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Supernova theory has struggled to explain the lightest known neutron star candidate with an accurate mass determination, the $1.174\mathrm{M}_\odot$ companion in the eccentric compact binary system J0453+1559. To improve the theoretical lower limit for neutron star birth masses, we perform 3D supernova simulations for five stellar models close to the minimum mass for iron core collapse. We obtain a record-low neutron star mass of $1.192\mathrm{M}_\odot$ and a substantial kick of $\mathord{\sim} 100\,\mathrm{km}\,\mathrm{s}^{-1}$. Given residual uncertainties in stellar evolution, a neutron star origin for the $1.174\mathrm{M}_\odot$ object remains plausible., Comment: 6 pages, 3 figures. Submitted to Physical Review Letters

Gravitational waveform predictions from 3D simulations of explosions of non-rotating massive stars with no magnetic fields have been extensively studied. However, the impact of magnetic fields and rotation on the core-collapse supernova gravitational-wave signal is not well understood beyond the core-bounce phase. Therefore, we perform four magnetohydrodynamical simulations of the explosion of a $15\,M_{\odot}$ star with the SFHx and SFHo equations of state. All of the models start with a weak magnetic field strength of $10^{8}$\,G, and two of the models are rapidly rotating. We discuss the impact of the rotation and magnetic fields on the gravitational-wave signals. We find that the weak pre-collapse fields do not have a significant impact on the gravitational-wave signal amplitude. With rapid rotation, the f/g-mode trajectory can change in shape, and the dominant emission band becomes broader. We include the low-frequency memory component of the gravitational-wave signal from both matter motions and neutrino emission anisotropy. We show that including the gravitational waves from anisotropic neutrino emission increases the supernova detection distances for the Einstein Telescope, and would also be detectable out to Mpc distances by a moon-based gravitational-wave detector.

Gravitational wave signals from core-collapse supernovae are one of the important observables for extracting the information of dense matter. To extract the properties of proto-neutron stars produced via core-collapse supernovae by asteroseismology, we perform a linear perturbation analysis using data obtained from two-dimensional numerical simulations. We employ 12 and 20 solar-mass progenitors and compare two different treatments of gravity. One is a general relativistic one with a conformal flatness condition and the other is an effective gravitational potential mimicking the Tolman-Oppenheimer-Volkoff solution. We discuss how the frequencies of the proto-neutron star oscillations corresponding to the gravitational wave signals in the simulations depend on the proto-neutron star properties. In our models, we find that the gravitational wave frequencies of the proto-neutron stars determined with the Cowling approximation can be expressed to very good approximation as a function of the proto-neutron star average density almost independently of the progenitor mass, treatment of gravity in the simulations, and the interpolations in the simulations. On the other hand, if one considers the gravitational wave frequencies as a function of the surface gravity of proto-neutron stars, such a relation appears sensitive to the treatment of gravity and other numerical details in the simulations. Thus, the average density of proto-neutron stars seems more suitable for universally expressing the supernova gravitational wave frequencies, instead of the surface gravity., Comment: Accepted for publication in RPD

We present a detailed analysis of the dynamics of proto-compact star (PCS) convection and the core ${}^2\!g_1$-mode in core-collapse supernovae based on general relativistic 2D and 3D neutrino hydrodynamics simulations. Based on 2D simulations, we derive a mode relation for the core $g$-mode frequency in terms of PCS and equation of state parameters, and discuss its limits of accuracy. This relation may prove useful for parameter inference from future supernova gravitational wave (GW) signals if the core $g$-mode or an emission gap at the avoided crossing with the fundamental mode can be detected. The current 3D simulation does not show GW emission from the core $g$-mode due to less power in high-frequency convective motions to excite the mode, however. Analysing the dynamics of PCS convection in 3D, we find that simple scaling laws for convective velocity from mixing-length theory (MLT) do not apply. Energy and lepton number transport is instead governed by a more complex balance between neutrino fluxes and turbulent fluxes that results in roughly uniform rates of change of entropy and lepton number in the PCS convection zone. Electron fraction and enthalpy contrasts in PCS convection are not well captured by the MLT gradient approximation. We find distinctly different spectra for the turbulent kinetic energy and turbulent fluctuations in the electron fraction, which scale approximately as $l^{-1}$ without a downturn at low $l$. We suggest that the different turbulence spectrum of the electron fraction is naturally expected for a passive scalar quantity.

Magnetohydrodynamic simulations of core-collapse supernovae have become increasingly mature and important in recent years. Magnetic fields take center stage in scenarios for explaining hypernova explosions, but are now also considered in supernova theory more broadly as an important factor even in neutrino-driven explosions, especially in the context of neutron star birth properties. Here we present an overview of simulation approaches currently used for magnetohydrodynamic supernova simulations and sketch essential physical concepts for understanding the role of magnetic fields in supernovae of slowly or rapidly rotating massive stars. We review progress on simulations of neutrino-driven supernovae, magnetorotational supernovae, and the relevant field amplification processes. Recent results on the nucleosynthesis and gravitational wave emission from magnetorotational supernovae are also discussed. We highlight efforts to provide better initial conditions for magnetohydrodynamic supernova models by simulating short phases of the progenitor evolution in 3D to address uncertainties in the treatment of rotation and magnetic fields in current stellar evolution models., Comment: 37 pages, 4 figures. Invited chapter for the edited book "New Frontiers in GRMHD Simulations" (Eds. C. Bambi, Y. Mizuno, S. Shashank and F. Yuan, Springer Singapore, expected in 2024)

Core-collapse supernova (CCSN) explosions powered by rotation and magnetic fields present an interesting astrophysical site for nucleosynthesis that potentially contributes to the production of $r$-process elements. Here we present yields of the innermost ejecta in 3D magnetorotational CCSN models simulated using the CoCoNuT-FMT code. Strong magnetic fields tap the rotational energy of the proto-neutron star and lead to earlier and more energetic ($\sim 3\times 10^{51}$ erg) explosions than typical neutrino-driven CCSNe. Compared to a reference non-magnetic model, the ejecta in the magnetorotational models have much more neutron-rich components with Ye down to $\sim$0.25. Our post-processing calculations with the reaction network SkyNet show significant production of weak $r$-process elements up to mass number $\sim$130. We find negligible differences in the synthesis of heavy elements between two magnetorotational models with different initial field strength of 10$^{10}$ and 10$^{12}$ G, in accord with their similar explosion dynamics. The magnetorotational models produce about $\sim$0.19 and 0.14 Msun of radioactive $^{56}$Ni, on the low end of inferred hypernova nickel masses. The yields are publicly available at Zenodo: doi:10.5281/zenodo.10578981 for comparison with stellar abundance patterns, inclusion in modelling galactic chemical evolution, and comparison with other yield calculations. Our results add to the yet restricted corpus of nucleosynthesis yields from 3D magnetorotational supernova simulations and will help quantify yield uncertainties., Comment: 19 pages, 9 figures, accepted by ApJ,yields available at doi.org/10.5281/zenodo.10578981

Gravitational waves are emitted from deep within a core-collapse supernova, which may enable us to determine the mechanism of the explosion from a gravitational-wave detection. Previous studies suggested that it is possible to determine if the explosion mechanism is neutrino-driven or magneto-rotationally powered from the gravitational-wave signal. However, long duration magneto-rotational waveforms, that cover the full explosion phase, were not available during the time of previous studies, and explosions were just assumed to be magneto-rotationally driven if the model was rapidly rotating. Therefore, we perform an updated study using new 3D long-duration magneto-rotational core-collapse supernova waveforms that cover the full explosion phase, injected into noise for the Advanced LIGO, Einstein Telescope and NEMO gravitational-wave detectors. We also include a category for failed explosions in our signal classification results. We then determine the explosion mechanism of the signals using three different methods: Bayesian model selection, dictionary learning, and convolutional neural networks. The three different methods are able to distinguish between neutrino-driven explosions and magneto-rotational explosions, even if the neutrino-driven explosion model is rapidly rotating. However they can only distinguish between the non-exploding and neutrino-driven explosions for signals with a high signal to noise ratio., Comment: Accepted in Physical Review D

We present a first 3D magnetohydrodynamic (MHD) simulation of oxygen, neon and carbon shell burning in a rapidly rotating 16 M_sun core-collapse supernova progenitor. We also run a purely hydrodynamic simulation for comparison. After 180s (15 and 7 convective turnovers respectively), the magnetic fields in the oxygen and neon shells achieve saturation at 10^{11}G and 5 x 10^{10}G. The strong Maxwell stresses become comparable to the radial Reynolds stresses and eventually suppress convection. The suppression of mixing by convection and shear instabilities results in the depletion of fuel at the base of the burning regions, so that the burning shell eventually move outward to cooler regions, thus reducing the energy generation rate. The strong magnetic fields efficiently transport angular momentum outwards, quickly spinning down the rapidly rotating convective oxygen and neon shells and forcing them into rigid rotation. The hydrodynamic model shows complicated redistribution of angular momentum and develops regions of retrograde rotation at the base of the convective shells. We discuss implications of our results for stellar evolution and for the subsequent core-collapse supernova. The rapid redistribution of angular momentum in the MHD model casts some doubt on the possibility of retaining significant core angular momentum for explosions driven by millisecond magnetars. However, findings from multi-D models remain tentative until stellar evolution calculations can provide more consistent rotation profiles and estimates of magnetic field strengths to initialise multi-D simulations without substantial numerical transients. We also stress the need for longer simulations, resolution studies, and an investigation of non-ideal effects., Comment: Submitted to MNRAS (14 pages, 11 Figures)

Spectroscopy is an important tool for providing insights into the structure of core-collapse supernova explosions. We use the Monte Carlo radiative transfer code ARTIS to compute synthetic spectra and light curves based on a two-dimensional explosion model of an ultra-stripped supernova. These calculations are designed both to identify observable fingerprints of ultra-stripped supernovae and as a proof-of-principle for using synthetic spectroscopy to constrain the nature of stripped-envelope supernovae more broadly. We predict very characteristic spectral and photometric features for our ultra-stripped explosion model, but find that these do not match observed ultra-stripped supernova candidates like SN 2005ek. With a peak bolometric luminosity of $6.8\times10^{41}\,\mathrm{erg}\,\mathrm{s}^{-1}$, a peak magnitude of $-15.9\,\mathrm{mag}$ in R-band, and $\Delta m_{15,\mathrm{R}}=3.50$, the model is even fainter and evolves even faster than SN 2005ek as the closest possible analogue in photometric properties. The predicted spectra are extremely unusual. The most prominent features are Mg II lines at 2,800 Angstrom and 4,500 Angstrom and the infrared Ca triplet at late times. The Mg lines are sensitive to the multi-dimensional structure of the model and are viewing-angle dependent. They disappear due to line blanketing by Fe group elements in a spherically averaged model with additional microscopic mixing. In future studies, multi-D radiative transfer calculations need to be applied to a broader range of models to elucidate the nature of observed Type Ib/c supernovae., Comment: 13 pages, 14 figures, submitted to MNRAS

The collapse of massive stars is one of the most-studied paths to black hole formation. In this chapter, we review black hole formation during the collapse of massive stars in the broader context of single and binary stellar evolution and the theory of supernova explosions. We provide a concise overview of the evolutionary channels that may lead to black hole formation -- the classical route of iron core collapse, collapse due to pair instability in very massive stars, and the hypothetical scenario of supermassive star collapse. We then review the current understanding of the parameter space for black hole formation and black hole birth properties that has emerged from theoretical and computational modelling of supernova explosions and transient observations. Finally, we discuss what the intricate interplay between stellar evolution, stellar explosions, and binary interactions implies for the formation of stellar-mass black holes., Comment: 53 pages, 9 figures. This chapter is the pre-print of the version currently in production. Please cite this chapter as the following: A.Heger, B. M\"uller, and I. Mandel. "Black holes as the end state of stellar evolution: Theory and simulations," in The Encyclopedia of Cosmology (Set 2): Black Holes, edited by Z. Haiman (World Scientific, New Jersey, 2023)

Using relativistic supernova simulations of massive progenitor stars with a quark-hadron equation of state (EoS) and a purely hadronic EoS, we identify a distinctive feature in the gravitational-wave signal that originates from a buoyancy-driven mode (g-mode) below the proto-neutron star convection zone. The mode frequency lies in the range $200\lesssim f\lesssim 800\,\text{Hz}$ and decreases with time. As the mode lives in the core of the proto-neutron star, its frequency and power are highly sensitive to the EoS, in particular the sound speed around twice saturation density., Comment: Accepted Phys. Rev. Lett. (29 September 2023)

Type IIP supernovae (SNe IIP) mark the explosive death of red supergiants (RSGs), evolved massive stars with an extended hydrogen envelope. They are the most common supernova type and allow for benchmarking of supernova explosion models by statistical comparison to observed population properties rather than comparing individual models and events. We construct a large synthetic set of SNe IIP light curves (LCs) using the radiation hydrodynamics code \texttt{SNEC} and explosion energies and nickel masses obtained from an efficient semi-analytic model for two different sets of stellar progenitor models. By direct comparison we demonstrate that the semi-analytic model yields very similar predictions as alternative phenomenological explosion models based on one-dimensional simulations. We find systematic differences of a factor of $\mathord{\sim}2$ in plateau luminosities between the two progenitor sets due to different stellar radii, which highlights the importance of the RSG envelope structure as a major uncertainty in interpreting LCs of SNe IIP. A comparison to a volume-limited sample of observed SNe IIP shows decent agreement in plateau luminosity, plateau duration and nickel mass for at least one of the synthetic LC sets. The models, however, do not produce sufficient events with very small nickel mass $M_\mathrm{Ni}<0.01\,M_\odot$ and predict an anticorrelation between plateau luminosity and plateau duration that is not present in the observed sample, a result that warrants further study. Our results suggest that a better understanding of RSG stellar structure is no less important for reliably explaining the light curves of SNe IIP than the explosion physics., Comment: 21 pages, 10 figures, 3 tables, accepted by ApJ, light curve parameter available at Zenodo:10.5281/zenodo.7354733

We perform three-dimensional simulations of magnetorotational supernovae using a $39\,M_{\odot}$ progenitor star with two different initial magnetic field strengths of $10^{10}$ G and $10^{12}$ G in the core. Both models rapidly undergo shock revival and their explosion energies asymptote within a few hundred milliseconds to values of $\gtrsim 2\times10^{51}$ erg after conservatively correcting for the binding energy of the envelope. Magnetically collimated, non-relativistic jets form in both models, though the jets are subject to non-axisymmetric instabilities. The jets do not appear crucial for driving the explosion, as they only emerge once the shock has already expanded considerably. Our simulations predict moderate neutron star kicks of about $150\, \mathrm{km}\,\mathrm{s}^{-1}$, no spin-kick alignment, and rapid early spin-down that would result in birth periods of about $20\, \mathrm{ms}$, too slow to power an energetic gamma-ray burst jet. More than $0.2\,M_\odot$ of iron-group material are ejected, but we estimate that the mass of ejected $^{56}\mathrm{Ni}$ will be considerably smaller as the bulk of this material is neutron-rich. Explosive burning does not contribute appreciable amounts of $^{56}\mathrm{Ni}$ because the burned material originates from the slightly neutron-rich silicon shell. The iron-group ejecta also show no pronounced bipolar geometry by the end of the simulations. The models thus do not immediately fit the characteristics of observed hypernovae, but may be representative of other transients with moderately high explosion energies. The gravitational-wave emission reaches high frequencies of up to 2000 Hz and amplitudes of over 100 cm. The gravitational-wave emission is detectable out to distances of $\sim4$ Mpc in the planned Cosmic Explorer detector.

Current prescriptions for supernova natal kicks in rapid binary population synthesis simulations are based on fits of simple functions to single pulsar velocity data. We explore a new parameterization of natal kicks received by neutron stars in isolated and binary systems developed by Mandel & M\"uller, which is based on 1D and 3D supernova simulations and accounts for the physical correlations between progenitor properties, remnant mass, and the kick velocity. We constrain two free parameters in this model using very long baseline interferometry velocity measurements of Galactic single pulsars. We find that the inferred values of natal kick parameters do not differ significantly between single and binary evolution scenarios. The best-fit values of these parameters are $v_{\rm ns} = 520$ km s$^{-1}$ for the scaling pre-factor for neutron star kicks, and $\sigma_{\rm ns}=0.3$ for the fractional stochastic scatter in the kick velocities., Comment: 8 pages, 8 figures, 1 table. Updated to match MNRAS version

We investigate the impact of strong initial magnetic fields in core-collapse supernovae of non-rotating progenitors by simulating the collapse and explosion of a 16.9 Msun star for a strong- and weak-field case assuming a twisted-torus field with initial central field strengths of ~1012 G and ~106 G. The strong-field model has been set up with a view to the fossil-field scenario for magnetar formation and emulates a pre-collapse field configuration that may occur in massive stars formed by a merger. This model undergoes shock revival already 100 s after bounce and reaches an explosion energy of 9.3 x 10^50 erg at 310 ms, in contrast to a more delayed and less energetic explosion in the weak-field model. The strong magnetic fields help trigger a neutrino-driven explosion early on, which results in a rapid rise and saturation of the explosion energy. Dynamically, the strong initial field leads to a fast build-up of magnetic fields in the gain region to 40% of kinetic equipartition and also creates sizable pre-shock ram pressure perturbations that are known to be conducive to asymmetric shock expansion. For the strong-field model, we find an extrapolated neutron star kick of ~350 km/s, a spin period of ~70 ms, and no spin-kick alignment. The dipole field strength of the proto-neutron star is 2 x 10^14 G by the end of the simulation with a declining trend. Surprisingly, the surface dipole field in the weak-field model is stronger, which argues against a straightforward connection between pre-collapse fields and the birth magnetic fields of neutron stars., Comment: 16 pages, 20 figures Accepted for publication in MNRAS

The hadron-quark phase transition in quantum chromodyanmics has been suggested as an alternative explosion mechanism for core-collapse supernovae. We study the impact of three different hadron-quark equations of state (EoS) with first-order (DD2F\_SF, STOS-B145) and second-order (CMF) phase transitions on supernova dynamics by performing 97 simulations for solar- and zero-metallicity progenitors in the range of $14\texttt{-}100\,\text{M}_\odot$. We find explosions only for two low-compactness models ($14 \text{M}_\odot$ and $16\,\text{M}_\odot$) with the DD2F\_SF EoS, both with low explosion energies of $\mathord{\sim}10^{50}\,\mathrm{erg}$. These weak explosions are characterised by a neutrino signal with several mini-bursts in the explosion phase due to complex reverse shock dynamics, in addition to the typical second neutrino burst for phase-transition driven explosions. The nucleosynthesis shows significant overproduction of nuclei such as $^{90}\mathrm{Zr}$ for the $14\,\text{M}_\odot$ zero-metallicity model and $^{94}\mathrm{Zr}$ for the $16\,\text{M}_\odot$ solar-metallicity model, but the overproduction factors are not large enough to place constraints on the occurrence of such explosions. Several other low-compactness models using the DD2F\_SF EoS and two high-compactness models using the STOS EoS end up as failed explosions and emit a second neutrino burst. For the CMF EoS, the phase transition never leads to a second bounce and explosion. For all three EoS, inverted convection occurs deep in the core of the proto-compact star due to anomalous behaviour of thermodynamic derivatives in the mixed phase, which heats the core to entropies up to $4k_\text{B}/\text{baryon}$ and may have a distinctive gravitational wave signature, also for a second-order phase transition.

Stripped-envelope stars can be observed as Wolf-Rayet (WR) stars, or as less luminous hydrogen-poor stars with low mass loss rates and transparent winds. Both types are potential progenitors of Type I core-collapse supernovae (SNe). We use grids of core-collapse models obtained from helium stars at different metallicities to study the effects of metallicity on the transients and remnants these stars produce. We characterise the surface and core properties of our core collapse models, and investigate their explodability employing three criteria. In cases where explosions are predicted, we estimate the ejecta mass, explosion energy, nickel mass and neutron star (NS) mass. Otherwise, we predict the mass of the resulting black hole (BH). We construct a simplified population model, and find that the properties SNe and compact objects depend strongly on metallicity. Ejecta masses and explosion energies for Type Ic SNe are best reproduced by models with Z=0.04 which exhibit strong winds during core helium burning. This implies that either their mass loss rates are underestimated, or that Type Ic SN progenitors experience mass loss through other mechanisms before exploding. The distributions of ejecta masses, explosion energies and nickel mass for Type Ib SNe are not well reproduced by progenitor models with WR mass loss, but are better reproduced if we assume no mass loss in progenitors with luminosities below the minimum WR star luminosity. We find that Type Ic SNe become more common as metallicity increases, and that the vast majority of progenitors of Type Ib SNe must be transparent-wind stripped-envelope stars. We find several models with pre-collapse CO-masses of up to $\sim 30 M_{\odot}$ may form $\sim 3 M_{\odot}$ BHs in fallback SNe. This may carry important consequences for our understanding of SNe, binary BH and NS systems, X-ray binary systems and gravitational wave transients., Comment: 30 pages, 20 figures, submitted to Astronomy & Astrophysics

Nearby core-collapse supernovae (CCSNe) are powerful multi-messenger sources for gravitational-wave, neutrino and electromagnetic telescopes as they emit gravitational waves in the ideal frequency band for ground based detectors. Once a CCSN gravitational-wave signal is detected, we will need to determine the parameters of the signal, and understand how those parameters relate to the source's explosion, progenitor and remnant properties. This is a challenge due to the stochastic nature of CCSN explosions, which is imprinted on their time series gravitational waveforms. In this paper, we perform Bayesian parameter estimation of CCSN signals using an asymmetric chirplet signal model to represent the dominant high-frequency mode observed in spectrograms of CCSN gravitational-wave signals. We use design sensitivity Advanced LIGO noise and CCSN waveforms from four different hydrodynamical supernova simulations with a range of different progenitor stars. We determine how well our model can reconstruct time-frequency images of the emission modes, and show how well we can determine parameters of the signal such as the frequency, amplitude, and duration. We show how the parameters of our signal model may allow us to place constraints on the proto-neutron star mass and radius, the turbulent kinetic energy onto the proto-neutron star, and the time of shock revival.

The next generation of ground-based gravitational-wave detectors will observe coalescences of black holes and neutron stars throughout the cosmos, thousands of them with exceptional fidelity. The Science Book is the result of a 3-year effort to study the science capabilities of networks of next generation detectors. Such networks would make it possible to address unsolved problems in numerous areas of physics and astronomy, from Cosmology to Beyond the Standard Model of particle physics, and how they could provide insights into workings of strongly gravitating systems, astrophysics of compact objects and the nature of dense matter. It is inevitable that observatories of such depth and finesse will make new discoveries inaccessible to other windows of observation. In addition to laying out the rich science potential of the next generation of detectors, this report provides specific science targets in five different areas in physics and astronomy and the sensitivity requirements to accomplish those science goals. This report is the second in a six part series of reports by the GWIC 3G Subcommittee: i) Expanding the Reach of Gravitational Wave Observatories to the Edge of the Universe, ii) The Next Generation Global Gravitational Wave Observatory: The Science Book (this report), iii) 3G R&D: R&D for the Next Generation of Ground-based Gravitational Wave Detectors, iv) Gravitational Wave Data Analysis: Computing Challenges in the 3G Era, v) Future Ground-based Gravitational-wave Observatories: Synergies with Other Scientific Communities, and vi) An Exploration of Possible Governance Models for the Future Global Gravitational-Wave Observatory Network., Comment: 69 pages, 18 figures

The first three observing runs with Advanced LIGO and Virgo have resulted in the detection of binary black hole mergers (BBH) with highly unequal mass components, which are difficult to reconcile with standard formation paradigms. The most representative of these is GW190814, a highly asymmetric merger between a 23 M$_{\odot}$ black hole and a 2.6 M$_{\odot}$ compact object. Here, we explore recent results suggesting that a sizeable fraction of stars with pre-collapse carbon-oxygen core masses above 10 M$_{\odot}$, and extending up to at least 30 M$_{\odot}$, may produce objects inside the so-called lower mass gap that bridges the division between massive pulsars and BHs in Galactic X-ray binaries. We demonstrate that such an explosion landscape would naturally cause a fraction of massive binaries to produce GW190814-like systems instead of symmetric-mass BBHs. We present examples of specific evolutionary channels leading to the formation of GW190814 and GW200210, a 24+2.8 M$_{\odot}$ merger discovered during the O3b observing run. We estimate the merger-rate density of these events in our scenario to be $\mathcal{O}$(5%) of the total BBH merger rate. Finally, we discuss the broader implications of this formation channel for compact object populations, and its possible relevance to less asymmetric merger events such as GW200105 and GW200115, Comment: A&A Letters, in press

Code comparisons are a valuable tool for the verification of supernova simulation codes and the quantification of model uncertainties. Here we present a first comparison of axisymmetric magnetohydrodynamic (MHD) supernova simulations with the CoCoNuT-FMT and Aenus-Alcar codes, which use distinct methods for treating the MHD induction equation and the neutrino transport. We run two sets of simulations of a rapidly rotating 35M gamma-ray burst progenitor model with different choices for the initial field strength, namely 10^12 G for the maximum poloidal and toroidal field in the strong-field case and 10^10 G in the weak-field case. We also investigate the influence of the Riemann solver and the resolution in CoCoNuT-FMT. The dynamics is qualitatively similar for both codes and robust with respect to these numerical details, with a rapid magnetorotational explosion in the strong-field case and a delayed neutrino-driven explosion in the weak-field case. Despite relatively similar shock trajectories, we find sizeable differences in many other global metrics of the dynamics, like the explosion energy and the magnetic energy of the proto-neutron star. Further differences emerge upon closer inspection, for example, the disk-like surface structure of the proto-neutron star proves highly sensitives to numerical details. The electron fraction distribution in the ejecta as a crucial determinant for the nucleosynthesis is qualitatively robust, but the extent of neutron- or proton-rich tails is sensitive to numerical details. Due to the complexity of the dynamics, the ultimate cause of model differences can rarely be uniquely identified, but our comparison helps gauge uncertainties inherent in current MHD supernova simulations., Comment: 16 pages, 20 figures, accepted for publication in MNRAS

We study differential rotation in late-stage shell convection in a 3D hydrodynamic simulation of a rapidly rotating $16M_\odot$ helium star with a particular focus on the convective oxygen shell. We find that the oxygen shell develops a quasi-stationary pattern of differential rotation that is neither described by uniform angular velocity as assumed in current stellar evolution models of supernova progenitors, nor by uniform specific angular momentum. Instead, the oxygen shell develops a positive angular velocity gradient with faster rotation at the equator than at the pole by tens of percent. We show that the angular momentum transport inside the convection zone is not adequately captured by a diffusive mixing-length flux proportional to the angular velocity or angular momentum gradient. Zonal flow averages reveal stable large-scale meridional flow and an entropy deficit near the equator that mirrors the patterns in the angular velocity. The structure of the flow is reminiscent of simulations of stellar surface convection zones and the differential rotation of the Sun, suggesting that similar effects are involved; future simulations will need to address in more detail how the interplay of buoyancy, inertial forces, and turbulent stresses shapes differential rotation during late-stage convection in massive stars. If convective regions develop positive angular velocity gradients, angular momentum could be shuffled out of the core region more efficiently, potentially making the formation of millisecond magnetars more difficult. Our findings have implications for neutron star birth spin periods and supernova explosion scenarios that involve rapid core rotation., Comment: 13 pages, 6 figures. Published in MNRAS

We investigate the impact of rotation and magnetic fields on the dynamics and gravitational wave emission in 2D core-collapse supernova simulations with neutrino transport. We simulate 17 different models of $15\,M_\odot$ and $39\,M_\odot$ progenitor stars with various initial rotation profiles and initial magnetic fields strengths up to $10^{12}\, \mathrm{G}$, assuming a dipolar field geometry in the progenitor. Strong magnetic fields generally prove conducive to shock revival, though this trend is not without exceptions. The impact of rotation on the post-bounce dynamics is more variegated, in line with previous studies. A significant impact on the time-frequency structure of the gravitational wave signal is found only for rapid rotation or strong initial fields. For rapid rotation, the angular momentum gradient at the proto-neutron star surface can appreciably affect the frequency of the dominant mode, so that known analytic relations for the high-frequency emission band no longer hold. In case of two magnetorotational explosion models, the deviation from these analytic relations is even more pronounced. One of the magnetorotational explosions has been evolved to more than half a second after the onset of the explosion and shows a subsidence of high-frequency emission at late times. Its most conspicuous gravitational wave signature is a high-amplitude tail signal. We also estimate the maximum detection distances for our waveforms. The magnetorotational models do not stick out for higher detectability during the post-bounce and explosion phase., Comment: 19 pages, 12 figures, substantially revised version. Model m15afb12 has been recalculated to remove numerical contamination of high-frequency tail of GW spectrum. One new model m15nrb11 and additional analysis added. Accepted for publiation in MNRAS

We present 3D core-collapse supernova simulations of massive Pop-III progenitor stars at the transition to the pulsational pair instability regime. We simulate two progenitor models with initial masses of $85\,\mathrm{M}_{\odot}$ and $100\,\mathrm{M}_\odot$ with the LS220, SFHo, and SFHx equations of state. The $85\,\mathrm{M}_{\odot}$ progenitor experiences a pair instability pulse coincident with core collapse, whereas the $100\,\mathrm{M}_{\odot}$ progenitor has already gone through a sequence of four pulses $1\mathord,500$ years before collapse in which it ejected its H and He envelope. The $85\,\mathrm{M}_{\odot}$ models experience shock revival and then delayed collapse to a black hole (BH) due to ongoing accretion within hundreds of milliseconds. The diagnostic energy of the incipient explosion reaches up to $2.7\times10^{51}\,\mathrm{erg}$ in the SFHx model. Due to the high binding energy of the metal core, BH collapse by fallback is eventually unavoidable, but partial mass ejection may be possible. The $100\,\mathrm{M}_\odot$ models have not achieved shock revival or undergone BH collapse by the end of the simulation. All models exhibit relatively strong gravitational-wave emission both in the high-frequency g-mode emission band and at low frequencies. The SFHx and SFHo models show clear emission from the standing accretion shock instability. For our models, we estimate maximum detection distances of up to $\mathord{\sim}46\,\mathrm{kpc}$ with LIGO and $\mathord{\sim} 850\,\mathrm{kpc}$ with Cosmic Explorer.

We present a first 3D magnetohydrodynamic (MHD) simulation of convective oxygen and neon shell burning in a non-rotating $18\, M_\odot$ star shortly before core collapse to study the generation of magnetic fields in supernova progenitors. We also run a purely hydrodynamic control simulation to gauge the impact of the magnetic fields on the convective flow and on convective boundary mixing. After about 17 convective turnover times, the magnetic field is approaching saturation levels in the oxygen shell with an average field strength of $\mathord{\sim}10^{10}\, \mathrm{G}$, and does not reach kinetic equipartition. The field remains dominated by small to medium scales, and the dipole field strength at the base of the oxygen shell is only $10^{9}\, \mathrm{G}$. The angle-averaged diagonal components of the Maxwell stress tensor mirror those of the Reynolds stress tensor, but are about one order of magnitude smaller. The shear flow at the oxygen-neon shell interface creates relatively strong fields parallel to the convective boundary, which noticeably inhibit the turbulent entrainment of neon into the oxygen shell. The reduced ingestion of neon lowers the nuclear energy generation rate in the oxygen shell and thereby slightly slows down the convective flow. Aside from this indirect effect, we find that magnetic fields do not appreciably alter the flow inside the oxygen shell. We discuss the implications of our results for the subsequent core-collapse supernova and stress the need for longer simulations, resolution studies, and an investigation of non-ideal effects for a better understanding of magnetic fields in supernova progenitors., Comment: 12 pages, 9 figures, revised version accepted for publication in MNRAS

Hypernovae powered by magnetic jets launched from the surface of rapidly rotating millisecond magnetars are one of the leading models to explain broad-lined Type Ic supernovae (SNe Ic-BL), and have been implicated as an important source of metal enrichment in the early Universe. We investigate the nucleosynthesis in such jet-driven hypernovae using a parameterised, but physically motivated, approach that analytically relates an artificially injected jet energy flux to the power available from the energy in differential rotation in the proto-neutron star. We find ejected $^{56}\mathrm{Ni}$ masses of $0.05\,\mathrm{M}_\odot - 0.45\,\mathrm{M}_\odot$ in our most energetic models with explosion energy $>10^{52}\,\mathrm{erg}$. This is in good agreement with the range of observationally inferred values for SNe Ic-BL. The $^{56}\mathrm{Ni}$ is mostly synthesised in the shocked stellar envelope, and is therefore only moderately sensitive to the jet composition. Jets with a high electron fraction $Y_\mathrm{e}=0.5$ eject more $^{56}\mathrm{Ni}$ by a factor of 2 than neutron-rich jets. We can obtain chemical abundance profiles in good agreement with the average chemical signature observed in extremely metal-poor (EMP) stars presumably polluted by hypernova ejecta. Notably, $\mathrm{[Zn/Fe]} \gtrsim 0.5$ is consistently produced in our models. For neutron-rich jets, there is a significant r-process component, and agreement with EMP star abundances in fact requires either a limited contribution from neutron-rich jets or a stronger dilution of r-process material in the interstellar medium than for the slow SN ejecta outside the jet. The high $\mathrm{[C/Fe]}\gtrsim 0.7$ observed in many EMP stars cannot be consistently achieved due to the large mass of iron in the ejecta, however, and remains a challenge for jet-driven hypernovae based on the magneto-rotational mechanism.

Based on a 3D supernova simulation of an $11.8\,M_\odot$ progenitor model with initial solar composition, we study the nucleosynthesis using tracers covering the innermost $0.1\,M_\odot$ of the ejecta. These ejecta are mostly proton-rich and contribute significant amounts of $^{45}$Sc and $^{64}$Zn. The production of heavier isotopes is sensitive to the electron fraction and hence the neutrino emission from the proto-neutron star. The yields of these isotopes are rather uncertain due to the approximate neutrino transport used in the simulation. In order to obtain the total yields for the whole supernova, we combine the results from the tracers with those for the outer layers from a suitable 1D model. Using the yields of short-lived radionuclides (SLRs), we explore the possibility that an $11.8\,M_\odot$ supernova might have triggered the formation of the solar system and provided some of the SLRs measured in meteorites. In particular, we discuss two new scenarios that can account for at least the data on $^{41}$Ca, $^{53}$Mn, and $^{60}$Fe without exceeding those on the other SLRs., Comment: 16 pages, 9 Figures, 4 Tables

We analyze the properties of 42 rapidly rotating, low metallicity, quasi-chemically homogeneously evolving stellar models in the mass range between 4 and 45 $\,\mathrm{M}_\odot$ at the time of core collapse. Such models were proposed as progenitors for both superluminous supernovae (SLSNe) and long duration gamma-ray bursts (lGRBs), and the Type Ic-BL supernovae (SNe) that are associated with them. Our findings suggest that whether these models produce a magnetar driven SLSN explosion or a near-critically rotating black hole (BH) is not a monotonic function of the initial mass. Rather, their explodability varies non-monotonically depending on the late core evolution, once chemical homogeneity is broken. Using different explodability criteria we find that our models have a clear preference to produce SLSNe at lower masses, and lGRBs at higher masses; but find several exceptions, expecting lGRBs to form from stars as low as 10 $\,\mathrm{M}_\odot$, and SLSNe with progenitors as massive as 30 $\,\mathrm{M}_\odot$. In general, our models reproduce the predicted angular momenta, ejecta masses and magnetic field strengths at core collapse inferred for SLSNe and lGRBs, and suggest significant interaction with their circumstellar medium, particularly for explosions with low ejecta mass., Comment: Accepted for publication in ApJ. 17 pages, 11 figures, 2 tables

We study the impact of a small-scale dynamo in core-collapse supernovae using a 3D neutrino magnetohydrodynamics simulation of a $15 M_\odot$ progenitor. The weak seed field is amplified exponentially in the gain region once neutrino-driven convection develops, and remains dominated by small-scale structures. About $250\, \mathrm{ms}$ after bounce, the field energy in the gain region reaches $\mathord{\sim} 50\%$ of kinetic equipartition. This supports the development of a neutrino-driven explosion with modest global anisotropy, which does not occur in a corresponding model without magnetic fields. Our results suggest that magnetic fields may play a beneficial subsidiary role in neutrino-driven supernovae even without rapid progenitor rotation. Further investigation into the nature of magnetohydrodynamic turbulence in the supernova core is required., Comment: 6 pages, 3 figures, accepted for publication in MNRAS Letters

We report on the impact of a probabilistic prescription for compact remnant masses and kicks on massive binary population synthesis. We find that this prescription populates the putative mass gap between neutron stars and black holes with low-mass black holes. However, evolutionary effects reduce the number of X-ray binary candidates with low-mass black holes, consistent with the dearth of such systems in the observed sample. We further find that this prescription is consistent with the formation of heavier binary neutron stars such as GW190425, but over-predicts the masses of Galactic double neutron stars. The revised natal kicks, particularly increased ultra-stripped supernova kicks, do not directly explain the observed Galactic double neutron star orbital period--eccentricity distribution. Finally, this prescription allows for the formation of systems similar to the recently discovered extreme mass ratio binary GW190814, but only if we allow for the survival of binaries in which the common envelope is initiated by a donor crossing the Hertzsprung gap, contrary to our standard model., Comment: Updated version as accepted by MNRAS

Based on recent results from three-dimensional supernova simulations and semi-analytical parametrised models, we develop analytical prescriptions for the dependence of the mass of neutron stars and black holes and the natal kicks, if any, on the pre-supernova carbon-oxygen core and helium shell masses. Our recipes are probabilistic rather than deterministic in order to account for the intrinsic stochasticity of stellar evolution and supernovae. We anticipate that these recipes will be particularly useful for rapid population synthesis, and we illustrate their application to distributions of remnant masses and kicks for a population of single stars., Comment: Version accepted to MNRAS

Fallback in core-collapse supernovae plays a crucial role in determining the properties of the compact remnants and of the ejecta composition. We perform three-dimensional simulations of mixing and fallback for selected non-rotating supernova models to study how explosion energy and asymmetries correlate with the remnant mass, remnant kick, and remnant spin. We find that the strongest kick and spin is imparted by partial fallback in an asymmetric explosion. Black hole (BH) kicks of several hundred $\mathrm{km}\,\mathrm{s}^{-1}$ and spin parameters of $\mathord{\sim}0.25$ can be obtained in this scenario. If the initial explosion energy barely exceeds the envelope binding energy, stronger fallback results, and the remnant kick and spin remain small. If the explosion energy is high with respect to the envelope binding energy, there is little fallback with a small effect on the remnant kick, but the spin-up by fallback can be substantial. For a non-rotating $12\,\mathrm{M}_\odot$ progenitor, we find that the neutron star (NS) is spun up to millisecond periods. The high specific angular momentum of the fallback material can also lead to disk formation around black holes. Fallback may thus be a pathway towards millisecond-magnetar or collapsar-type engines for hypernovae and gamma-ray bursts that does not require rapid progenitor rotation. Within our small set of simulations, none reproduced the peculiar layered fallback necessary to explain the metal-rich iron-poor composition of many carbon-enhanced metal-poor (CEMP) stars. Models with different explosion energy and different realisations of asymmetries may, however, be compatible with CEMP abundance patterns., Comment: 12 pages, 13 figures, accepted for publication in MNRAS

We introduce a new discrete-ordinate scheme for solving the general relativistic Boltzmann transport equation in the context of core-collapse supernovae. Our algorithm avoids the need to spell out the complicated advection terms in energy and angle that arise when the transport equation is formulated in spherical polar coordinates, in the comoving frame, or in a general relativistic spacetime. We instead approach the problem by calculating the advection of neutrinos across momentum space using an intuitive particle-like approach that has excellent conservation properties and fully accounts for Lorentz boosts, general relativistic effects, and grid geometry terms. In order to avoid the need for a global implicit solution, time integration is performed using a locally implicit Lax-Wendroff scheme that correctly reproduces the diffusion limit. This will facilitate the use of our method on massively parallel distributed-memory architectures. We have verified the accuracy and stability of our scheme with a suite of test problems in spherical symmetry and axisymmetry. To demonstrate that the new algorithm works stably in core-collapse supernova simulations, we have coupled it to the general relativistic hydrodynamics code CoCoNuT and present a first demonstration run of a $20M_\odot$ progenitor with a reduced set of neutrino opacities., Comment: 22 pages, 15 figures, accepted for publication in MNRAS

We present three-dimensional simulations of the core-collapse of massive rotating and non-rotating progenitors performed with the general relativistic neutrino hydrodynamics code CoCoNuT-FMT and analyse their explosion properties and gravitational-wave signals. The progenitor models include Wolf-Rayet stars with initial helium star masses of $39\,M_{\odot}$ and $20\,M_{\odot}$, and an $18\,M_{\odot}$ red supergiant. The $39\,M_{\odot}$ model is a rapid rotator, whereas the two other progenitors are non-rotating. Both Wolf-Rayet models produce healthy neutrino-driven explosions, whereas the red supergiant model fails to explode. By the end of the simulations, the explosion energies have already reached $1.1\times 10^{51}\,\mathrm{erg}$ and $0.6\times 10^{51}\,\mathrm{erg}$ for the $39\,M_{\odot}$ and $20\,M_{\odot}$ model, respectively. The explosions produce neutron stars of relatively high mass, but with modest kicks. Due to the alignment of the bipolar explosion geometry with the rotation axis, there is a relatively small misalignment of $30^\circ$ between the spin and the kick in the $39\,M_{\odot}$ model. In terms of gravitational-wave signals, the massive and rapidly rotating $39\,M_{\odot}$ progenitor stands out by large gravitational-wave amplitudes that would make it detectable out to almost 2 Mpc by the Einstein Telescope. For this model, we find that rotation significantly changes the dependence of the characteristic gravitational-wave frequency of the f-mode on the proto-neutron star parameters compared to the non-rotating case. The other two progenitors have considerably smaller detection distances, despite significant low-frequency emission in the most sensitive frequency band of current gravitational-wave detectors due to the standing accretion shock instability in the $18\,M_{\odot}$ model.

For high-throughput cell culture and associated analytics, droplet-based cultivation systems open up the opportunities for parallelization and rapid data generation. In contrast to microfluidics with continuous flow, sessile droplet approaches enhance the flexibility for fluid manipulation with usually less operational effort. Generating biologically favorable conditions and promoting cell growth in a droplet, however, is particularly challenging due to mass transfer limitations, which has to be solved by implementing an effective mixing technique. Here, capillary waves induced by vertical oscillation are used to mix inside a sessile droplet micro-bioreactor (MBR) system avoiding additional moving parts inside the fluid. Depending on the excitation frequency, different patterns are formed on the oscillating liquid surface, which are described by a model of a vibrated sessile droplet. Analyzing mixing times and oxygen transport into the liquid, a strong dependency of mass transfer on the oscillation parameters, especially the excitation frequency, is demonstrated. Oscillations at distinct capillary wave resonant frequencies lead to rapid homogenization with mixing times of 2 s and volumetric liquid-phase mass transfer coefficients of more than 340 h-1. This shows that the mass transfer in a droplet MBR can be specifically controlled via capillary waves, what is subsequently demonstrated for cultivations of Escherichia coli BL21 cells. Therefore, the presented MBR in combination with vertical oscillation mixing for intensified mass transfer is a promising tool for highly parallel cultivation and data generation.

We calculate the mean evolution of the iron-peak abundance ratios [(Cr,Mn,Co,Zn)/Fe] in the Galaxy, using modern supernova and hypernova chemical yields and a Galactic Chemical Evolution code that assumes homogeneous chemical evolution. We investigate a range of hypernova occurrence rates and are able to produce a chemical composition that is a reasonable fit to the observed values in metal-poor stars. This requires a hypernova occurence rate that is large (50%) in the early Universe, decreasing throughout evolution to a value that is within present day observational constraints (>~ 1%). A large hypernova occurence rate is beneficial to matching the high [Zn/Fe] observed in the most metal-poor stars, although including hypernovae with progenitor mass >= 60 solar masses is detrimental to matching the observed [(Mn,Co)/Fe] evolution at low [Fe/H]. A significant contribution from HNe seems to be critical for producing supersolar [(Co,Zn)/Fe] at low metallicity, though more work will need to be done in order to match the most extreme values. We also emphasise the need to update models for the enrichment sources at higher metallicity, as the satisfactory recovery of the solar values of [(Cr,Mn,Co,Zn)/Fe] still presents a challenge., Comment: 17 pages, 14 figures

We present a seven-minute long $4\pi$-3D simulation of a shell merger event in a non-rotating $18.88\, M_\odot$ supernova progenitor before the onset of gravitational collapse. The key motivation is to capture the large-scale mixing and asymmetries in the wake of the shell merger before collapse using a self-consistent approach. The $4\pi$ geometry is crucial as it allows us to follow the growth and evolution of convective modes on the largest possible scales. We find significant differences between the kinematic, thermodynamic and chemical evolution of the 3D and the 1D model. The 3D model shows vigorous convection leading to more efficient mixing of nuclear species. In the 3D case the entire oxygen shell attains convective Mach numbers of $\mathord{\approx}\, 0.1$, whereas in the 1D model, the convective velocities are much lower and there is negligible overshooting across convective boundaries. In the 3D case, the convective eddies entrain nuclear species from the neon (and carbon) layers into the deeper part of the oxygen burning shell, where they burn and power a violent convection phase with outflows. This is a prototypical model of a convective-reactive system. Due to the strong convection and the resulting efficient mixing, the interface between the neon layer and the silicon-enriched oxygen layer disappears during the evolution, and silicon is mixed far out into merged oxygen/neon shell. Neon entrained inwards by convective downdrafts burns, resulting in lower neon mass in the 3D model compared to the 1D model at time of collapse. In addition, the 3D model develops remarkable large-scale, large-amplitude asymmetries, which may have important implications for the impending gravitational collapse and the subsequent explosion., Comment: 23 pages, 18 figure, Accepted to The ApJ (matches the accepted version)

Observations with next-generation ground-based detectors further enhanced with multi-messenger (electromagnetic and neutrino) detections will allow us to probe new extreme astrophysics. Target sources included: core-collapse supernovae, continuous emission from isolated or accreting neutron stars, and bursts from magnetars and other pulsars., Comment: 13 pages, 1 figure, White Paper Submitted to Astro2020 (2020 Astronomy and Astrophysics Decadal Survey) by GWIC 3G Science Case Team (GWIC: Gravitational Wave International Committee)

State-of-the-art numerical simulations of core-collapse supernovae reveal that the main source of gravitational waves is the excitation of proto-neutron star modes during post-bounce evolution. In this work we derive universal relations that relate the frequencies of the most common oscillation modes observed, i.e. g-modes, p-modes and the f-mode, with fundamental properties of the system, such as the surface gravity of the proto-neutron star or the mean density in the region enclosed by the shock. These relations are independent of the equation of state, the neutrino treatment, and the progenitor mass and hence can be used to build methods to infer proto-neutron star properties from gravitational-wave observations alone. We outline how these measurements could be done and the constraints that could be placed on the proto-neutron star properties.

It has recently been proposed that global or local turbulence models can be used to simulate core-collapse supernova explosions in spherical symmetry (1D) more consistently than with traditional approaches for parameterised 1D models. However, a closer analysis of the proposed schemes reveals important consistency problems. Most notably, they systematically violate energy conservation as they do not balance buoyant energy generation with terms that reduce potential energy, thus failing to account for the physical source of energy that buoyant convection feeds on. We also point out other non-trivial consistency requirements for viable turbulence models. The model of Kuhfuss (1986) proves more consistent than the newly proposed approaches for supernovae, but still cannot account naturally for all the relevant physics for predicting explosion properties. We perform numerical simulations for a $20 M_\odot$ progenitor to further illustrate problems of 1D turbulence models. If the buoyant driving term is formulated in a conservative manner, the explosion energy of $\mathord{\sim}2\times 10^{51}\, \mathrm{erg}$ for the corresponding non-conservative turbulence model is reduced to $<10^{48}\,\mathrm{erg}$ even though the shock expands continuously. This demonstrates that the conservation problem cannot be ignored. Although plausible energies can be reached using an energy-conserving model when turbulent viscosity is included, it is doubtful whether the energy budget of the explosion is regulated by the same mechanism as in multi-dimensional models. We conclude that 1D turbulence models based on a spherical Reynolds decomposition cannot provide a more consistent approach to supernova explosion and remnant properties than other phenomenological approaches before some fundamental problems are addressed., Comment: 15 pages, 4 figures, accepted for publication in MNRAS. Revised version includes substantial improvements; the non-inclusion of the turbulent mass flux in the Kuhfuss model is justified rigorously by means of a Favre decomposition of the fluid equations, and the model is shown to be compatible with the second law of thermodynamics

Understanding gravitational wave emission from core-collapse supernovae will be essential for their detection with current and future gravitational wave detectors. This requires a sample of waveforms from modern 3D supernova simulations reaching well into the explosion phase, where gravitational wave emission is expected to peak. However, recent waveforms from 3D simulations with multi-group neutrino transport do not reach far into the explosion phase, and some are still obtained from non-exploding models. We therefore calculate waveforms up to 0.9\,s after bounce using the neutrino hydrodynamics code \textsc{CoCoNuT-FMT}. We consider two models with low and normal explosion energy, namely explosions of an ultra-stripped progenitor with an initial helium star mass of $3.5\,M_{\odot}$, and of an $18\,M_{\odot}$ single star. Both models show gravitational wave emission from the excitation of surface g-modes in the proto-neutron star with frequencies between $\mathord{\sim}800\,\mathrm{Hz}$ and 1000\,Hz at peak emission. The peak amplitudes are about $6\, \mathrm{cm}$ and $10\, \mathrm{cm}$, respectively, which is somewhat higher than in most recent 3D models of the pre-explosion or early explosion phase. Using a Bayesian analysis, we determine the maximum detection distances for our models in simulated Advanced LIGO, Advanced Virgo, and Einstein Telescope design sensitivity noise. The more energetic $18 M_\odot$ explosion will be detectable to about $17.5 \,\mathrm{kpc}$ by the LIGO/Virgo network and to about $180\, \mathrm{kpc}$ with the Einstein Telescope.

The solution of the Poisson equation is a ubiquitous problem in computational astrophysics. Most notably, the treatment of self-gravitating flows involves the Poisson equation for the gravitational field. In hydrodynamics codes using spherical polar grids, one often resorts to a truncated spherical harmonics expansion for an approximate solution. Here we present a non-iterative method that is similar in spirit, but uses the full set of eigenfunctions of the discretized Laplacian to obtain an exact solution of the discretized Poisson equation. This allows the solver to handle density distributions for which the truncated multipole expansion fails, such as off-center point masses. In three dimensions, the operation count of the new method is competitive with a naive implementation of the truncated spherical harmonics expansion with $N_\ell \approx 15$ multipoles. We also discuss the parallel implementation of the algorithm. The serial code and a template for the parallel solver are made publicly available., Comment: 9 pages, 4 figures, accepted for publication in ApJ. Added convergence tests and included some other minor revisions