five regimes of nuclear burning in dense stellar matter

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!