# Jet - counter-jet asymmetry in the jittering jets explosion mechanism of
supernovae

Noam Soker  Department of Physics, Technion, Haifa, 3200003, Israel;
<EMAIL_ADDRESS>
###### Abstract

I identify a point-symmetric morphology composed of three pairs of ears (small
lobes) in the X-ray images of the core-collapse supernova remnant (CCSNR) N63A
and argue that this morphology supports the jittering jets explosion mechanism
(JJEM). The opposite two ears in each of the three pairs of SNR N63A are not
equal to each other as one is larger than the other. From the morphology of
SNR N63A, I infer that this asymmetry is due to asymmetrical opposite jets at
launching. Namely, the newly born neutron star that launches the jets that
explode the star, does it in many cases with one jet more powerful than its
counter-jet. I propose that this asymmetry results from that the accretion
disk that launches the jets has no time to fully relax during a jet-launching
episode. This implies that if the disk is born with two unequal sides as
expected in the JJEM, then during a large fraction, or even all, of the jet-
launching episode the two sides remain unequal. I also show that the magnetic
reconnection timescale, which is about the timescale for the magnetic field to
relax, is not much shorter than the jet-launching episode, therefore the two
sides of the accretion disk might have a different magnetic structure. The
unequal sides of the accretion disk launch two opposite jets with different
energy from each other.

###### keywords:

stars: massive – stars: neutron – supernovae: general – stars: jets – ISM:
supernova remnants

##  1 Introduction

In core-collapse supernovae (CCSNe) the inner core collapses to form a neutron
(NS), a process that releases a gravitational energy of $\simeq{\rm few}\times
10^{53}{~{}\rm erg}$. Most of this energy is carried by neutrinos, while the
rest explodes the star with explosion energies of $E_{\rm exp}\approx
10^{49}-10^{52}{~{}\rm erg}$. Studies in recent years discuss one of two
explosion mechanisms that utilize a small fraction of the gravitational energy
towards explosion. These are the delayed neutrino explosion mechanism (e.g.,
Bethe & Wilson 1985; Heger et al. 2003; Janka 2012; Nordhaus et al. 2012;
Müller et al. 2019; Fujibayashi et al. 2021; Fryer, Olejak, & Belczynski 2022;
Boccioli et al. 2022; Nakamura, Takiwaki, & Kotake 2022; Olejak et al. 2022;
Boccioli et al. 2023; Burrows, Vartanyan, & Wang 2023) and the jittering jets
explosion mechanism (JJEM; e.g., Soker 2010, 2020, 2022a, 2023a; Papish &
Soker 2011; Gilkis & Soker 2014, 2016; Quataert et al. 2019; Shishkin & Soker
2021, 2023; Antoni & Quataert 2022, 2023).

In the JJEM the explosion is driven by jets that intermittent accretion disks,
or even sub-Keplerian belts (e.g., Schreier & Soker 2016) around the newly
born NS launch at 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). There are $\approx{\rm few}$ to $\approx 30$ jet-
launching episodes, in each the jets carry a mass of $\approx
10^{-3}M_{\odot}$. In each episode, the accretion disk launches two opposite
jets along an axis that (almost) stochastically varies from one episode to the
next. If there is pre-explosion core rotation then the jets’ axis variation is
not completely stochastic (e.g., Soker 2023a). Also, the back reaction of the
jets on the accreted mass acts to have the jets’ axis in the same plane that
is defined by the jets’ axes of the two previous episodes (Papish & Soker,
2014). The total jet-activity phase lasts for $\simeq 1-10{~{}\rm s}$ or even
longer in some electron capture CCSNe (Wang, Shishkin, & Soker 2024). Each
jet-launching episode lasts for $\tau_{\rm jet}\simeq 0.01-0.1\sec$, a
timescale that is central to the present study.

The angular momentum of the accreted mass in the JJEM starts with stochastic
pre-collapse core convection motion (e.g., Soker 2010; Papish & Soker 2014;
Gilkis & Soker 2015; Soker 2019a; Shishkin & Soker 2022; Soker 2022b), or in
some cases with envelope convection motion (e.g., Quataert et al. 2019; Antoni
& Quataert 2022, 2023), in particular in electron capture CCSNe (Wang,
Shishkin, & Soker, 2024). According to the JJEM, the seed angular momentum
perturbations of the pre-collapse convective cells are substantially amplified
by instabilities between the newly born NS and the stalled shock at $\simeq
100{~{}\rm km}$ (e.g., see discussion by Shishkin & Soker 2021).

One prediction of the delayed neutrino explosion mechanism is the existence of
failed CCSNe (e.g., Kuroda & Shibata 2023 for a very recent paper). The JJEM
predicts no failed CCSNe (e.g., Soker 2022c for a review). Recent studies that
find no observational evidence for the existence of a large failed CCSN
population (e.g., Byrne & Fraser 2022; Strotjohann, Ofek, & Gal-Yam 2024)
indirectly support the JJEM.

The JJEM implies that in some (but not all) cases several pairs of jets, the
last jets to be launched, shape the CCSN remnant (CCSNR) to have a point-
symmetric morphology. Namely, a supernova remnant (SNR) structure where there
are two or more morphological features each with a counter-morphological
feature on the opposite side of the center of the CCSNR. Such point-symmetry
is not possible to form by jet-driven explosions that operate only for rare
cases of rapidly rotating pre-collapse cores (e.g., Khokhlov et al. 1999;
Maeda et al. 2012; López-Cámara et al. 2013; Bromberg & Tchekhovskoy 2016;
Nishimura et al. 2017; Wang, Wang, & Dai 2019; Grimmett et al. 2021; Gottlieb
et al. 2022; Obergaulinger & Reichert 2023; Urrutia, De Colle, & López-Cámara
2023) because in these cases the jets maintain a fixed axis. Instabilities
alone, as in the delayed neutrino explosion mechanism (e.g., Wongwathanarat,
Müller, & Janka 2015; Wongwathanarat et al. 2017; Burrows & Vartanyan 2021;
Vartanyan, Coleman, & Burrows 2022), cannot account for point-symmetric
morphologies because instabilities form stochastic morphological features
rather than pairs on opposite sides of the center of the explosion.

In three recent studies, I explored the point-symmetric morphology of three
CCSNRs and argue that these strongly support the JJEM, SNR 0540-69.3 (Soker,
2022a), the Vela SNR (Soker, 2023b), and possibly SN 1987A (Soker, 2023c). In
this paper, I present the point-symmetric morphology of SNR N63A (section 2)
as I identify by six ears in its images (e.g., Karagöz et al. 2023 for recent
images), and use the unequal ears within each pair to infer about the
jittering jet properties at launching (section 3). I summarize this study in
section 4.

##  2 Pairs of ears in supernova remnant N63A

I examine Chandra X-ray observations (e.g., Warren, Hughes, & Slane 2003;
Schenck, Park, & Post 2016) and analyze the morphology of the Large Magellanic
Cloud SNR N63A, which is a CCSNR (e.g., Warren, Hughes, & Slane 2003;
Yamaguchi et al. 2014). Optical (e.g., Chu & Kennicutt 1988) and radio (e.g.,
Sano et al. 2019) images reveal only small areas of SNR N63A, and do not help
the present analysis.

In Figure 1 I present an X-ray image from Figure 2C of Karagöz et al. (2023).
I added the three red rectangles that connect the two ears of the three pairs.
The asterisk inside each rectangle marks its center. I label the ears by three
pairs 1a-1b, 2a-2b, and 3a-3b. The blue-dashed ellipse is by-eye fitting to
the outskirt of the SNR. The thick blue-dashed line along the minor axis of
the ellipse splits the plane into region A in the northeast and region B in
the southwest. The double-headed blue-dashed line marks what might be the
projected (on the plane of the sky) long axis of the SNR. It might more or
less coincide with a slow pre-collapse angular momentum of the core because in
such a case the jets might jitter around the pre-collapse angular momentum
axis. This requires further study. In Figure 2 I present an X-ray image based
on three energy bands, and with an optical image that shows the presence of an
ISM or a CSM cloud (e.g., Chu 2001; Sano et al. 2019). I do not refer to this
cloud in the morphological analysis. I added three lines in Figure 2 that
connect the tips of opposite ears.

Figure 1: A logarithmic-scale $0.3-7.0{~{}\rm keV}$ X-ray Chandra image of SNR
N63A adapted from figure 2C of Karagöz et al. (2023). The green lines and the
small-yellow writings are from the original figure of Karagöz et al. (2023). I
added the red-solid lines, the dashed-blue lines, and the red and the blue
writing.  Figure 2: A Chandra X-ray (red, green, blue for different X-ray
energy bands). The light brown region to the upper right of the three red
lines is optical light detected by Hubble. (Credit: Enhanced Image by Judy
Schmidt based on images provided courtesy of NASA/CXC/SAO & NASA/STScI.) I
added three lines that I drew between the tips of opposite ears.

Considering that none of the ears has a symmetrical structure around the axis
that connects it to its counter ear, it is expected that the centers of the
three pairs of ears, as marked by three red asterisks on Figure 1, and the
center of the ellipse, where the two blue-dashed lines cross each other, do
not exactly overlap. Nonetheless, the centers are sufficiently close to each
other to define a point-symmetric morphology for SNR N63A that is based on
ears.

The morphology of SNR N63A reveals the following prominent properties and
their relevance to the analysis to follow in section 3.

  1. 1.

It has a point symmetric structure defined by the six ears (for morphological
classification according to shaping by jets see Soker 2023b). This supports
the JJEM as instabilities alone and fixed-axis jets do not form such
morphologies (section 1).

  2. 2.

There is a small signature of elongation along the northeast (region A) to
southwest (region B) direction, as indicated by the double-headed blue-dashed
line in Figure 1. As said, it might indicate a slow pre-collapse core rotation
around which the late jets that shape the SNR jitter (Soker, 2023a). The same
symmetry defines region A where ears 1a-3a reside and region B where ears
1b-3b reside.

  3. 3.

Opposite ears do not have the same size, i.e., the projected area on the plane
of the sky of an ear is not equal to that of its counter-ear. Two types of
processes can cause this asymmetry, either the two opposite jets are unequal
at launching or the two sides of the SNR with which equal opposite jets
interact are not equal to each other. It does not seem that the effect is due
to asymmetrical material in regions A and B because while $S_{\rm 2a}<S_{\rm
2b}$ and $S_{\rm 3a}<S_{\rm 3b}$, for pair number 1 the inequality is $S_{\rm
1a}>S_{\rm 1b}$. I take this to imply that the asymmetry between two opposite
ears results from jet-counter-jet asymmetry during the jets’ launching process
rather than the influence of the medium with which the jets interact. This is
the subject of section 3.

##  3 Accounting for unequal pairs of jets

###  3.1 Short jet-launching episodes

The conclusion of section 2 is that the three pairs of ears that compose the
point-symmetric morphology of SNR N63A were shaped by three pairs of jittering
jets wherein each of the jet-launching episodes there was a jet-counter-jet
asymmetry. Namely, in the launching process, one jet was more energetic than
the other. Many other CCSNRs, in most of them there is only one pair of ears
(Soker, 2023b), have unequal opposite ears (e.g, Bear, Grichener, & Soker
2017; Grichener & Soker 2017; Soker 2023b). This jet-counter-jet asymmetry is
unlike most other astrophysical objects, from young stellar objects to active
galactic nuclei, where in most (but not all) cases the the two opposite jets
are about equal to each other, i.e., having no or only a small asymmetry. I am
discussing here a possible explanation of the unique physical conditions of
the JJEM.

I attribute the asymmetrical jets to the relatively (to other types of
systems) small ratio of the total lifetime of the accretion disk to the
orbital period of the accretion disk that launches the jets. The accretion
disk is extended and therefore I scale the orbital period with a typical
radius of the accretion disk around the newly born NS, which has not relaxed
yet to its final radius of $\simeq 12{~{}\rm km}$. Each accretion disk that
launches one pair of jets in a jet-launching episode in the JJEM lasts for a
typical time of $\tau_{\rm jet}\simeq 0.01-0.1{~{}\rm s}$ (section 1). The
orbital period of a test particle that orbits the newly born NS, of mass
$M_{\rm NS}\simeq 1.4M_{\odot}$, at a radius of $r\simeq 20{~{}\rm km}$ is
$\tau_{\rm Kep}\simeq 2\pi r^{3/2}/\sqrt{GM_{\rm NS}}\simeq 0.0013(r/20{~{}\rm
km})^{3/2}{~{}\rm s}$. I take from now on $M_{\rm NS}\simeq 1.4M_{\odot}$ as
the analysis is weakly sensitive to the exact NS mass. I neglect relativistic
effects which are small, $\simeq 10\%$ effect, compared with the other
uncertainties to follow, like the viscosity in the disk and the magnetic
reconnection rate. The important ratio in the JJEM is

$\left(\frac{\tau_{\rm jet}}{\tau_{\rm Kep}}\right)_{\rm JJ}\simeq
40\left(\frac{r}{20{~{}\rm km}}\right)^{-3/2}\left(\frac{\tau_{\rm
jet}}{0.05{~{}\rm s}}\right).$ (1)

For the relevant parameters of the JJEM, this can also be expressed as

$1\lesssim\log\left(\frac{\tau_{\rm jet}}{\tau_{\rm Kep}}\right)_{\rm
JJ}\lesssim 2.$ (2)

In most other astrophysical systems the accretion disk lives much longer and
the ratio is $\log({\tau_{\rm jet}}/{\tau_{\rm Kep}})\gg 2$. The relatively
small (with respect to other astrophysical systems) ratio in equation (2)
explains the jet-counter-jet asymmetry, as I explain now by considering two
other timescales that are related to $\tau_{\rm Kep}$.

###  3.2 The viscous relaxation timescale

Consider the supply of material with specific angular momentum $j$ that
corresponds to a circular orbit at $r\simeq j^{2}/GM_{\rm NS}$. The material
settled into a more or less steady-state accretion disk on a viscosity
timescale. There are large uncertainties in the value of the viscosity in the
accretion disk. In relaxed (stead-state) thin accretion disks where the scale
height of the disk at radius $r$ is $H(r)$ and with the usage of the $\alpha$
parameter (e.g., Shakura & Sunyaev 1973), the viscous timescale is

$\tau_{\rm vis}\simeq\left(\frac{r}{H}\right)^{2}\frac{1}{2\pi\alpha}\tau_{\rm
Kep},$ (3)

Considering that the disk would settle to a thin accretion disk, $H(r)\simeq
0.1r$, if has enough time, the viscous time is

$\tau_{\rm vis}\simeq
0.02\alpha^{-1}\left(\frac{r}{10H}\right)^{2}\left(\frac{r}{20{~{}\rm
km}}\right)^{3/2}{~{}\rm s}.$ (4)

This leads to the ratio of

$0\la\log\left(\frac{\tau_{\rm jet}}{\tau_{\rm vis}}\right)_{\rm JJ}\lesssim
1.$ (5)

This implies that for a relatively long time during a jet-launching episode,
or even during the entire episode, the accretion disk is not relaxed. If the
perturbations, that must exist in the JJEM, form initial two unequal sides of
the accretion disk, for a large fraction, possibly for most or even all, of
the jet-launching episode they remain unequal. They will therefore launch
unequal opposite jets, i.e., one will be more powerful than the other.

The relation in equation (5) is in contrast with the majority of other
astrophysical objects launching jets for which $\log\left({\tau_{\rm
jet}}/{\tau_{\rm vis}}\right)\gg 1$, and therefore the two sides of the
accretion disk have time to relax to the same structure and the same physical
conditions with each other during a short fraction of the jet launching
episode duration. In those other cases, the accretion disk will launch two
symmetrical opposite jets. However, from equation (5) the jets will not be
equal to each other in many cases of the JJEM.

###  3.3 The magnetic reconnection timescale

Magnetic fields play important roles in the launching process of jets. The
rearrangement of magnetic fields involves reconnection. The typical timescale
of reconnection is (e.g., Parker 1979) $\tau_{\rm rec}\simeq l_{B}/(\epsilon
v_{\rm A})$, where $l_{B}$ is the size of the reconnecting magnetic field,
$v_{\rm A}=B/\sqrt{4\pi\rho}$ is the Alfven speed, $\rho$ is the density, and
$\epsilon\approx 0.1$. If the accretion disk is supported by the pressure of
the magnetic field, namely, $v_{\rm A}>C_{s}$, where $C_{s}$ is the sound
speed, then the height of the disk is $H(r)\simeq rv_{\rm A}/v_{\rm Kep}$,
where $v_{\rm Kep}$ is the orbital velocity of the gas around the newly born
NS (I neglect relativistic effects). The reconnection timescale is

$\tau_{\rm rec}\simeq\frac{l_{B}}{\epsilon v_{\rm A}}\simeq
1.6\left(\frac{l_{B}}{H}\right)\left(\frac{\epsilon}{0.1}\right)^{-1}\tau_{\rm
Kep}.$ (6)

If the magnetic pressure is smaller than the thermal plus radiation pressure,
then the reconnection timescale is larger even. Overall, the reconnection
timescale might be not much shorter than the jet-activity period of one jet-
launching episode. This relation reads

$0\lesssim\log\left(\frac{\tau_{\rm jet}}{\tau_{\rm rec}}\right)_{\rm
JJ}\lesssim 1.5.$ (7)

This shows that during a large fraction of the jet-launching episode, the
accretion disk might not relax to have a symmetrical magnetic structure on
both its sides. This is different from most other astrophysical systems where
$\log(\tau_{\rm jet}/\tau_{\rm rec})\gg 2$ and for which the two sides of the
accretion disk reach symmetrical magnetic fields with respect to each other.

##  4 Summary

I analyzed the X-ray morphology of the CCSNR N63A and concluded that it
possesses a point-symmetric structure of three pairs of ears. I also argued in
section 2 that the only viable explanation is the JJEM. Namely, N63A was
exploded by jittering jets. In that, CCSNR N63A is the fourth CCSNR with
point-symmetric morphology; the others are SNR 0540-69.3 (Soker, 2022a), the
Vela SNR (Soker, 2023b), and possibly SN 1987A (Soker, 2023c). All these
strongly support the JJEM and pose challenges to the delayed neutrino
explosion mechanism.

The opposite two ears in each of the three pairs of SNR N63A are not equal to
each other. This is a common property of opposite pairs of ears in CCSNRs,
including those with only one pair of ears (e.g., Soker (2023b)). The ears in
a pair are not equal to each other in one or more of their properties,
including size, intensity, and distance from the center (e.g., Soker 2023b). I
used the morphology of SNR N63A to infer that this asymmetry is due to
asymmetrical opposite jets at launching, rather than the unequal environment
with which the jets interact as they inflate the ears. In section 3 I proposed
an explanation for the observation that in most CCSNRs the two ears (or lobes)
in a pair are not equal to each other.

I proposed that the different powers of the two opposite jets at launching
results from that the accretion disk that launches the jets has no time to
fully relax during a jet-launching episode. This implies that if the disk is
born with two unequal sides, then during a large fraction, or even all, of the
jet-launching episode the two sides remain unequal. In the JJEM that is based
on instabilities and angular momentum fluctuations of the accrete gas, it is
very likely that each accretion disk is born with unequal sides. I showed that
the viscous relaxation timescale is not much shorter than the jet-launching
episode (equation 5). I also showed that the magnetic reconnection timescale,
which is about the timescale for the magnetic field to relax, is not much
shorter than the jet-launching episode in the JJEM (equation 7).

I propose that the two unequal sides of the accretion disk in each jet-
launching episode are likely to launch unequal jets that in turn inflate
unequal ears. This assertion requires further study.

Overall, the morphology of CCSNR N63A supports the JJEM and offers an
explanation for the common occurrence of unequal opposite ears in CCSNRs.

## Acknowledgements

This research was supported by a grant from the Pazy Research Foundation.

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