FIVE REGIMES OF NUCLEAR BURNING IN DENSE STELLAR MATTERFIVE REGIMES OF NUCLEAR BURNING IN DENSE STELLAR MATTER

D.G. Yakovlev

Ioffe Physical Technical Institute, St.-Petersburg, Russia

Thermonuclear burning

Physical conditions

Summary

Moscow, December, 2004

Screening in thermonuclearreactions

Pycnonuclear burning

General outlook and applications

PHYSICAL CONDITIONS

i

ippp

mL

i

m

neZT

Ta

eZT

na

aT

eZ

22

22

3/122

4,

175;1

.4

3,

...21 cZZZ

PHYSICAL STATES OF IONS

Gas Strongly coupledclassical system

Strongly coupledquantum system

1

22

a

eZT

1

22

a

eZTp

1

22

a

eZT p

Classical theory of thermonuclear reactions

...21 cZZZ

Reaction rate:

scm

reactions3

12

21

1

v

nnR

)(/3

0

Evv TE

ed

Z1 Z2

exp)(,)()(

EPE

EPESE

v

eZZrprE

a

b

2212

)(d2

Classical theory of thermonuclear reactions

-expT

ES

M

Ev pkpk )(

3

24

12

2733/1

2

422

21

2

T

eZMZ

T

Epk

Reaction rate R depends mainly on T

History

Example

G. Gamow, H. Bethe, C. Critchfield, E. Salpeter,

C. Von Weizsacker, A. Cameron, W. Fowler, G. Rivers

Carbon burning: ...MgCC *241212 Rnt i /,cmg10 3-9 = burning time

T=109 K t~ 1 min

T=108 K t~1036 yr No burning at low T!

Nobel Prize, 1967

1938

PLASMA SCREENING IN THERMONUCLEAR REACTIONS

)()(2

21 rr

eZZrU

Created byneighbors

ar ~

Consider: pt TTar

Then trrconstr for )(

Two-stage process: (1) approaching the barrier(2) penetrating the barrier

The reaction rate: R=R0E

E>1 enhancement factor

TffffE j

j

),exp( 1221

Basic ideas:Salpeter 1954, 1961Salpeter & Van Horn 1969 DeWitt, Graboske & Cooper 1973

Thermodynamic function

STRONG PLASMA SCREENING

122

pTTa

eZ Thermonuclear regimewith strong screening

1exp 1221 fffE

1for 9.0)(with

Carlo, Monte OCP from - )(

4

3,,

)( :rule additive;

3/1

3/122

f

f

naZaa

Ta

eZ

ffT

f

eeej

j

jj

jjj

j

+ 1

Salpeter’s model:

1 and for )057.1exp( 21 ZZE

21 ZZ

1 2 12

Pycnonuclear reactions

exp)(,)()(

EPE

EPESE

6/1

2

0

1)(d

2

r

drprE

a

b

Coulomb lattice of nuclei, T=0 d

Zero-point vibrations,

m

rE

~,~ 0

m

neZ ip

224~

=ion plasma frequency

WKB tunneling:

?1~

The reaction rate exponentiallyincreases with growing density!

PYCNONUCLEAR BURNING OF DENSE STELLAR MATTERPYCNONUCLEAR BURNING OF DENSE STELLAR MATTER

tburn~1075 yrs tburn~0.1 s

Gamow and Wildhack

Later History

Zel’dovich (1957)

Cameron (1959)

Kirzhnits (1960)

Kopyshev (1964)

Wolf (1965)

Van Horn (1966)

Salpeter & Van Horn (1969)

Schramm & Koonin (1990)

Err-brr-mrr!!

THERMALLY ENHANCED PYCNONUCLEAR BURNING

Increase T from T=0: )0(/)( RTREpyc = enhancement factor

Salpeter and Van Horn 1969

a

eZ

Ta

eZE

T

EfnE

pk

nnn

220

22

0

exp

1exp;2

1

INTERMEDIATE THERMO-PYCNONUCLEAR BURNING

const)( ;Z

~;~ ;~22

ra

eEarTT pktp

Most difficult for the theory!Many attempts!

FIVE REGIMES OF BURNING IN DENSE MATTER

Thermonuclear

Intermediate

Pycnonuclear

Cla

ssic

al

Str

on

g

scre

enin

g

T-e

nh

ance

d

T=

0

1 2

3

4 5

TEMPERATURE DEPENDENCE

GENERAL OUTLOOK

CARBON IGNITION CURVE

1. Accreting massive white dwarfs -- SNIa

2. Accreting neutron stars -- superbursts

Applications of pycnonuclear burning

White dwarfs and neutron stars (particularly, accreting)

Mas

s de

nsit

y, g

cm

-3

106

109

1010

1012

1013

HHe

C

ASHES

BURN!

No hydrogen in WDsWDs as SN IaX-ray bursters

Accreting neutronstars – soft X-raytransients

48Mg+48Mg -> 96CrDeepest burning:

SUMMARY

1. There are five regimes of nuclear burning 2. Classical thermonuclear regime is well elaborated; other regimes – much less 3. The problem belongs to the physics of strongly coupled Coulomb plasma: quantum tunneling in random and fluctuating plasma potential 4. Theory goes back in time!