Hydrogen burning under extreme conditions
Scenarios:
• Hot bottom burning in massive AGB stars (> 4 solar masses)
(T9 ~ 0.08)
• Nova explosions on accreting white dwarfs
(T9 ~ 0.4)
• X-ray bursts on accreting neutron stars
(T9 ~ 2)
• accretion disks around low mass black holes ?
• neutrino driven wind in core collapse supernovae ?
further discussion assumes a density of 106 g/cm3 (X-ray burst conditions)
“Cold” CN(O)-Cycle T9 < 0.08
Mg (12)
Na (11)
Ne (10)
F (9)
O (8)
Energy production rate:
  v 14 N ( p , )
N (7)
C (6)
14
11 1213
9 10
3 4 5 6 7 8
Ne-Na cycle !
Hot CN(O)-Cycle
T9 ~ 0.08-0.1
Mg (12)
Na (11)
Ne (10)
F (9)
O (8)
“beta limited CNO cycle”
  1 /(1
14O (   )
 151O (   ) )  const
Note: condition for hot CNO cycle
depend also on density and Yp:
 p ,  
 Yp N A  v   
on 13N:
N (7)
C (6)
14
11 1213
9 10
3 4 5 6 7 8
Very Hot CN(O)-Cycle T9 ~ 0.3
Mg (12)
Na (11)
Ne (10)
F (9)
O (8)
still “beta limited”
N (7)
C (6)
14
T1/2=1.7s
11 1213
9 10
3 4 5 6 7 8
3a flow
Breakout
Mg (12)
Na (11)
Ne (10)
F (9)
O (8)
processing beyond CNO cycle
after breakout via:
T9 >~ 0.3
15O(a,)19Ne
T9 >~ 0.6
18Ne(a,p)21Na
N (7)
C (6)
14
11 1213
9 10
3 4 5 6 7 8
3a flow
Multizone Nova model
(Starrfield 2001)
Current 15O(a,) Rate
with X10 variation
5
10
New lower limit for
density from B. Davids et al.
(PRC67 (2003) 012801)
4
Density (g/cm3)
10
3
10
Breakout
2
10
1
10
No
Breakout
0
100.0
0.5
1.0
Temperature (GK)
1.5
X-ray binaries
Outline – nuclear physics at the extremes
1. Observations
2. Model
3. Open Questions
4. Nuclear Physics – the rp process
X-rays
Wilhelm Konrad Roentgen,
First Nobel Price 1901 for
discovery of X-rays 1895
First X-ray image from 1890
(Goodspeed & Jennings, Philadelphia)
Ms Roentgen’s hand, 1895
Cosmic X-rays: discovered end of 1960’s:
0.5-5 keV (T=E/k=6-60 x 106 K)
Again Nobel Price in Physics 2002
for Riccardo Giacconi
Discovery
First X-ray pulsar: Cen X-3 (Giacconi et al. 1971) with UHURU
T~ 5s
Today:
~50
First X-ray burst: 3U 1820-30 (Grindlay et al. 1976) with ANS
Today:
~40
Total ~230 X-ray binaries known
10 s
Typical X-ray bursts:
• 1036-1038 erg/s
• duration 10 s – 100s
• recurrence: hours-days
• regular or irregular
Frequent and very bright
phenomenon !
(stars 1033-1035 erg/s)
X-ray binaries
Others
(e.g. no bursts found yet)
X-ray pulsars
Regular pulses with
periods of 1- 1000 s
(Bursting pulsar:
GRO J1744-28)
X-ray bursters
Frequent Outbursts of 10-100s duration
with lower, persistent X-ray flux inbetween
Type I bursts
Type II bursts
Burst energy proportional
to duration of preceeding
inactivity period
Burst energy proportional
to duration of following
inactivity period
By far most of the bursters
“Rapid burster”
and GRO J1744-28 ?
The Model
Neutron stars:
1.4 Mo, 10 km radius
(average density: ~ 1014 g/cm3)
Neutron Star
Donor Star
(“normal” star)
Accretion Disk
Typical systems:
• accretion rate 10-8/10-10 Mo/yr (0.5-50 kg/s/cm2)
• orbital periods 0.01-100 days
• orbital separations 0.001-1 AU’s
Mass transfer by Roche Lobe Overflow
Star expands on main sequence.
when it fills its Roche Lobe mass transfer happens
through the L1 Lagrangian point
John Blondin, NC State, http://wonka.physics.ncsu.edu/~blondin/AAS/
Energy generation: thermonuclear energy
4H
4He
6.7 MeV/u
3 4He
12C
0.6 MeV/u
(“triple alpha”)
5 4He + 84 H
104Pd
6.9 MeV/u
(rp process)
Energy generation: gravitational energy
E=
G M mu
R
= 200 MeV/u
Ratio gravitation/thermonuclear ~ 30 - 40
Observation of thermonuclear energy:
Unstable, explosive burning in bursts (release over short time)
Burst energy
thermonuclear
Persistent flux
gravitational energy
Ignition and thermonuclear runaway
Burst trigger rate is “triple alpha reaction”
Ignition:
10
-1
2 -1
dcool
>
dT
nuc
cool ~ T4
12C
Nuclear energy generation rate
Cooling rate
Triple alpha reaction rate
-9
reaction rate (cm s mole )
dnuc
dT
3 4He
-10
10
Ignition < 0.4 GK:
unstable runaway
(increase in T increases
nuc that increases T …)
-11
10
-12
10
-13
10
-14
10
degenerate e-gas helps !
-15
10
0
1
temperature (GK)
10
BUT: energy release dominated by subsequent reactions !
Arguments for thermonuclear origin of type I bursts:
• ratio burst energy/persistent X-ray flux ~ 1/30 – 1/40
(ratio of thermonuclear energy to gravitational energy)
• type I behavior: the longer the preceeding fuel accumulation
the more intense the burst
• spectral softening during burst decline (cooling of hot layer)
Arguments for neutron star as burning site
• consistent with optical observations (only one star, binary)
• Stefan-Boltzmann L = A T4eff gives typical neutron star radii
• Maximum luminosities consistent with Eddington luminosity
for a neutron star (radiation pressure balances gravity)
Ledd = 4pcGM/k=2.5 x 1038(M/M . )(1+X)-1 erg/s
(this is non relativistic – relativistic corrections need to be applied)
kopacity, X=hydrogen mass fraction
What happens if “ignition temperature” > 0.4 GK
0.24
(medd generates luminosity Ledd)
0.23
temperature (GK)
at high local
accretion rates m > medd
0.22
0.21
0.2
0.19
0.18
0.17
0.16
-2
10
Triple alpha reaction rate
-9
-1
10
accretion rate (L_edd)
2 -1
-1
reaction rate (cm s mole )
10
-10
10
-11
10
Stable nuclear burning
-12
10
-13
10
-14
10
-15
10
0
1
temperature (GK)
10
0
10
X-ray pulsar
> 1012 Gauss !
High local accretion rates due to magnetic funneling of material on small surface area
Why do we care about X-ray binaries ?
• Basic model seems to work but many open questions
• Unique laboratories to probe neutron stars:
• Over larger mass range as they get heavier
• Over larger spin range as they get spun up
• Over larger temperature range as they get heated
Some current open questions
• Burst timescale variations
why do they vary from ~10 s to ~100 s
• Superbursts (rare, 1000x stronger and longer bursts)
what is their origin ?
• Contribution of X-ray bursts to galactic nucleosynthesis ?
• NCO’s (300-600Hz oscillations during bursts, rising by ~Hz)
what is their origin ?
• Crust composition – what is made by nuclear burning ?
• Magnetic field evolution ?
(why are there bursters and pulsars)
• Thermal structure ?
(what does observed thermal radiation tell us ?)
• Detectable gravitatioal wave emission ?
(can crust reactions deform the crust so that the spinning
neutron star emits gravitational waves ?)
(1735-444)
24 s
Normal type I bursts:
• duration 10-100 s
• ~1039 erg
(rapid burster)
3 min
Superbursts:
(4U 1735-44)
• duration …
• ~1043 erg
• rare (every 3.5 yr ?)
4.8 h
time (days) 18
(discovered 2001, so far 7 seen in 6 sources)
18.5
Spin up of neutron stars in X-ray binaries
Unique opportunity to study NS at various stages of spin-up (and mass)
4U1728-34
Rossi X-ray Timing Explorer
Picture: T. Strohmeyer, GSFC
Frequency (Hz)
331
330
329
328
F. Weber
327
10
15
20
Time (s)
• Quark matter/Normal matter phase transition ? (Glendenning, Weber 2000)
• Gravitational wave emission from deformed crust ? (Bildsten, 1998)
Chandra observations of transients
KS 1731-260 (Wijands 2001)
Bright X-ray burster from 1988 -early 2001
Accretion shut off early 2001
Detect thermal X-ray flux from cooling crust:
• Too cold ! (only 3 mio K)
• Constraints on duration of previous quiescent phase
• Constraints on neutron star cooling mechanisms
Nuclear physics overview
Accreting Neutron Star Surface
n’s
X-ray’s
H,He
fuel
~1 m
Thermonuclear H+He burning
(rp process)
gas
ashes
~10 m
ocean
~100 m
outer
crust
~1 km
10 km
Inner
crust
core
Deep burning
(EC on H, C-flash)
Crust processes
(EC, pycnonuclear fusion)
Nuclear reaction networks
Mass fraction of nuclear species X
Abundance
Y = X/A (A=mass number)
Number density
n =  NAY (=mass density, NA=Avogadro)
(note NA is really 1/mu – works only in CGS units)
Astrophysical model (hydrodynamics, ….)
Temperature T and Density
Network: System of differential equations:
dYi
  N ij  jY j   N ijk  N A   v  Y jYk  ...
dt
j
jk
1 body
2 body
Nuclear energy generation
Ni…: number of nuclei of species I produced (positive) or destroyed (negative) per reaction
Visualizing reaction network solutions
Proton
number
(a,)
(p,)
14
27Si
13
(a,p)
(,)
neutron number
dY j
 dYi
Lines = Flow = Fi , j  
  dt i  j  dt

 dt
j  i 
Temperature (GK)
Models: Typical temperatures and densities
2
1
0
300
400
500
600
300
400
500
600
Density (g/cm3)
7
10
6
10
5
10
time (s)
Al (13)
Mg (12)
Na (11)
Ne (10)
Burst Ignition:
15 16
13 14
F (9)
O (8)
N (7)
C (6)
B (5)
Be (4)
Li (3)
He (2)
3 4 5
H (1)
n (0)
2
0 1
11 12
9 10
8
7
6
Prior to ignition
~0.20 GK Ignition
: hot CNO cycle
: 3a
: Hot CNO cycle II
~ 0.68 GK breakout 1: 15O(a,)
~0.77 GK breakout 2: 18Ne(a,p)
(~50 ms after breakout 1)
Leads to rp process and
main energy production
Models: Typical reaction flows
Schatz et al. 2001 (M. Ouellette) Phys. Rev. Lett. 68 (2001) 3471
Xe (54)
I (53)
Te (52)
Sb (51)
Sn (50)
In (49)
Cd (48)
Ag (47)
Pd (46)
Rh (45)
Ru (44)
Schatz et al. 1998
59
5758
Tc (43)
Mo (42)
Nb (41)
Zr (40)
Y (39)
Sr (38)
5455
Rb (37)
Kr (36)
Br (35)
Se (34)
Wallace and Woosley 1981
Hanawa et al. 1981
Koike et al. 1998
Most calculations
(for example Taam 1996)
56
53
5152
4950
As (33)
Ge (32)
Ga (31)
Zn (30)
45464748
424344
41
Cu (29)
37383940
Ni (28)
Co (27)
33343536
Fe (26)
Mn (25)
3132
Cr (24)
V (23)
2930
Ti (22)
Sc (21)
25262728
Ca (20)
K (19)
2324
Ar (18)
Cl (17)
2122
S (16)
P (15)
17181920
Si (14)
Al (13)
1516
Mg (12)
Na (11)
14
Ne (10)
F (9)
11 1213
O (8)
N (7)
9 10
C (6)
B (5)
7 8
Be (4)
ap process:
14O+a
17F+p
17F+p
18Ne
18Ne+a
Li (3)
He (2)
5 6
H (1)
3 4
0 1 2
3a reaction
a+a+a
12C
…
rp process:
41Sc+p
42Ti
+p
+p
44Cr
44V+p …
43V
44Cr
44V+e++n
e
In detail: ap process
Ge (32)
Ga (31)
Zn (30)
Cu (29)
Ni (28)
333
Co (27)
Fe (26)
3132
Mn (25)
Cr (24)
2930
V (23)
Ti (22)
25262728
Sc (21)
Ca (20)
2324
K (19)
Ar (18)
2122
Cl (17)
S (16)
17181920
P (15)
Si (14)
12C
a+a+a
1516
Al (13)
Mg (12)
14O+a
17F+p
14
Na (11)
17F+p
18Ne
Ne (10)
18Ne+a …
11 1213
F (9)
O (8)
9 10
N (7)
Alternating (a,p) and (p,) reactions:
C (6)
For each proton capture there is an
7 8
B (5)
Be (4)
(a,p) reaction releasing a proton
Li (3)
5 6
He (2)
Net effect: pure He burning
3 4
H (1)
0 1 2
3a reaction
ap process:
In detail: rp process
Nuclear lifetimes: (average time between a …)
• proton capture
: t = 1/(Yp  NA <v>)
•  decay
: t = T1/2/ln2
• photodisintegration : t = 1/(,p)
Z
43 (Tc)
(for =106 g/cm3, Yp=0.7)
42 (Mo)
10
10
8
10
41 (Nb)
10
40 (Zr)
10
6
Lifetime (s)
4
39 (Y)
2
10
0
10
-2
10
-4
38 (Sr)
10
-6
10
N=41
-8
10
-10
10
38
39
40
41
neutron number
Proton number
42
43
The endpoint of the rp process
Possibilities:
• Cycling (reactions that go back to lighter nuclei)
• Coulomb barrier
• Runs out of fuel
• Fast cooling
Proton capture lifetime of nuclei near the drip line
4
Event
timescale
10
2
10
lifetime (s)
0
10
-2
10
-4
10
-6
10
-8
10
-10
10
0
10
20
30
40
50
charge number Z
60
70
80
Endpoint: Limiting factor I – SnSbTe Cycle
The Sn-Sb-Te cycle
Known ground state
a emitter
(,a)
105Te
106Te
107Te
108Te
104Sb
105Sb
106
107Sb
Sb
Sb (51)
Sn (50)
In (49)
Cd (48)
Ag (47)
Pd (46)
Rh (45)
Ru (44)
(p,)
103Sn
102In
104Sn
103In
105Sn
104In
106Sn
59
5758
Tc (43)
Mo (42)
Nb (41)
Zr (40)
Y (39)
Sr (38)

56
5455
Rb (37)
Kr (36)
Br (35)
Se (34)
105In
As (33)
Ge (32)
Ga (31)
Zn (30)
Cu (29)
37383940
Ni (28)
Co (27)
33343536
Fe (26)
Mn (25)
3132
Cr (24)
V (23)
2930
Ti (22)
Sc (21)
25262728
Ca (20)
K (19)
2324
Ar (18)
Cl (17)
2122
S (16)
P (15)
17181920
Si (14)
Al (13)
1516
Mg (12)
Na (11)
14
Ne (10)
F (9)
11 1213
O (8)
N (7)
9 10
C (6)
B (5)
7 8
Be (4)
Li (3)
He (2)
5 6
H (1)
3 4
0 1 2
Xe (54)
I (53)
Te (52)
53
5152
4950
45464748
424344
41
The endpoint for full hydrogen consumption:
Xe (54)
I (53)
Te (52)
Solar H/He ratio ~ 9
He burning: 10 He -> 41Sc
Sb (51)
Sn (50)
In (49)
Cd (48)
Ag (47)
Pd (46)
Rh (45)
Ru (44)
90 H per 41Sc available
59
5758
Tc (43)
Mo (42)
Nb (41)
Zr (40)
Y (39)
Sr (38)
if all captured in rp process
reaches A=90 + 41 = 131
(but stuck in cycle)
56
5455
Rb (37)
Kr (36)
Br (35)
Se (34)
As (33)
Ge (32)
Ga (31)
Zn (30)
Cu (29)
37383940
Ni (28)
Co (27)
33343536
Fe (26)
Mn (25)
3132
Cr (24)
V (23)
2930
Ti (22)
Sc (21)
25262728
Ca (20)
K (19)
2324
Ar (18)
Cl (17)
2122
S (16)
P (15)
17181920
Si (14)
Al (13)
1516
Mg (12)
Na (11)
14
Ne (10)
F (9)
11 1213
O (8)
N (7)
9 10
C (6)
B (5)
7 8
Be (4)
53
5152
4950
45464748
424344
41
Lower temperature:
Assume only 5He->21Na
45H per 21Na available
reach A=45+21=66 !
Li (3)
He (2)
5 6
H (1)
3 4
0 1 2
Endpoint varies with conditions:
• peak temperature
• amount of H available at ignition
Production of nuclei in the rp process – waiting points
Movie X-ray burst
Te (52)
Sb (51)
Sn (50)
In (49)
Cd (48)
Ag (47)
Pd (46)
Rh (45)
Ru (44)
Final Composition:
slow  decay
(waiting point)
6162636465
5960
104
5758
Tc (43)
Mo (42)
Nb (41)
Zr (40)
Y (39)
Sr (38)
56
5455
Rb (37)
Kr (36)
Br (35)
Se (34)
53
76
5152
80
4950
As (33)
45464748
Ge (32)
72 424344
Ga (31)
272829303132333435363738394041
-2
10
68
64
-3
abundance
10
-4
10
-5
10
-6
10
0
20
40
60
80
100
120
Mass number
• Abundances of
waiting points
luminosity (erg/g/s)
• Luminosity:
abundance
X-ray burst:
1e+ 17
cycle
5e+ 16
0e+ 00
-1
10
300
-2
10
-3
10
400
64Ge
56Ni
500
68Se
600
104Sn
72Kr
-4
10
-5
• H, He abundance
fuel abundance
10
0
10
300
10
-2
500
600
400
500
600
1H
-1
10
400
4He
-3
10
300
time (s)
Xe (54)
I (53)
Te (52)
Sb (51)
Sn (50)
In (49)
Cd (48)
Ag (47)
Pd (46)
Rh (45)
Ru (44)
Nuclear data needs:
Masses (proton separation energies)
-decay rates
Reaction rates (p-capture and a,p)
Some recent mass measurenents
-endpoint at ISOLDE and ANL
Ion trap (ISOLTRAP)
5758
Tc (43)
Mo (42)
Nb (41)
Zr (40)
Y (39)
Sr (38)
56
5455
Rb (37)
Kr (36)
Br (35)
Se (34)
53
5152
4950
As (33)
Ge (32)
Ga (31)
Zn (30)
45464748
424344
41
Cu (29)
37383940
Ni (28)
Co (27)
33343536
Fe (26)
Mn (25)
3132
Cr (24)
V (23)
2930
Ti (22)
Sc (21)
25262728
Ca (20)
K (19)
2324
Ar (18)
Cl (17)
2122
S (16)
P (15)
17181920
Si (14)
Al (13)
1516
Mg (12)
Na (11)
14
Ne (10)
F (9)
11 1213
O (8)
N (7)
9 10
C (6)
B (5)
7 8
Be (4)
Separation energies
Experimentally known
up to here
59
Many lifetime measurements at
radioactive beam facilities
(for example at LBL,GANIL, GSI, ISOLDE,
MSU, ORNL)
Know all -decay rates (earth)
Location of drip line known (odd Z)
Indirect information about rates
from radioactive and stable beam experiments
(Transfer reactions, Coulomb breakup, …)
Li (3)
He (2)
5 6
H (1)
3 4
0 1 2
Direct reaction rate measurements
with radioactive beams have begun
(for example at ANL,LLN,ORNL,ISAC)