Lecture 13

Presupernova Models, Core Collapse and Bounce

Density Profiles of Supernova Progenitor Cores

2D SASI-aided, Neutrino-Driven Explosion?

These should beeasy to explode

These make the heavy elements

Poelarends, Herwig, Langer and Heger (2008)

Ignite carbon burning > 7.25 Me

Heaviest to lose envelope

by winds and thermal pulses 9.0 Me

Ignite Ne and O burning 9.25 Me

Range of e-capture NeO SNe 9.0 - 9.25 Me

Expected number 4%; Maximum number 20%

Larger percentage at lower metallicity

7 −12 Me Stars

12 Me Model has binding 1 x 1050 erg

external to 1.7 Me baryon; 1 x 1049 erg

external to 2.6 Me

Mα =2.2 Me i.e., main sequence mass ≈9 Me

O, Ne, Mg core develops - residual of carbon burning, but not

hot enough to ignite Ne or O burning. Degenerate core (may) grow by thin helium shell burning. M → 1.375 Me if envelope not lost

24Mg(e−,νe)24 Na, 20Ne(e−,νe)

20 Na reduce Ye hence ρ ↑ runaway collapse

At about 2 × 1010 g cm-3, ignite oxygen burning, but matter is already falling in rapidly. Very degenerate runaway. Burn to iron group but kT < εFermi. No appreciable overpressure. Instead capture electrons on Fe group nuclei. Collapse accelerates.

Oxygen burning continues, but in a thin shell through which matter

is falling supersonically. Collapse continues to nuclear density without

ever having formed a large iron core.

Original model due to Miyaji et al (1980). Studied many times since.

A similar evolution may occur for accreting Ne-O white dwarfs (or very rapidly accreting CO-white dwarfs) in binary systems - analternate outcome to Type Ia supernovae. This phenomena in a binaryis generally referred to as “Accretion Induced Collapse (AIC)”.

Once the collapse is well underway, the outcome does not vary appreciably from what one would expect for a collapsingiron core of the same (zero temperature Chandrasekhar)mass.

The energy release from oxygen burning and silicon burning is small compared with the gravitational potential at which the burning occurs

Miyaji et al, PASJ, 32, 303 (1980)Nomoto, ApJ, 277, 791(1984)Nomoto, ApJ, 322, 206 (1987)Mayle and Wilson, ApJ, 334, 909 (1988)Baron et al, ApJ, 320, 304, (1987)

MMS

≈9 Me

MHe ≈2.2 Me

Nomoto, ApJ, 322, 206, (1987)

Kitaura, Janka, and Hillebrandt(2006) using 2.2 solar mass Hecore from Nomoto (1984, 1987)

Explosion ~1050 erg,basically the neutrino wind.Very little Ni or heavy elements ejected.

Faint supernova(?)

Star of ~ 10 solar masses suggested as progenitor of the Crab nebula by Nomoto et al. (1982, Nature, 299, 803)

Observed for Crab: KE = 0.6 to 1.5 x 1050 erg in 4.6+- 1.8 solar masses of ejecta (Davidson and Fesen 1985)

8 – 10 solar masses

Woosley and Weaver (1980)

Total nuclear energyliberated 3 x 1050 erg

Si - ignition at 5 x 108 g cm-3 in a core of almost pure 30Si (Ye = 0.46).

Very degenerate but notso degenerate as a Ia.T ~ 2.5 x 109 at runaway.Peak T = 6 x 109 K.

10 Me Woosley

and Heger (2009)

Fine zoning and carefultreatment of nuclear physics(250 isotope network)

Final kinetic energy3.7 x 1049 erg

L ~ 3 - 10 x 1040 erg/sfor ~ 1 year.

Typical ejection speeds few x 107 cm s-1.

Leaves 1.63 solar masses

One year later, SN ofabout 1050 erg inside 8solar masses of ejecta already at 1015 cm.

Thermonuclear supernova!

Results for stars near 10 solar masses at death

Mass He CO Fe comment core core core

9.2 1.69 1.43 1.22 envelope intact 10 2.2 1.58 1.29 envelope ejected10.5 2.47 1.68 1.29 envelope ejected

Caveat: Multi-D effects not explored!

In a calculation that included current approximationsto all known mechanisms of angular momentum transportin the study, the final angular momentum in the iron coreof the 10 solar mass star when it collapsed was 7 x 1047 erg s

This corresponds to a pulsar period of 11 ms, about half of what the Crab is believed to have been born with.

Spruit (2006) suggests modifications to original modelthat may result in still slower spins.

The explosion of the CrabSN was not (initially) powered by rotation andfall back was minimal.

What about rotation?

Heger, Woosley, & Spruit (2004)using magnetic torques as derived inSpruit (2002)

Stellar evolution including approximate magnetic torques gives slow rotation for common supernova progenitors.

times 2 ?

11 Solar Masses - PreSN

(note thin shells of heavy elements outside Fe core)

Density Temperature Structure – 11 solar masses

Distribution of collapse velocity and Ye (solid line) in the inner2.5 solar masses of a 15 solar mass presupernova star. A collapsespeed of 1000 km/s anywhere in the iron core is a working definition of “presupernova”. The cusp at about 1.0 solar masses is the extent of convective core silicon burning.

Ye

vcollapse

HHe

O

FeSi

Stars of larger mass have thicker, more massive shells of heavy elementssurrounding the iron core when it collapses.

Note that the final masses of the 15 and 25 solar mass main sequence starsare nearly the same – owing to mass loss.

HHeO

Fe Si

Woosley, Heger, and Weaver (2003)

Woosley and Weaver (1995)

Models having a large variety ofmain sequence masses converge on a very similar final structure in their inner solar mass.

The fall off in density around the ironcore is more gradual for higher mass stars (owing to their greater entropy).

Neutron stars?

Black holes?

Timmes, Woosley, and Weaver (1995)

The iron core mass is a (nucleosynthetic) lower limit to the baryonic mass of the neutron star. A large entropy jump characterizes the base of the oxygen shell andmay provide a natural location for the mass cut. Naively the baryonic mass of the remnant may be between these two – but this is very crude and ignores fall back.Above some remnant mass (1,7? 2.2?) a black hole will result. For the most abundantsupernovae (10 to 20 solar masses) the range of iron core masses is1.2 to 1.55 solar masses.For the oxygen shell it is 1.3 to 1.7. From these numbers subtract about 15% for neutrinolosses. Across all masses the iron core varies only from 1.2 to 1.65 solar masses.

range of iron core masseslower bound to remnant mass

Gravitational Binding Energy of the Presupernova Star

This is just the binding energy outside the iron core. Bigger stars are more tightly bound and will be harder to explode. The effect is morepronounced in metal-deficient stars.

solar

low Z

Core Collapse

Once the collapse is fully underway, the time scale becomesvery short. The velocity starts at 108 cm s-1 (definition of the presupernova link) and will build up to at least c/10 = 30,000 km s-1 beforewe are through. Since the iron core only has a radius of 5,000 to10,000 km, the next second is going to be very interesting.

Neutrino Trapping

Trapping is chiefly by way of elastic neutral current scattering on heavy nuclei. Freedman, PRD, 9, 1389 (1974) gives the crosssection

22 2 44 20

22 44 2 -1

coh

219 2 2 -1

0

220 2 -1

2 4 20

1.5 10 cmMeV

hence

1.5 10 cm gmMeV

5.0 10 cm gm56 MeV

2.6 10 cm gm56 MeV

if one takes sin ( ) (0.229) 0

coh

o A

coh

W

a A

a A N

Aa

A

a

ν

ν

ν

ν

εσ

εκ

ε

εκ

θ

−

−

−

−

⎛ ⎞≈ ×⎜ ⎟⎝ ⎠

⎛ ⎞≈ ×⎜ ⎟⎝ ⎠

⎛ ⎞⎛ ⎞= × ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

⎛ ⎞⎛ ⎞= × ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

= = =

g

g

.0524

20

W

sin ( ) where

is the "Weinberg

angle", a measure of the

importance of weak

neutral currents

Wa θθ

=

Therefore neutrino trapping will occur when

κν ρR~1 R~2 ×106 cm

10−19( ) 102( )ρ 106( )~1 ⇒ ρ~1011 gcm-3

(for A~100)

From this point on the neutrinos will not freely stream but must diffuse. Neutrino producing reactions will be inhibited by the filling of neutrino phase space. The total lepton number

YL = Ye +Y

will be conserved, not necessarily the individual terms. At the pointwhere trapping occurs YL = Ye ~ 0.37. At bounce Ye~ 0.29; Y~ 0.08.

1/37

11 -3

1.11( ) MeV

~ 30 MeV at

=10 g cm

F eYε ρ

ρ

=

Bounce

Up until approximately nuclear density the structural adiabaticindex of the collapsing star is governed by the leptons – the electrons and neutrinos, both of which are highly relativistic,hence nearly =4/3.

As nuclear density is approached however, the star first experiencesthe attactive nuclear force and goes briefly but dramaticallybelow 4/3.

At still higher densities, above ρnuc, the repulsive hard corenuclear force is encountered and abruptly>> 4/3.

In general, favor the curves K = 220. For densities significantlybelow nuclear is due to relativistic positrons and electrons.

As the density reaches and surpasses nuclear )(2.7 x 1014 gmcm-3), the effects of the strong force become important. One first experiences attraction and anacceleration of the collapse, then a very strong repulsion leading to >> 4/3 and a sudden halt to the collapse.

15 -3 -3

39 1

1.66 10 (fm ) g cm

( 10 ) "A

n

N

ρ− −

= ×

=

The collapse of the “iron” core continues until densities nearthe density of the atomic nucleus are reached. There is a portion of the core called the “homologous core” that collapses subsonically (e.g., Goldreich & Weber, ApJ, 238, 991 (1980); Yahil ApJ, 265, 1047 (1983)). This is also approximately equivalent to the “sonic core”.

This part of the core is called homologous because it can be shown that within it, vcollapse is proportional to radius. Thus the homologouscore collapses in a sef similar fashion. Were = 4/3 for the entire ironcore, the entire core would contract homologously, but because becomessignificantly less than 4/3, part of the inner core pulls away from the outer core. As the center of this inner core approaches and exceeds ρnuc the resistanceof the nuclear force is communicated throughout its volume by sound waves,but not beyond its edge. Thus the outer edge of the homologous core iswhere the shock is first born. Typically, MHC = 0.6 – 0.8 solar masses.

The larger MHC and the smaller the mass of the iron core, the lessdissipation the shock will experience on its way out.

at about point b) on previous slide

Factors affecting the mass of the homologous core:

• YL – the “lepton number”, the sum of neutrino and electron more numbers after trapping. Larger YL gives larger MHC and is more conducive to explosion. Less electron capture, less neutrino escape, larger initial Ye could raise YL.

• GR – General relativistic effects decrease MHC, presumably by strengthening gravity. In one calulation 0.80 solar masses without GR became 0.67 with GR. This may be harmful for explosion but overall GR produces more energetic bounces and this is helpful.

• Neutrino transport – how neutrinos diffuse out of the core and how many flavors are carried in the calculation.

Relevant Physics To Shock Survival

Photodisintegration:

As the shock moves through the outer core, the temperature rises to the point where nuclear statistical equilibrium favors neutrons and protons over bound nuclei or even -particles

56 17

18 -1

51

492.26 MeV( 26 ,30 ) 9.65 10

56

8.5 10 erg gm

1.7 10 erg/0.1 M

nucq Fe p n ⎛ ⎞→ = × ⎜ ⎟⎝ ⎠

= ×

= × e

Neutrino losses

Especially as the shock passes to densities below 1012 g cm-3, neutrinolosses from behind the shock can rob it of energy. Since neutrinos oflow energy have long mean free paths and escape more easily, reactionsthat degrade the mean neutrino energy, especially neutrino-electron scatteringare quite important. So too is the inclusion of andflavored neutrinos

The Mass of the Presupernova Iron Core

Unless the mass of the iron core is unrealistically small (less than about 1.1 solar masses) the prompt shock dies

The Equation of State and General Relativity

A softer nuclear equation of state is “springier” and gives a larger amplitude bounce and larger energy to the initial shock.General relativity can also help by making the bounce go “deeper”.

Stellar Structure and the Mass of the Homologous Core

A larger homologous core means that the shock is born fartherout with less matter to photodisintegrate and less neutrino losseson its way out.

Collapse and bounce in a 13 solar mass supernova.Radial velocity vs. enclosedmass at 0.5 ms, +0.2 ms,and 2.0 ms with respect tobounce. The blip at 1.5 solar masses is due to explosive nuclear burningof oxygen in the infall(Herant and Woosley 1996).

It is now generally agreed (despite what you may read in old astronomy text books), that the so called “promptshock mechanism” – worked on extensively by Bethe,Brown, Baron, Cooperstein, and colleagues in the 1980’s – does not work. The shock fails and becomes in a short time(< 10 ms) an accretion shock.

It will turn to neutrinos and other physics to actually blow up the star. But the success of the neutrino model will depend, in part,upon the conditions set up in the star by the failureof the first shock. How far out did it form? What is the neutrino luminosity? Does convection occur beneath the neutrinosphere? So all the factors listed on the previouspages are still important.