Open Issues in Core Collapse Supernova Theory (Proceedings from the Institute for Nuclear Theory 14)

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This has a strong impact in many other astrophysical fields, like fireballs detection, minor planet studies, the search for extra-solar planets, the monitoring of variable stars in our Galaxy, the study of active galactic nuclei, the detection and monitoring of supernovae, and the immediate follow-up of high-energy transients such as cosmic gamma-ray bursts, besides the search of neutrino and gravitational waves electromagnetic counterparts. Last, but not least, space debris surveillance and tracking is another field of increasing interest.

Educational aspects will be also covered. Thus, the main focus of the workshop will be on the new and existing astronomical facilities whose goal is to observe a wide variety of astrophysical targets with no or very little human interaction. As in the past 10 years, we expect the workshop will continue as an international forum for researchers to summarize the most recent developments and ideas in the field, with a special emphasis given to the Technical and Scientific results obtained within the last two years and future developments, with specific sessions on Educational Activities and Space Surveillance and Tracking.

Contact: Email: astrorob iaa. The nuclear symmetry energy and its density dependence are known to govern to a large extent the physics of nuclear masses and radii, the collective excitations at moderate excitation energies, up to the dynamics and observables of the high-energy heavy-ion collisions that explore regimes characterized by higher densities and isospin asymmetry of nuclear matter, especially, with radioactive beams.

Last but not least, the understanding of the density dependence of nuclear symmetry energy is of paramount importance in the context of the forefront research related to the astrophysical modelling of the stellar and explosive nucleosynthesis, of supernovae and kilonovae first observed in the aftermath of GW , as well as of the properties of neutron stars and their mergers.

The purpose of the workshop is to study in detail the application of the Scarlet pipeline for de-blending sources in different astrophysical contexts of interest for the LSST community. Contact: Email: loc-lsst-scarlet inaf. We will do this by bringing together all the numerous groups in Aotearoa who already have dark sky accreditation from the International Dark Sky Association, or who aspire to do so in the near future.

We invite scientists who focus on atmospheres, fundamental parameters, formation mechanisms and beyond of brown dwarfs, exoplanets, and solar system objects to gather for a two day conference. Our aim is to build upon the first two meetings which engaged attendees in lively discussions of the current, future, and overlap status of the fields. The workshop is a short two-day meeting aimed at students in their final bachelor studies, postgraduate students, and researchers already familiar with General Relativity and Cosmology. The main lectures will be complemented with seminars and poster session.

In this third edition the invited countries are Scotland and Italy. The main objective of III-MCTPCosmoGrav is to promote discussions centering on the themes of the invited lectures and talks focused on recent developments in areas related to Gravitation and Cosmology, in topics such as: Gravitational Waves observations and data analysis and Dark Matter nature and distribution. Contact: Email: celia. It will be held from October 28th to November 1st, in Antofagasta, Chile.

It is an introductory school oriented at students and researchers of all levels. Current theories succeed in reproducing the observed mass distribution of galaxies only by introducing powerful stellar and black hole feedback that alleviate the rapid gas cooling and condensation into stars. An emergent alternative is that a large fraction of the gas internal energy is stored in turbulent motions instead of being radiated away and lost. Turbulence however adds a huge level of complexity to the physics of baryonic matter because cosmic turbulence involves magnetic fields and the plasma nature of the gas and because it pervades all the thermal phases from the hottest at more than one million Kelvin to the coldest at about 10 Kelvin in which stars form.

The prodigious development of new facilities on the observational side, and the fast increase of computing power on the modeling side are opening up the field, calling for new multi-disciplinary approaches. The meeting will gather astrophysicists, observers and theorists of the local and high-redshift universe, with experts of turbulence and plasma physics to trigger cross-pollination between research fields usually discussed separately. The format of the workshop will include not only reports but also a series of lectures and several special sessions for discussion and hands-off.

The Conference is organized in cooperation with various Physics Departments in Malaysia. The scientific objective of the Conference is to provide a forum for interaction involving world-renowned researchers as to stimulate and enhance interest in Physics around the Asia Pacific region. The school is aimed primarily at students and young researchers wishing to build or perfect their knowledge of cosmic rays. The main purpose is to provide a good opportunity for young scientists, master and PhD students coming from universities and institutes in the Asia-Pacific region to develop regional exchange activities, mutual understanding and cooperation, as well as stimulate scientific training and education.

TeVPA aims to bring together leading scientists in the field to discuss the latest results and ideas, and prospects for progress in Astroparticle Physics. The conference will feature invited plenary talks covering the topics of recent interest. A number of parallel and poster sessions will provide an opportunity for junior scientists to present their work. Contact: Email: tevpa.

This will make possible a multi-messenger approach, capitalizing on multiple probes that capture phenomena of the Universe in different observational channels over a large range of redshifts and will open the opportunity to study the synergies between different experiments. The conference will bring researchers working on theoretical aspects, statistical methods and observational cosmology and will discuss the new directions of fundamental physics and cosmological mysteries which can be addressed from these multi-messenger multi-frequency probes.

Along with probing the fundamental aspect of gravity, nature of dark energy, properties of dark matter, primordial gravitational waves, neutrino masses and hierarchy, next-generation missions will also be powerful probes to learn about the astrophysical aspects such as the population of black holes, properties of first stars, reionization history of the Universe, galaxy evolution and the interplay between cosmological and astrophysical effects.

The meeting will also discuss future statistical tools and machine learning techniques which will be required to make robust measurements from the data which will be available from the upcoming missions on astrophysical gravitational waves, cosmic microwave background, large scale structure, line intensity mapping, supernovae and many others. Topics: Cosmic microwave background, gravitational waves, large scale structure, line intensity mapping, standard candles. The School is addressed to advanced masters students, graduate students enrolled in a PhD program, and postdocs. A limited amount of financial help to attend the School is available see registration page.

Topics: Neutrino Cosmology, Non-linear perturbation theory, Testing dark energy with current and future observations, CMB polarisation and spectral distortions. Proposed neutrino species can also in principle constitute the bulk of the dark matter.

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They may moreover leave different signatures on astrophysical scales than the hitherto standard WIMP-based cold dark matter. As the parameter space for the latter is increasingly constrained experimentally, such alternates become more relevant, along with others such as the lately topical ultra-light axions.

The NDM aims to be a forum for the discussion and exchange of ideas regarding the particle phenomenology, astrophysical signatures and experimental constraints related to those two fundamental and actively studied issues in particle and astroparticle physics, namely neutrinos and dark matter, and their possible connections. The format for this symposium consists of invited and contributed oral and poster presentations in several themed sessions. We encourage your participation and hope that you will share this announcement with colleagues. Important topics that will be covered include hidden sector model building in the LHC era, thermalization of the universe following inflation, possibilities of post-inflation cosmic history prior to nucleosynthesis, and associated experimental signatures.

The conference aims to attract researchers in different areas to develop new directions in model building and establish new experimental paths for probing early universe cosmology and dark matter phenomenology. If this is to succeed it will require the active participation of the major projects and observatories around the world. This constitutes undoubtly a new era through a move from object- to data-driven astrophysics.

We can distinguish two types of challenges: the first one is related to the exploration of the data space and the second one is the physical interpretation of the results of this exploration. Astrostatistics cannot be reduced to the technical issues brought by methods and algorithms required to analyse the data. Despite these tools are not part of the cursus of astronomers, things are changing rapidly through schools, training sessions, collaborations with experts statisticians as well as developments of specific tools adapted to astronomical data. The use of new techniques pervades the astronomical literature.

To convince more and more astronomers to switch to this new approach to do science, it is important to demonstrate the relevance of astrostatistics results.

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The Large Area Telescope LAT has discovered more than a thousand new sources and many new source classes, bringing the importance of gamma-ray astrophysics to an ever-broadening community. Along this path, the formation of complex organic molecules necessary to construct the building blocks of life brings us a step closer to the understanding of the evolution of life. The advancement in the understanding of these vast intricacies of space lies in the development of varied laboratory techniques and astrophysical modelling in close connection with space exploration and astronomical observations.

Return of extra-terrestrial samples is one of the drivers of these missions e. The ECLA conference will provide the opportunity for interdisciplinary exchanges between scientists active in different research fields, which range from astronomy to geology and from chemistry to instrumentation. Contact: Email: vito. It will connect the observations to theoretical modeling of galaxy formation on large scales and star formation on small scales.

The topics for discussion will include the efficiency of star cluster formation as a function of environment, and the origins of the cluster age and metallicity distributions. The meeting will aim to highlight the similarities and differences in star formation in low-redshift and high-redshift galaxies. Galactic foregrounds are an issue in different observational contexts for the Cosmic Microwave Background CMB , the HI 21cm signal from the epoch of reionization EoR , line intensity mapping and lensing surveys. The more general coverage of topics in nuclear astrophysics by the lecturers at this school is intended to broadly familiarize young theoretical and experimental nuclear astrophysicists with exciting and challenging current problems.

The workshop is focused on subjects related to statistical nuclear physics. By bringing together scientists working in various areas of this diverse field -- including astrophysics, technology, theory, and experiment. Announcement Website Registration. In light of this special occasion we have invited a number of speakers to review historical development and present the latest experimental and theoretical results on low energy proton and alpha capture reactions for the CNO cycles in main sequence stars and stellar helium burning.

It is a collaborative effort between CARINA and JINA with the goal to develop an updated and unified nuclear reaction data base for modeling a wide variety of stellar nucleosynthesis scenarios. This workshop will review experimental methods for mass determinations, theoretical modeling of nuclear masses, and their implications for outstanding questions in both nuclear structure and nuclear astrophysics. The objectives of the proposed School are to enable younger researchers to gain the background knowledge and to provide real experience in the use of modern direct reaction methods and codes.

Announcement Application Program Dining Photos. Charlie Barnes is one of the great pioneers in the field of experimental nuclear astrophysics. On the occasion of his 85th birthday we are planning to organize this special workshop on the "Status of 12 C a,y 16 O" to honor him and his contributions and achievements to the field. This informal two day workshop is intended to bring together diverse parts of the nuclear astrophysics community interested in the physics of massive stellar progenitors and their ability to collapse and later explode as a Supernovae or make a GRB.

Announcement Agenda Talks.

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This workshop covered the basic theoretical methods and computational tools used for shell model configuration mixing calculations. The emphasis was on a "hands-on" use of computer codes. Announcement Registration Lectures Pictures. This is the first of a series of meetings, to be held every other year, that aim to bring together all of JINA, JINA collaborators and other interested researchers to discuss current research activities. Website Program Talks Pictures More. The primary aim of the Workshop is to bring together interested physicists from the areas of Astrophysics, Giant Resonances, and Heavy-Ion Reactions, to discuss current status of experiments and theoretical models related to nuclear incompressibility and the equation of state, and to explore what experiments might be needed to clarify some of the outstanding issues.

Announcement Registration Program Participants Talks. The school focused on "Nuclear Reaction Network Techniques". This workshop intends to strengthen the communication and collaboration between four research directions to improve our understanding of s-process nucleosynthesis. Important theoretical and numerical issues include.

To date, collapse simulations generally include state-of-the-art treatments of only one or two of the above physics issues often because of numerical constraints. For example, those studies that include advanced microphysics have often been run with Newtonian gravity and approximate evaluation of the GW emission; see Section 2. A 3D, general relativistic collapse simulation that includes all significant physics effects is not feasible at present. However, good progress has been made on the majority of the issues listed above; the more recent work will be reviewed in some detail here.

The remainder of this article is structured as follows. Each of these sections 2 , 3 , 4 , 5 , 6 is divided into subsection topics: collapse scenario, formation rate, GW emission mechanisms, and numerical predictions of GW emission. In the subsections on numerical predictions, the detectability of the GW emission from various phenomena associated with collapse is examined. In particular, the predicted characteristics of GW emission are compared to the sensitivities of LIGO for sources with frequencies of 1 to 10 4 Hz and LISA for sources with lower frequencies in the range of 10 -4 to 1 Hz.

For those white dwarfs in binaries, binary accretion can reheat the white dwarf. If the accreted material ignites degenerately, the resultant nuclear explosion produces a nova and ejects all of the accreted material. But if this material burns non-degenerately, the white dwarf will gain mass. When the mass of the white dwarf exceeds the Chandrasekhar stability limit, it will begin to collapse. Two possible fates await this collapsing white dwarf.

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If the collapsing core can achieve high enough temperatures, nuclear burning will begin and the stellar pressure will increase. However, neutrino emission from electron capture e. The result of this collapse is the formation of a neutron star. For O-Ne-Mg white dwarfs, electron capture may be stronger than nuclear burning under most conditions if a Rayleigh-Taylor instability does not produce a turbulent burn front [ , ].

For more details about the conditions under which AIC occurs, see [ , , 32 , 31 , ]. The dynamics of the collapse itself are somewhat similar to the dynamics of core collapse SNe: the collapse proceeds until the core reaches nuclear densities, the core then bounces and sends out a bounce shock that stalls when it becomes optically thin to neutrinos and loses its thermal energy.

However, there is very little envelope around this core to prevent an explosion and the shock can easily be revived to drive a low-mass explosion. Exactly how much matter is ejected depends upon the details of the collapse calculation compare [ , , 82 ]. The AIC occurrence rate is difficult to determine for a number of reasons. These include incomplete understanding of binary star evolution and determining how much matter is truly accreted onto the white dwarf versus the amount that is ejected through novae [ 48 , , ].

Another uncertainty is whether the collapse of an accreting Chandrasekhar mass white dwarf results in a supernovae explosion or a complete AIC with accompanying neutron star formation. New results continue to alter the dividing lines between these fates [ ]. The final fate of accretion OMgNe white dwarfs as a function of the initial white dwarf mass and the accretion rate onto the white dwarf. Figure 3 of [ ]; used with permission. The AIC rate can be indirectly inferred from the observed amount of rare, neutron rich isotopes present in the Galaxy. Binary population synthesis analysis can be used to determine which accreting white dwarfs will undergo AIC.

Thus, a reasonable occurrence rate can be found for an observation distance of Mpc. The convective time is likely to be brief, so it is unlikely that post-bounce convection will produce GWs. However, GWs will also be produced if the collapsing star or neutron star remnant develops rotational or pulsational instabilities [ , , , , ]. These include global rotational mode, r -mode, f -mode, and fragmentation instabilities.

Here, T rot is the rotational kinetic energy and W is the gravitational potential energy. Dynamical rotational instabilities, driven by Newtonian hydrodynamics and gravity, develop on the order of the rotation period of the object. Secular rotational instabilities are driven by dissipative processes such as gravitational radiation reaction and viscosity. When this type of instability arises, it develops on the timescale of the relevant dissipative mechanism, which can be much longer than the rotation period e. In an attempt to reduce these high rotation requirements, there has been increasing work studying bar-mode instabilities driven by dynamical sheer in differentially rotating neutron stars.

Sheer instabilities excite the co-rotating f -mode. In rotating stars, gravitational radiation reaction drives the r -modes toward unstable growth [ 5 , 77 ]. In hot, rapidly rotating neutron stars, this instability may not be suppressed by internal dissipative mechanisms such as viscosity and magnetic fields [ ].

The emitted GWs carry away angular momentum, and will cause the newly formed neutron star to spin down over time. Some research suggests that magnetic fields, hyperon cooling, and hyperon bulk viscosity may limit the growth of the r -mode instability, even in nascent neutron stars [ , , , , , , , 6 ] significant uncertainties remain regarding the efficacy of these dissipative mechanisms. Furthermore, a study of a simple barotropic neutron star model by Arras et al.

There is some numerical evidence that a collapsing star may fragment into two or more orbiting clumps [ 96 ]. If this does indeed occur, the orbiting fragments would be a strong GW source. The accretion-induced collapse of white dwarfs has been simulated by a number of groups [ 14 , , , 82 ]. The most sophisticated are those carried out by Fryer et al. FHH used both numerical and analytical techniques to estimate the peak amplitude h pk , energy E GW , and frequency f GW of the gravitational radiation emitted during the collapse simulations they studied.

For direct numerical computation of the GWs emitted in these simulations, FHH used the quadrupole approximation, valid for nearly Newtonian sources [ ]. This approximation is standardly used to compute the GW emission in Newtonian simulations. The reduced or traceless quadrupole moment of the source can be expressed as. The energy E GW is a function of. However, successive application of numerical derivatives generally introduces artificial noise. Methods for computing and without taking numerical time derivatives have been developed [ 74 , 25 , ].

Thus, instantaneous values for and can be computed on a single numerical time slice see [ , ] for details. Note that FHH define h pk as the maximum value of the rms strain , where angular brackets indicate that averages have been taken over both wavelength and viewing angle on the sky. Neglect of general relativity in rotational collapse studies is of special concern because relativistic effects counteract the stabilizing effects of rotation see Section 3. Because the code used in the collapse simulations examined by FHH [ 82 ] was axisymmetric, their use of the numerical quadrupole approximation discussed above does not account for GW emission that may occur due to non-axisymmetric mass flow.

The GWs computed directly from their simulations come only from polar oscillations which are significant when the mass flow during collapse [or explosion] is largely aspherical. In order to predict the GW emission produced by non-axisymmetric instabilities, FHH employed rough analytical estimates. FHH vary the mass m assumed to be enclosed by the bar which has a corresponding length 2 r and compute the characteristics of the GW emission as a function of this enclosed mass.

For simplicity, FHH assumed that a fragmentation instability will cause a star to break into two clumps although more clumps could certainly be produced. Their estimates for the rms strain and power radiated by the orbiting binary fragments are. This approach is detailed in FHH. If the neutron star mass and initial radius are taken to be 1. For sources that persist for N cycles,. See the text for details regarding the computations of h. Secular bar-mode sources are identified with an s , dynamical bar-modes with a d. The SMS sources are assumed to be located at a luminosity distance of 50 Gpc.

The bar-mode source is a dynamical bar-mode. The simulation of Fryer et al. The choice of initial angular momentum J for the progenitor in an AIC simulation can affect this outcome. Fryer et al. Higher angular momenta are certainly possible. If higher values of J exist in accreting white dwarfs, bar-mode instabilities may be more likely to occur see the discussion of work by Liu and Lindblom below. FHH compute h f GW for coherent observation of the neutron star as it spins down over the course of a year. The track moves down and to the left i.

In addition to full hydrodynamics collapse simulations, many studies of gravitational collapse have used hydrostatic equilibrium models to represent stars at various stages in the collapse process. Some investigators use sequences of equilibrium models to represent snapshots of the phases of collapse e. Others use individual equilibrium models as initial conditions for hydrodynamical simulations e. Such simulations represent the approximate evolution of a model beginning at some intermediate phase during collapse or the evolution of a collapsed remnant.

These studies do not typically follow the intricate details of the collapse itself. Instead, their goals include determining the stability of models against the development of nonaxisymmetric modes and estimation of the characteristics of any resulting GW emission. Liu and Lindblom [ , ] have applied this equilibrium approach to AIC. Their investigation began with a study of equilibrium models built to represent neutron stars formed from AIC [ ].

All three models are uniformly rotating, with the maximum allowed angular velocities. The realistic equation of state used to construct the white dwarfs is a Coulomb corrected, zero temperature, degenerate gas equation of state [ , 52 ]. In the second step of their process, Liu and Lindblom [ ] built equilibrium models of the collapsed neutron stars themselves. The mass, total angular momentum, and specific angular momentum distribution of each neutron star remnant is identical to that of its white dwarf progenitor see Section 3 of [ ] for justification of the specific angular momentum conservation assumption.

These models were built with two different realistic neutron star equations of state. Comparison of the results of these two studies could indicate that the equation of state may play a significant role in determining the structure of collapsed remnants. Or it could suggest that the assumptions employed in the simplified investigation of Liu and Lindblom are not fully appropriate.

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In a continuation of the work of Liu and Lindblom, Liu [ ] used linearized hydrodynamics to perform a stability analysis of the cold neutron star AIC remnants of Liu and Lindblom [ ]. These values are for a source located at Mpc. Note that this value for h is merely an upper limit as it assumes that the amplitude and frequency of the GWs do not change over the 7 s during which they are emitted. Of course, they will change as angular momentum is carried away from the object via GW emission. Details of the approximations on which these estimates are based can be found in [ ].

This would make bar formation less likely. The AIC scenario is generally discussed in terms of the collapse of an accreting white dwarf to a neutron star. However, Shibata, Baumgarte, and Shapiro have examined the collapse of a rotating, supramassive neutron star to a black hole [ ]. Such supramassive neutron stars with masses greater than the maximum mass for a nonrotating neutron star could be formed and pushed to collapse via accretion from a binary companion.

They performed 3D, fully general relativistic hydrodynamics simulations of uniformly rotating neutron stars. Dynamical non-axisymmetric instabilities such as the bar-mode did not have time to grow in their simulations prior to black hole formation. The gravitational energy released during the collapse is believed to be the power source behind a large subset of supernovae for reviews, see [ 8 , 23 , 79 , 81 , ]. This section studies the gravitational waves produced during the stellar collapse and supernova explosion mechanism.

If rotating, the collapsing stars may form an accretion disk around their black hole core. We will discuss these collapsars and their resultant gravitational waves further in Section 4. However, if we include the effects of winds, these stars lose much of their mass through winds during their nuclear-burning lifetimes. These objects also produce a variant of the collapsar engine for gamma-ray bursts GRBs.

Although the discussion of GW production from the collapse and supernova explosion phase will be discussed in this section, the GWs produced during the fallback and black hole accretion disk phase will be discussed in Section 4. The density and temperature of such a core will eventually rise, due to the build up of matter consumed by thermonuclear burning, to the point where electron capture and photodissociation of nuclei begin.

Electron capture reduces the electron degeneracy pressure. One or both of these processes will trigger the collapse of the core. The relative importance of dissociation and electron capture in instigating collapse is determined by the mass of the star [ 71 ]. The more massive the core, the bigger is the role played by dissociation. The outer core collapses at supersonic speeds [ 71 , ].

It takes just 1 s for an earth-sized core to collapse to a radius of 50 km [ 8 ]. The core overshoots its equilibrium position and bounces. A shock wave is formed when the supersonically infalling outer layers hit the rebounding inner core. Inclusion of general relativistic effects in collapse simulations can increase the success of the prompt mechanism in some cases [ 13 , ]. Both dissociation of nuclei and electron capture can reduce the ejection energy, causing the prompt mechanism to fail.

The shock will then stall at a radius in the range — km. Colgate and White [ 55 ] suggested that energy from neutrinos emitted by the collapsed core could revive the stalled shock. See Burrows and Thompson [ 44 ] for a review of core collapse neutrino processes. Wilson and collaborators were the first to perform collapse simulations with successful delayed ejections [ 30 , 29 , , 24 , , ]. However, their 1-dimensional simulations and those of others had difficulty producing energies high enough to match observations [ 53 , 36 , ].

It was not until Herant and collaborators modelled the collapse and bounce phase with neutrinotransport in 2-dimensions that convection began to be accepted as a necessary puzzle piece in understanding the supernova explosion mechanism [ ]. Observations of SN a show that significant mixing occurred during this supernovae see Arnett et al. Such mixing can be attributed to nonradial motion resulting from fluid instabilities.

Convective instabilities play a significant role in the current picture of the delayed explosion mechanism. The outer regions of the nascent neutron star are convectively unstable after the shock stalls for an interval of 10— ms after bounce due to the presence of negative lepton and energy gradients []. This has been confirmed by both 2D and 3D simulations [ , 42 , , , , 78 , 83 , , , , 91 , 85 , 26 , 39 , 92 , 80 , , ]. Convective motion is more effective at transporting neutrinos out of the proto-neutron star than is diffusion.

Some simulations that include advanced neutrino transport methods have cast doubt on the ability of convection to ensure the success of the delayed explosion mechanism [ , , , 39 ] and this problem is far from solved. But progress not only in neutrino transport, but in understanding new features in the convection [ 26 , 43 , 75 ] some including the effect of magnetic fields is leading to new ideas about the supernova mechanism [ 3 ]. We will discuss the effects of this new physics on the GW signal at the end of this section.

In addition to the mixing seen in SN a, observations of i polarization in the spectra of several core collapse SNe, ii jets in the Cas A remnant, and iii kicks in neutron stars suggest that supernovae are inherently aspherical see [ 8 , 3 , , , ] and references therein. If due to the mechanism itself, these asymmetries may provide clues into the true engine behind supernova explosions. Already, the observations partly motivated the multi-dimensional studies of convection in the delayed explosion mechanism as well as work on magnetic field engines [ 17 , , 3 ].

Observations have also driven the work on jets and collapsars 4.

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  6. Hungerford and collaborators have argued that the asymmetries required are not so extreme [ , ], arguments that have now been confirmed [ ]. This debate is crucial to our understanding of the supernova mechanism. If jets are required, magnetic field mechanisms are the likely source of the asymmetry. If jets are not required, the convective engine can produce asymmetries via a number of channels from low mode convection [ 26 , , 43 ] to rotation e.

    The most thorough computation of SN rates is that of Cappellaro et al. Their sample includes SNe from five different SN searches. Thus, a reasonable occurrence rate can be found for an observation distance of 10 Mpc. Note that a infrared survey estimates that the rate may actually be an order of magnitude higher [ ].

    What this rate might exclude are those stars that collapse to form neutron stars, but have sufficiently weak explosions that they eject very little nickel and hence are not very bright. However, it does include those stars that collapse to black holes directly and form GRBs producing supernova-like outbursts. We will discuss the GWs from such collapses in Section 4. Excluding them from this sample will not change the above numbers. A rough description of the possible evolution of the quadrupole moment is given in the remainder of this paragraph.

    The contraction speeds up over the next 20 ms and the density distribution becomes a centrally condensed torus [ ]. If centrifugal forces play a role in halting the collapse, the bounce can last up to several ms [ ]. The shape of the core, the depth of the bounce, the bounce timescale, and the rotational energy of the core all strongly affect the GW emission.

    For further details see [ 71 , ]. A neutron star remnant will likely also be susceptible to the radiation reaction driven r-modes. Both of these types of instabilities will emit GWs, as will a fragmentation instability if one occurs. See Section 2. The collapse of the progenitors of core collapse supernovae has been investigated as a source of gravitational radiation for more than three decades.

    In an early study published in , Ruffini and Wheeler [ ] identified mechanisms related to core collapse that could produce GWs and provided order-of-magnitude estimates of the characteristics of such emission. Quantitative computations of GW emission during the infall phase of collapse were performed by Thuan and Ostriker [ ] and Epstein and Wagoner [ 66 , 65 ], who simulated the collapse of oblate dust spheroids.

    Thuan and Ostriker used Newtonian gravity and computed the emitted radiation in the quadrupole approximation. Epstein and Wagoner discovered that post-Newtonian effects prolonged the collapse and thus lowered the GW luminosity. Subsequently, Novikov [ ] and Shapiro and Saenz [ , ] included internal pressure in their collapse simulations and were thus able to examine the GWs emitted as collapsing cores bounced at nuclear densities.

    The quadrupole GWs from the ringdown of the collapse remnant were initially investigated by the perturbation study of Turner and Wagoner [ ] and later by Saenz and Shapiro [ , ]. He found that differential rotation enhanced the efficiency of the GW emission. Stark and Piran [ , ] were the first to compute the GW emission from fully relativistic collapse simulations, using the ground-breaking formalism of Bardeen and Piran [ 11 ]. They followed the pressure-cut induced collapse of rotating polytropes in 2D. Their work focused in part on the conditions for black hole formation and the nature of the resulting ringdown waveform, which they found could be described by the quasi-normal modes of a rotating black hole.

    Seidel and collaborators also studied the effects of general relativity on the GW emission during collapse and bounce [ , ]. They employed a perturbative approach, valid only in the slowly rotating regime. The gravitational radiation from non-axisymmetric collapse was investigated by Detweiler and Lindblom, who used a sequence of non-axisymmetric ellipsoids to represent the collapse evolution [ 57 ].

    They found that the radiation from their analysis of non-axisymmetric collapse was emitted over a more narrow range of frequency than in previous studies of axisymmetric collapse. For further discussion of the first two decades of study of the GW emission from stellar collapse see [ 72 ]. In the remainder of Section 3. The shortcomings of their investigation included initial models that were not in rotational equilibrium, an equation of state that was somewhat stiff in the subnuclear regime, and the use of Newtonian gravity.

    Each of their four models had a different initial angular momentum profile. The rotational energies of the models ranged from 0. They also determined that a subnuclear bounce produced larger amplitude oscillations in density and radius, with larger oscillation periods, than a bounce initiated by nuclear forces alone. They pointed out that these differences in timescale and oscillatory behavior should affect the GW signal. Therefore, the GW emission could indicate whether the bounce was a result of centrifugal or nuclear forces.

    The waveforms they categorized as Type I similar to those observed in previous collapse simulations [ , 74 ] are distinguished by a large amplitude peak at bounce and subsequent damped ringdown oscillations. They noted that Type I signals were produced by cores that bounced at nuclear densities or bounced at subnuclear densities if the cores had small ratios of radial kinetic to rotational kinetic energies. The vertical dotted line marks the time at which the first bounce occurred.

    Figure 5d of [ ]; used with permission. The vertical dotted line marks the time at which bounce occurred. Figure 5a of [ ]; used with permission. In order to make this large survey tractable, they used a simplified equation of state and did not explicitly account for electron capture or neutrino transport. The equation of state used during the collapse evolution had both polytropic and thermal contributions note that simulations using more sophisticated equations of state get similar results [ ]. Their waveforms were computed with the same technique used in [ ].

    Figure 5e of [ ]; used with permission. This is because the deformation of the core is larger for faster rotators. These models bounce at subnuclear densities. Thus, the resulting acceleration at bounce and the GW amplitude are smaller. However, they did find that models with soft equations of state emitted stronger signals as the degree of differential rotation increased. The peaks of their power spectra were between Hz and 1 kHz. The GW emission from non-axisymmetric hydrodynamics simulations of stellar collapse was first studied by Bonazzola and Marck [ , 28 ].

    They used a Newtonian, pseudo-spectral hydrodynamics code to follow the collapse of polytropic models. Their simulations covered only the pre-bounce phase of the collapse. They found that the magnitudes of h pk in their 3D simulations were within a factor of two of those from equivalent 2D simulations and that the gravitational radiation efficiency did not depend on the equation of state. At that point, 2. Before the 3D simulations started, non-axisymmetric density perturbations were imposed to seed the growth of any non-axisymmetric modes to which the configuration was unstable.

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    The growth of this particular mode was instigated by the cubical nature of the computational grid. These arms carried mass and angular momentum away from the center of the core. Significant non-axisymmetric structure was visible only within the inner 40 km of the core. The findings of Centrella et al. Centrella et al. The simulations carried out by Centrella and collaborators were not full collapse simulations, but rather began with differentially rotating equilibrium models.

    He performed 3D hydrodynamical simulations of the post-bounce configurations resulting from 2D simulations of core collapse. The angular velocity profiles of their pre-collapse progenitors were broad and Gaussian-like. This is likely a result of the larger degree of differential rotation in the model of Rampp et al. Brown refers to the Rampp et al. This suggests that the mode growth in their simulations was a result of the large perturbations they imposed. Fryer and Warren [ 91 ] performed the first 3D collapse simulations to follow the entire collapse through explosion. They used a smoothed particle hydrodynamics code, a realistic equation of state, the flux-limited diffusion approximation for neutrino transport, and Newtonian spherical gravity.

    Their initial model was nonrotating. Thus, no bar-mode instabilities could develop during their simulations. The only GW emitting mechanism present in their models was convection in the core. By the launch of the explosion, no bar instabilities had developed. These models have been further studied for the GW signals [ 87 ]. Fryer and collaborators have also modeled asymmetric collapse and asymmetric explosion calculations in 3 dimensions [ 80 , 90 ]. These calculations will be discussed in Section 3. The GW emission from nonradial quasinormal mode oscillations in proto-neutron stars has been examined by Ferrari, Miniutti, and Pons [ 70 ].

    They found that the frequencies of emission f GW during the first second after formation — Hz for the first fundamental and gravity modes are significantly lower than the corresponding frequencies for cold neutron stars and thus reside in the bandwidths of terrestrial interferometers. General relativistic effects oppose the stabilizing influence of rotation in pre-collapse cores. Thus, stars that might be prevented from collapsing due to rotational support in the Newtonian limit may collapse when general relativistic effects are considered. Furthermore, general relativity will cause rotating stars undergoing collapse to bounce at higher densities than in the Newtonian case [ , , , 37 ].

    The full collapse simulations of Fryer and Heger [ 83 ] are the most sophisticated axisymmetric simulations from which the resultant GW emission has been studied [ 86 , 88 ]. Fryer and Heger include the effects of general relativity, but assume for the purposes of their gravity treatment only that the mass distribution is spherical.

    The GW emission from these simulations was evaluated with either the quadrupole approximation or simpler estimates see below. The work of Fryer and Heger [ 83 ] is an improvement over past collapse investigations because it starts with rotating progenitors evolved to collapse with a stellar evolution code which incorporates angular momentum transport via an approximate diffusion scheme [ ], incorporates realistic equations of state and neutrino transport, and follows the collapse to late times.

    The values of total angular momentum of the inner cores of Fryer and Heger 0. Note that the total specific angular momentum of these core models may be lower by about a factor of 10 if magnetic fields were included in the evolution of the progenitors [ 3 , , ]. The cores in the simulations of Fryer and Heger [ 83 ] are not compact enough or rotating rapidly enough to develop bar instabilities during the collapse and initial bounce phases. However, the explosion phase ejects a good deal of low angular momentum material along the poles in their evolutions.

    As mentioned above, the proto-neutron stars of Fryer and Heger are likely to be unstable to the development of secular bar instabilities. The GW emission from proto-neutron stars that are secularly unstable to the bar-mode has been examined by Lai and Shapiro [ , ]. Because the timescale for secular evolution is so long, 3D hydrodynamics simulations of the nonlinear development of a secular bar can be impractical.

    To bypass this difficulty, Lai [ ] considers only incompressible fluids, for which there are exact solutions for Dedekind and Jacobi-like bar development. The maximum f GW of the emitted radiation is in the range 10 2 —10 3 Hz. This type of signal should be easily detected by LIGO-I although detection may require a technique like the fast chirp transform method of Jenet and Prince [ ] due to the complicated phase evolution of the emission. Alternatively, Ou et al. They found that a bar instability was maintained for several orbits before sheer flows, producing GW emission that would have a signal-to-noise ratio greater than 8 for LIGO-II out to 32 Mpc.

    For video see appendix. FHH predict that a fragmentation instability is unlikely to develop during core collapse SNe because the cores have central density maxima see also [ 88 ]. Multiple GW bursts will occur as material falls back onto the neutron star and results in repeat episodes of r -mode growth note that a single r -mode episode can have multiple amplitude peaks [ ].

    They estimate the emitted energy to exceed 10 52 erg. In all, they have followed the collapse evolution of 26 different models, with both Newtonian and general relativistic simulations. They use the conformally flat metric to approximate the space time geometry [ 56 ] in their relativistic hydrodynamics simulations. Thus, as long as the collapse is not significantly aspherical, the approximation is relatively accurate. However, the conformally flat condition does eliminate GW emission from the spacetime.

    The general relativistic simulations of Dimmelmeier et al.

    Open Issues in Core Collapse Supernova Theory (Proceedings from the Institute for Nuclear Theory 14) Open Issues in Core Collapse Supernova Theory (Proceedings from the Institute for Nuclear Theory 14)
    Open Issues in Core Collapse Supernova Theory (Proceedings from the Institute for Nuclear Theory 14) Open Issues in Core Collapse Supernova Theory (Proceedings from the Institute for Nuclear Theory 14)
    Open Issues in Core Collapse Supernova Theory (Proceedings from the Institute for Nuclear Theory 14) Open Issues in Core Collapse Supernova Theory (Proceedings from the Institute for Nuclear Theory 14)
    Open Issues in Core Collapse Supernova Theory (Proceedings from the Institute for Nuclear Theory 14) Open Issues in Core Collapse Supernova Theory (Proceedings from the Institute for Nuclear Theory 14)
    Open Issues in Core Collapse Supernova Theory (Proceedings from the Institute for Nuclear Theory 14) Open Issues in Core Collapse Supernova Theory (Proceedings from the Institute for Nuclear Theory 14)
    Open Issues in Core Collapse Supernova Theory (Proceedings from the Institute for Nuclear Theory 14) Open Issues in Core Collapse Supernova Theory (Proceedings from the Institute for Nuclear Theory 14)
    Open Issues in Core Collapse Supernova Theory (Proceedings from the Institute for Nuclear Theory 14) Open Issues in Core Collapse Supernova Theory (Proceedings from the Institute for Nuclear Theory 14)

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