PYCNONUCLEAR REACTIONS in dense stellar matter

PYCNONUCLEAR REACTIONS
in dense stellar matter
D.G. Yakovlev
Ioffe Physical Technical Institute, St.-Petersburg, Russia
Main collaborators:
L. Gasques – JINA, Notre Dame
P. Haensel – CAMK, Warsaw
K.P. Levenfish – Ioffe Institute
M. Wiescher – JINA, Notre Dame
Talk outline:
• Thermonuclear reactions
• Pycnonuclear reactions
• From thermo to pycno
• Applications
Notre Dame, JINA, August 21, 2007

THERMONUCLEAR REACTIONS
Z
1
+ Z2
→ Zc
→
...
Reaction rate:
n1n2
R =
1+
δ
12
vσ
reactions
cm
3
s
Z 1 Z 2
∞
∫
0
dv
v
3
e
−E / T
σ
( E)
S(
E)
P(
E)
σ −η
E
( E) = , P(
E)
= exp( )
a
2 Z1Z
η ( E)
= 2 dr
p(
r)
π
h
∫ =
hv
b
2
e
2

2E
pk
S(
E
pk
)
vσ = 4
exp -τ
3M
T
τ =
3
E pk
T
2
⎛ 27π
MZ
=
⎜
⎝ 2Th
2
1
2
Z
2
2
e
4
⎞
⎟
⎠
1/3
( )
>> 1
Reaction rate R depends mainly on T
History
1938
Test
Example
ρ =
10 9
g cm -3
,
G. Gamow, H. Bethe, C. Critchfield, E. Salpeter,
C. Von Weizsacker, A. Cameron, W. Fowler, G. Rivers
Stellar evolution
Carbon burning:
12 12 24
C + C ⇒
*
Mg ⇒ ...
t = n / i
R
T=10 9 K t~ 1 min
= burning time
Nobel Prize, 1967
T=10 8 K t~10 36 yr No burning at low T!

Coulomb lattice of nuclei, T=0
Zero-point vibrations,
ω ~ ω =
p
2
4πZ
e
m
WKB tunneling:
PYCNONUCLEAR REACTIONS
2
h ω,
r ~
S(
E)
P(
E)
σ −η
E
n
( E) = , P(
E)
= exp( )
i
E
~
0
En
= hω
⎛
⎜n+
⎝
h
mω
=ion plasma frequency
1
2
⎞
⎟
⎠
d
η
a
2
⎛ d ⎞
=
h
∫ ⎜ ⎟
⎝ r
b
0 ⎠
( E) dr
p(
r)
= α⎜
⎟ ∝
1/ 6
α ~ 1 =
?
2
1
ρ
The reaction rate exponentially
increases with growing density!

DENSITY DEPENDENCE OF CARBON BURNING RATES
t burn
~10 75 yrs
t burn
~0.1 s

Gamow and Wildhack

Later History
Zeldovich (1957)
Cameron (1959) – “pycnos”
Kirzhnits (1960)
Kopyshev (1964)
Wolf (1965)
Van Horn (1966)
Salpeter & Van Horn (1969)
Schramm & Koonin (1990)

PHYSICAL CONDITIONS
Z
1
+ Z2
→ Zc
→
...
Γ =
T
T
L
p
=
2
Z e
aT
2
2
Z e
a
p
2
= hω
,
⎛ 3 ⎞
, a =
⎜
4πn
⎟
⎝ i ⎠
⇒ Γ = 1;
ω
p
=
T
m
1/3
2
4πZ
e
m
⇒ Γ = 175
i
2
.
n
i

PHYSICAL STATES OF IONS
T
Gas
2 2
Z e
>> a
Γ > 1

FIVE REGIMES OF BURNING IN DENSE MATTER
1 2
Thermonuclear
Classical
Strong
screening
3
Intermediate
Pycnonuclear
T-enhanced
4 5
T=0

GENERAL OUTLOOK for Carbon Burning

Applications of pycnonuclear burning
White dwarfs and neutron stars (particularly, accreting)
Mass density, g cm -3
H
10 6
10 9
10 10
10 12
10 13
He
ASHES
BURN!
C
WDs as SN Ia
NSs: X-ray bursters
NSs: superbursts
Accreting neutron
stars – soft X-ray
transients

CARBON IGNITION CURVE IN WHITE DWARFS
Talk by
David Chamulak

Soft X-ray X
transients
• Active states: L X
= 10 36 -10 39 erg/s
weeks – months – years; X-ray bursts
• Quiescent states: L X = 10 30 –10 34 ergs/s
years - decades
• SXRTs belong to LMXRBs
Donor star: main-sequence or
subgiant, M ≤ M SUN
• P ORB : a few hours – a few days
• ‹M› ≈ 10 -11 –10 -9 M SUN /yr
.
Brown, Bildsten & Rutledge (1998):
Aql X-1 T S ~ 10 6 K

Accreted Crust
Reactions:
1. Beta captures
2. Neutron emission
and absorption
3. Pycnonuclear
reactions

Accreted crust: Starting from 56 Fe (Haensel & Zdunik 1990)

SUMMARY
• Cold dense matter undergoes pycnonuclear burning
• Pycnonuclear burning is not efficient in ordinary stars but can be
important in cores of white dwarfs and envelopes of neutron stars
• Applications of pycnonuclear burning include:
(a) explosions of white dwarfs as Ia type supernovae
(b) deep crustal heating of transiently accreting neutron stars
(c) superbursts of accreting neutron stars
• The theory of pycnonuclear burning is not perfect;
new theories, implementations, observations and theoretical
interpretation are ahead