arXiv subjects

Ondrej Pejcha

Publications and source records attributed to Ondrej Pejcha.

At least 19 recordsLinked to original sources

arXiv2024

Journey to the center of the common envelope evolution. Inner dynamics of the post-dynamical inspiral

Three-dimensional hydrodynamical simulations of common envelope evolution are often terminated soon after the initial dynamical plunge of the companion transitions into a long-lasting post-dynamical inspiral with slowly varying semi-major axis, $a_\text{b}$. This premature termination is often due to insufficient numerical resolution and challenges associated with the softening of the gravitational potential of the two cores. In this work, we use statically-refined 3D hydrodynamical simulations to study binaries orbiting inside a common envelope, exploring the effects of varying numerical resolution, $δ$, gravitational potential softening prescriptions, and the associated softening lengthscale, $ε$. We find that quantities such as the binary inspiral timescale or the volume-averaged shearing rate typically converge to asymptotic values only for $ε\le 0.1 a_\text{b}$ and $δ\le 6 \times 10^{-3}a_\text{b}$ with smaller $ε$ requiring correspondingly smaller $δ$. After a few tens of binary orbits, the two cores become surrounded by a corotating, nearly hydrostatic gas structure, resembling the shared envelope of a contact binary. We propose that this structure is responsible for the slowing down of the dynamical inspiral, leading to an asymptotic inspiral timescale of approximately $10^5$ orbital periods for a binary mass ratio $q=1/3$, and approximately $10^6$ orbital periods for a binary mass ratio $q=1$. By investigating kinetic helicity, we argue that the magnetic field is unlikely to organize into large-scale structures via the usual $α$--effect during the post-dynamical phase. Even in the absence of magnetic fields, we observe intermittent polar outflows collimated by partially centrifugally evacuated polar funnels. (abridged)

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arXiv2023

Post-dynamical inspiral phase of common envelope evolution. The role of magnetic fields

During common envelope evolution, an initially weak magnetic field may undergo amplification by interacting with spiral density waves and turbulence generated in the stellar envelope by the inspiralling companion. Using 3D magnetohydrodynamical simulations on adaptively refined spherical grids with excised central regions, we studied the amplification of magnetic fields and their effect on the envelope structure, dynamics, and the orbital evolution of the binary during the post-dynamical inspiral phase. About $95\%$ of magnetic energy amplification arises from magnetic field stretching, folding, and winding due to differential rotation and turbulence while compression against magnetic pressure accounts for the remaining $\sim 5\%$. Magnetic energy production peaks at a scale of $3a_\text{b}$, where $a_\text{b}$ is the semimajor axis of the central binary's orbit. Because the magnetic energy production declines at large radial scales, the conditions are not favorable for the formation of magnetically collimated bipolar jet-like outflows unless they are generated on small scales near the individual cores, which we did not resolve. Magnetic fields have a negligible impact on binary orbit evolution, mean kinetic energy, and the disk-like morphology of angular momentum transport, but turbulent Maxwell stress can dominate Reynolds stress when accretion onto the central binary is allowed, leading to an $α$-disk parameter of $\simeq 0.034$. Finally, we discovered accretion streams arising from the stabilizing effect of the magnetic tension from the toroidal field about the orbital plane, which prevents overdensities from being destroyed by turbulence and enables them to accumulate mass and eventually migrate toward the binary.

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arXiv2022

The luminous red nova AT 2018bwo in NGC 45 and its binary yellow supergiant progenitor

Luminous Red Novae (LRNe) are astrophysical transients associated with the partial ejection of a binary system's common envelope (CE) shortly before its merger. Here we present the results of our photometric and spectroscopic follow-up campaign of AT2018bwo (DLT18x), a LRN discovered in NGC45, and investigate its progenitor system using binary stellar-evolution models. The transient reached a peak magnitude of $M_r=-10.97\pm0.11$ and maintained this brightness during its optical plateau of $t_p = 41\pm5$days. During this phase, it showed a rather stable photospheric temperature of ~3300K and a luminosity of ~$10^{40}$erg/s. The photosphere of AT2018bwo at early times appeared larger and cooler than other similar LRNe, likely due to an extended mass-loss episode before the merger. Towards the end of the plateau, optical spectra showed a reddened continuum with strong molecular absorption bands. The reprocessed emission by the cooling dust was also detected in the mid-infrared bands ~1.5 years after the outburst. Archival Spitzer and Hubble Space Telescope data taken 10-14 years before the transient event suggest a progenitor star with $T_{prog}\sim 6500$K, $R_{prog}\sim 100R_{\odot}$ and $L_{prog}\sim 2\times10^4L_{\odot}$, and an upper limit for optically thin warm (1000 K) dust mass of $M_d<10^{-6}M_{\odot}$. Using stellar binary-evolution models, we determined the properties of binary systems consistent with the progenitor parameter space. For AT2018bwo, we infer a primary mass of 12-16 $M_{\odot}$, which is 9-45% larger than the ~11$M_{\odot}$ obtained using single-star evolution models. The system, consistent with a yellow-supergiant primary, was likely in a stable mass-transfer regime with -2.4<log ($\dot{M}/M_{\odot}$/yr)<-1.2 a decade before the main instability occurred. During the dynamical merger, the system would have ejected 0.15-0.5$M_{\odot}$ with a velocity of ~500 km/s.

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arXiv2021

Pre-explosion spiral mass loss of a binary star merger

Binary stars commonly pass through phases of direct interaction which result in the rapid loss of mass, energy, and angular momentum. Though crucial to understanding the fates of these systems, including their potential as gravitational wave sources, this short-lived phase is poorly understood and has thus far been unambiguously observed in only a single event, V1309 Sco. Here we show that the complex and previously-unexplained photometric behavior of V1309 Sco prior to its main outburst results naturally from the runaway loss of mass and angular momentum from the outer Lagrange point, which lasts for thousands of orbits prior to the final dynamical coalescence, much longer than predicted by contemporary models. This process enshrouds the binary in a "death spiral" outflow, which affects the amplitude and phase modulation of its light curve, and contributes to driving the system together. The total amount of mass lost during this gradual phase ($\sim 0.05 M_\odot$) rivals the mass lost during the subsequent dynamical interaction phase, which has been the main focus of "common envelope" modeling so far. Analogous features in related transients suggest that this behavior is ubiquitous.

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arXiv2019

On the triple-star origin of the planetary nebula Sh 2-71

Recent studies have indicated that triple star systems may play a role in the formation of an appreciable number of planetary nebulae, however only one triple central star is known to date (and that system is likely too wide to have had much influence on the evolution of its component stars). Here, we consider the possibility that Sh 2-71 was formed by a triple system which has since broken apart. We present the discovery of two regions of emission, seemingly aligned with the proposed tertiary orbit (i.e. in line with the axis formed by the two candidate central star systems previously considered in the literature). We also perform a few simple tests of the plausibility of the triple hypothesis based on the observed properties (coordinates, radial velocities, distances and proper motions) of the stars observed close to the projected centre of the nebula, adding further support through numerical integrations of binary orbits responding to mass loss. Although a number of open questions remain, we conclude that Sh 2-71 is currently one of the best candidates for planetary nebula formation influenced by triple-star interactions.

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arXiv2019

Kinematics of Mass Loss from the Outer Lagrange Point L2

We investigate kinematics of mass loss from the vicinity of the second Lagrange point L2 with applications to merging binary stars, common envelope evolution and the associated transient brightenings. For ballistic particle trajectories, we characterize initial velocities and positional offsets from L2 which lead to unbound outflow, fall back followed by a formation of a decretion disk, collision with the binary surface, or a hydrodynamic shock close to the binary, where some particle trajectories loop and self-intersect. The latter two final states occur only when the trajectories are initiated with offset from L2 or with velocity vector different from corotation with the binary. We find that competition between the time-dependent and steeply radially decreasing tidal torques from the binary, Coriolis force and initial conditions lead to a non-trivial distribution of outcomes in the vicinity of L2. Specifically, even for initial velocities slower than corotation, we find that a set of initial position offsets lead to unbound outflows. Our results will aid in the interpretation of the morphology of mass loss streams in hydrodynamic simulations.

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arXiv2019

The Type II-P Supernova 2017eaw: from explosion to the nebular phase

The nearby SN 2017eaw is a Type II-P (``plateau') supernova showing early-time, moderate CSM interaction. We present a comprehensive study of this SN including the analysis of high-quality optical photometry and spectroscopy covering the very early epochs up to the nebular phase, as well as near-UV and near-infrared spectra, and early-time X-ray and radio data. The combined data of SNe 2017eaw and 2004et allow us to get an improved distance to the host galaxy, NGC 6946, as $D \sim 6.85$ $\pm 0.63$ Mpc; this fits in recent independent results on the distance of the host and disfavors the previously derived (30% shorter) distances based on SN 2004et. From modeling the nebular spectra and the quasi-bolometric light curve, we estimate the progenitor mass and some basic physical parameters for the explosion and the ejecta. Our results agree well with previous reports on a RSG progenitor star with a mass of $\sim15-16$ M$_\odot$. Our estimation on the pre-explosion mass-loss rate ($\dot{M} \sim3 \times 10^{-7} -$ $1\times 10^{-6} M_{\odot}$ yr$^{-1}$) agrees well with previous results based on the opacity of the dust shell enshrouding the progenitor, but it is orders of magnitude lower than previous estimates based on general light-curve modeling of Type II-P SNe. Combining late-time optical and mid-infrared data, a clear excess at 4.5 $μ$m can be seen, supporting the previous statements on the (moderate) dust formation in the vicinity of SN 2017eaw.

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arXiv2017

The Nickel Mass Distribution of Normal Type II Supernovae

Core-collapse supernova explosions expose the structure and environment of massive stars at the moment of their death. We use the global fitting technique of Pejcha & Prieto (2015a,b) to estimate a set of physical parameters of 19 normal Type II SNe, such as their distance moduli, reddenings, $^{56}$Ni masses $M_{\rm Ni}$, and explosion energies $E_{\rm exp}$ from multicolor light curves and photospheric velocity curves. We confirm and characterize known correlations between $M_{\rm Ni}$ and bolometric luminosity at 50 days after the explosion, and between $M_{\rm Ni}$ and $E_{\rm exp}$. We pay special attention to the observed distribution of $M_{\rm Ni}$ coming from a joint sample of 38 Type~II SNe, which can be described as a skewed-Gaussian-like distribution between $0.005~M_{\odot}$ and $0.280~M_{\odot}$, with a median of $0.031~M_{\odot}$, mean of $0.046~M_{\odot}$, standard deviation of $0.048~M_{\odot}$ and skewness of $3.050$. We use two-sample Kolmogorov-Smirnov test and two-sample Anderson-Darling test to compare the observed distribution of $M_{\rm Ni}$ to results from theoretical hydrodynamical codes of core-collapse explosions with the neutrino mechanism presented in the literature. Our results show that the theoretical distributions obtained from the codes tested in this work, KEPLER and Prometheus Hot Bubble, are compatible with the observations irrespective of different pre-supernova calibrations and different maximum mass of the progenitors.

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arXiv2017

Shock-powered light curves of luminous red novae as signatures of pre-dynamical mass loss in stellar mergers

Luminous red novae (LRN) are a class of optical transients believed to originate from the mergers of binary stars, or "common envelope" events. Their light curves often show secondary maxima, which cannot be explained in the previous models of thermal energy diffusion or hydrogen recombination without invoking multiple independent shell ejections. We propose that double-peaked light curves are a natural consequence of a collision between dynamically-ejected fast shell and pre-existing equatorially-focused material, which was shed from the binary over many orbits preceding the dynamical event. The fast shell expands freely in the polar directions, powering the initial optical peak through cooling envelope emission. Radiative shocks from the collision in the equatorial plane power the secondary light curve peak on the radiative diffusion timescale of the deeper layers, similar to luminous Type IIn supernovae and some classical novae. Using a detailed 1D analytic model, informed by complementary 3D hydrodynamical simulations, we show that shock-powered emission can explain the observed range of peak timescales and luminosities of the secondary peaks in LRN for realistic variations in the binary parameters and fraction of the binary mass ejected. The dense shell created by the radiative shocks in the equatorial plane provides an ideal location for dust nucleation consistent with the the inferred aspherical geometry of dust in LRN. For giant stars, the ejecta forms dust when the shock-powered luminosity is still high, which could explain the infrared transients recently discovered by Spitzer. Our results suggest that pre-dynamical mass loss is common if not ubiquitous in stellar mergers, providing insight into the instabilities responsible for driving the binary merger.

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arXiv2016

Binary Stellar Mergers with Marginally-Bound Ejecta: Excretion Disks, Inflated Envelopes, Outflows, and their Luminous Transients

We study mass loss from the outer Lagrange point (L2) in binary stellar mergers and their luminous transients by means of radiative hydrodynamical simulations. Previously, we showed that for binary mass ratios 0.06 < q < 0.8, synchronous L2 mass loss results in a radiatively inefficient, dust-forming unbound equatorial outflow. A similar outflow exists irrespective of q if the ratio of the sound speed to the orbital speed at the injection point is sufficiently large, ε= c_T/v_orb > 0.15. By contrast, for cold L2 mass-loss (ε< 0.15) from binaries with q < 0.06 or q > 0.8, the equatorial outflow instead remains marginally-bound and falls back to the binary over tens to hundreds of binary orbits, where it experiences additional tidal torqueing and shocking. As the bound gas becomes virialized with the binary, the luminosity of the system increases slowly at approximately constant photosphere radius, causing the temperature to rise. Subsequent evolution depends on the efficiency of radiative cooling. If the bound atmosphere is able to cool efficiently, as quantified by radiative diffusion time being shorter than the advection time (t_diff/t_adv < 1), then the virialized gas collapses to an excretion disk, while for t_diff/t_adv > 1 an isotropic wind is formed. Between these two extremes, an inflated envelope transports the heat generated near the binary to the surface by meridional flows. In all cases, the radiated luminosity reaches a fraction ~0.01 to 0.1 of Mdot v_orb^2/2, where Mdot is the mass outflow rate. We discuss the implications of our results for transients in the luminosity gap between classical novae and supernovae, such as V1309 Sco and V838 Mon.

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arXiv2015

Cool and Luminous Transients from Mass-Losing Binary Stars

We study transients produced by equatorial disk-like outflows from catastrophically mass-losing binary stars with an asymptotic velocity and energy deposition rate near the inner edge which are proportional to the binary escape velocity v_esc. As a test case, we present the first smoothed-particle radiation-hydrodynamics calculations of the mass loss from the outer Lagrange point with realistic equation of state and opacities. The resulting spiral stream becomes unbound for binary mass ratios 0.06 < q < 0.8. For synchronous binaries with non-degenerate components, the spiral-stream arms merge at a radius of ~10a, where a is the binary semi-major axis, and the accompanying shock thermalizes about 10% of the kinetic power of the outflow. The mass-losing binary outflows produce luminosities reaching up to ~10^6 L_Sun and effective temperatures spanning 500 < T_eff < 6000 K, which is compatible with many of the class of recently-discovered red transients such as V838 Mon and V1309 Sco. Dust readily forms in the outflow, potentially in a catastrophic global cooling transition. The appearance of the transient is viewing angle-dependent due to vastly different optical depths parallel and perpendicular to the binary plane. We predict a correlation between the peak luminosity and the outflow velocity, which is roughly obeyed by the known red transients. Outflows from mass-losing binaries can produce luminous (10^5 L_Sun) and cool (T_eff < 1500 K) transients lasting a year or longer, as has potentially been detected by Spitzer surveys of nearby galaxies.

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arXiv2015

On The Intrinsic Diversity of Type II-Plateau Supernovae

Hydrogen-rich Type II-Plateau supernovae exhibit correlations between the plateau luminosity $L_{\rm pl}$, the nickel mass $M_{\rm Ni}$, the explosion energy $E_{\rm exp}$, and the ejecta mass $M_{\rm ej}$. Using our global, self-consistent, multi-band model of nearby well-observed supernovae, we find that the covariances of these quantities are strong and that the confidence ellipsoids are oriented in the direction of the correlations, which reduces their significance. By proper treatment of the covariance matrix of the model, we discover a significant intrinsic width to the correlations between $L_{\rm pl}$, $E_{\rm exp}$, and $M_{\rm Ni}$, where the uncertainties due to the distance and the extinction dominate. For fixed $E_{\rm exp}$, the spread in $M_{\rm Ni}$ is about 0.25 dex, which we attribute to the differences in the progenitor internal structure. We argue that the effects of incomplete $γ$-ray trapping are not important in our sample. Similarly, the physics of the Type II-Plateau supernova light curves leads to inherently degenerate estimates of $E_{\rm exp}$ and $M_{\rm ej}$, which makes their observed correlation weak. Ignoring the covariances of supernova parameters or the intrinsic width of the correlations causes significant biases in the slopes of the fitted relations. Our results imply that Type II-Plateau supernova explosions are not described by a single physical parameter or a simple one-dimensional trajectory through the parameter space, but instead reflect the diversity of the core and surface properties of their progenitors. We discuss the implications for the physics of the explosion mechanism and possible future observational constraints.

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arXiv2015

The Landscape of the Neutrino Mechanism of Core-Collapse Supernovae: Neutron Star and Black Hole Mass Functions, Explosion Energies and Nickel Yields

If the neutrino luminosity from the proto-neutron star formed during a massive star core collapse exceeds a critical threshold, a supernova (SN) results. Using spherical quasi-static evolutionary sequences for hundreds of progenitors over a range of metallicities, we study how the explosion threshold maps onto observables, including the fraction of successful explosions, the neutron star (NS) and black hole (BH) mass functions, the explosion energies (E_SN) and nickel yields (M_Ni), and their mutual correlations. Successful explosions are intertwined with failures in a complex pattern that is not simply related to initial progenitor mass or compactness. We predict that progenitors with initial masses of 15 +/- 1, 19 +/- 1, and 21-26 M_Sun are most likely to form BHs, that the BH formation probability is non-zero at solar-metallicity and increases significantly at low metallicity, and that low luminosity, low Ni-yield SNe come from progenitors close to success/failure interfaces. We qualitatively reproduce the observed E_SN-M_Ni correlation, we predict a correlation between the mean and width of the NS mass and E_SN distributions, and that the means of the NS and BH mass distributions are correlated. We show that the observed mean NS mass of ~1.33 M_Sun implies that the successful explosion fraction is higher than 0.35. Overall, we show that the neutrino mechanism can in principle explain the observed properties of SNe and their compact objects. We argue that the rugged landscape of progenitors and outcomes mandates that SN theory should focus on reproducing the wide ranging distributions of observed SN properties.

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arXiv2014

A Global Model of The Light Curves and Expansion Velocities of Type II-Plateau Supernovae

We present a new self-consistent and versatile method that derives photospheric radius and temperature variations of Type II-Plateau supernovae based on their expansion velocities and photometric measurements. We apply the method to a sample of 26 well-observed, nearby supernovae with published light curves and velocities. We simultaneously fit ~230 velocity and ~6800 magnitude measurements distributed over 21 photometric passbands spanning wavelengths from 0.19 to 2.2 microns. The light curve differences among the Type II-Plateau supernovae are well-modeled by assuming different rates of photospheric radius expansion, which we explain as different density profiles of the ejecta and we argue that steeper density profiles result in flatter plateaus, if everything else remains unchanged. The steep luminosity decline of Type II-Linear supernovae is due to fast evolution of the photospheric temperature, which we verify with a successful fit of SN1980K. Eliminating the need for theoretical supernova atmosphere models, we obtain self-consistent relative distances, reddenings, and nickel masses fully accounting for all internal model uncertainties and covariances. We use our global fit to estimate the time evolution of any missing band tailored specifically for each supernova and we construct spectral energy distributions and bolometric light curves. We produce bolometric corrections for all filter combinations in our sample. We compare our model to the theoretical dilution factors and find good agreement for the B and V filters. Our results differ from the theory when the I, J, H, or K bands are included. We investigate the reddening law towards our supernovae and find reasonable agreement with standard R_V ~ 3.1 reddening law in UBVRI bands. Results for other bands are inconclusive. We make our fitting code publicly available.

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arXiv2014

Burying a Binary: Dynamical Mass Loss and a Continuous Optically-Thick Outflow Explain the Candidate Stellar Merger V1309 Scorpii

V1309 Sco was proposed to be a stellar merger and a common envelope transient based on the pre-outburst light curve of a contact eclipsing binary with a rapidly decaying orbital period. Using published data, I show that the period decay timescale P/Pdot of V1309 Sco decreased from ~1000 to ~170 years in less than about 6 years, which implies a very high value of second period derivative. I argue that V1309 Sco experienced an onset of dynamical mass loss through the outer Lagrange point, which eventually obscured the binary. The photosphere of the resulting continuous optically-thick outflow expands as the mass-loss rate increases, explaining the ~200 day rise to optical maximum. The model yields the mass-loss rate of the binary star as a function of time and fits the observed light curve remarkably well. It is also possible to observationally constrain the properties of the surface layers undergoing the dynamical mass loss. V1309 Sco is thus a prototype of a new class of stellar transients distinguished by a slow rise to optical maximum that are driven by dynamical mass loss from a binary. I discuss implications of these findings for stellar transients and other suggested common envelope events.

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arXiv2013

Greatly Enhanced Eccentricity Oscillations in Quadruple Systems Composed of Two Binaries: Implications for Stars, Planets, and Transients

We study the orbital evolution of hierarchical quadruple systems composed of two binaries on a long mutual orbit, where each binary acts as a Kozai-Lidov (KL) perturber on the other. We find that the coupling between the two binaries qualitatively changes the behavior of their KL cycles. The binaries can experience coherent eccentricity oscillations as well as excursions to very high eccentricity that occur over a much larger fraction of the parameter space than in triple systems. For a ratio of outer to inner semi-major axes of 10 to 20, about 30 to 50% of equal-mass quadruples reach eccentricity 1-e < 10^{-3} in one of the binaries. This is about 4 to 12 times more than for triples with equivalent parameters. Orbital "flips" and collisions without previous tidal interaction are similarly enhanced in quadruples relative to triples. We argue that the frequency of evolutionary paths influenced by KL cycles is comparable in the triple and quadruple populations even though field quadruples are a factor of ~5 less frequent than triples. Additionally, quadruples might be a non-negligible source of triples and provide fundamentally new evolutionary outcomes involving close binaries, mergers, collisions, and associated transients, which occur without any fine tuning of parameters. Finally, we study the perturbations to a planetary orbit due to a distant binary and we find that the fraction of orbital flips is a factor of 3 to 4 higher than for the corresponding triple system given our fiducial parameters with implications for hot Jupiters and star-planet collisions.

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arXiv2012

Effect of Collective Neutrino Oscillations on the Neutrino Mechanism of Core-Collapse Supernovae

In the seconds after collapse of a massive star, the newborn proto-neutron star (PNS) radiates neutrinos of all flavors. The absorption of electron-type neutrinos below the radius of the stalled shockwave may drive explosions (the "neutrino mechanism"). Because the heating rate is proportional to the square of neutrino energy, flavor conversion of mu and tau neutrinos to electron-type neutrinos via collective neutrino oscillations (CnuO) may in principle increase the heating rate and drive explosions. In order to assess the potential importance of CnuO for the shock revival, we solve the steady-state boundary value problem of spherically-symmetric accretion between the PNS surface (r_nu) and the shock (r_S), including a scheme for flavor conversion via CnuO. For a given r_nu, PNS mass (M), accretion rate (Mdot), and assumed values of the neutrino energies from the PNS, we calculate the critical neutrino luminosity above which accretion is impossible and explosion results. We show that CnuO can decrease the critical luminosity by a factor of at most ~1.5, but only if the flavor conversion is fully completed inside r_S and if there is no matter suppression. The magnitude of the effect depends on the model parameters (M, Mdot, and r_nu) through the shock radius and the physical scale for flavor conversion. We quantify these dependencies and find that CnuO could lower the critical luminosity only for small M and Mdot, and large r_nu. However, for these parameter values CnuO are suppressed due to matter effects. By quantifying the importance of CnuO and matter suppression at the critical neutrino luminosity for explosion, we show in agreement with previous studies that CnuO are unlikely to affect the neutrino mechanism of core-collapse supernovae significantly.

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arXiv2012

The observed neutron star mass distribution as a probe of the supernova explosion mechanism

The observed distribution of neutron star (NS) masses reflects the physics of core-collapse supernova explosions and the structure of the massive stars that produce them at the end of their evolution. We present a Bayesian analysis that directly compares the NS mass distribution observed in double NS systems to theoretical models of NS formation. We find that models with standard binary mass ratio distributions are strongly preferred over independently picking the masses from the initial mass function, although the strength of the inference depends on whether current assumptions for identifying the remnants of the primary and secondary stars are correct. Second, NS formation models with no mass fallback are favored because they reduce the dispersion in NS masses. The double NS system masses thus directly point to the mass coordinate where the supernova explosion was initiated, making them an excellent probe of the supernova explosion mechanism. If we assume no fallback and simply vary the mass coordinate separating the remnant and the supernova ejecta, we find that for solar metallicity stars the explosion most likely develops at the edge of the iron core at a specific entropy of about 2.8 k_B. The primary limitations of our study are the poor knowledge of the supernova explosion mechanism and the lack of broad range of SN model explosions of LMC to solar metallicity.

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