Stalled Shock Research Articles

Low-energy Explosions in a Gravitational Field: Implications for Sub-energetic Supernovae and Fast X-Ray Transients

Observations and theory suggest that core-collapse supernovae can span a range of explosion energies, and when sub-energetic the shockwave initiating the explosion can decelerate to speeds comparable to the escape speed of the progenitor. In these cases, gravity will complicate the explosion hydrodynamics and conceivably cause the shock to stall at large radii within the progenitor star. To understand these unique properties of weak explosions, we develop a perturbative approach for modeling the propagation of an initially strong shock into a time-steady, infalling medium in the gravitational field of a compact object. This method writes the shock position and the post-shock velocity, density, and pressure as series solutions in the (time-dependent) ratio of the freefall speed to the shock speed, and predicts that the shock stalls within the progenitor if the explosion energy is below a critical value. We show that our model agrees very well with hydrodynamic simulations, and accurately predicts (for example) the time-dependent shock position and velocity and the radius at which the shock stalls. Our results have implications for black hole formation and the newly detected class of fast X-ray transients (FXTs). In particular, we propose that a “phantom shock breakout”—where the outer edge of the star falls through a stalled shock—can yield a burst of X-rays without a subsequent optical/UV signature, similar to FXTs. This model predicts the rise time of the X-ray burst, t d, and the mean photon energy, kT, are anticorrelated, approximately as T∝td−5/8 .

Gravitational-wave signature of core-collapse supernovae

We calculate the gravitational-wave (GW) signatures of detailed 3D core-collapse supernova simulations spanning a range of massive stars. Most of the simulations are carried out to times late enough to capture more than 95% of the total GW emission. We find that the f/g-mode and f-mode of proto-neutron star oscillations carry away most of the GW power. The f-mode frequency inexorably rises as the proto-neutron star (PNS) core shrinks. We demonstrate that the GW emission is excited mostly by accretion plumes onto the PNS that energize modal oscillations and also high-frequency (``haze") emission correlated with the phase of violent accretion. The duration of the major phase of emission varies with exploding progenitor and there is a strong correlation between the total GW energy radiated and the compactness of the progenitor. Moreover, the total GW emissions vary by as much as three orders of magnitude from star to star. For black-hole formation, the GW signal tapers off slowly and does not manifest the haze seen for the exploding models. For such failed models, we also witness the emergence of a spiral shock motion that modulates the GW emission at a frequency near $\sim$100 Hertz that slowly increases as the stalled shock sinks. We find significant angular anisotropy of both the high- and low-frequency (memory) GW emissions, though the latter have very little power.

Comparison of the Core-collapse Evolution of Two Nearly Equal-mass Progenitors

We compare the core-collapse evolution of a pair of 15.8 M ☉ stars with significantly different internal structures, a consequence of the bimodal variability exhibited by massive stars during their late evolutionary stages. The 15.78 and 15.79 M ☉ progenitors have core masses (masses interior to an entropy of 4 k B baryon−1) of 1.47 and 1.78 M ☉ and compactness parameters ξ 1.75 of 0.302 and 0.604, respectively. The core-collapse simulations are carried out in 2D to nearly 3 s postbounce and show substantial differences in the times of shock revival and explosion energies. The 15.78 M ☉ model begins exploding promptly at 120 ms postbounce when a strong density decrement at the Si–Si/O shell interface, not present in the 15.79 M ☉ progenitor, encounters the stalled shock. The 15.79 M ☉ model takes 100 ms longer to explode but ultimately produces a more powerful explosion. Both the larger mass accretion rate and the more massive core of the 15.79 M ☉ model during the first 0.8 s postbounce time result in larger ν e / luminosities and RMS energies along with a flatter and higher-density heating region. The more-energetic explosion of the 15.79 M ☉ model resulted in the ejection of twice as much 56Ni. Most of the ejecta in both models are moderately proton rich, though counterintuitively the highest electron fraction (Y e = 0.61) ejecta in either model are in the less-energetic 15.78 M ☉ model, while the lowest electron fraction (Y e = 0.45) ejecta in either model are in the 15.79 M ☉ model.

Spherically symmetric accretion on to a compact object through a standing shock: the effects of general relativity in the Schwarzschild geometry

ABSTRACT A core-collapse supernova is generated by the passage of a shock wave through the envelope of a massive star, where the shock wave is initially launched from the ‘bounce’ of the neutron star formed during the collapse of the stellar core. Instead of successfully exploding the star, however, numerical investigations of core-collapse supernovae find that this shock tends to ‘stall’ at small radii (≲10 neutron star radii), with stellar material accreting on to the central object through the standing shock. Here, we present time-steady, adiabatic solutions for the density, pressure, and velocity of the shocked fluid that accretes on to the compact object through the stalled shock, and we include the effects of general relativity in the Schwarzschild metric. Similar to previous works that were carried out in the Newtonian limit, we find that the gas ‘settles’ interior to the stalled shock; in the relativistic regime analysed here, the velocity asymptotically approaches zero near the Schwarzschild radius. These solutions can represent accretion on to a material surface if the radius of the compact object is outside of its event horizon, such as a neutron star; we also discuss the possibility that these solutions can approximately represent the accretion of gas on to a newly formed black hole following a core-collapse event. Our findings and solutions are particularly relevant in weak and failed supernovae, where the shock is pushed to small radii and relativistic effects are large.

Magnetic support for neutrino-driven explosion of 3D non-rotating core-collapse supernova models

ABSTRACT The impact of the magnetic field on post-bounce supernova dynamics of non-rotating stellar cores is studied by performing 3D magnetohydrodynamics simulations with spectral neutrino transport. The explodability of strongly and weakly magnetized models of 20 and 27 M⊙ pre-supernova progenitors are compared. We find that although the efficiency for the conversion of the neutrino heating into turbulent energy including magnetic fields in the gain region is not significantly different between the strong and weak field models, the amplified magnetic field due to the neutrino-driven convection on large hot bubbles just behind stalled shock results in a faster and more energetic explosion in the strongly magnetized models. In addition, by comparing the difference between the 2nd- and 5th-order spatial accuracy of the simulation in the strong field model for 27 M⊙ progenitor, we also find that the higher order accuracy in space is beneficial to the explosion because it enhances the growth of neutrino-driven convection in the gain region. Based on our results of core-collapse supernova simulations for the non-rotating model, a new possibility for the origin of the magnetic field of the protoneutron star (PNS) is proposed. The magnetic field is accumulated and amplified to magnetar level, that is, $\mathcal {O}(10^{14})$ G, in the convectively stable shell near the PNS surface.

Boosting Jittering Jets by Neutrino Heating in Core Collapse Supernovae

I estimate the energy that neutrino heating adds to the outflow that jets induce in the collapsing core material in core collapse supernovae (CCSNe), and find that this energy crudely doubles the energy that the jets deposit into the outer core. I consider the jittering jets explosion mechanism where there are several stochastic jet-launching episodes, each lasting for about 0.01–0.1 s. The collapsing core material passes through the stalled shock at about 100 km and then slowly flows onto the proto-neutron star (NS). I assume that the proto-NS launches jittering jets, and that the jets break out from the stalled shock. I examine the boosting process by which the high-pressure gas inside the stalled shock, the gain region material, expands alongside the jets and does work on the material that the jets shock, the cocoon. This work is crudely equal to the energy that the original jets carry. I argue that the coupling between instabilities, stochastic rotation, magnetic fields, and jittering jets leads to most CCSN explosions. In other cases, the pre-collapse core is rapidly rotating and therefore ordered rotation replaces stochastic rotation and fixed jets replace jittering jets.

Supplying angular momentum to the jittering jets explosion mechanism using inner convection layers

ABSTRACT We conduct one-dimensional stellar evolution simulations in the mass range 13–20 M⊙ to late core collapse times and find that an inner vigorous convective zone with large specific angular momentum fluctuations appears at the edge of the iron core during the collapse. The compression of this zone during the collapse increases the luminosity there and the convective velocities, such that the specific angular momentum fluctuations are of the order of $j_{\rm conv} \simeq 5 \times 10^{15} {~\rm cm}^2 {~\rm s}^{-1}$. If we consider that three-dimensional simulations show convective velocities that are three to four times larger than what the mixing length theory gives, and that the spiral standing accretion shock instability in the post-shock region of the stalled shock at a radius of ${\simeq}100 {~\rm km}$ amplifies perturbations, we conclude that the fluctuations that develop during core collapse are likely to lead to stochastic (intermittent) accretion discs around the newly born neutron star. In reaching this conclusion, we also make two basic assumptions with uncertainties that we discuss. Such intermittent discs can launch jets that explode the star in the frame of the jittering jets explosion mechanism.

On the Development of Multidimensional Progenitor Models for Core-collapse Supernovae

Abstract Multidimensional hydrodynamic simulations of shell convection in massive stars suggest the development of aspherical perturbations that may be amplified during iron core collapse. These perturbations have a crucial and qualitative impact on the delayed neutrino-driven core-collapse supernova explosion mechanism by increasing the total stress behind the stalled shock. In this paper, we investigate the properties of a 15 model evolved in one, two, and three dimensions (3D) for the final ∼424 s before gravitational instability and iron core collapse using Modules for Experiments in Stellar Astrophysics (MESA) and the FLASH simulation framework. We find that just before collapse, our initially perturbed fully 3D model reaches angle-averaged convective velocity magnitudes of ≈240–260 km s−1 in the Si- and O-shell regions with a Mach number of ≈0.06. We find the bulk of the power in the O-shell resides at large scales, characterized by spherical harmonic orders (ℓ) of 2–4, while the Si-shell shows broad spectra on smaller scales of . Both convective regions show an increase in power at near collapse. We show that the 1D MESA model agrees with the convective velocity profile and speeds of the Si-shell when compared to our highest resolution 3D model. However, in the O-shell region, we find that MESA predicts speeds approximately four times slower than all of our 3D models suggest. All eight of the multidimensional stellar models considered in this work are publicly available.

Is the SNR HESS J1731-347 Colliding with Molecular Clouds?

Abstract The supernova remnant HESS J1731-347 is a young supernova remnant (SNR) that displays a nonthermal X-ray and TeV shell structure. A molecular cloud at a distance of ∼3.2 kpc is spatially coincident with the western part of the SNR, and it was likely hit by the SNR. The X-ray emission from this part of the shell is much lower than from the rest of the SNR. Moreover, a compact GeV emission region coincident with the cloud has been detected with a soft spectrum. These observations seem to imply a shock-cloud collision scenario at this area, where the stalled shock can no longer accelerate super-TeV electrons or maintain strong magnetic turbulence downstream, while the GeV cosmic rays (CRs) are released through this stalled shock. To test this hypothesis, we have performed a detailed Fermi-LAT reanalysis of the HESS J1731-347 region with over nine years of data. Two distinct GeV components are found, one displaying a soft spectrum is from the compact GeV emission region, the other one displaying a hard spectrum is from the rest of the SNR (excluding the cloud region). A hadronic model involving a shock-cloud collision scenario is built to explain the γ-ray emission from this area. It consists of three CR sources: run-away super-TeV CRs that have escaped from the fast shock, leaked GeV CRs from the stalled shock, and the local CR sea. The X-ray and γ-ray emission of the SNR excluding the shock-cloud interaction region is explained in a one-zone leptonic model. Our shock-cloud collision model explains the GeV–TeV observations from the clouds around HESS J1731-347, i.e., a cloud in contact with the SNR and a distant cloud in spatial coincidence to the TeV source HESS J1729-345. We find however that the leaked GeV CRs from the shock-cloud collision do not necessarily dominate the GeV emission from the clouds, due to a comparable contribution from the local CR sea.

Wave heating from proto-neutron star convection and the core-collapse supernova explosion mechanism

ABSTRACT Our understanding of the core-collapse supernova explosion mechanism is incomplete. While the favoured scenario is delayed revival of the stalled shock by neutrino heating, it is difficult to reliably compute explosion outcomes and energies, which depend sensitively on the complex radiation hydrodynamics of the post-shock region. The dynamics of the (non-)explosion depend sensitively on how energy is transported from inside and near the proto-neutron star (PNS) to material just behind the supernova shock. Although most of the PNS energy is lost in the form of neutrinos, hydrodynamic and hydromagnetic waves can also carry energy from the PNS to the shock. We show that gravity waves excited by core PNS convection can couple with outgoing acoustic waves that present an appreciable source of energy and pressure in the post-shock region. Using one-dimensional simulations, we estimate the gravity wave energy flux excited by PNS convection and the fraction of this energy transmitted upwards to the post-shock region as acoustic waves. We find wave energy fluxes near $10^{51}\, \mathrm{erg}\, \mathrm{s}^{-1}\,$ are likely to persist for $\sim \! 1\, \mathrm{s}$ post-bounce. The wave pressure on the shock may exceed $10{{\ \rm per\ cent}}$ of the thermal pressure, potentially contributing to shock revival and, subsequently, a successful and energetic explosion. We also discuss how future simulations can better capture the effects of waves, and more accurately quantify wave heating rates.

Reviving the stalled shock by jittering jets in core collapse supernovae: jets from the standing accretion shock instability

I present a scenario by which an accretion flow with alternating angular momentum on to a newly born neutron star in a core collapse supernova (CCSN) efficiently amplifies magnetic fields and by that launches jets. The accretion flow of a collapsing core on to the newly born neutron star suffers spiral standing accretion shock instability (SASI). This instability leads to a stochastically variable angular momentum of the accreted gas, which in turn forms an accretion flow with alternating directions of the angular momentum, and hence alternating shear, at any given time. I study the shear in this alternating-shear sub-Keplerian inflow in published simulations, and present a new comparison with Keplerian accretion disks. From that comparison I argue that it might be as efficient as Keplerian accretion disks in amplifying magnetic fields by a dynamo. I suggest that although the average specific angular momentum of the accretion flow is small, namely, sub-Keplerian, this alternating-shear accretion flow can launch jets with varying directions, namely, jittering jets. Neutrino heating is an important ingredient in further energizing the jets. The jittering jets locally revive the stalled accretion shock in the momentarily polar directions, and by that they explode the star. I repeat again my call for a paradigm shift from a neutrino-driven explosion of CCSNe to a jet-driven explosion mechanism that is aided by neutrino heating.

Storing magnetic fields in pre-collapse cores of massive stars

We argue that the radiative zone above the iron core in pre-collapse cores of massive stars can store strong magnetic fields. To reach this conclusion we use the stellar evolutionary code MESA to simulate the evolution of two stellar models with initial masses of 15Mo and 25Mo, and reveal the entropy profile above the iron core just before core collapse. Just above the iron core there is a thin zone with convective shells. We assume that a dynamo in these convective shells amplifies magnetic fields and forms magnetic flux loops. By considering the buoyancy of magnetic flux loops we show that the steep entropy rise in the radiative zone above the dynamo can prevent buoyancy of flux loops with magnetic fields below about 10^{13}G. When this radiative zone collapses on to the newly born neutron star the converging inflow further amplifies the magnetic fields by a factor of about a hundred. After passing through the stalled shock at about a hundred kilometres from the center, these strong magnetic fields together with instabilities can facilitate the launching of jets that explode the star in the frame of the jittering jets explosion mechanism. Our study further supports the claim for the necessity to include magnetic fields in simulating the explosion of CCSNe.

Three-dimensional Core-collapse Supernova Simulations with Multidimensional Neutrino Transport Compared to the Ray-by-ray-plus Approximation

Abstract Self-consistent, time-dependent supernova (SN) simulations in three spatial dimensions (3D) are conducted with the Aenus-Alcar code, comparing, for the first time, calculations with fully multidimensional (FMD) neutrino transport and the ray-by-ray-plus (RbR+) approximation, both based on a two-moment solver with algebraic M1 closure. We find good agreement between 3D results with FMD and RbR+ transport for both tested grid resolutions in the cases of a 20 M ⊙ progenitor, which does not explode with the employed simplified set of neutrino opacities, and of an exploding 9 M ⊙ model. This is in stark contrast to corresponding axisymmetric (2D) simulations, which confirm previous claims that the RbR+ approximation can foster explosions in 2D, particularly in models with powerful axial sloshing of the stalled shock due to the standing accretion shock instability. However, while local and instantaneous variations of neutrino fluxes and heating rates can still be considerably higher with RbR+ transport in 3D, the time-averaged quantities are very similar to FMD results, because of the absence of a fixed, artificial symmetry axis that channels the flow. Therefore, except for stochastic fluctuations, the neutrino signals and the postbounce evolution of 3D simulations with FMD and RbR+ transport are also very similar, particularly for our calculations with the better grid resolution. Higher spatial resolution clearly has a more important impact than the differences due to the two transport treatments. Our results back up the use of the RbR+ approximation for neutrino transport in 3D SN modeling.

Three-dimensional supernova explosion simulations of 9-, 10-, 11-, 12-, and 13-M⊙ stars

Abstract Using the new state-of-the-art core-collapse supernova (CCSN) code fornax, we have simulated the three-dimensional dynamical evolution of the cores of 9-, 10-, 11-, 12-, and 13-M⊙ stars from the onset of collapse. Stars from 8 to 13 M⊙ constitute roughly 50 per cent of all massive stars, so the explosive potential for this mass range is important to the overall theory of CCSNe. We find that the 9-, 10-, 11-, and 12-M⊙ models explode in 3D easily, but that the 13-M⊙ model does not. From these findings, and the fact that slightly more massive progenitors seem to explode, we suggest that there is a gap in explodability near 12 to 14 M⊙ for non-rotating progenitor stars. Factors conducive to explosion are turbulence behind the stalled shock, energy transfer due to neutrino–matter absorption and neutrino–matter scattering, many-body corrections to the neutrino–nucleon scattering rate, and the presence of a sharp silicon–oxygen interface in the progenitor. Our 3D exploding models frequently have a dipolar structure, with the two asymmetrical exploding lobes separated by a pinched waist where matter temporarily continues to accrete. This process maintains the driving neutrino luminosity, while partially shunting matter out of the way of the expanding lobes, thereby modestly facilitating explosion. The morphology of all 3D explosions is characterized by multiple bubble structures with a range of low-order harmonic modes. Though much remains to be done in CCSN theory, these and other results in the literature suggest that, at least for these lower mass progenitors, supernova theory is converging on a credible solution.

Effects of Rotation and Magnetic Field on the Revival of a Stalled Shock in Supernova Explosions

Abstract We investigate axisymmetric steady solutions of (magneto)hydrodynamics equations that approximately describe accretion flows through a standing shock wave onto a protoneutron star and discuss the effects of rotation and magnetic field on the revival of the stalled shock wave in supernova explosions. We develop a new powerful numerical method to calculate the two-dimensional steady accretion flows self-consistently. We first confirm the results of preceding papers that there is a critical luminosity of irradiating neutrinos, above which there exists no steady solution in spherical models. If a collapsing star is rotating and/or has a magnetic field, the accretion flows are no longer spherical owing to the centrifugal force and/or Lorentz force, and the critical luminosity is modified. In fact, we find that the critical luminosity is reduced by about 50%–70% for very rapid rotations; the rotation frequencies are 0.2–0.45 s−1 at the radius of r = 1000 km (equivalent to spin periods ∼0.5–0.22 ms at r = 10 km) and about 20%–50% for strong toroidal magnetic fields (the strengths of which are 1.0 × 1012–3.0 × 1012 G at r = 1000 km), depending on the mass accretion rate. These results may also be interpreted as the existence of a critical specific angular momentum or critical magnetic field, above which there exists no steady solution and the standing shock wave will be revived for a given combination of mass accretion rate and neutrino luminosity.

Heavy sterile neutrinos in stellar core-collapse

We perform spherically symmetric simulations of the core collapse of a single progenitor star of zero age main sequence mass $M_{\rm ZAMS} = 15 \, M_{\odot}$ with two models of heavy sterile neutrinos in the mass range of hundred MeV$/c^2$. According to both models, these hypothetical particles are copiously produced in the center, stream outwards a subsequently decay releasing energy into final states (including neutrinos) of the Standard Model. We find that they can lead to a successful explosion in otherwise non-exploding progenitors. Depending on their unknown parameters (e.g., mass and coupling constants with matter), we obtain either no explosion or an explosion of one of two types, i.e., through heating of gas downstream of the stalled shock wave, similarly to the standard scenario for supernova explosions or through heating of gas at higher radii that ejects matter from the outer core or the envelope while the center continues to accrete matter. In both cases, the explosion energies can be very high. We presume that this new type of explosion would produce an electromagnetic signal that significantly differs from common events because of the relative absence of heavy elements in the ejecta. The combination of core-collapse simulations and astrophysical observations may further constrain the parameters of the sterile neutrinos.

Revival of the fittest: exploding core-collapse supernovae from 12 to 25 M⊙

We present results of 2D axisymmetric core-collapse supernova simulations, employing the FORNAX code, of nine progenitor models spanning 12 to 25 M$_{\odot}$ and evolved over a 20,000-km grid. We find that four of the nine models explode with inelastic scattering off electrons and neutrons as well as the many-body correction to neutrino-nucleon scattering opacities. We show that these four models feature sharp Si-O interfaces in their density profiles, and that the corresponding dip in density reduces the accretion rate around the stalled shock and prompts explosion. The non-exploding models lack such a steep feature, suggesting that Si-O interface is one key to explosion. Furthermore, we show that all of the non-exploding models can be nudged to explosion with modest changes to macrophysical inputs, including moderate rotation and perturbations to infall velocities, as well as to microphysical inputs, including changes to neutrino-nucleon interaction rates, suggesting that all the models are perhaps close to criticality. Exploding models have energies of few $\times$10$^{50}$ ergs at the end of our simulation, and are rising, suggesting the need to continue these simulations over larger grids and for longer times to reproduce the energies seen in Nature. We find that the morphology of the explosion contributes to the explosion energy, with more isotropic ejecta producing larger explosion energies. However, we do not find evidence for the Lepton-number Emission Self-Sustained Asymmetry. Finally, we look at PNS properties and explore the role of dimension in our simulations. We find that convection in the proto-neutron star (PNS) produces larger PNS radii as well as greater "$\nu_\mu$" luminosities in 2D compared to 1D.

A Parametric Study of the Acoustic Mechanism for Core-collapse Supernovae

Abstract We investigate the criterion for the acoustic mechanism to work successfully in core-collapse supernovae. The acoustic mechanism is an alternative to the neutrino-heating mechanism. It was proposed by Burrows et al., who claimed that acoustic waves emitted by g-mode oscillations in proto-neutron stars (PNS) energize a stalled shock wave and eventually induce an explosion. Previous works mainly studied to which extent the g-modes are excited in the PNS. In this paper, on the other hand, we investigate how strong the acoustic wave needs to be if it were to revive a stalled shock wave. By adding the acoustic power as a new axis, we draw a critical surface, which is an extension of the critical curve commonly employed in the context of neutrino heating. We perform both 1D and 2D parametrized simulations, in which we inject acoustic waves from the inner boundary. In order to quantify the power of acoustic waves, we use the extended Myers theory to take neutrino reactions into proper account. We find for the 1D simulations that rather large acoustic powers are required to relaunch the shock wave, since the additional heating provided by the secondary shocks developed from acoustic waves is partially canceled by the neutrino cooling that is also enhanced. In 2D, the required acoustic powers are consistent with those of Burrows et al. Our results seem to imply, however, that it is the sum of neutrino heating and acoustic powers that matters for shock revival.

PROGENITOR-DEPENDENT EXPLOSION DYNAMICS IN SELF-CONSISTENT, AXISYMMETRIC SIMULATIONS OF NEUTRINO-DRIVEN CORE-COLLAPSE SUPERNOVAE

ABSTRACT We present self-consistent, axisymmetric core-collapse supernova simulations performed with the Prometheus-Vertex code for 18 pre-supernova models in the range of 11–28 M ⊙, including progenitors recently investigated by other groups. All models develop explosions, but depending on the progenitor structure, they can be divided into two classes. With a steep density decline at the Si/Si–O interface, the arrival of this interface at the shock front leads to a sudden drop of the mass-accretion rate, triggering a rapid approach to explosion. With a more gradually decreasing accretion rate, it takes longer for the neutrino heating to overcome the accretion ram pressure and explosions set in later. Early explosions are facilitated by high mass-accretion rates after bounce and correspondingly high neutrino luminosities combined with a pronounced drop of the accretion rate and ram pressure at the Si/Si–O interface. Because of rapidly shrinking neutron star radii and receding shock fronts after the passage through their maxima, our models exhibit short advection timescales, which favor the efficient growth of the standing accretion-shock instability. The latter plays a supportive role at least for the initiation of the re-expansion of the stalled shock before runaway. Taking into account the effects of turbulent pressure in the gain layer, we derive a generalized condition for the critical neutrino luminosity that captures the explosion behavior of all models very well. We validate the robustness of our findings by testing the influence of stochasticity, numerical resolution, and approximations in some aspects of the microphysics.

Supernova deleptonization asymmetry: Impact on self-induced flavor conversion

During the accretion phase of a core-collapse supernova (SN), the deleptonization flux has recently been found to develop a global dipole pattern (LESA---Lepton Emission Self-sustained Asymmetry). The $\nu_e$ minus $\bar\nu_e$ flux essentially vanishes in one direction, potentially facilitating self-induced flavor conversion. On the other hand, below the stalled shock wave, self-induced flavor conversion is typically suppressed by multi-angle matter effects, preventing any impact of flavor conversion on SN explosion dynamics. In a schematic model of SN neutrino fluxes, we study the impact of modified $\bar\nu_e$-$\nu_e$ flux asymmetries on collective flavor conversion. In the parameter space consisting of matter density and effective neutrino density, the region of instability with regard to self-induced flavor conversion is much larger for a vanishing lepton number flux, yet this modification does not intersect a realistic SN profile. Therefore, it appears that, even in the presence of LESA, self-induced flavor conversion remains suppressed below the shock front.