FIVE REGIMES OF NUCLEAR BURNING IN DENSE STELLAR MATTER
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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
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PHYSICAL CONDITIONS
i
ippp
mL
i
m
neZT
Ta
eZT
na
aT
eZ
22
22
3/122
4,
175;1
.4
3,
...21 cZZZ
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PHYSICAL STATES OF IONS
Gas Strongly coupledclassical system
Strongly coupledquantum system
1
22
a
eZT
1
22
a
eZTp
1
22
a
eZT p
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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
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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
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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
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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
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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!
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PYCNONUCLEAR BURNING OF DENSE STELLAR MATTERPYCNONUCLEAR BURNING OF DENSE STELLAR MATTER
tburn~1075 yrs tburn~0.1 s
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Gamow and Wildhack
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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!!
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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
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INTERMEDIATE THERMO-PYCNONUCLEAR BURNING
const)( ;Z
~;~ ;~22
ra
eEarTT pktp
Most difficult for the theory!Many attempts!
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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
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TEMPERATURE DEPENDENCE
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GENERAL OUTLOOK
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CARBON IGNITION CURVE
1. Accreting massive white dwarfs -- SNIa
2. Accreting neutron stars -- superbursts
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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:
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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!