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Lorenzo Roberti

Publications and source records attributed to Lorenzo Roberti.

At least 19 recordsLinked to original sources

Explodability matters: how realistic neutrino-driven explosions change explosive nucleosynthesis yields

Explosive nucleosynthesis is affected by many uncertainties, particularly regarding assumptions and prescriptions adopted during the evolution of the star. Moreover, simple explosion models are often used in the literature, which can introduce large errors in the assumed explosion energy and mass cut. In this paper, our goal is to analyze the explosion properties and nucleosynthesis of a large range of progenitors from three different stellar evolution codes: FRANEC, KEPLER, and MESA. In particular, we will show the differences between the neutrino-driven explosions simulated in this work with the much simpler bomb and piston models that are typically widely used in the literature. We will then focus on the impact of different explodabilities and different explosion dynamics on the nucleosynthetic yields. We adopt the neutrino-driven core-collapse supernova explosion code GR1D+, i.e. a spherically symmetric model with state-of-the-art microphysics and neutrino transport and a time-dependent mixing-length model for neutrino-driven convection. We carry out explosions up to several seconds after bounce, and then calculate the nucleosynthetic yields with the post-processing code SkyNet. We find that our 1D+ simulations yield explosion energies and remnant masses in agreement with observations of type II-P, IIb, and Ib supernovae, as well as with the most recent 3D simulations of the explosion. We provide a complete set of yields for all the stars simulated, including rotating, low-metallicity, and binary progenitors. Finally, we find that piston and bomb models, compared to more realistic neutrino-driven explosions, can artificially increase the production of Fe-peak elements, whereas the different explodability tends to cause discrepancies in the lighter elements.

astro-ph.HE

An updated picture of pre-solar history from short-lived radioactive isotopes and inferences on the birth of the Sun

We examine the origin of the short-lived radionuclides (SLRs, defined as having half-lives between 0.1 and 100 Ma) present in the early Solar System (ESS) by investigating how predictions of their abundances in the interstellar medium (ISM) from steady-state equilibrium relate to their ESS values. For this, we take into account the non-negligible time $t_{\mathrm{iso}}$ elapsed between the isolation of the pre-solar molecular cloud and the formation of the ESS, during which the SLRs decayed freely. We also consider the alternative scenario in which the pre-solar molecular cloud remained partially mixed with the ISM, with a mixing timescale $t_{\mathrm{mix}}$. We find that the ESS abundances of $^{107}$Pd and $^{182}$Hf produced by \textit{slow} neutron captures (\textit{s}-process), and of $^{53}$Mn and $^{60}$Fe produced by explosive nucleosynthesis, can be consistently explained within these scenarios. Their required $t_{\mathrm{iso}}$ is 9-12 Ma, and their required $t_{\mathrm{mix}}$ is 11-14 Ma (with one potential exception of $t_{\mathrm{mix}}$ = 38 Ma), depending on galactic uncertainties, such as the galactic star formation history and efficiency and the star-to-gas mass ratio. Another \textit{s}-process SLR, $^{205}$Pb has a more uncertain ESS value, and falls within only some of these time values. The same applies to the SLRs produced by the $p$-process ($^{92}$Nb and $^{146}$Sm), depending on the latter's half-life. In agreement with previous studies, we find that the ESS abundances of the \textit{rapid} neutron-capture isotopes ($^{129}$I, $^{244}$Pu, and $^{247}$Cm) and of the most short-lived radionuclides ($^{26}$Al, $^{36}$Cl and $^{41}$Ca) cannot be explained by assuming steady-state equilibrium in the ISM.

astro-ph.SR

Production of heavy $α$-elements and $^{44}$Ti in Cas A: comparison to abundances from 1D core-collapse supernova models and evidence for Carbon-Oxygen shell mergers

The merger between the carbon (C) and oxygen (O) shells hours to days before the collapse of a massive star significantly changes its nucleosynthesis, which is reflected in the elemental ratios observed in supernova remnants (SNRs). We present a nucleosynthesis study of $^{44}$Ti production in core-collapse supernovae (CCSNe), highlighting large silicon (Si), sulfur (S), calcium (Ca), and, most importantly, argon (Ar) to neon (Ne) ratios as diagnostics for carbon-oxygen (C--O) shell mergers. We compare yields from eight different sets of CCSNe models to observations of Cassiopeia A (Cas A), and show that C--O shell mergers are consistently the models that best match X-ray and infrared observations. These models produce high Ar/Ne ratios ($\gtrsim 0.1$), due to $^{20}$Ne depletion and production of $^{36}$Ar and $^{38}$Ar, while lower ratios are obtained from non-merger cases. Based on the Ar/Ne diagnostic, we compare the range of expected $^{44}$Ti produced by C--O shell mergers, which is up to $\sim 20 - 30 \%$ of the overall $^{44}$Ti, but expected to be located outside the reverse shock. Based on the sets of models considered, the photon flux expected from the $^{44}$Ti synthesized in the C--O shell merger in Cas A is below the $NuSTAR$ and $COSI$ detection limits, compatible with current limits locating most of the $^{44}$Ti interior to the reverse shock, but might be detectable from proposed missions like $ASCENT$. Finally, for the SNR of 1987A, a dominant C--O merger origin of the observed $^{44}$Ti is unlikely based on the observed redshift in its $^{44}$Ti line.

astro-ph.HE

Stellar Interpretation of Meteoritic Data and PLotting for Everyone (SIMPLE): Isotope Mixing Lines for Six Sets of Core-Collapse Supernova Models

Bulk meteorites and their inclusions exhibit, for many chemical elements, isotopic variability produced by nucleosynthetic events in stars and supernovae before the formation of the Sun. While the exact astrophysical origins of these variations are still a matter of debate, their identification provides insights on the environment of the Sun's birth and the formation of the Solar System. Here we present a new Python tool called SIMPLE (Stellar Interpretation of Meteoritic Data and Plotting for Everyone) designed to compare the isotopic composition of the ejecta from core-collapse supernovae (CCSNe) with meteoritic data. In the present version, the SIMPLE toolkit includes a dataset of 18 CCSN models, from 6 different published sets, with initial masses of 15, 20, and 25 M$_{\odot}$ and solar metallicity. SIMPLE is designed to easily extract the isotopic abundances predicted by each CCSN model for any elements and post-process them into the format needed to compare to the meteoritic data, therefore, facilitating their interpretation. As an example of how to use SIMPLE, we analyze the composition of the Ni isotopes in the 18 models and confirm that bulk meteorite Ni anomalies are compatible with material from the innermost Si-rich region of CCSN ejecta. Designed as a collaborative platform, SIMPLE is open-source and welcomes community contributions to enhance its development and dissemination for stellar nucleosynthesis and meteoritic studies. Future enhancements include addition of more model predictions and inclusion of mixing between different layers of supernova ejecta.

astro-ph.SR

The role of rotation on the yields of the two γ-ray emitters 26Al and 60Fe ejected by massive stars

We show that the observed 60Fe/26Al flux ratio provided by the SPectrometer on INTEGRAL satellite (0.24 +- 0.04) can be reproduced only if rotation is taken into account in the computation of the stellar models. Predictions from non-rotating stellar models yield to a significantly lower ratio (0.062), which is incompatible with the observed value. The adopted models and the associated yields are based on a combination of models already published by Limongi & Chieffi (2018) complemented by additional ones fully consistent with the original grid, allowing a finer resolution in the initial rotational velocity distribution.

astro-ph.SR

Strontium-84 Enrichments in Presolar Grains Provide First Evidence of p-process Nucleosynthesis in Core-collapse Supernovae

This study reports detection of rare p-process isotopes within presolar grains. Presolar grains are relic dust grains from dying stars. These microscopic dust particles are found in primitive solar system materials. Their distinct isotopic compositions record the nucleosynthetic processes in their parent stars and the Galactic chemical environment in which these stars formed. We studied presolar graphite grains of high-density type from the Murchison meteorite and found five grains with subgrains that show enrichments in 84Sr compared to the solar abundance.84Sr is the neutron-deficient isotope of strontium that can be produced in the deep oxygen-rich interior of high-mass stars that end their lives as core-collapse supernovae. The observed 84Sr excesses cannot be produced in low-mass asymptotic giant branch stars, the source of most high-density presolar graphites found in meteorites. High-density graphites with embedded 84Sr excesses are, instead, compatible with a core-collapse supernovae origin. The graphite subgrains condensed from carbon-rich materials in the outer layers of core-collapse supernovae, where 84Sr was destroyed by neutron captures during hydrostatic evolution of the stars and their final explosion. Based on current theoretical stellar models, a few percent of contribution from the inner regions of core-collapse supernovae, which are enriched in p-process nuclides, to the outer carbon-rich regions is the most likely explanation for the observed enrichment of 84Sr in the subgrains of the high-density graphites. In this study, we present the first observational evidence that core-collapse supernovae produce and eject isotopes made by the p-process.

astro-ph.SR

Impact of Newly Measured Nuclear Reaction Rates on $^{26}$Al Ejected Yields from Massive Stars

Over the last three years, the rates of all the main nuclear reactions involving the destruction and production of $^{26}$Al in stars ($^{26}$Al(n, p)$^{26}$Mg, $^{26}$Al(n, $α$)$^{23}$Na, $^{26}$Al(p, $γ$)$^{27}$Si and $^{25}$Mg(p, $γ$)$^{26}$Al) have been re-evaluated thanks to new high-precision experimental measurements of their cross sections at energies of astrophysical interest, considerably reducing the uncertainties in the nuclear physics affecting their nucleosynthesis. We computed the nucleosynthetic yields ejected by the explosion of a high-mass star (20 Msun, Z = 0.0134) using the FRANEC stellar code, considering two explosion energies, 1.2 10$^{51}$ erg and 3 10$^{51}$ erg. We quantify the change in the ejected amount of $^{26}$Al and other key species that is predicted when the new rate selection is adopted instead of the reaction rates from the STARLIB nuclear library. Additionally, the ratio of our ejected yields of 26Al to those of 14 other short-lived radionuclides (36Cl, 41Ca, 53Mn, 60Fe, 92Nb, 97Tc, 98Tc, 107Pd, 126Sn, 129I, 36Cs, 146Sm, 182Hf, 205Pb) are compared to early solar system isotopic ratios, inferred from meteorite measurements. The total ejected 26Al yields vary by a factor of ~3 when adopting the new rates or the STARLIB rates. Additionally, the new nuclear reaction rates also impact the predicted abundances of short-lived radionuclides in the early solar system relative to $^{26}$Al. However, it is not possible to reproduce all the short-lived radionuclide isotopic ratios with our massive star model alone, unless a second stellar source could be invoked, which must have been active in polluting the pristine solar nebula at a similar time of a core-collapse supernova.

astro-ph.SR

Impact of the latest 22Ne+α reaction rates on nucleosynthesis in massive stars and galactic chemical evolution

In massive stars (initial mass of > 9 solar masses), the weak s (slow neutron capture) process produces elements between Fe and Zr, enriching the Galaxy with these elements through core-collapse supernova explosions. The weak s-process nucleosynthesis is driven by neutrons produced in the 22Ne(α, n)25Mg reaction during convective He-core and C-shell burning. The yields of heavy elements thus depend on the 22Ne(α, n)25Mg and the competitive 22Ne(α, γ)26Mg reaction rates which are dominated by several narrow-resonance reactions. While the accuracy of these rates has been under debate for decades, recent experimental efforts, including ours, drastically reduced these uncertainties. In this work, we use a set of 280 massive star nucleosynthesis models calculated using different 22Ne(α, n)25Mg and 22Ne(α, γ)26Mg rates, and a galactic chemical evolution (GCE) study to probe their impact on the weak s-process elemental abundances in the Galaxy. The GCE was computed with the OMEGA+ code, using the new sets of stellar yields with different 22Ne+α rates. From GCE, we find that these rates are causing up to 0.45 dex of variations in the [Cu/Fe], [Ga/Fe], and [Ge/Fe] ratios predicted at solar metallicity. The greatest impact on the stellar nucleosynthesis and GCE results derives from uncertainties in the (α,n) strength (ωγ(α,n)) of the Ex=11.32 MeV resonance. We show that the variations observed in the GCE calculations for the weak s-proess elements become negligibly smaller than dispersions found in observations once the ωγ(α,n) is accurately determined within the uncertaintiy of 10 to 20% (typically reported experimental errors for the resonance) in future nuclear physics experiments.

astro-ph.SR

The chemical yields of stars in the range 9-15 Msun

In Limongi et al. (2024) we presented and discussed the main evolutionary properties and final fate of stars in the mass range 7-15 Msun. The evolutions of those models were computed by means of a medium size nuclear network that guaranteed a proper calculation of the nuclear energy generation and hence a good modeling of the physical evolution of these stars. In the present paper, we extend this study by computing the detailed chemical yields of stars in the mass range 9-15 Msun, i.e., those stars that explode as core collapse supernovae (CCSNe). The explosive nucleosynthesis is then computed in the framework of the thermal bomb induced explosion by means of the HYPERION code (Limongi and Chieffi 2020). We find that: (1) the yields of the intermediate mass elements (i.e., O to P) show a steep decrease as the inital mass decreases; (2) the yields of s-weak component, i.e., those produced by the slow neutron captures from Ga to to the first neutron closure shell, decrease almost linearly as a function of the initial mass with respect to the ones produced by the more massive stars; (3) the global contribution of the stars in the mass range 9.22-13 Msun to the yields of a generation of massive stars averaged over a standard initial mass function is negligible for essentially all the isotopes. In spite of this, however, the models of stars in this mass range can be fundamental to interpret the observations of specific supernovae.

astro-ph.SR

Stellar population modelling of neutron stars and black holes: spatially-resolved graveyards in MaNGA/SDSS-IV galaxies

We update our stellar population models for the time evolution of the number and mass of massive remnants - neutron stars and black holes - with a new initial mass-remnant mass relation for core collapse supernovae. The calculations are based on hydrodynamical simulations and induced explosions of a subset of previously published pre-supernovae models spanning a wide range of stellar mass, metallicity and different values for rotation velocity. The resulting stellar population models predict lower numbers of neutron stars (by up to 0.3 dex) and higher numbers of black holes (by up to 0.8 dex), especially when stellar rotation is considered. The mass fraction locked in neutron stars and black holes is lowest in high-metallicity populations, with the largest number of remnants found at about half-solar metallicity. This mirrors the amount of available gas, ranging from 35 per cent to 45 per cent. We then apply our new models to IFU spectra for ~10,000 galaxies from the SDSS-IV/MaNGA survey for which we previously published spatially-resolved star formation histories. This allows us to probe spatially-resolved graveyards in galaxies of different types. The number and radial distribution of remnants depend on a galaxy's mass, star formation history and metal content. More massive and hence more metal-rich galaxies are found to host fewer remnants. Radial gradients in the number of remnants depend on galaxy mass mostly because of the mass-dependent profiles in mass density: the gradients are flat in low-mass galaxies, and negative in high-mass galaxies, particularly in Milky Way analogues.

astro-ph.GA

The impact of asteroseismically calibrated internal mixing on nucleosynthetic wind yields of massive stars

Asteroseismology gives us the opportunity to look inside stars and determine their internal properties. Based on these observations, estimations can be made for the amount of the convective boundary mixing and envelope mixing of such stars, and the shape of the mixing profile in the envelope. However, these results are not typically included in stellar evolution models. We aim to investigate the impact of varying convective boundary mixing and envelope mixing in a range based on asteroseismic modelling in stellar models, both for the stellar structure and for the nucleosynthetic yields. In this first study, we focus on the pre-explosive evolution of a 20Msun star and evolve the models to the final phases of carbon burning. We vary the convective boundary mixing, implemented as step-overshoot, with the overshoot parameter in the range 0.05-0.4 and the amount of envelope mixing in the range 1-10$^{6}$ with a mixing profile based on internal gravity waves. We use a large nuclear network of 212 isotopes to study the nucleosynthesis. We find that enhanced mixing according to asteroseismology of main-sequence stars, both at the convective core boundary and in the envelope, has significant effects on the nucleosynthetic wind yields. Our evolutionary models beyond the main sequence diverge in yields from models based on rotational mixing, having longer helium burning lifetimes and lighter helium-depleted cores. We find that the asteroseismic ranges of internal mixing calibrated from core hydrogen burning stars lead to similar wind yields as those resulting from the theory of rotational mixing. Adopting the seismic mixing levels beyond the main sequence, we find earlier transitions to radiative carbon burning compared to models based on rotational mixing. This influences the compactness and the occurrence of shell-mergers, which may affect the supernova properties and explosive nucleosynthesis.

astro-ph.SR

Zero and extremely low metallicity rotating massive stars: evolution, explosion, and nucleosynthesis up to the heaviest nuclei

We present the evolution and the explosion of two massive stars, 15 and 25 M$_{\odot}$, spanning a wide range of initial rotation velocities (from 0 to 800 km/s) and three initial metallicities: Z=0 ([Fe/H]=$-\infty$), $3.236\times10^{-7}$ ([Fe/H]=-5), and $3.236\times10^{-6}$ ([Fe/H]=-4). A very large nuclear network of 524 nuclear species extending up to Bi has been adopted. Our main findings may be summarized as follows: a) rotating models above Z=0 are able to produce nuclei up to the neutron closure shell at N=50, and in a few cases up to N=82; b) rotation drastically inhibits the penetration of the He convective shell in the H rich mantle, phenomenon often found in zero metallicity non rotating massive stars; c) vice versa rotation favors the penetration of the O convective shell in the C rich layers with the consequence of altering significantly the yields of the products of the C, Ne, and O burning; d) none of the models that reach the critical velocity while in H burning, loses more the 1 M$_{\odot}$ in this phase; e) conversely, almost all models able to reach their Hayashi track exceed the Eddington luminosity and lose dynamically almost all their H rich mantle. These models suggest that rotating massive stars may have contributed significantly to the synthesis of the heavy nuclei in the first phase of enrichment of the interstellar medium, i.e., at early times.

astro-ph.SR

The $γ$-process nucleosynthesis in core-collapse supernovae II. Effect of the explosive recipe

The $γ$-process in core-collapse supernovae (CCSNe) can produce a number of neutron-deficient stable isotopes heavier than iron (p-nuclei). However, current model predictions do to not fully reproduce the solar abundances. We investigate the impact of different explosion energies and parameters on the nucleosynthesis of p-nuclei, by studying stellar models with different initial masses and CCSN explosions. We find that the total p-nuclei yields are only marginally affected by the CCSN explosion prescriptions if the $γ$-process production is already efficient in the stellar progenitors due to a C-O shell merger. In most of CCSN explosions from progenitors without C-O shell merger, the $γ$-process yields increase with the explosion energy up to an order of magnitude, depending on the progenitor structure and the CCSN prescriptions. The trend of the p-nuclei production with the explosion energy is more complicated if we look at the production of single p-nuclei. The light p-nuclei tend to be the most enhanced with increasing the explosion energy. In particular, for the CCSN models where the $α$-rich freeze-out component is ejected, the yields of the lightest p-nuclei increase by up to three orders of magnitude. We provide the first extensive study using different sets of massive stars of the impact of varying CCSN explosion prescriptions on the production of the p-nuclei. Unlike previous expectations and recent results in the literature, we find that the average production of p-nuclei tends to increase with the explosion energy. We also confirm that the pre-explosive production of p-nuclei in C-O shell mergers is a robust result, independently from the subsequent explosive nucleosynthesis. A realistic range of variations in the evolution of stellar progenitors and in the CCSN explosions might boost the CCSN contribution to the galactic chemical evolution of p-nuclei.

astro-ph.SR

Presupernova evolution and explosive nucleosynthesis of rotating massive stars II: the Super Solar models at [Fe/H]=0.3

We present an extension of the set of models published in Limongi & Chieffi, 2018, ApJS, 237, 13, at metallicity two times solar, i.e. [Fe/H]=0.3. The key physical properties of these models at the onset of the core collapse are mainly due to the higher mass loss triggered by the higher metallicity: the super solar metallicity (SSM) models reach the core collapse with smaller He- and CO-core masses, while the amount of 12C left by the central He burning is higher. These results are valid for all the rotation velocities. The yields of the neutron capture nuclei expressed per unit mass of Oxygen (i.e. the X/O) are higher in the SSM models than in the SM ones in the non rotating case while the opposite occurs in the rotating models. The trend shown by the non rotating models is the expected one, given the secondary nature of the n-capture nucleosynthesis. Vice versa, the counter intuitive trend obtained in the rotating models is the consequence of the higher mass loss present in the SSM models that removes the H rich envelope faster than in the SM ones while the stars are still in central He burning, dumping out the entanglement (activated by the rotation instabilities) and therefore a conspicuous primary n-capture nucleosynthesis.

astro-ph.SR

The physics of Core-Collapse Supernovae: explosion mechanism and explosive nucleosynthesis

Recent developments in multi-dimensional simulations of core-collapse supernovae have considerably improved our understanding of this complex phenomenon. In addition to that, one-dimensional (1D) studies have been employed to study the explosion mechanism and its causal connection to the pre-collapse structure of the star, as well as to explore the vast parameter space of supernovae. Nonetheless, many uncertainties still affect the late stages of the evolution of massive stars, their collapse, and the subsequent shock propagation. In this review, we will briefly summarize the state-of-the-art of both 1D and 3D simulations and how they can be employed to study the evolution of massive stars, supernova explosions, and shock propagation, focusing on the uncertainties that affect each of these phases. Finally, we will illustrate the typical nucleosynthesis products that emerge from the explosion.

astro-ph.SR

Evolution and final fate of solar metallicity stars in the mass range 7-15 Msun. I. The transition from AGB to SAGB stars, Electron Capture and Core Collapse Supernovae progenitors

According to a standard initial mass function, stars in the range 7-12 Msun constitute ~50% (by number) of the stars more massive than ~7 Msun, but, in spite of this, their evolutionary properties, and in particular their final fate, are still scarcely studied. In this paper we present a detailed study of the evolutionary properties of solar metallicity, non rotating stars in the range 7-15 Msun, from the pre main sequence phase up to the presupernova stage or up to an advanced stage of the thermally pulsing phase, depending on the initial mass. We find that (1) the 7.00 Msun develops a degenerate CO core and evolves as a classical AGB star in the sense that it does not ignite the C burning reactions; (2) stars with the initial mass M >= 9.22 Msun end their life as core collapse supernovae; (3) stars in the range 7.50 <= M/Msun <= 9.20 develop a degenerate ONeMg core and evolve through the thermally pulsing SAGB phase; 4) stars in the mass range 7.50 <= M/Msun <= 8.00 end their life as hybrid CO/ONeMg- or ONeMg- WD; (5) stars with the initial mass in the range 8.50 <= M/Msun <= 9.20 may potentially explode as electron capture supernovae.

astro-ph.SR

On the origin of the Galactic thin and thick discs, their abundance gradients and the diagnostic potential of their abundance ratios

Using a semi-analytical model of the evolution of the Milky Way, we show how secular evolution can create distinct overdensities in the phase space of various properties (e.g. age vs metallicity or abundance ratios vs age) corresponding to the thin and thick discs. In particular, we show how key properties of the Solar vicinity can be obtained by secular evolution, with no need for external or special events, like galaxy mergers or paucity in star formation. This concerns the long established double-branch behaviour of [alpha/Fe] vs metallicity and the recently found non-monotonic evolution of the stellar abundance gradient, evaluated at the birth radii of stars. We extend the discussion to other abundance ratios and we suggest a classification scheme, based on the nature of the corresponding yields (primary vs secondary or odd elements) and on the lifetimes of their sources (short-lived vs long-lived ones). The latter property is critical in determining the single- or double- branch behavior of an elementary abundance ratio in the Solar neighborhood. We underline the high diagnostic potential of this finding, which can help to separate clearly elements with sources evolving on different timescales and help determining the site of e.g. the r-process(es). We define the "abundance distance" between the thin and thick disc sequences as an important element for such a separation. We also show how the inside-out evolution of the Milky Way disc leads rather to a single-branch behavior in other disc regions.

astro-ph.GA

Explosion mechanism of core-collapse supernovae: role of the Si/O interface

We present a simple criterion to predict the explodability of massive stars based on the density and entropy profiles before collapse. If a pronounced density jump is present near the Si/Si-O interface, the star will likely explode. We develop a quantitative criterion by using $\sim 1300$ 1D simulations where $ν$-driven turbulence is included via time-dependent mixing-length theory. This criterion correctly identifies the outcome of the supernova more than $90 \%$ of the time. We also find no difference in how this criterion performs on two different sets of progenitors, evolved using two different stellar evolution codes: FRANEC and KEPLER. The explodability as a function of mass of the two sets of progenitors is very different, showing: (i) that uncertainties in the stellar evolution prescriptions influence the predictions of supernova explosions; (ii) the most important properties of the pre-collapse progenitor that influence the explodability are its density and entropy profiles. We highlight the importance that $ν$-driven turbulence plays in the explosion by comparing our results to previous works.

astro-ph.HE