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 10-7 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.

K 10 3 T ;cm gm102 As 8-39 xx

sun1212

nuc M 1.38 M plasma);(S C)C(S

29

89

A Successful Model Must:

• Produce approximately 0.6 solar masses of 56Ni (0.1 to 1 Msun )

• Produce at least 0.2 solar masses of SiSArCa

• Not make more than about 0.1 solar masses of 54Fe and 58Ni combined

• And probably not have too much unburned oxygen in close proximity to 56Ni

• 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 flamethat starts slowly, pre-expands the star (so asto avoid too much electron capture) then moves very rapidly when

Unfortunately the laminar flame has just the opposite behavior.

-37 cm gm10

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 highdensity 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 108 K

Pressure scale height: 400 km

Nuclear time scale: 102 s

Convective time scale: 102 s

Convective speed: 5 km s-1

Binding energy: 4 x 1050 erg

Density: 2 x 109 g cm-3

Burning 0.05 solar masses can causeexpansion 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 detonationone 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 constantacross the flame surface. Temperature rises, densitydecreases. 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 109 Kassuring 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 109 gm cm-3

only 1015 gm. That is, a length scale of 70 cm.

Why doesn't it happen?

T

T

r

r

In the absence of externalforces, the only way an isolated region can developa detonation is to have asupersonic phase velocityimposed 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.

Snuc crd

d

1

To serve as a detonator, a region must run awayas a unit in approximately a sound crossing time.

Nuclear burning time scales as approximately T26

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 108 K,the same total time to within 0.01 s/100 s = 0.01%.In fact, this must be divided by the power of Tto which the nuclear energy generation is sensitive.

So temperature fluctuations greater than 5 x 10-6

are not allowed.

Speculation

How many points and when and whereeach ignites may have dramatic consequencesfor the supernova (origin of diversity?)

2/L km 200 r P

Multi-point Ignition

Depends on: C/O

ign

Blobs of various sizesand released from varying altitudes allrunaway at 100 km to 300 km

Garcia-Senz and WoosleyApJ, 454, 895, (1995)

Igniting the star at a single point off center gives very different results than ignitingprecisely at the center orin a spherical volume.

This "single point ignition"model did not produce a supernova (pulsation would have ensued)

Ignition at 5 pointsdid produce a successfulsupernova with 0.65 solar masses of burnedmaterial, 0.5 solar masses of which was56Ni.

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 ToDetonation Happen?

• Could have desireable consequences if it happened at r = 107 - 108 g cm-3

• The critical mass for ignition is not large (about 50 m at 3 x 107 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:

lGib

is defined by:

As density decreases , vcond

decreases dramatically and

dcond

also increases dramatically.

Eventually l

Gib <

cond

L

3/1

vv

L

ll

cm10 Lat

s cm10v6

-17L

condlGibuv

L

3/1

vu i.e.,

L

lGibcond L

v

u3

L

cond

Gibl

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...

1.0

0.5 XC=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 ~ 107 - 108 cm/s

e.g. but, and

D = 2.33 which implies veff = vL

S

cond

c

ur

Area

2eff 4v

cond

D

ul

R2

effv

R

v

3

L

cond

Gib

ull

2) Zeldovich detonation (Khokhlov 1990)

At e.g., 3 x 107 g cm-3, one must prepare a regionlarger 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

tBURN

(lcrit

) > teddy

(lcrit

) evaluated at Tash

but tBURN << tHD

"Sharp-Wheeler Model"

g

Model OK, but deficient in Si, S, Ar, Ca

2SW

2SW

1.0v

05.0r

tg

tg

eff

eff

Why is there a Philipps Relation?

Broader = BrighterPinto & Eastman (2000)astro/ph-0006171

at peak light

Photons must diffuse through a forest of lines in a differentially expanding medium.

Doppler shift causes amigration from line to line.

The trapped radiation is mostly uv and the uv optical depth is very large.

Photons escape chiefly by fluorescence.

More 56Ni implies a larger luminosity at peak. (Arnett's rule)

But more 56Ni 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 56Ni

• The mass of 54Fe, 58Ni, and other stable members of the iron group

• The mass of SiSArCa

• The explosion energyContained 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 of1.38 solar masses, a centraldensity of 2 x 109 g cm-3

and a C/O ratio of 1::2

The final composition (3variables) then defines the model.

The final velocity distributionis not very sensitive to how the energy is deposited(especially for the ironcontaining region).

First results indicate the need for mixing: