower
panel, and the mark of the faint-strip by a black line in the upper left
panel. The two parallel dashed lines mark the boundary of the
$1.5^{\prime\prime}$ wide X-shooter slit (Larsson et al. 2021).

I can identify the same main jet-axis in earlier Hubble Space Telescope (HST)
observations by Morse et al. (2006), as I mark on the two panels of Fig. 2
that I reproduce from figure 1 of Morse et al. (2006). I discuss the meaning
of the red arrows of the NS natal kick velocity in section 3.

Figure 2: My identification of the main jet-axis (yellow double-headed arrows)
in the HST observations from Morse et al. (2006). In red double-lined arrow I
mark my suggestion for the transverse (projected on the plane of the sky) NS
natal kick velocity $v_{\rm k,T}$ that I derive from the velocity component
perpendicular to the main jet-axis $v_{\rm k,per}$ and the component along the
slit $v_{\rm k,slit}$ (section 3).

My identification of the faint strip as the axis (or plane) of jittering jets
that exploded the CCSN is new. In the past, studies (e.g., Serafimovich et al.
2004; Brantseg et al. 2014) attributed this plane to the plane of the assumed
torus of the PWN. These studies also identified two opposite jets
perpendicular to this torus (e.g., Serafimovich et al. 2004; Lundqvist et al.
2021). On the other hand, De Luca et al. (2007) suggested that the direction
along the faint strip is the direction of the pulsar jets (see also discussion
by Lundqvist et al. 2011). As I show next, I attribute this direction to the
plane of the jittering jets that exploded the CCSN of SNR 0540-69.3 rather
than to the jets of the pulsar.

###  2.2 A point-symmetric Morphology

####  2.2.1 Point-symmetry in planetary nebulae

Larsson et al. (2021) present a thorough analysis of the properties of the
clumps and the rings that they reveal in SNR 0540-69.3. I here only
concentrate on what I identify as a point-symmetric structure that I attribute
to jittering jets. My claim for jets is based in large parts on the shaping by
jets of the point-symmetric morphologies of planetary nebulae (e.g. Sahai &
Trauger 1998; Sahai, Morris, & Villar 2011).

In Fig. 3 I present two examples of planetary nebulae with a point-symmetric
structure. On the left is the planetary nebula He2-138 (PN G320.1-09.6) from
Sahai & Trauger (1998) that presents a point symmetric structure that the
authors attribute to shaping by jets. This PN demonstrates four pairs of
opposite protrusions. In this case most of the brightest regions are the arcs
at the front of the protrusions. On the right is the planetary nebula PN M1-37
(PN G002.6-03.4) from Sahai (2000), who also marked the three straight lines
and named the three pairs of protrusions (lobes). In this case most of the
brightest regions are to the sides of the lines connecting the tips of the
opposite protrusions.

Figure 3:  Two-planetary nebulae that demonstrate a point-symmetric structure
that the authors of the respective papers attribute to jets. On the left is
the PN He2-138 (PN G320.1-09.6) from Sahai & Trauger (1998) and on the right
is PN M1-37 (PN G002.6-03.4) from Sahai (2000). The three lines on the right
panel are on the original image by Sahai (2000).

The point to take from these two planetary nebulae is that jets can form
point-symmetric structures, but that the brightest regions might be on
different regions with respect to what researchers identify as the jets’ axes.

####  2.2.2 Point-symmetry in SNR 0540-69.3

From their VLT/X-shooter spectroscopic observation along the slit as marked by
two parallel dashed lines in two panels of Fig. 1 and from their derived age
of $\simeq 1100{~{}\rm yr}$ for SNR 0540-69.3, Larsson et al. (2021) build a
velocity map in a plane perpendicular to the plane of the sky, i.e., along the
line of sight. I present their figure 4 in Fig. 4. I identify 8 clumps that
form a point-symmetric structure (although not perfect) along four lines that
go through four pairs of clumps A-D, B-E, C-F and Gs-Gn. Larsson et al. (2021)
mark clumps A-F and I mark also clumps Gn and Gs.

Figure 4: Two-dimensional velocity maps as Larsson et al. (2021) present in
their figure 4 along the slit that the two dashed lines mark in two panels of
Fig. 1. The velocity along the slit $v_{\rm slit}$ is positive to the
northeast, and $v_{\rm z}$ is the velocity along the line of sight. I added 4
lines on all panels (same 4 lines), P1-P4, to mark 4 pairs of opposite clumps
that form the point-symmetric morphology that I identify here (A-D; B-E; C-F;
Gn-Gs). The marks of clumps A to F in the lower left panel are from Larsson et
al. (2021), while I added the marks to clumps Gn and Gs. The pulsar is at
$v_{\rm slit}=0$ in these panels. The dashed horizontal yellow line at the
location of the pulsar indicates that the line of sight velocity of the pulsar
is not determined here.

I define the four different lines by connecting bright clumps. I identify the
line ‘P1’ in the images of [O II] and [S III], the line ‘P2’ in the image of
[Fe II], the line ‘P3’ in the image of the [O II], and the line ‘P4’ in the
image of [Fe II]. I then copy the lines to other images to form the same
structure of the 4 lines in all images of Fig. 4. The strong point is that the
lines cross also clumps that I did not use to define them. For example, line
‘P2’ crosses also clumps in the [O II] image and in the H$\alpha$ image.

Because I define the lines by the bright clumps, the 4 lines do not cross
exactly at the same point. However, that the four lines cross each other at
almost the same point, despite that I define them by the clumps, supports my
claim for a point-symmetric structure.

A point-symmetric structure of an outflowing nebula very strongly suggests
shaping by precessing jets or jittering (stochastic) jets. I therefore take
the point symmetric structure in the plane of the slit to be a plane of
jittering jets. The slit direction is at $12^{\circ}$ to the main jet-axis
that I take along the faint strip (Fig. 2). Because the faint strip is wide,
to the accuracy of the present analysis I can take the slit direction to be as
the main jet-axis. This implies that the main jet-axis represent a jittering
plane along the line of sight (perpendicular to the planes of Figs. 1 and 2).

From the two point-symmetric planetary nebulae in Fig. 3 we learn that the
dense clumps might be at the tip of the jets or to to the sides o the jets.
Without numerical simulations of the explosion (which are extremely demanding)
I cannot tell whether there were two, three or fours pairs of jittering jets
in the plane of Fig. 4. The reason is that each jet might form a clump at its
head, a case that implies four pairs of jets, or each jet can inflate a bubble
that form clumps on its boundary, a case that allows for only two pairs of
jets.

Let me consider the case where four pairs of jittering jets formed the point-
symmetric structure that I identify in the plane of Fig. 4. According to the
jittering jets explosion mechanism several to few tens of jet-launching
episodes explode the star (e.g. Papish & Soker 2011, 2014a). However, the
jittering direction might not be completely chaotic. Papish & Soker (2014b)
conducted three-dimensional hydrodynamical numerical simulations of the
jittering jets explosion mechanism and showed that early jittering jets
channel the gas that the newly born NS continues to accrete to inflow in
directions perpendicular to the early jets. The direction of the angular
momentum that this in-flowing gas carries, therefore, tends to be in the same
plane as the first two pairs of jittering jets. Namely, later jets are more
likely to be in the same plane as the first four jets (two pairs of jets). For
that, the presence of four pairs of jets in a similar plane is compatible with
the jittering jets explosion mechanism. This must not be the case with all
jets, as large fluctuations of the angular momentum of the accreted gas onto
the NS might tilt the accretion disk by a large angle so that the jet-axis of
the newly launched jets is outside the earlier jittering plane. Therefore,
other jet-axes are possible beside the jittering plane of Fig. 4. In section 4
I suggest that one such jet-axis might be perpendicular to the [O III]
irregular ring-like structure.

My conclusion is that the point-symmetric morphology that I identify in Fig. 4
is compatible with, and strongly support, the jittering jets explosion
mechanism.

##  3 On the natal kick direction

In what follows I deal only with the angle between the pulsar natal kick
direction and the main jet-axis as it is projected on the plane of the sky.
Therefore, the natal kick velocity component along the line of sight is not
relevant.

Serafimovich et al. (2004) estimated a pulsar transverse velocity of $1190\pm
560{~{}\rm km}{~{}\rm s}^{-1}$ in a south east direction. However, Mignani et
al. (2010) constraint the transverse velocity to be $<250{~{}\rm km}s^{-1}$.

If my identification of the jittering jet axis/plane holds, I can use it to
estimate the pulsar natal kick velocity component on the plane of the sky. The
pulsar is at a transverse distance of $d_{\rm per}\simeq 0.8^{\prime\prime}D$
from the main jet-axis. For an age of $\tau=1100{~{}\rm yr}$ as Larsson et al.
(2021) use (note that Serafimovich et al. 2004 take $\tau=1660{~{}\rm yr}$),
and a distance to the CCSN of $D=50{~{}\rm kpc}$ this displacement corresponds
to a transverse kick velocity component perpendicular to the main jet-axis of
$v_{\rm k,per}=d_{\rm per}/\tau=171{~{}\rm km}{~{}\rm s}^{-1}$. I mark this
direction by thick red arrow on Fig. 2. Larsson et al. (2021) take the pulsar
at the center of the explosion. From Fig. 4 I find the velocity along the
X-shooter of the pulsar relative to the center of the point-symmetric
structure to be $v_{\rm k,slit}=165{~{}\rm km}{~{}\rm s}^{-1}$ in the south-
west direction, as I mark by a second red arrow on Fig. 2, and by the white
arrow in the middle-lower panel of Fig. 4. The slit is tilted at $12^{\circ}$
to the main jet-axis. From these I find the transverse (i.e., projected on the
plane of the sky) pulsar velocity relative to the center of the point-
symmetric structure to be $v_{\rm k,T}=|\vec{v}_{\rm k,slit}+\vec{v}_{\rm
k,per}|=235{~{}\rm km}{~{}\rm s}^{-1}$. I mark the transverse pulsar velocity
that I estimate here by a double-lined red arrow in Fig. 2. This velocity is
below the upper limit that Mignani et al. (2010) deduce.

The angle of this transverse kick velocity to the main jet-axis is
$\alpha\simeq 47^{\circ}$. I also note that the transverse component of the
natal kick velocity of the pulsar that I deduce here is almost opposite to the
direction that Serafimovich et al. (2005) argued for and that was refuted by
Mignani et al. (2010).

Bear & Soker (2018a) present the distribution of the projected angles $\alpha$
between the jets’ axis and the NS kick velocity for 12 SNRs. They conclude
that the cumulative distribution function fits the random distribution (kick
velocity is random with respect to the main jet-axis) at large angles, and is
missing systems with small angles relative to the random distribution. I add
the angle of $\alpha=47^{\circ}$ for SNR 0540-69.3 that I estimate above to
have now a sample of 13 SNRs. Note again that I deal here only with the
projected angle on the plane of the sky as Bear & Soker (2018a) do in their
analysis, and for that the natal kick velocity component along the line of
sight is not relevant. I present the new cumulative distribution function in
Fig. 5. The new addition of SNR 0540-69.3 is compatible with the conclusion of
Bear & Soker (2018a) and strengthens it.

Figure 5: The cumulative distribution function ${\rm W}_{\alpha}$ of projected
angles between the jets’-axis and the NS natal kick for 13 SNRs. The angles of
12 SNRs are from Bear & Soker (2018a) and the new addition is my estimate of
$\alpha\simeq 47^{\circ}$ for SNR 0540-69.3. The straight orange line is the
expected random cumulative distribution function, while the convex blue line
is the expected cumulative distribution function when in all cases the three-
dimensional NS kick velocity is perpendicular to the jets’ axis.

The reason that in the jittering jets explosion mechanism the NS kick velocity
tends to be at a large angle to the main jet-axis is that dense ejecta clumps
accelerate the NS by the gravitational tug-boat mechanism (Nordhaus et al.
2010; Wongwathanarat et al. 2013; Janka 2017; for a different explanation for
kick velocities see, e.g., recent studies by Yao et al. 2021 and Xu et al.
2021). Bear & Soker (2018a) argue that either the jets prevent the formation
of dense clumps along their propagation direction, or that the dense clumps
also supply the gas to the accretion disk that launches the jets. In either
cases the jet-axis and the natal kick velocity direction cannot be too close
to each other.

##  4 Discussion and Summary

I examined the images and velocity maps of SNR 0540-69.3 that Larsson et al.
(2021) present in a recent study. I defined a faint strip (upper left panel of
Fig. 1) in the images of the different spectral lines, and based on similar
structures in a few other SNRs and in some planetary nebulae (e.g., Akashi et
al. 2018) I attributed the shaping of the faint strip to one or more pairs of
opposite jets. I termed this axis the main jet-axis.

Larsson et al. (2021) obtain the velocity maps, which I present here in Fig.
4, in a plane perpendicular to the plane of the sky by a slit that the two
dashed lines in two panels of Fig. 1 mark. In the velocity maps I identified a
point-symmetric structure that is defined by 8 clumps (Fig. 4). The four lines
that connect opposite clumps cross each other at what I identified as the
center of the structure. The direction of the slit almost coincides with the
main jet-axis, and therefore I take the main jet-axis to be part of the point
symmetric structure. Namely, the main jet-axis was shaped by two to four pairs
of jittering jets.

In section 2.2 I argued that the point symmetric structure in the plane of
Fig. 4 is compatible with the jittering jets explosion mechanism of CCSNe.
Actually, the jittering jets explosion mechanism predicts the common
occurrence of point-symmetric morphological features in remnants of CCSNe.
More than that, according to the jittering jets explosion mechanism in some
cases several consecutive pairs of jets will jitter in the same plane (Papish
& Soker 2014b). According to the interpretation I suggest here the elongation
of the PWN (e.g., Brantseg et al. 2014) in the same direction as the main jet-
axis results from the process by which the PWN plasma fills the less dense
volume that the jittering jets that exploded the star shaped (the faint
strip).

From the location of the pulsar relative to the main jet axis and the age of
$1100{~{}\rm yr}$ for SNR 0540-69.3 that Larsson et al. (2021) estimate, I
estimated the transverse (projected on the plane of the sky) pulsar natal kick
velocity to be $v_{\rm k,T}\simeq 235{~{}\rm km}{~{}\rm s}^{-1}$ at
$\alpha\simeq 47^{\circ}$ to the direction of the main jet-axis (red double-
lined arrow on the right panel of Fig. 2).

In Fig. 5 I present the cumulative distribution function of the jet-kick
angles of 13 SNRs, 12 SNRs from Bear & Soker (2018a) and the new addition of
$\alpha\simeq 47^{\circ}$ for SNR 0540-69.3. This distribution shows that the
NS natal kick direction and the main jets’-axis avoid small angles with
respect to each other. I discussed in section 3 the explanation for the
missing small values of $\alpha$ in the frame of the jittering jets explosion
mechanism.

Each jet inflates a bubble as it interacts with the core material that it
accelerates, and the interactions with each other of the bubbles that the
jittering jets inflate form a complicated flow structure in the exploding
core, i.e., vortexes (Papish & Soker 2014b). This implies that in addition to
instabilities (e.g., Utrobin et al. 2019) that occur also in the jittering
jets explosion mechanism, the jittering jets also mix elements in the
exploding core.

I here analysed only the inner ejecta with expanding velocities from the
explosion site of $\la 1000{~{}\rm km}{~{}\rm s}^{-1}$. I did not analyse the
[O III] irregular ring-like structure at a velocity of $\simeq 1600{~{}\rm
km}{~{}\rm s}^{-1}$ that Larsson et al. (2021) study in details. Larsson et
al. (2021) mention that the [O III] irregular ring-like structure of SNR
0540-69.3 might be similar to the CO torus expanding with a velocity of
$\simeq 1700{~{}\rm km}{~{}\rm s}^{-1}$ that ALMA observations reveal in SNR
1987A (Abellán et al. 2017). Bear & Soker (2018b) attributed the shaping of
the CO torus in SNR 1987A to jittering jets. I therefore propose here the
possibility that the [O III] irregular ring-like structure of SNR 0540-69.3
was compressed by two opposite jets with a jets’ axis perpendicular to the
plane of the [O III] irregular ring-like structure. This pair of jets was
launched at a different angle than the 4 pairs of jets in the plane of Fig. 4.

I also note that in a recent paper Leonard et al. (2021) interpret their
polarisation observation of Type II-P/L SN 2013ej as resulting from the
formation of high velocity ($\simeq 4000{~{}\rm km}{~{}\rm s}^{-1}$) nickel-56
clumps in the explosion. The jittering jets might explain such fast clumps.

Larsson et al. (2021) write in their conclusions that their results “add to
the growing evidence that rings and clumps are ubiquitous features of SN
ejecta, likely reflecting hydrodynamical instabilities in the explosions.” I
would add that these clumps, rings, and mixing reflect hydrodynamical
instabilities and jets in the explosion mechanism.

## Acknowledgments

I thank an anonymous referee for good suggestions. 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. (2018) Akashi, M., Bear, E., & Soker, N. 2018, MNRAS, 475, 4794. doi:10.1093/mnras/sty029
  * Aschenbach et al. (1995) Aschenbach, B., Egger, R., & Trümper, J. 1995, Nature, 373, 587
  * 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
  * 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
  * Blondin & Mezzacappa (2007) Blondin, J. M., & Mezzacappa, A. 2007, Nature, 445, 58
  * Brantseg et al. (2014) Brantseg, T., McEntaffer, R. L., Bozzetto, L. M., Filipovic, M., & Grieves, N., 2014, ApJ, 780, 50. doi:10.1088/0004-637X/780/1/50
  * De Luca et al. (2007) De Luca, A., Mignani, R. P., Caraveo, P. A., et al. 2007, ApJ, 667, L77. doi:10.1086/522033
  * Fernández (2015) Fernández, R. 2015, MNRAS, 452, 2071
  * Fransson et al. (2015) Fransson, C., Larsson, J., Migotto, K., et al. 2015, ApJ, 806, L19
  * Fransson et al. (2016) Fransson, C., Larsson, J., Spyromilio, J., Leibundgut, B., McCray, R., and Jerkstrand, A, 2016, ApJ, 821, L5
  * Gabler et al. (2021) Gabler, M., Wongwathanarat, A., & Janka, H.-T. 2021, MNRAS, 502, 3264. doi:10.1093/mnras/stab116
  * 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
  * Gilkis & Soker (2016) Gilkis, A., & Soker, N. 2016, ApJ, 827, 40
  * 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
  * Grichener & Soker (2017) Grichener, A., & Soker, N. 2017, MNRAS, 468, 1226
  * 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
  * Kazeroni et al. (2017) Kazeroni, R., Guilet, J., & Foglizzo, T. 2017, MNRAS, 471, 914
  * Kjær et al. (2010) Kjær, K., Leibundgut, B., Fransson, C., Jerkstrand, A., & Spyromilio, J. 2010, A&A, 517, A51
  * 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, arXiv:2109.03683
  * 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
  * Leonard et al. (2021) Leonard D. C., Dessart L., Hillier D. J., Pignata G., Williams G. G., Hoffman J. L., Milne P., et al., 2021, ApJL, 921, L35. doi:10.3847/2041-8213/ac31bf
  * Lopez et al. (2013) Lopez, L. A., Ramirez-Ruiz, E., Castro, D., & Pearson, S. 2013, ApJ, 764, 50
  * Lundqvist et al. (2011) Lundqvist, N., Lundqvist, P., Björnsson, C.-I., Olofsson, G., Pires, S., Shibanov, Y. A., & Zyuzin D. A. 2011, MNRAS, 413, 611. doi:10.1111/j.1365-2966.2010.18159.x
  * Lundqvist et al. (2021) Lundqvist, P., Lundqvist, N., & Shibanov, Y. A. 2021, arXiv:2109.03287
  * Matsuura et al. (2017) Matsuura, M., Indebetouw, R., Woosley, S., et al. 2017, MNRAS, 469, 3347
  * Mignani et al. (2010) Mignani, R. P., Sartori, A., de Luca, A., Rudak, B., Słowikowska, A., Kanbach, G., & Caraveo, P. A. 2010, A&A, 515, A110. doi:10.1051/0004-6361/200913870
  * Morse et al. (2006) Morse, J. A., Smith, N., Blair, W. P., Kirshner, R. P., Winkler, P. F., & Hughes, J. P. 2006, ApJ, 644, 188. doi:10.1086/503313
  * Nordhaus et al. (2010) Nordhaus, J., Brandt, T. D., Burrows, A., Livne, E., & Ott, C. D. 2010, Phys. Rev. D, 82, 103016
  * Orlando et al. (2016) Orlando, S., Miceli, M., Pumo, M. L., & Bocchino, F. 2016, ApJ, 822, 22
  * 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
  * Papish & Soker (2011) Papish, O., & Soker, N. 2011, MNRAS, 416, 1697
  * Papish & Soker (2014a) Papish, O., & Soker, N. 2014a, MNRAS, 438, 1027
  * Papish & Soker (2014b) Papish, O., & Soker, N. 2014b, MNRAS, 443, 664
  * Papish et al. (2015a) Papish, O., Gilkis, A., & Soker, N. 2015a, arXiv:1508.00218
  * Park et al. (2007) Park, S., Hughes, J. P., Slane, P. O., Burrows, D. N., Gaensler, B. M. and Ghavamian, P.. 2007, ApJ, 670, L121
  * 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
  * Rantsiou et al. (2011) Rantsiou, E., Burrows, A., Nordhaus, J., & Almgren, A. 2011, ApJ, 732, 57
  * Sahai (2000) Sahai R., 2000, ApJL, 537, L43. doi:10.1086/312748
  * 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
  * Serafimovich et al. (2005) Serafimovich, N. I., Lundqvist, P., Shibanov, Y. A., & Sollerman, J. 2005, Advances in Space Research, 35, 1106. doi:10.1016/j.asr.2005.01.071
  * Serafimovich et al. (2004) Serafimovich, N. I., Shibanov, Y. A., Lundqvist, P., & Sollerman, J. 2004, A&A, 425, 1041. doi:10.1051/0004-6361:20040499
  * Shishkin & Soker (2021) Shishkin, D. & Soker, N. 2021, MNRAS. doi:10.1093/mnrasl/slab105
  * Soker (2017) Soker, N. 2017, Research in Astronomy and Astrophysics, 17, 113. doi:10.1088/1674-4527/17/11/113
  * Utrobin et al. (2019) Utrobin, V. P., Wongwathanarat, A., Janka, H.-T., Müller, E., Ertl, T., & , S. E. 2019, A&A, 624, A116. doi:10.1051/0004-6361/201834976
  * Wang et al. (2002) Wang, L., Wheeler, J. C., Höflich, P., et al. 2002, ApJ, 579, 671
  * Wongwathanarat et al. (2013) Wongwathanarat, A., Janka, H.-T., & Müller, E. 2013, A&A, 552, A126
  * Wongwathanarat et al. (2017) Wongwathanarat, A., Janka, H.-T., Müller, E., Pllumbi, E., & Wanajo, S. 2017, ApJ, 842, 13
  * Wongwathanarat et al. (2015) Wongwathanarat, A., Müller, E., & Janka, H.-T. 2015, A&A, 577, A48. doi:10.1051/0004-6361/201425025
  * Xu et al. (2021) Xu, F., Geng, J.-J., Wang, X., Li, L., & Huang, Y.-F., 2021, arXiv:2109.11485
  * Yao et al. (2021) Yao, J., Zhu, W., Manchester, R. N., Coles, W. A., Li, D., Wang, N., Kramer, M., et al., 2021, Nature Astronomy, 5, 788. doi:10.1038/s41550-021-01360-w