The First Second of a TypeI I Sup ernova Convection Accretion and Sho ck Propagation HTHOMAS JANKA Department of Astronomy and Astrophysics University of Chicago S Ellis Avenue Chicago Illinois USA Email thomasgrantauchicagoedu AND EWALD MULLER MaxPlanckInstitut f urAstrophysik KarlSchwarzschildStr D Garching Germany Email ewaldmpagarchingmpgde ABSTRACT One and twodimensional hydrodynamical simulations of the neutrinodriven sup ernova explosion of a M star are p erformed for the phase b etween the stagnation of the prompt sho ck and ab out one second after core b ounce Systematic variation of the neutrino uxes from the neutrino sphere shows that the explosion energy explosion time scale initial mass of the protoneutron star and explosive nucleosynthesis of iron group elements dep end sensitively on the strength of the neutrino heating during the rst few ms after sho ck formation Convective overturn in the neutrinoheated region b ehind the sho ck is a crucial help for the explosion only in a narrow window of neutrino luminosities Here p owerful explosions can b e obtained only in the multi dimensional case primarily b ecause the overturn increases the eciency of neutrino energy dep osition by allowing co ol p ostsho ck matter to p enetrate inward to the region astro-ph/9503015 3 Mar 1995 of strongest heating while heated gas can quickly rise outward thus reducing its energy loss due to reemission of neutrinos This interpretation is supp orted by the dierent rise of the explosion energy as a function of time in D and D mo dels For higher core neutrino uxes also spherically symmetrical mo dels yield energetic explosions while for lower luminosities even with convection no strong explosions o ccur The co ol matter in the downows from the sho ck to the heating zone loses lepton number by emission but gains energy by interactions with the coreneutrino uxes e However since the gas do es not b ecome very neutronrich and its entropy increases it is not accreted into the lowentropy neutronized surface layer of the neutron star Due to the absence of signicant accretion while the explosions develop on a time scale of only a few ms the initial protoneutron star masses in our mo dels are only ab out M Turbulent activity around the protoneutron star is a transient phenomenon at On leave from MaxPlanckInstitut f ur Astrophysik KarlSchwarzschildStr D Garching Germany ms after sho ck formation the turbulent shell decouples from the neutrinoheated zone and moves outward b ehind the sup ernova sho ck The sho ck shows deformation on large scales and the inhomogeneities of temp erature density and velocity with contrasts o o of order unity on scales of to in the layer b ehind the sho ck can help to explain the anisotropies and radial mixing observed in SN A When the sup ernova sho ck reaches the entropy step of the SiOinterface at km ab out ms after b ounce the density inversion b etween the dense inhomogeneous shell b ehind the sho ck and the low density hotbubble region around the neutron star b egins to steep en into a strong reverse sho ck This reverse sho ck forms a sharp discontinuity in the neutrinodriven wind from the nascent neutron star The deceleration of the wind expansion might trigger signicant anisotropic matter fallback to the neutron star on a time scale of several seconds Sub ject headings sup ernovae general hydrodynamics sho ck waves convection turbulence INTRODUCTION There is a variety of observational hints that largescale mixing pro cesses o ccurred and played an imp ortant role in SN A even during the early phase of the explosion Xrays eg Dotani et al Sunyaev et al and rays eg Matz et al Mahoney et al from the decay of Ni and Co and strongly Dopplershifted infrared emission lines of iron eg Erickson et al Haas et al were observed at a stage when Ni and Fe should have still b een obscured by the overlying expanding material of the progenitor star This indicated that radioactive elements must have b een mixed out with very high velocities from the place of their formation close to the center of the sup ernova far into the stellar mantle and envelope The structure of the infrared emission lines was interpreted as an indication that the ironp eak elements were mixed outward macroscopically and inhomogeneously in form of ab out to identical clumps Li et al The smo othness of the light curve of SN A provided indirect evidence for the existence and strength of the mixing pro cess Mixing of hydrogen towards the center helps to explain the smo oth and broad light curve maximum by the timespread of the lib eration of recombination energy Shigeyama Nomoto Mixing of heavy elements into the hydrogenrich envelope homogenizes the opacity and again smo oths the light curve Arnett et al and references therein Moreover the observation of a large number of fastmoving young pulsars Lyne Lorimer might indicate the existence of violent nonspherical pro cesses in the early moments of the sup ernova explosion when the neutron star is formed The large dense explosion fragments seen on ROSAT Xray images outside of the sho ck front in the Vela sup ernova remnant Aschenbach et al might p ossibly also originate from such early instabilities Numerical simulations of RayleighTaylor instabilities at the comp osition interfaces metalHe HeH in the stellar mantle and envelope after sho ck passage eg Arnett et al Den et al Herant Benz could neither explain the extent of the required mixing nor could they account for the observed high velocities and the large scales of inhomogeneities and anisotropies M uller et al This inspired sup ernova mo dellers to p erform multidimensional calculations of the early phases of the sup ernova explosion ie the corecollapse sho ckformation and neutrinoheating phases Spherically symmetrical mo dels had indeed shown that convectively unstable layers are present in the collapsed stellar core after formation and propagation of the prompt sho ck Burrows Lattimer Theoretical considerations conrmed the p ossible imp ortance of overturn and mixing in these layers for the evolution of the sho ck Bethe MULTIDIMENSIONAL MODELS OF THE EXPLOSION Herant et al rst demonstrated by a hydrodynamical simulation that strong turbulent overturn o ccurs in the neutrinoheated layer outside of the protoneutron star and that this helps the stalled sho ck front to start reexpansion as a result of energy dep osition by neutrinos Although the existence and fast growth of these instabilities was conrmed by Janka M uller and M uller Janka the results of their simulations in D and in D indicated a very strong sensitivity to the conditions at the protoneutron star and to the details of the description of neutrino interactions and neutrino transp ort Since the knowledge ab out the highdensity equation of state in the nascent neutron star and ab out the neutrino opacities of dense matter is incomplete Raelt Seckel Keil et al the inuence of a contraction of the neutron star and of the size of the neutrino uxes on the evolution of the explosion has to b e tested by systematic studies In the following we rep ort the main results of a set of calculations of D and D Newtonian mo dels with dierent coreneutrino luminosities and with varied temp oral contraction of the inner b oundary The latter is placed somewhat inside the neutrino sphere and is used instead of simulating the evolution of the very dense inner core of the nascent neutron star This gives us the freedom to set the neutrino uxes to chosen values at the inner b oundary and also enables us to follow the D simulations until ab out one second after core b ounce with a reasonable number O of time steps and an acceptable computation time ie several h on one pro cessor of a CrayYMP with a grid of zones and a highly ecient implementation of the microphysics Doubling the angular resolution multiplies the computational load by a factor of Our simulations are started at ab out ms after sho ck formation using an initial mo del that was evolved through core collapse and b ounce by Bruenn The b oundary luminosities of all neutrino kinds are set to values near those obtained by Bruenn and in Newtonian computations by Bruenn et al For details and information ab out the numerical treatment see Janka M ullera Our approach and aims dier from those chosen by other groups who recently p erformed D simulations of sup ernova explosions Herant et al Burrows et al These groups attempted a selfconsistent treatment that includes the central highdensity part of the neutron star up to a certain stage in the evolution typically ms after core b ounce but they did not reveal the dep endence of their results on uncertain asp ects of the input physics or its numerical description RESULTS OneDimensional Mo dels The evolution of the stalled prompt sup ernova sho ck in D mo dels turns out to b e extremely sensitive to the size of the neutrino luminosities and to the corresp onding strength of neutrino heating exterior to the gain radius Increasing the coreneutrino uxes from low to higher values has the eect that the sho ck is pushed further and further out to reach a successively larger maximum radius during a phase of ab out ms of slow expansion Nevertheless it nally recedes again to b ecome a standing accretion sho ck at a much smaller radius For a suciently high threshold luminosity however neutrino heating is strong enough to drive the sho ck front outwards and to cause a successful explosion For even higher neutrino uxes the explosion develops faster