Timmes (1996)

Ignition Conditions Flame Propagation Detonation, Deflagration, Delayed Detonation, Pulsational Detonation Light curves and cosmology Topics

Progenitor Hoyle & Fowler (1960) Arnett (1968, 1969) Nomoto, Sugimoto, & Neo (1976) C,O white dwarf grows by accretion Supersoft X-ray source? Accretion rate about solar masses/yr Not a classical nova Thin H,He shells (< 0.01 solar masses) Ignition near center to avoid nucleosynthesis problems to avoid collapse (Iwamoto et al. 1999; Woosley 1996) n.b.

A Successful Model Must: Produce approximately 0.6 solar masses of 56 Ni (0.1 to 1 M sun ) Produce at least 0.2 solar masses of SiSArCa Not make more than about 0.1 solar masses of 54 Fe and 58 Ni combined And probably not have too much unburned oxygen in close proximity to 56 Ni Allow for some diversity For the light For the spectrum For the nucleosynthesis For the spectrum (Starting from 1.38 solar masses of carbon and oxygen)

It has been known for some time that the way to achieve such results is with a flame that starts slowly, pre-expands the star (so as to avoid too much electron capture) then moves very rapidly when Unfortunately the laminar flame has just the opposite behavior.

The laminar flame slows down with time and density and gets thicker

Brachwitz et al. (2000)

For over 25 years the search has been for the correct physics that would describe this solution, i.e., a little burning at high density and a lot of burning at low density. Rayleigh-Taylor Instability Turbulence Delayed Detonation Pulsational Detonation Off-center burning

Ignition Conditions Supernova preceded by 1000 years of convection Last "good convective model" is when the central temperature has risen to 7 x 10 8 K Pressure scale height: 400 km Nuclear time scale: 10 2 s Convective time scale: 10 2 s Convective speed: 5 km s -1 Binding energy: 4 x erg Density: 2 x 10 9 g cm -3 Burning 0.05 solar masses can cause expansion by a factor of three URCA Process?

Turbulent Convection

Kercek, Hillebrandt, & Truran (1998)

Detonation Deflagration Burning propagated by a shock wave. Pressure, density, and temperature all rise in the shock. To initiate a detonation one needs either an external piston or for a region to runaway coherently in less than a sonic crossing time. Burning as a subsonic flame. Pressure is constant across the flame surface. Temperature rises, density decreases. Such a flame sheet in a white dwarf is Rayleigh-Taylor unstable, and that makes things hard. In both cases, the burning temperature is 9 x 10 9 K assuring that burning goes to nuclear statistical equilibrium.

Once ignited, a central detonation will consume the entire star. Converting it entirely to iron group elements. Woosley (1990) The critical mass for a self- sustaining detonation in carbon at 2 x 10 9 gm cm -3 only gm. That is, a length scale of 70 cm. Why doesn't it happen?

T T r r In the absence of external forces, the only way an isolated region can develop a detonation is to have a supersonic phase velocity imposed by the initial conditions. That means that the reciprocal of the gradient of the nuclear burning time scale must be supersonic within a critical mass But there can be no temperature fluctuations in the region that would lead to premature burning.

To serve as a detonator, a region must run away as a unit in approximately a sound crossing time. Nuclear burning time scales as approximately T 26 A region 100 km across can run away supersonically then if all its components have the same burning time to within 0.01 s, or, starting at 7 x 10 8 K, the same total time to within 0.01 s/100 s = 0.01%. In fact, this must be divided by the power of T to which the nuclear energy generation is sensitive. So temperature fluctuations greater than 5 x are not allowed.

Speculation How many points and when and where each ignites may have dramatic consequences for the supernova (origin of diversity?)

Multi-point Ignition Depends on: C/O  ign

Blobs of various sizes and released from varying altitudes all runaway at 100 km to 300 km Garcia-Senz and Woosley ApJ, 454, 895, (1995)

Igniting the star at a single point off center gives very different results than igniting precisely at the center or in a spherical volume. This "single point ignition" model did not produce a supernova (pulsation would have ensued)

Ignition at 5 points did produce a successful supernova with 0.65 solar masses of burned material, 0.5 solar masses of which was 56 Ni. Note - this was a 2D calculation.

Recent simulations by Hillebrandt, Reinecke, and Niemeyer show successful explosions (in 2D), but the results are resolution sensitive.

Does a Transition To Detonation Happen? Could have desireable consequences if it happened at r = g cm -3 The critical mass for ignition is not large (about 50 m at 3 x 10 7 g cm -3 ) But a region larger than this must be well mixed (nearly isothermal) and burn in a sound crossing time. Not possible while the flame is still alive!

The Gibson Length For a standard Kolmogorov picture of turbulence: l Gib is defined by: As density decreases, v cond decreases dramatically and d cond also increases dramatically. Eventually l Gib <  cond

Three possibilities: Precondition the star so that a large fraction ignites nearly simultaneously Mix a critical mass thoroughly, then wait for it to run away again as the star continues to expand Pulsational detonation Or maybe there is no detonation X C =0.2

Difficulties 1) Volume detonation (Woosley 1993) Try to generate sufficient area so that: The problem is that (for constant turbulent energy) the area always adjusts so that v eff = v L ~ cm/s e.g. but, and D = 2.33 which implies v eff = v L

2) Zeldovich detonation (Khokhlov 1990) At e.g., 3 x 10 7 g cm -3, one must prepare a region larger than M crit with small enough temperature variations that burning occurs in a sound crossing time. Moreover, this burning must occur in << t HD. This is very difficult. Must have an isolated eddy such that t BURN (l crit ) > t eddy (l crit ) evaluated at T ash but t BURN << t HD

"Sharp-Wheeler Model" g Model OK, but deficient in Si, S, Ar, Ca

Why is there a Philipps Relation? Broader = Brighter Pinto & Eastman (2000) astro/ph  at peak light Photons must diffuse through a forest of lines in a differentially expanding medium. Doppler shift causes a migration from line to line. The trapped radiation is mostly uv and the uv optical depth is very large. Photons escape chiefly by fluorescence.

More 56 Ni implies a larger luminosity at peak. (Arnett's rule) But more 56 Ni also implies higher temperature in the interior. This in turn implies that Fe, Co, Ni are more highly ionized (III rather than II) The more highly ionized Fe is less effective at "Photon Splitting" than less ionized Fe Hence hotter implies more optical opacity (actually less optical efficiency)

Light Curves What matters? There are potentially four major parameters (and several minor ones) The mass of 56 Ni The mass of 54 Fe, 58 Ni, and other stable members of the iron group The mass of SiSArCa The explosion energy Contained within these are a number of other parameters: The ignition density, C/O ratio, detonation transition density, etc.

An idealized model Assume a starting mass of 1.38 solar masses, a central density of 2 x 10 9 g cm -3 and a C/O ratio of 1::2 The final composition (3 variables) then defines the model.

The final velocity distribution is not very sensitive to how the energy is deposited (especially for the iron containing region).

First results indicate the need for mixing: