Supernovae, Their Collapsing Cores and Nuclear Physics

Sam M. Austin Mitchell 4/14/06

Supernovae, Their Collapsing Cores and Nuclear Physics

Nature of Supernova Progenitors

Their sensitivity to nuclear properties

How these properties are determined

Ongoing experiments


Evolution of Stellar Core for Heavy Stars

After initial formation

A gravitational collapse, interrupted by long nuclear burning stages.

Eventually form “Fe”core, and no further nuclear energy available.

Log Central Density

Log

Cen

tral

Den

sity

Woosley & Janke--Nature

Temperature vs Density


Problem since Baade/Zwicky in 1930’s suggested SN powered by gravitational energy from collapse of normal star to neutron-star

Supernova EvolutionThe special case of Fe

Previously products of f usion were lighter than the constituents, excess mass appeared as energy.

Fe is most tightly bound f orm of matter. Fusing two Fe takes energy, No more nuclear energy available.

Core collapses and keeps on collapsing

At about density of nuclei, collapse stops, bounces out. Resulting shock wave blows off the surf ace of star?

Huge amount of energy released, a suddenly bright star, a supernova.

“Fe”-Core Collapse

Bounce-Form Shock Wave

Shock--Dissociates Overlying “Fe”



















"Fe" core Collapses

Bounce--Form Shock Wave

Shock moves out

Loses energy. Fe p's , n's in outer part of Fe core; neutrino emission

Stalls

Time

Supernovae Core Collapse—The Mechanism


Difficulty Of The Supernova Problem

A commentInsufficient knowledge of nuclear physics properties causes changes at the 1-few% level

Dangerous to assume that the effects are always cancelled by negative feedback processes

Nature of the energetics—the 1% problem?Only 1% of the available gravitational energy (1053 ergs) is emitted as explosion energy, rest as neutrinos. (Burrows argues it’s a 10% problem--90% of gravitational energy emitted prior to critical phase). But, either way, it may mean we have to do things very well.

What’s been tried

Delayed shock– re-energized by neutrinos from proto-neutron star Better neutrino transport, better weak interactions, 2 and 3-D (limitations), acoustic coupling, ……

Scheck, Janka


Triple makes 12C, 12C()16O turns it into 16O. Their ratio determines the amounts of C and O made and affects the nature of a star and of its iron core

An Example--Helium Burning

Rehm-ANL 10:10

WMU-MSU


SNII--Pre-collapse Fe Core Size

Pre-supernova evolution

Vary rate of 12C()16O (or Triple alpha)?

All else constant

Fe core mass changes by >0.2 M over the interesting range

Important?Naively, yes. If homologous core mass constant, need 3 x 1051 erg to dissociate extra 0.2 M to nucleons

Fe C

ore

Siz

e (

Sola

r M

ass

es)

0.5

1.0

1

.5

2.0

1.0 1.5 2.0 2.5 12C()16O Multiplier

or 1/Triple alpha?

25 MHeger, Woosley, Boyes

Need ratio of rates to 10%

() 160 ±40 keV b Brune 2006

3 alpha Fynbo 2006


Element Production in a Supernovae

Shell Burning

When He is exhausted in the core the core collapses, T increases, core carbon and oxygen burning begin. H and He burning in shells

The successive core stages are H He, gravity He C,O, gravity C,O Mg, Si--gravity, Si Fe.

How Sun Evolves

Hydrogen burning ends after 1010 yrs

Consumed central 10% of star

No heat source, pressure decreases and gravity wins. Core collapses, releases gravitational energy which heats the core.

Helium burning starts

Core gets hot enough to overcome Coulomb repulsion of two 4He (Z=2).

Helium fuses into 12C and 16O

Hydrogen consumed in a shell

He burning core T=108 K=107 kg/m3

H burning shell

Non-burning envelope

He Burning Core T=108 K = 107 kg/m3

The Result (Stellar Onion)

SN blows off outer layers Need detailed element distribution/abundances to predict SN element production


Detailed Models-Heger and Woosley 2001

It’s more complex than the onion even in 1D: M= 22 Msun. Along the x-axis sequential episodes of convective carbon, neon, oxygen, and silicon burning. Affected by rates of He-burning reactions.


SNII Nucleosynthesis A=16-40

12C()16O Multiplier (xBuchmann 1996)

Pro

duct

ion

Fact

or

Heger, Woosley,

Boyes

25 M

Explosion of 25 M star

Vary rate of 12C()16O

All else same

Production Factor“Same” PF for 1.2 x standard12C()16O rate

170 keV b


Weak Strength and Supernovae Core Collapse

Gamow-Teller (GT) Strength?

Mediates -decay, electron capture(EC), n induced reactions

GT (allowed) Strength S=1; L = 0, e.g. 0+ 1+; GT+,GT-

Lies in giant resonances

(n,p)

(p,n)

GT+ dominates process

Situation

After silicon burning, Tcore 3.3 x 109 K, density108 g/cm3. e- Fermi energy allows capture into GT+. Reduces e- pressure emits neutrinos. Speeds collapse.

At higher T, GT+ thermally populated, - decays back to ground state. - E.C.


Effects of Changed Weak Rates-Heger et al. Ap.J. 560 (2001) 307

2

4

6

8

T (

109

K)

T

4105106

Time till collapse (s)

10-8

10-7

10-6

10-5

10-4

10-3

dY

e

dt (

s1

)

LMP-ECLMP-

10010110210310

0.44

0.46

0.48

0.50

Ye

WWLMP

15 M

URCA

IPM vs Shell Model

WW standard Wallace-Weaver rates based on independent particle model (FFN)

LMP-from large basis shell model calculations. (Langanke and Martinez-Pinedo)

Significant differencesLarger, lower entropy "Fe" pre-collapse core More e-'s (Ye larger), lower T core. Larger homologous core


Important Electron Capture Nuclei

Pre-Collapse: Nuclei in the Fe-Ni region

Collapse: Heavier nuclei are important, including many with N>40


Do (N>40) Nuclei Undergo Electron Capture?

From Martinez-Pinedo

Independent particle model: No for N>40Transitions Pauli blocked

Shell model at finite T: Blocking removed—Has

important effects


Results of New Calculations--Langanke et al PRL

Nature of calculations

Shell model Monte Carlo + RPA

Results

Capture on nuclei dominates by x10

Neutrino energies are lower

Mass enclosed by the shock is smaller by 0.1 Msun

Shock is weaker

Ye varies with enclosed mass


Reliability of Nuclear Models for e-CaptureFor pre-collapse calculations

Quite good, some problemsFurther validation of models requires data for unstable isotopes especially odd-odd nuclei

: FFN (IPM)

: data (n,p) (TRIUMF)

: Caurier et al. (1999) Large basis SM : Caurier et al. folded with experimental resolution

?

?

?

(Caurier, et al NPA 653, 439(99


Reliability of Nuclear Models for e-Capture-cont.

For heavier nuclei--less firmly based and not validated

General Comment

Can’t measure everything, 1000s of transitions, many from thermally excited states

But need to do enough checks to have confidence in models

Nature of measurements: Hadronic charge exchange reactions

Operators similar to decay operator; (n,p), (d,2He), (t,3He) measure e-capture strength

B(GT) = CEX(q = 0)/unit , unit calibrated from known transitions

Accuracies in 10-20% range, better for strong transitions

Require energy of >100 MeV/nucleon to minimize 2-step processes

Reactions studied: In past (n,p), (d,2He), (t,3He); presently only (t,3He)


Charge Exchange Options

(t, 3He)Secondary triton beams 106-

7/sec at MSU/NSCL, 115 MeV/A tritons

Resol: 160 keV achievedData on 24,26Mg, 58Ni, 63Cu,

94Mo

90

0

10

20

30

40

50

60

70

80

0.0

MeV

1+

4.5

MeV

2-

7.7

MeV

1-

160 keV

12C(t,3He)12B

lab=0o1.7o

0

10

20

30

40

50

60

70

80

90

-2 0 2 4 6 8 10 12

0.0

MeV

1+

4.5

MeV

2-

7.7

MeV

1-

230 keV

12C(t,3He)12B

labo =1.7 3.4o

E(MeV)

Sherrill, et al

Counts

Unique beam-spectrometer(S800), simple analysis, calibration from (3He, t) reaction at Osaka. More beam nice

Future (Zegers, et al.)Develop techniques for using radioactive beams:

(p,n), (7Li, 7Be) in inverse kinematics to study -decay, electron capture, respectively. Test (7Li, 7Be) expt in near future.


(t,3He), (3He,t) vs (p,n) and Shell Model


II

Q2= -287 keV

+8Be

Hoyle state

Back to The Triple Alpha Process-More Formally

Step I: 8BeEquilibrium abundance of

8Be

Step II: 8Be + 12C(7.65)

Present Interests—3 and SNII (Iron core size, nucleosynthesis) 5% AGB Stars (Carbon production and carbon stars) 5% Limits on variation of “fundamental” constants

r3 rad(7.65)e-Q/kt

rad = + , -Q = Q1+Q2

Rate depends on properties of Hoyle state (7.65), mostly on rad

I

Q1 = -92 keV


How Well Do We Know rad

rad

2.7% 9.2% 6.4%2.7%

12%

Least well known quantity is

A WMU, MSU collaboration is undertaking a new measurement:

WMU Alan Wuosmaa, Jon Lighthall, Scott Marley, Nicholas Goodman

MSU/NSCL Clarisse Tur, SMA


Measuring A hard measurement: Branch is small ~6 x 10-6

New measurement: WMU/MSUWMU Tandem, (p,p’) at 135o, 10.56 MeV (strong resonance for 7.65 state)

pairs/#-7.65

protons)Aim: ± 5% accuracy

PMPM

PM Si, 1 of 4

PMPM

PM

PMPM

PM Si, 1 of 4Side View

Top ViewPM

PM

PMPM

Plastic Scint

Liner

12C Target

BeamPM

PM

PMPM

Plastic Scint

Liner

Beam

Improved version of Robertson, et al PRC 15,1072(77)


WMU-MSU/NSCL Detector


Final Comments

Discussed two cases were nuclear uncertainties are important

Helium burning (expts on 12C( and 3alpha rates ongoing)

Electron capture (expts ongoing)

Others have not been much investigated12C+12C reaction rate poorly known—sensitivity of progenitor structure?r-process nucleosynthesis could provide a diagnostic of conditions at its site—nuclear properties need to be better understood


Cocktail beam

78Ni

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

70 120 170 220

Mass (A)

Ab

un

da

nc

e (

A.U

.)

Observed Solar Abundances

Model Calculation: Half-Lives fromMoeller, et al. 97

Series4

Measured half-life of 78Ni with 11 events Acceleration of the r-process

excess of heavy elements with the new shorter 78Ni half-life

Result: 110 +100-60 ms

(Theory: 460 ms)

T1/2 measurement at NSCL

Beta Lifetimes are important--Example: doubly magic 78Ni

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

70 120 170 220

Mass (A)

Ab

un

da

nc

e (

A.U

.)

Observed Solar Abundances

Model Calculation: Half-Lives fromMoeller, et al. 97

Same but with present 78Ni Result

En

erg

y los s

velocity

r-process calculation

P. Hosmer et al. 2005 (NSCL, Mainz, Maryland collaboration)


Some Comments

Discussed two cases were nuclear uncertainties are important

Helium burning (expts on 12C(a,g) and 3alpha rates ongoing)

Electron capture (expts ongoing)

Others have not been much investigated12C+12C reaction rate poorly known—sensitivity of progenitor structure?r-process nucleosynthesis could provide a diagnostic of conditions at its site—nuclear properties need to be better understood

2D and 3D calculations of progenitor evolutionIn their beginning phasesWill surely change the nature of the pre-SN starNote: present 1-D models differ somewhat from group to group

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Supernovae, Their Collapsing Cores and Nuclear Physics

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