Probing the Core-Collapse Supernova Mechanism with Gravitational Waves
C. D. Ott
备注：
13 pages, 5 figures. Submitted to the special issue of Class. Quant. Grav. for the 13th Gravitational Wave Data Analysis Workshop (GWDAW13). A version with high-resolution figures is available from http://stellarcollapse.org/papers/OTT_gwdaw13.pdf
The mechanism of core-collapse supernova explosions must draw on the energy provided by gravitational collapse and transfer the necessary fraction to the kinetic and internal energy of the ejecta. Despite many decades of concerted theoretical effort, the detailed mechanism of core-collapse supernova explosions is still unknown, but indications are strong that multi-D processes lie at its heart. This opens up the possibility of probing the supernova mechanism with gravitational waves, carrying direct dynamical information from the supernova engine deep inside a dying massive star. I present a concise overview of the physics and primary multi-D dynamics in neutrino-driven, magnetorotational, and acoustically-driven core-collapse supernova explosion scenarios. Discussing and contrasting estimates for the gravitational-wave emission characteristics of these mechanisms, I argue that their gravitational-wave signatures are clearly distinct and that the observation (or non-observation) of gravitational waves from a nearby core-collapse event could put strong constraints on the supernova mechanism.
Gravitational waves are a potential direct probe for the multi-dimensional flow during the first second of core-collapse supernova explosions. Here we outline the structure of the predicted gravitational wave signal from neutrino-driven supernovae of non-rotating progenitors from recent 2D and 3D simulations. We sketch some quantitative dependencies that govern the amplitudes of this signal and its evolution in the time-frequency domain.
We present gravitational wave emission predictions based on three core collapse supernova simulations corresponding to three different progenitor masses. The masses span a large range, between 9.6 and 25 Solar masses, are all initially non-rotating, and are of two metallicities: zero and Solar. We compute both the temporal evolution of the gravitational wave strains for both the plus and the cross polarizations, as well as their spectral decomposition and characteristic strains.
We constructed 70 SuperNova IDentification (SNID; Blondin & Tonry 2007) supernova (SN) templates using 640 spectra of stripped-envelope core-collapse SNe (SESNe) published by Modjaz et al. (2014). Fifty-six SN templates which are constructed from 458 spectra are brand new, increasing the number of SESNe and the number of SESNe spectra in the current SNID database by a factor of 2.6 and 2.0, respectively. We also made some type and phase refinements to templates in the current SNID database.
Core-collapse supernovae are among Nature's most energetic events. They mark the end of massive star evolution and pollute the interstellar medium with the life-enabling ashes of thermonuclear burning. Despite their importance for the evolution of galaxies and life in the universe, the details of the core-collapse supernova explosion mechanism remain in the dark and pose a daunting computational challenge. We outline the multi-dimensional, multi-scale, and multi-physics nature of the core-collapse supernova problem and discuss computational strategies and requirements for its solution. Specifi…
We report on a method, PUSH, for triggering core-collapse supernova (CCSN) explosions of massive stars in spherical symmetry. This method provides a framework to study many important aspects of core collapse supernovae: the effects of the shock passage through the star, explosive supernova nucleosynthesis and the progenitor-remnant connection. Here we give an overview of the method, compare the results to multi-dimensional simulations and investigate the effects of the progenitor and the equation of state on black hole formation.
Multi-dimensional fluid flow plays a paramount role in the explosions of massive stars as core-collapse supernovae. In recent years, three-dimensional (3D) simulations of these phenomena have matured significantly. Considerable progress has been made towards identifying the ingredients for shock revival by the neutrino-driven mechanism, and successful explosions have already been obtained in a number of self-consistent 3D models. These advances also bring new challenges, however. Prompted by a need for increased physical realism and meaningful model validation, supernova theory is now moving t…
We evolve models of rotating massive stars up to the stage of iron core collapse using the MESA code and find a shell with a mixed composition of primarily helium and oxygen in some cases. In the parameter space of initial masses of 13-40 Mo and initial rotation velocities of 0-450 km/s that we investigate, we find a mixed helium-oxygen shell with a significant mass only for a small fraction of the models. While the shell is formed due to rotational mixing, the pre-collapse rotation rate is not very high, as required for an energetic collapse-induced thermonuclear explosion. Our results sugges…
In this study we include axions in stellar evolution models adopting the current stringest constraints for their coupling to photons and electrons. We obtain that the minimum stellar mass of Core Collapse Supernova (CCSN) progenitors is shifted up by nearly 2 Mo. This result seems to be in tension with the observationaly derived minimum mass of CCSN progenitors.
The death of massive stars is shrouded in many mysteries. One of them is the mechanism that overturns the collapse of the degenerate iron core into an explosion, a process that determines the supernova explosion energy, properties of the surviving compact remnant, and the nucleosynthetic yields. The number of core-collapse supernova observations has been growing with an accelerating pace thanks to modern time-domain astronomical surveys and new tests of the explosion mechanism are becoming possible. We review predictions of parameterized supernova explosion models and compare them with explosi…
Stellar collapse and the subsequent development of a core-collapse supernova explosion emit bursts of gravitational waves (GWs) that might be detected by the advanced generation of laser interferometer gravitational-wave observatories such as Advanced LIGO, Advanced Virgo, and LCGT. GW bursts from core-collapse supernovae encode information on the intricate multi-dimensional dynamics at work at the core of a dying massive star and may provide direct evidence for the yet uncertain mechanism driving supernovae in massive stars. Recent multi-dimensional simulations of core-collapse supernovae exp…
We investigate effects of aspherical energy deposition in core-collapse supernovae on the light curve of the supernova shock breakout. We performed two-dimensional hydrodynamical calculations of an aspherical supernova explosion to obtain the time when a shock wave generated in the stellar interior reaches the stellar surface in each radial direction. Using results of the calculations, light curves during the shock breakout are derived in an approximate way. We show that the light curve during the shock breakout can be a strong indicator of aspherical properties of core-collapse supernovae.
Recent observations of a large fraction of Type II supernovae show traces of dense circumstellar medium (CSM) very close to the progenitor star. If this CSM is created by eruptive mass loss several months before core-collapse, the eruption itself may be visible as a precursor, helpful as an early warning of a near-future supernova. Using radiation hydrodynamical simulations based on the open-source code CHIPS, we theoretically model the emission from mass eruption of a red supergiant star. We find that for a modest mass eruption the luminosity is typically on the order of $10^{39}$ erg s$^{-1}…
We present a search for core-collapse supernovae in the Milky Way galaxy, using the MiniBooNE neutrino detector. No evidence is found for core-collapse supernovae occurring in our Galaxy in the period from December 14, 2004 to July 31, 2008, corresponding to 98% live-time for collection. We set a limit on the core-collapse supernova rate out to a distance of 13.5 kpc to be less than 0.69 supernovae per year at 90% CL.
With the advent of modern neutrino and gravitational wave detectors, the promise of multi-messenger detections of the next galactic core-collapse supernova has become very real. Such detections will give insight into the core-collapse supernova mechanism, the structure of the progenitor star, and may resolve longstanding questions in fundamental physics. In order to properly interpret these detections, a thorough understanding of the landscape of possible core-collapse supernova events, and their multi-messenger signals, is needed. We present detailed predictions of neutrino and gravitational …
In a previously presented proof-of-principle study we established a parametrized spherically symmetric explosion method (PUSH) that can reproduce many features of core-collapse supernovae. The present paper goes beyond a specific application that is able to reproduce observational properties of SN1987A and performs a systematic study of the explosion properties for an extensive set of non-rotating, solar metallicity stellar progenitor models in the mass range from 10.8 to 120 M$_\odot$.This includes the transition from neutron stars to black holes as the final result of the collapse of massive…
The explosion outcome and diagnostics of core-collapse supernovae depend sensitively on the nature of the stellar progenitor, but most studies to date have focused exclusively on one-dimensional, spherically-symmetric massive star progenitors. We present some of the first core-collapse supernovae simulations of three-dimensional massive star supernovae progenitors, a 12.5- and a 15-M$_{\odot}$ model, evolved in three-dimensions from collapse to bounce through explosion with the radiation-hydrodynamic code F{\sc{ornax}}. We compare the results using those starting from three-dimensional progeni…
The Swift UV-Optical Telescope (UVOT) has been observing Core-Collapse Supernovae (CCSNe) of all subtypes in the UV and optical since 2005. We present here 50 CCSNe observed with the Swift UVOT, analyzing their UV properties and behavior. Where we have multiple UV detections in all three UV filters (λc = 1928 - 2600 Å), we generate early time bolometric light curves, analyze the properties of these light curves, the UV contribution to them, and derive empirical corrections for the UV-flux contribution to optical-IR based bolometric light curves.
We review recent progress in the theoretical predictions of gravitational waves (GWs) of core-collapse supernovae. Following a brief summary of the methods in the numerical modeling, we summarize multiple physical elements that determine the GW signatures which have been considered to be important in extracting the information of the long-veiled explosion mechanism from the observation of the GWs. We conclude with a summary of the most urgent tasks to make the dream come true.
The stationary accretion shock instability (SASI) plays a central role in modern simulations of the explosion phase of core-collapse supernovae (CCSNe). It may be key to realizing neutrino powered explosions, and possibly links birth properties of pulsars (e.g., kick, spin, and magnetic field) to supernova dynamics. Using high-resolution magnetohydrodynamic simulations, we study the development of turbulence, and subsequent amplification of magnetic fields in a simplified model of the post-bounce core-collapse supernova environment. Turbulence develops from secondary instabilities induced by t…
The explosion of a core-collapse supernova can be approximated by the breakdown of steady-state solutions for accretion onto a proto-neutron star (PNS). We analytically show that as the neutrino luminosity exceeds a critical value L_c, the neutrinosphere pressure exceeds the hydrostatic limit even for an optimal shock radius R. This yields L_c \propto M^2 T^2 (with logarithmic corrections) and R \propto M/T, in agreement with numerical results, where M, T are the PNS mass, neutrino temperature. The near-critical flow can be approximated as a ballistic shell on top of an isothermal layer.
Many core-collapse supernova progenitors are presumed to be in binary systems. If a star explodes in a binary system, the early supernova light curve can be brightened by the collision of the supernova ejecta with the companion star. The early brightening can be observed when the observer is in the direction of the hole created by the collision. Based on a population synthesis model, we estimate the fractions of core-collapse supernovae in which the light-curve brightening by the collision can be observed. We find that 0.19% of core-collapse supernova light curves can be observed with the coll…
Most massive stars experience binary interactions in their lifetimes that can alter both the surface and core structure of the stripped star with significant effects on their ultimate fate as core-collapse supernovae. However, core-collapse supernovae simulations to date have focused almost exclusively on the evolution of single stars. We present a systematic simulation study of single and binary-stripped stars with the same initial mass as candidates for core-collapse supernovae (11 - 21 M$_{\odot}$). Generally, we find that binary-stripped stars core tend to be less compact, with a more prom…
We highlight developments in the domain of supernova neutrinos. We discuss the importance of the future observation, by running and upcoming experiments, of the neutrino signals from the next supernova as well as of the diffuse supernova neutrino background.
A detection of a core-collapse supernova signal with an Advanced LIGO and Virgo gravitational-wave detector network will allow us to measure astrophysical parameters of the source. In real advanced gravitational-wave detector data there are transient noise artifacts that may mimic a true gravitational-wave signal. In this paper, we outline a procedure implemented in the Supernova Model Evidence Extractor (SMEE) that determines if a core-collapse supernova signal candidate is a noise artefact, a rapidly-rotating core-collapse supernova signal, or a neutrino explosion mechanism core-collapse sup…
Most existing criteria derived from progenitor properties of core-collapse supernovae are not very accurate in predicting explosion outcomes. We present a novel look at identifying the explosion outcome of core-collapse supernovae using a machine learning approach. Informed by a sample of 100 2D axisymmetric supernova simulations evolved with Fornax, we train and evaluate a random forest classifier as an explosion predictor. Furthermore, we examine physics-based feature sets including the compactness parameter, the Ertl condition, and a newly developed set that characterizes the silicon/oxygen…
Much progress in realistic modeling of core-collapse supernovae has occurred recently through the availability of multi-teraflop machines and the increasing sophistication of supernova codes. These improvements are enabling simulations with enough realism that the explosion mechanism, long a mystery, may soon be delineated. We briefly describe the CHIMERA code, a supernova code we have developed to simulate core-collapse supernovae in 1, 2, and 3 spatial dimensions. We then describe the results of an ongoing suite of 2D simulations initiated from a 12, 15, 20, and 25 solar mass progenitor. The…
We investigate several aspects of black hole formation in failing core-collapse supernovae using 1D general-relativistic hydrodynamic simulations. We use the open-source code GR1D and incorporate into it nucleon-nucleon Bremsstrahlung, a crucial neutrino pair-production channel. We focus on how various thermal effects can influence the postbounce supernova evolution towards black hole formation. By performing simulations with and without nucleon-nucleon Bremsstrahlung, we investigate the sensitivity of black hole formation to thermal support in the protoneutron star. We also investigate delaye…
We have made core-collapse supernova simulations that allow oscillations between electron neutrinos (or their anti particles) with right-handed sterile neutrinos. We have considered a range of mixing angles and sterile neutrino masses including those consistent with sterile neutrinos as a dark matter candidate. We examine whether such oscillations can impact the core bounce and shock reheating in supernovae. We identify the optimum ranges of mixing angles and masses that can dramatically enhance the supernova explosion by efficiently transporting electron anti-neutrinos from the core to behind…
We investigate light-curve and spectral properties of ultra-stripped core-collapse supernovae. Ultra-stripped supernovae are the explosions of heavily stripped massive stars which lost their envelopes via binary interactions with a compact companion star. They eject only ~ 0.1 Msun and may be the main way to form double neutron-star systems which eventually merge emitting strong gravitational waves. We follow the evolution of an ultra-stripped supernova progenitor until iron core collapse and perform explosive nucleosynthesis calculations. We then synthesize light curves and spectra of ultra-s…
The explosion mechanism of core-collapse supernovae is a long-standing problem in stellar astrophysics. We briefly outline the main contenders for a solution and review recent efforts to model core-collapse supernova explosions by means of multi-dimensional simulations. We discuss several suggestions for solving the problem of missing or delayed neutrino-driven explosions in three-dimensional supernova models, including -- among others -- variations in the microphysics and large seed perturbations in convective burning shells. Focusing on the neutrino-driven mechanism, we summarise currents ef…
We optimize the third-generation gravitational-wave detector to maximize the range to detect core-collapse supernovae. Based on three-dimensional simulations for core-collapse and the corresponding gravitational-wave waveform emitted, the corresponding detection range for these waveforms is limited to within our galaxy even in the era of third-generation detectors. The corresponding event rate is two per century. We find from the waveforms that to detect core-collapse supernovae with an event rate of one per year, the gravitational-wave detectors need a strain sensitivity of 3$\times10^{-27}~$…
Core-collapse supernovae are among Nature's grandest explosions. They are powered by the energy released in gravitational collapse and include a rich set of physical phenomena involving all fundamental forces and many branches of physics and astrophysics. We summarize the current state of core-collapse supernova theory and discuss the current set of candidate explosion mechanisms under scrutiny as core-collapse supernova modeling is moving towards self-consistent three-dimensional simulations. Recent work in nuclear theory and neutron star mass and radius measurements are providing new constra…
Core-collapse supernovae produce copious low-energy neutrinos and are also predicted to radiate gravitational waves. These two messengers can give us information regarding the explosion mechanism. The gravitational wave detection from these events are still elusive even with the already advanced detectors. Here we give a concise and timely introduction to a new method that combines triggers from GW and neutrino observatories; more details shall be given in a forthcoming paper [1]. Keywords: multimessenger, supernova, core-collapse, low-energy neutrino, gravitational wave.
Massive stars unable to sustain gravitational collapse, at the end of nuclear burning stage, turns out into core-collapse supernovae, leaving behind compact objects like neutron stars or black holes. The progenitor properties like mass and metallicity primarily governs the explosion parameters and type of compact remnant. In this contribution we summarize observational study of three Core Collapse type IIP SNe 2012aw, 2013ab and 2013ej, which are rigorously observed from ARIES and other Indian observatories and discuss their progenitor and explosion properties.
Using 250 neutron star merger simulations with microphysics, we explore for the first time the role of nuclear incompressibility in the prompt collapse threshold for binaries with different mass ratios. We demonstrate that observations of prompt collapse thresholds, either from binaries with two different mass ratios or with one mass ratio but combined with the knowledge of the maximum neutron star mass or compactness, will constrain the incompressibility at the maximum neutron star density, $K_{\rm max}$, to within tens of percent. This, otherwise inaccessible, measure of $K_{\rm max}$ can po…
We present a core-collapse supernova model for the extremely luminous Type Ic supernova 2007bi. By performing numerical calculations of hydrodynamics, nucleosynthesis, and radiation transport, we find that SN 2007bi is consistent with the core-collapse supernova explosion of a 43 Msun carbon and oxygen core obtained from the evolution of a progenitor star with a main sequence mass of 100 Msun and metallicity of Z = Zsun/200, from which its hydrogen and helium envelopes are artificially stripped. The ejecta mass and the ejecta kinetic energy of the models are 40 Msun and 3.6*10^{52} erg. The ej…
We present gravitational wave and neutrino signatures obtained in our first principle 3D core-collapse supernova simulation of 15M non-rotating progenitor with Chimera code. Observations of neutrinos emitted by the forming neutron star, and gravitational waves, which are produced by hydrodynamic instabilities is the only way to get direct information about the supernova engine. Both GW and neutrino signals show different phases of supernova evolution.
A notable feature of the two standard models for thermonuclear and core-collapse supernovae is that, although these two models are fundamentally different, the respective supernova types have quite similar rates and appearances. For instance, both types occur one to several times per century per typical galaxy and both types seed the universe with the heavy elements essential to life. In spite of this, neither standard model provides a reasonably problem-free description of its target phenomenon. A major obstacle to providing a unified picture of supernovae would seem to be the fact that type …
I summarize what we have learned about the nature of stars that ultimately explode as core-collapse supernovae from the examination of images taken prior to the explosion. By registering pre-supernova and post-supernova images, usually taken at high resolution using either space-based optical detectors, or ground-based infrared detectors equipped with laser guide star adaptive optics systems, nearly three dozen core-collapse supernovae have now had the properties of their progenitor stars either directly measured or (more commonly) constrained by establishing upper limits on their luminosities…
Future galactic supernovae will provide an extremely long baseline for studying the properties and interactions of neutrinos. In this paper, we discuss the possibility of using such an event to constrain (or discover) the effects of exotic physics in scenarios that are not currently constrained and are not accessible with reactor or solar neutrino experiments. In particular, we focus on the cases of neutrino decay and quantum decoherence. We calculate the expected signal from a core-collapse supernova in both current and future water Cerenkov, scintillating, and liquid argon detectors, and fin…
Large neutrino detectors like IceCube monitor for core-collapse supernovae using low energy (MeV) neutrinos, with a reach to a supernova neutrino burst to the Magellanic Cloud. However, some models predict the emission of high energy neutrinos (GeV-TeV) from core-collapse supernovae through the interaction of ejecta with circumstellar material and (TeV-PeV) through choked jets. In this paper, we explore the detection horizon of IceCube for core-collapse supernovae using high-energy neutrinos from these models. We examine the potential of two high-energy neutrino data samples from IceCube, one …
Current surveys are underway to utilize gravitational lensing by galaxy clusters with Einstein radii >35" in the search for the highest redshift galaxies. Associated supernova from the epoch of reionization would have their fluxes boosted above the detection threshold, extending their duration of visibility. We predict that the James Webb Space Telescope (JWST) will be able to discover lensed core-collapse supernovae at redshifts exceeding z=7-8.
Past high-energy density laboratory experiments provided insights into the physics of supernovae, supernova remnants, and the destruction of interstellar clouds. In a typical experimental setting, a laser-driven planar blast wave interacts with a compositionally-homogeneous spherical or cylindrical target. In this work we propose a new laboratory platform that accounts for curvature of the impacting shock and density stratification of the target. Both characteristics reflect the conditions expected to exist shortly after a supernova explosion in a close binary system. We provide details of a p…
Mapping supernovae to their progenitors is fundamental to understanding the collapse of massive stars. We investigate the red supergiant problem, which concerns why red supergiants with masses $\sim16$-$30 M_\odot$ have not been identified as progenitors of Type IIP supernovae, and the supernova rate problem, which concerns why the observed cosmic supernova rate is smaller than the observed cosmic star formation rate. We find key physics to solving these in the compactness parameter, which characterizes the density structure of the progenitor. If massive stars with compactness above $ξ_{2.5} \…
The recent discovery that the Fe-K line luminosities and energy centroids observed in nearby SNRs are a strong discriminant of both progenitor type and circumstellar environment has implications for our understanding of supernova progenitor evolution. Using models for the chemical composition of core-collapse supernova ejecta, we model the dynamics and thermal X-ray emission from shocked ejecta and circumstellar material, modeled as an $r^{-2}$ wind, to ages of 3000 years. We compare the X-ray spectra expected from these models to observations made with the Suzaku satellite. We also model the …
The joint observation of core-collapse supernovae with gamma-ray bursts shows that jets can be launched in the aftermath of stellar core collapse, likely by a newly formed black hole that accretes matter from the star. Such gamma-ray bursts have only been observed accompanying Type Ibc supernovae, indicating a stellar progenitor that lost its Hydrogen envelope before collapse. According to recent hypothesis it is possible that jets are launched in core-collapse events even when the progenitors still retain their Hydrogen envelopes, however, such jets are not able to burrow through the star and…
We investigate the role of hyperons in the dynamical collapse of a non-rotating massive star to a black hole(BH) using one dimensional general relativistic $GR1D$ code. We follow the dynamical formation and evolution of a protoneutron star (PNS) to a black hole using various progenitor models, adopting a hyperonic equation of state (EoS) generated by Shen et. al. We compare the results with those of nuclear EoS by Shen et. al. and understand the role of strange hyperons in the core collapse supernova. We discuss the neutrino signals that may be used as a probe to core collapse. Further, an exo…
With myriads of detection events from a prospective Galactic core-collapse supernova, current and future neutrino detectors will be able to sample detailed, time-dependent neutrino fluxes and spectra. This offers enormous possibilities for inferring supernova physics from the various phases of the neutrino signal from the neutronization burst through the accretion and early explosion phase to the cooling phase. The signal will constrain the time evolution of bulk parameters of the young proto-neutron star like its mass and radius as well as the structure of the progenitor, probe multi-dimensio…
How do massive stars explode? Progress toward the answer is driven by increases in compute power. Petascale supercomputers are enabling detailed three-dimensional simulations of core-collapse supernovae. These are elucidating the role of fluid instabilities, turbulence, and magnetic field amplification in supernova engines.
We discuss the possible impact of strange quark matter on the evolution of core-collapse supernovae with emphasis on low critical densities for the quark-hadron phase transition. For such cases the hot proto-neutron star can collapse to a more compact hybrid star configuration hundreds of milliseconds after core-bounce. The collapse triggers the formation of a second shock wave. The latter leads to a successful supernova explosion and leaves an imprint on the neutrino signal. These dynamical features are discussed with respect to their compatibility with recent neutron star mass measurements w…
The equation of state and composition of matter are calculated for conditions typical for pre-collapse and early collapse stages in core collapse supernovae. The composition is evaluated under the assumption of nuclear statistical equilibrium, when the matter is considered as an `almost' ideal gas with corrections due to thermal excitations of nuclei, to free nucleon degeneracy, and to Coulomb and surface energy corrections. The account of these corrections allows us to obtain the composition for densities a bit below the nuclear matter density. Through comparisons with the equation of state (…
The design and analysis of time-domain sky surveys requires the ability to simulate accurately realistic populations of core collapse supernova (SN) events. We present a set of spectral time-series templates designed for this purpose, for both hydrogen-rich (type II, IIn, IIb) and stripped envelope (types Ib, Ic, Ic-BL) core collapse supernovae. We use photometric and spectroscopic data for 67 core collapse supernovae from the literature, and for each generate a time-series spectral template. The techniques used to build the templates are fully data-driven with no assumption of any parametric …
IceCube is a cubic kilometer neutrino detector array in the Antarctic ice that was designed to search for astrophysical, high-energy neutrinos. It has detected a diffuse flux of astrophysical neutrinos that appears to be of extragalactic origin. A possible contribution to this diffuse flux could stem from core-collapse supernovae. The high-energy neutrinos could either come from the interaction of the ejecta with a dense circumstellar medium or a jet, emanating from the star's core, that stalls in the star's envelope. Here, we will present results of a stacking analysis to search for this high…
A mechanism of formation of gravitational waves in the Universe is considered for a nonspherical collapse of matter. Nonspherical collapse results are presented for a uniform spheroid of dust and a finite-entropy spheroid. Numerical simulation results on core-collapse supernova explosions are presented for the neutrino and magnetorotational models. These results are used to estimate the dimensionless amplitude of the gravitational wave with a frequency ν~1300 Hz, radiated during the collapse of the rotating core of a pre-supernova with a mass of 1:2M(sun) (calculated by the authors in 2D). Thi…
