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supernovae, Type Ia

tive region is trapped near the proto-neutron star by the ram pressure of infalling material. The explosion occurs only when the energy in the convective region overcomes this ram pressure. The neutrino-driven wind implies a more steady state ejection of material, not a sudden burst as occurs in the delayed neutrino supernova mechanism. Unlike the neutrino-driven wind mechanism, the electron fraction of the ejecta from the delayed-neutrino mechanism depends both upon the relative absorption and emission rates of electron neutrinos and anti-neutrinos.

supernovae, neutrinos The emission of neutrinos in core collapse supernovae (Type Ib/c and Type II) is dominated by electron capture onto protons and by electron/positron annihilation. As the core collapses, its pressure is sufﬁcient to overcome nuclear forces and capture electrons onto protons, producing a neutron and an electron neutrino. These neutrinos dominate the initial neutrino burst. As the core collapses further, it becomes so dense that it is optically thick to neutrinos, and the neutrinos become trapped in the core. The temperatures rise sufﬁciently to produce positron pairs, and the annihilation of electrons and positrons form neutrino/antineutrino pairs. In the ﬁrst 20 s after collapse, neutrinos release over 1053 ergs of energy.

supernovae, prompt shock mechanism

When the collapsing core of a massive star reaches nuclear densities (see supernovae, core collapse mechanism), nuclear forces halt the collapse causing the infalling material to rebound. A bounce shock then propogates out of the star. The prompt shock mechanism argues that this shock carries sufﬁcient energy to power a supernova explosion (1% of the gravitational potential energy released). However, as the shock expands outward, it loses energy through neutrino emission and the dissociation of outer material it hits. In most simulations, the shock stalls at 100 to 500 km; thus, failing to produce and explosion.

supernovae, spectra The spectra from supernovae are the dominant characteristic used to classify supernovae types (see supernovae, classiﬁcation). The spectral lines are generally broad (>10,000km/s) and blue-shifted due

to the rapid expansion velocities with different lines having different characteristic velocities. For a review, see Filippenko (1997).

supernovae, thermonuclear explosions

Type Ia supernovae are powered by the thermonuclear explosion of a white dwarf. The current “favored” model is the thermonuclear explosion of an accreting white dwarf which reaches the Chandrasekhar mass, triggering nuclear burning near the core (see supernovae, white dwarf accretion). This mechanism is further subdivided into several models: detonation, delayed-detonation, deﬂagration, etc. These models differ on the type of burning that occurs in the core. For instance, the delayed-detonation model is initiated by a core burning with a deﬂagration ﬂame front (ﬂame speed less than the sound speed) which then evolves into a detonation (ﬂame speed greater than the sound speed).

Sub-Chandrasekhar thermonuclear explosions occur in white dwarfs less massive than the Chandrasekhar mass. The accreting material builds a helium layer on the white dwarf and ignites. The detonation of the helium layer drives pressure waves into the core, ultimately causing the white dwarf core to detonate. Currently, this mechanism has difﬁculty explaining the spectra of Type Ias and, hence, is not the favored Type Ia supernova mechanism.

supernovae, Type Ia The kind of stellar explosion that occurs in all kinds of galaxies (not just ones with young stars) and whose spectra show no evidence for the presence of hydrogen. The cause of the explosion is the ignition of carbon and oxygen burning within degenerate material in a white dwarf. The star is completely disrupted; most of the carbon and oxygen fuses to iron and nearby elements releasing about 1051 ergs of energy, about 1% of which appears as visible light, and the rest of which blows the gas out into space at speeds of about 10,000 km/sec. Type Ia supernovae have no hydrogen in their spectra but exhibit strong silicon lines (most notably Si II λλ6347, 6371). At late times, iron and cobalt lines become prominent. The expansion velocities inferred from the spectra are roughly 11,000 to 13,000 km s−1. The absolute peak magnitudes of Type Ia show little scatter !MV" = −18.5 ± 0.3 mag. The differences

supernovae, Type Ib/Ic

in the peak magnitude have been correlated to the decline rate of the supernova luminosity (see supernovae, M15/Phillips relation). Using this correlation, the peak magnitude variations can be removed, and Type Ia can thus be used as standard candles for measuring the Hubble constant, and other cosmological parameters.

The luminosity is powered by the decay of 56Ni produced in the explosion. Some of the low luminosity outbursts (e.g., 1991bg) may be explained by the accretion induced collapse of white dwarfs (see supernovae, accretion induced collapse). Type Ia supernovae do not occur in extremely young stellar populations but do occur in all types of galaxies at a rate of 0.005 yr−1 per Milky Way-sized galaxy, consistent with the assumption that the progenitors of these systems come from low-mass stars. At peak brightness, a Ia SN can be as bright as its entire host galaxy. The precise nature of the progenitors is not clear. One popular candidate is a pair of white dwarfs whose total mass exceeds the Chandrasekhar limit in a binary system with orbit period less than about one day. Such a pair will spiral together in less than the age of the universe and explode as required when they merge, but we have not yet actually seen any white dwarf binaries with the required properties. Tycho’s and Kepler’s supernovae were probably Type Ia events.

supernovae, Type Ib/Ic Type Ib/Ic supernovae exhibit neither hydrogen lines nor silicon lines. Type Ib supernovae are characterized by the existence of helium lines, absent in Type Ic supernovae. These two types of supernovae are otherwise very similar (both have oxygen and calcium in their late-time spectra) and are generally lumped together. They occur at a rate of 0.002 yr−1 per Milky Way-sized galaxy.

Type Ib/Ic supernovae are similar to Type II supernovae in that they are caused by the collapse of massive stars (> 10M ). However, at the time of collapse, Type Ib/Ic supernovae have lost most/all of their hydrogen envelope either through stellar winds or during binary evolution through a common envelope phase. Type Ic supernovae have lost not only their hydrogen envelope but most of their helium envelope as well. The connection between Type II supernovae and Type Ib/Ic supernovae comes from supernovae 1987K and 1993J which both ex-

hibited hydrogen in their spectra but mimicked Type Ib supernovae at late times. The two progenitors of these supernovae appear to have lost most, but deﬁnitely not all, of their hydrogen before collapse, implying a smooth continuum between Type Ib/Ic and Type II supernovae.

supernovae, Type II The kind of supernova that results when the core of a massive star collapses to a neutron star or black hole (see core collapse). They are the primary source of new heavy elements (those beyond hydrogen and helium) made by nuclear reactions over the life of the star and expelled when energy from the core collapse blows off the outer layers of the star. The spectrum is dominated by lines of hydrogen gas, from the envelope of the star, but oxygen and other heavy elements are also seen. Core collapse, when the star has already lost its hydrogen envelope, produces hydrogen-free supernovae of Types Ib and Ic. It is estimated that about one SNII occurs in our galaxy each century. This class of supernovae is subdivided into two major groups based on their light curves: Type II-Linear (II-L) supernovae peak and then decay quickly, and Type II-Plateau (II-P) which, after their peak, decay only 1 magnitude and then reach a plateau for 100 days before a latetime decay similar to type II-L supernovae. The expansion velocities inferred from the spectra are roughly 7000 km s−1. The absolute peak visual magnitudes of Type II supernovae have considerable scatter (!MV" = −17 ± 2 mag.). However, models of Type II-P supernovae allow a physical calibration of these objects, allowing them to be used as “standard” candles without relying upon a local calibrator such as Cepheid Variables.

Type II supernovae are caused by the core collapse of massive stars (> 10M ) and are powered by the potential energy released during this collapse (see supernovae, core collapse mechanism). Because their progenitors are short-lived, they only occur in young stellar populations, and none have been observed in elliptical galaxies. Type II (and Type Ib/Ic) supernovae form the bulk of the neutron stars in the universe and occur at a rate of 0.0125 yr−1 per Milky Way-sized galaxy.

superposition principle

supernovae, white dwarf accretion Type Ia supernovae are powered by the thermonuclear explosion of accreting white dwarfs (see supernovae, thermonuclear explosions). The favored Type Ia supernova model requires that the white dwarf accrete up to a Chandrasekhar mass. However, accreting white dwarfs tend to lose mass during nova eruptions. Only for accretion rates greater than 10−9 − 10−8M yr−1 are white dwarfs thought to gain mass from accretion. Rapidly accreting ( 10−6M yr−1) C/O white dwarfs and most accreting OMgNe white dwarfs, which gain enough matter to exceed the Chandrasekhar mass, are thought to collapse to neutron stars (Nomoto & Kondo) before nuclear burning can drive a thermonuclear explosion. Neutrino Urca processes prevent these white dwarfs from getting hot enough to burn efﬁciently. For more common accretion rates, C/O white dwarfs are thought to ignite their cores, initiating a thermonuclear explosion.

supernova rates The rate at which supernovae of different types occur remains uncertain by factors of 2. These rates can be indirectly determined by observing metal abundances (metals are produced almost entirely in supernovae) of galaxies and using a theoretically derived production rate of metals per supernova. Alternatively, the rate of core-collapse supernovae (Type II + Type Ib/c) can be calculated by combining the theoretical estimates of the mass range of stars with observations of the initial mass function and the star formation rate. However, the most direct and most accurate technique to determine these rates is to simply observe the supernovae that occur in the universe and correct for the biases intrinsic to the observed sample. Unfortunately, a large supernova sample does not exist, and biases such as luminosity differences and obscuration, make it difﬁcult to exactly determine the supernova rate. Recent estimates of supernova rates are printed in the following table. (Cappellaro et al., 1997.) The units are per 1010 solar luminosities (in the blue) per century.

supernova remnant (SNR) The expanding gas blown out during any type of supernova SN explosion. Masses can range from a few tenths to a few tens of solar masses. Expan-

Supernova Rates

Galaxy Type

Supernova Type

Type Ia

Type Ib/c

Type II

E-SO

0.15 ± 0.06

SOa-Sb

0.20 ± 0.07

0.11 ± 0.06

0.40 ± 0.19

Sbc-Sd

0.24 ± 0.09

0.16 ± 0.08

0.88 ± 0.37

Early time spectra of supernovae. Type II supernovae have hydrogen lines. Type Ia supernovae have strong silicon lines whereas Type Ib/c supernovae do not. Type Ib supernovae exhibit helium lines which are absent in Type Ic supernovae. Figure courtesy of Alex Filippenko.

sion velocities range from 2,000 to about 20,000 km/sec. Young SNRs sometimes have pulsars in them (meaning that the SN was a core collapse event). A few hundred SNRs are known in our galaxy, from their emission line spectra, radio, and X-ray radiation which occurs by synchrotron and/or bremsstrahlung processes. Their spectrum sometimes shows emission lines characteristic of shocked and photoionized gas. SNRs add kinetic energy and heat to the interstellar medium and contribute to accelerating cosmic rays.

superposition principle In linear systems any collection of solutions to a physical problem can be added to produce another solution. An example is adding Fourier harmonics to describe oscillations in the electromagnetic ﬁeld in a cavity. In particular situations a limited form of superposition is possible in speciﬁc nonlinear systems.

supersonic

Typical supernovae light curves. Type II supernovae have a large amount of scatter ( 4 magnitudes in the peak luminosity). Type II supernovae are separated into two groups (Plateau and Linear) based on the light curve. Figure courtesy of Mario Hamuy.

25M core-collapse simulation 20 ms after bounce. In this simulation, the convective region stretches from roughly 50 km to 300 km.

supersonic Involving speeds in excess of the local speed of sound.

supersonic string model	See elastic string
model.

superspace The space of inequivalent (under general coordinate transformations) spatial geometries and matter ﬁelds associated to the ADM decomposition of space-time (see geometrodynamics). Since the metric of space is a symmetric tensor of rank 2, there are apparently six gravitational degrees of freedom per space point. However, the latter are subjected to one Hamiltonian and three super-momentum

constraints which correspond to the transformations of the reference frame which leave the geometry unaltered. This leaves the equivalent of two degrees of freedom per space point or a total of (∞3)2 gravitational degrees of freedom. A (generally time dependent) solution to Einstein’s equations traces out a 1-parameter path through superspace.

One usually needs to impose some further restriction to the metric in order to handle the constraints and obtain manageable results. See minisuperspace, ADM form of the Einstein–Hilbert action.

surface boundary layer The usually “weakly stratiﬁed” layer at the top of natural water, which is immediately and directly affected by either wind or convection.

surface gravity The limiting value of the force applied at inﬁnity to keep a unit mass at rest on the black hole horizon. For an explicit example, see Schwarzschild metric. The surface gravity is also related to the temperature of Hawking radiation. See black hole horizon.

surface tension (σ ) Molecules in the surface of liquid water are subjected to a net inward force due to hydrogen bonding with the water molecules below the surface. Surface tension is equal to the magnitude of that force divided by the distance over which it acts.

surface waves Seismic waves that propagate along the surface of the Earth (as opposed to body waves). Surface waves are either Rayleigh (longitudinal, with a vertical component) or Love transverse waves. Surface waves are primarily responsible for the damage associated with earthquakes; they propagate more slowly than body waves so that the body waves provide a short precursory warning of the arrival of the destructive surface waves.

surf zone The region at a coast where breaking waves are found.

surge In solar physics, a relatively narrow active region jet of material in which plasma is accelerated outward at 50 to 200 km s−1 for a few tens of minutes. Surges reach coronal heights