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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)
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3 4 5 6 7 8
9 10
11 12 13
14
C (6) N (7)
O (8) F (9)
N e (10)N a (11)
M g (12)
3 4 5 6 7 8
9 10
11 12 13
14
C (6) N (7)
O (8) F (9)
N e (10)N a (11)
M g (12)
“Cold” CN(O)-Cycle
Hot CN(O)-Cycle
),(14 pNv Energy production rate:
T9 < 0.08
T9 ~ 0.08-0.1
const)/(1 11
)(15)(14
OO
“beta limited CNO cycle”
Note: condition for hot CNO cycledepend also on density and Yp:
,pon 13N:
vNY Ap
Ne-Na cycle !
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3 4 5 6 7 8
9 10
11 12 13
14
C (6) N (7)
O (8) F (9)
N e (10)N a (11)
M g (12)Very Hot CN(O)-Cycle
still “beta limited”
T9 ~ 0.3
T1/2=1.7s
3 flow
3 4 5 6 7 8
9 10
11 12 13
14
C (6) N (7)
O (8) F (9)
N e (10)N a (11)
M g (12)Breakout
processing beyond CNO cycleafter breakout via:
3 flow
T9 >~ 0.3 15O(,)19Ne
18Ne(,p)21NaT9 >~ 0.6
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0.0 0.5 1.0 1.5100
101
102
103
104
105
Temperature (GK)
Den
sity
(g/
cm3 )
Current 15O(a,) Ratewith X10 variation
Multizone Nova model(Starrfield 2001)
Breakout
NoBreakout
New lower limit for density from B. Davids et al. (PRC67 (2003) 012801)
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Outline
X-ray binaries – nuclear physics at the extremes
1. Observations2. Model3. Open Questions4. Nuclear Physics – the rp process
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X-rays
Wilhelm Konrad Roentgen,First Nobel Price 1901 fordiscovery of X-rays 1895
First X-ray image from 1890(Goodspeed & Jennings, Philadelphia)
Ms Roentgen’s hand, 1895
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0.5-5 keV (T=E/k=6-60 x 106 K)
Cosmic X-rays: discovered end of 1960’s:
Again Nobel Price in Physics 2002for Riccardo Giacconi
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Discovery
First X-ray pulsar: Cen X-3 (Giacconi et al. 1971) with UHURU
First X-ray burst: 3U 1820-30 (Grindlay et al. 1976) with ANS
Today:~50
Today:~40
Total ~230 X-ray binaries knownTotal ~230 X-ray binaries known
T~ 5s
10 s
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Typical X-ray bursts:
• 1036-1038 erg/s• duration 10 s – 100s• recurrence: hours-days• regular or irregular
Frequent and very brightphenomenon !
(stars 1033-1035 erg/s)
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X-ray binariesX-ray binaries
X-ray pulsarsRegular pulses withperiods of 1- 1000 s
X-ray pulsarsRegular pulses withperiods of 1- 1000 s
X-ray burstersFrequent Outbursts of 10-100s durationwith lower, persistent X-ray flux inbetween
X-ray burstersFrequent Outbursts of 10-100s durationwith lower, persistent X-ray flux inbetween
Type I burstsBurst energy proportionalto duration of preceedinginactivity period
By far most of the bursters
Type I burstsBurst energy proportionalto duration of preceedinginactivity period
By far most of the bursters
Type II burstsBurst energy proportionalto duration of followinginactivity period
“Rapid burster”and GRO J1744-28 ?
Type II burstsBurst energy proportionalto duration of followinginactivity period
“Rapid burster”and GRO J1744-28 ?
(Bursting pulsar:GRO J1744-28)
Others(e.g. no bursts found yet)
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Neutron Star
Donor Star(“normal” star)
Accretion Disk
The Model
Neutron stars:1.4 Mo, 10 km radius(average density: ~ 1014 g/cm3)
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
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Mass transfer by Roche Lobe Overflow
Star expands on main sequence.when it fills its Roche Lobe mass transfer happensthrough the L1 Lagrangian point
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John Blondin, NC State, http://wonka.physics.ncsu.edu/~blondin/AAS/
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Energy generation: thermonuclear energy
Ratio gravitation/thermonuclear ~ 30 - 40
4H 4He
5 4He + 84 H 104Pd
6.7 MeV/u
0.6 MeV/u
6.9 MeV/u
Energy generation: gravitational energy
E = G M mu
R= 200 MeV/u
3 4He 12C (“triple alpha”)
(rp process)
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Observation of thermonuclear energy:
Unstable, explosive burning in bursts (release over short time)
Burst energythermonuclear
Persistent fluxgravitational energy
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Ignition and thermonuclear runaway
0 1 10te m p e ra ture (G K)
10-15
10-14
10-13
10-12
10-11
10-10
10-9
rea
ctio
n ra
te (c
m2 s-1
mo
le-1
)
Burst trigger rate is “triple alpha reaction” 3 4He 12C
Ignition: dnuc
dTdcool
dT>
nuc
cool ~ T4
Ignition < 0.4 GK: unstable runaway (increase in T increases nuc that increases T …)
degenerate e-gas helps !
Triple alpha reaction rate
BUT: energy release dominated by subsequent reactions !
Nuclear energy generation rate
Cooling rate
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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 T4
eff gives typical neutron star radii• Maximum luminosities consistent with Eddington luminosity for a neutron star (radiation pressure balances gravity)
Ledd = 4cGM/=2.5 x 1038(M/M )(1+X)-1 erg/s
(this is non relativistic – relativistic corrections need to be applied)
.
opacity, X=hydrogen mass fraction
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What happens if “ignition temperature” > 0.4 GK
10-2
10-1
100
accretion rate (L_edd)
0.16
0.17
0.18
0.19
0.2
0.21
0.22
0.23
0.24
tem
per
atur
e (G
K)
0 1 10te m p e ra ture (G K)
10-15
10-14
10-13
10-12
10-11
10-10
10-9
rea
ctio
n ra
te (c
m2 s-1
mo
le-1
)
Triple alpha reaction rate
at high localaccretion rates m > medd
(medd generates luminosity Ledd)
Stable nuclear burning
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X-ray pulsar
> 1012 Gauss !
High local accretion rates due to magnetic funneling of material on small surface area
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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
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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 ?)
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(1735-444)
18 18.5time (days)
(rapid burster)
(4U 1735-44)
Normal type I bursts:• duration 10-100 s• ~1039 erg
Superbursts:(discovered 2001, so far 7 seen in 6 sources)
• duration …• ~1043 erg• rare (every 3.5 yr ?)
24 s
3 min
4.8 h
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Spin up of neutron stars in X-ray binaries
Unique opportunity to study NS at various stages of spin-up (and mass)
• Quark matter/Normal matter phase transition ? (Glendenning, Weber 2000)• Gravitational wave emission from deformed crust ? (Bildsten, 1998)
331
330
329
Fre
quen
cy (
Hz)
328
32710 15 20
Time (s)
4U1728-34Rossi X-ray Timing ExplorerPicture: T. Strohmeyer, GSFC
F. Weber
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KS 1731-260 (Wijands 2001)
Chandra observations of transients
Bright X-ray burster from 1988 -early 2001Accretion 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
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Nuclear physics overview
Accreting Neutron Star Surface
fuel
ashesocean
Innercrust
outercrust
H,He
gas
core
’sX-ray’s
~1 m
~10 m
~100 m
~1 km
10 km
Thermonuclear H+He burning(rp process)
Deep burning(EC on H, C-flash)
Crust processes(EC, pycnonuclear fusion)
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Nuclear reaction networks
Mass fraction of nuclear species XAbundance 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)
Temperature T and Density
Nuclear energy generation
Astrophysical model (hydrodynamics, ….)
... kjk
jAijkjj
j
ij
i YYvNNYNdt
dY
Network: System of differential equations:
1 body 2 body
Ni…: number of nuclei of species I produced (positive) or destroyed (negative) per reaction
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Visualizing reaction network solutions
27Si
neutron number13
Protonnumber
14
(p,) (,p)
(,)
(,)
Lines = Flow = dtdt
dY
dt
dYF
ij
j
ji
iji
,
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Models: Typical temperatures and densities
300 400 500 6000
1
2
300 400 500 60010
5
106
107
Tem
pera
ture
(G
K)
Den
sity
(g/
cm3 )
time (s)
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0 1
2
3 4 5
6
7
8
9 10
11 12
13 14
15 16
17 18 19 20
21 22
23 24
25 26 27 28
29 30
31 32
33 34 35 36
37 38 39 40
41 42 43 44
45 46
47 48 49 50
51 52 53 54
n (0)
H (1)
H e (2)
L i (3)
Be (4)
B (5 )
C (6)
N (7)
O (8)
F (9 )
N e (10)
N a (11)
M g (12)
A l (13)
S i (14)
P (15)
S (16)
C l (17)
A r (18)
K (19)
C a (20)
Sc (21)
Ti (22)
V (23)
C r (24)
M n (25)
Fe (26)
C o (27)
N i (28)
C u (29)
Zn (30)
G a (31)
G e (32)
As (33)
Se (34)
B r (35)
K r (36)
R b (37)
S r (38)
Y (39)
Zr (40)
N b (41)
M o (42)
Tc (43)
R u (44)
R h (45)
Pd (46)
Ag (47)
C d (48)
In (49)
Sn (50)
Burst Ignition:
Prior to ignition : hot CNO cycle~0.20 GK Ignition : 3
: Hot CNO cycle II
~ 0.68 GK breakout 1: 15O()
~0.77 GK breakout 2: 18Ne(,p)
(~50 ms after breakout 1)Leads to rp process and main energy production
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0 1 2
3 45 6
7 8
9 10
11 12 13
14
15 16
17 18 19 20
21 22
23 24
25 26 27 28
29 30
31 32
33 34 35 36
37 38 39 4041
42 43 44
45 46 47 48
49 5051 52
5354 55
56
57 58
59
H (1)H e (2)L i (3)
Be (4) B (5) C (6) N (7)
O (8) F (9)
N e (10)N a (11)
M g (12)A l (13)S i (14) P (15)
S (16)C l (17)
A r (18) K (19)
C a (20)Sc (21)
Ti (22) V (23)
C r (24)M n (25)
Fe (26)C o (27)
N i (28)C u (29)
Zn (30)G a (31)
G e (32)As (33)
Se (34)B r (35)K r (36)R b (37)
S r (38) Y (39)
Zr (40)N b (41)
M o (42)Tc (43)
R u (44)R h (45)Pd (46)Ag (47)
C d (48)In (49)
Sn (50)Sb (51)
Te (52) I (53)
Xe (54)
3 reaction++ 12C
p process: 14O+ 17F+p17F+p 18Ne18Ne+ …
rp process:41Sc+p 42Ti +p 43V +p 44Cr44Cr 44V+e++e
44V+p …
Most calculations(for example Taam 1996)
Wallace and Woosley 1981Hanawa et al. 1981Koike et al. 1998
Schatz et al. 2001 (M. Ouellette) Phys. Rev. Lett. 68 (2001) 3471
Models: Typical reaction flows
Schatz et al. 1998
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0 1 2
3 45 6
7 8
9 10
11 12 13
14
15 16
17 18 19 20
21 22
23 24
25 26 27 28
29 30
31 32
33 34 35 36
37 38 39 4041
42 43 44
45 46 47 48
49 5051 52
5354 55
56
57 58
59
H (1)H e (2)L i (3 )
Be (4) B (5) C (6) N (7)
O (8) F (9)
N e (10)N a (11)
M g (12)A l (13)S i (14) P (15)
S (16)C l (17)
A r (18) K (19)
C a (20)Sc (21)
Ti (22) V (23)
C r (24)M n (25)
Fe (26)C o (27)
N i (28)C u (29)
Zn (30)G a (31)
G e (32)As (33)
Se (34)B r (35)K r (36)R b (37)
S r (38) Y (39)
Zr (40)N b (41)
M o (42)Tc (43)
R u (44)R h (45)Pd (46)Ag (47)
C d (48)In (49)
Sn (50)Sb (51)
Te (52) I (53)
Xe (54)
3 reaction++ 12C p process:
14O+ 17F+p17F+p 18Ne18Ne+ …
In detail:p process
Alternating (,p) and (p,) reactions:For each proton capture there is an (,p) reaction releasing a proton
Net effect: pure He burning
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In detail: rp process
38 39 40 41 42 43neutron num ber
10-10
10-8
10-6
10-4
10-2
100
102
104
106
108
1010
Life
time
(s)
N=41
38 (Sr)
39 (Y)
40 (Zr)
41 (Nb)
42 (Mo)
43 (Tc)
Z
Proton number
Nuclear lifetimes: (average time between a …)• proton capture : = 1/(Yp NA <v>)• decay : = T1/2/ln2• photodisintegration : = 1/p
(for =106 g/cm3, Yp=0.7)
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Possibilities: • Cycling (reactions that go back to lighter nuclei)• Coulomb barrier• Runs out of fuel• Fast cooling
Possibilities: • Cycling (reactions that go back to lighter nuclei)• Coulomb barrier• Runs out of fuel• Fast cooling
The endpoint of the rp process
0 10 20 30 40 50 60 70 80charge num ber Z
10-10
10-8
10-6
10-4
10-2
100
102
104
lifet
ime
(s)
Proton capture lifetime of nuclei near the drip line
Eventtimescale
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0 1 2
3 45 6
7 8
9 10
11 12 13
14
15 16
17 18 19 20
21 22
23 24
25 26 27 28
29 30
31 32
33 34 35 36
37 38 39 4041
42 43 44
45 46 47 48
49 5051 52
5354 55
56
57 58
59
H (1)H e (2)L i (3)
Be (4) B (5) C (6) N (7)
O (8) F (9)
N e (10)N a (11)
M g (12)A l (13)S i (14) P (15)
S (16)C l (17)
A r (18) K (19)
C a (20)Sc (21)
Ti (22) V (23)
C r (24)M n (25)
Fe (26)C o (27)
N i (28)C u (29)
Zn (30)G a (31)
G e (32)As (33)
Se (34)B r (35)K r (36)R b (37)
S r (38) Y (39)
Zr (40)N b (41)
M o (42)Tc (43)
R u (44)R h (45)Pd (46)Ag (47)
C d (48)In (49)
Sn (50)Sb (51)
Te (52) I (53)
Xe (54)
The Sn-Sb-Te cycle
1 0 4S b 1 0 5S b 1 0 6 1 0 7S b
1 0 3S n 1 0 4S n 1 0 5S n 1 0 6S n
1 0 5Te 1 0 6Te 1 0 7Te 1 0 8Te
1 0 2In 1 0 3In 1 0 4In 1 0 5In
(,a )
S b
(p , )
Known ground state emitter
Endpoint: Limiting factor I – SnSbTe Cycle
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The endpoint for full hydrogen consumption:
0 1 23 4
5 6
7 8
9 10
11 12 13
14
15 16
17 18 19 20
21 22
23 24
25 26 27 28
29 30
31 32
33 34 35 36
37 38 39 4041
42 43 44
45 46 47 48
49 5051 52
5354 55
56
57 58
59
H (1)H e (2)L i (3)
Be (4) B (5) C (6) N (7)
O (8) F (9)
N e (10)N a (11)
M g (12)A l (13)S i (14) P (15)
S (16)C l (17)
A r (18) K (19)
C a (20)Sc (21)
Ti (22) V (23)
C r (24)M n (25)
Fe (26)C o (27)
N i (28)C u (29)
Zn (30)G a (31)
G e (32)As (33)
Se (34)B r (35)K r (36)R b (37)
S r (38) Y (39)
Zr (40)N b (41)
M o (42)Tc (43)
R u (44)R h (45)Pd (46)Ag (47)
C d (48)In (49)
Sn (50)Sb (51)
Te (52) I (53)
Xe (54)Solar H/He ratio ~ 9
90 H per 41Sc available
Endpoint varies with conditions:• peak temperature• amount of H available at ignition
He burning: 10 He -> 41Sc
if all captured in rp process reaches A=90 + 41 = 131 (but stuck in cycle)
Assume only 5He->21Na45H per 21Na availablereach A=45+21=66 !
Lower temperature:
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Production of nuclei in the rp process – waiting points
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Movie X-ray burst
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27282930 3132 333435 3637383940 4142 4344
45 464748
495051 52
535455
56
5758
5960
61 62 6364 656667 68697071 727374
75 76 7778
7980 8182
G a (31)G e (32)As (33)
Se (34)Br (35)Kr (36)Rb (37)
Sr (38) Y (39)
Zr (40)Nb (41)
M o (42)Tc (43)
Ru (44)Rh (45)Pd (46)Ag (47)
Cd (48)In (49)
Sn (50)Sb (51)
Te (52) I (53)
Xe (54)
0 20 40 60 80 100 12010
-6
10-5
10-4
10-3
10-2
68
72
76
abun
danc
e
64
104
80
Final Composition:
Mass number
slow decay (waiting point)
![Page 39: Hydrogen burning under extreme conditions Scenarios: Hot bottom burning in massive AGB stars (> 4 solar masses) (T 9 ~ 0.08) Nova explosions on accreting](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649d005503460f949d2278/html5/thumbnails/39.jpg)
300 400 500 60010
-3
10-2
10-1
100 300 400 500 600
10-5
10-4
10-3
10-2
10-1 300 400 500 600
0e + 00
5e + 16
1e + 17
lum
inos
ity
(erg
/g/s
)
cycle
fuel
abu
ndan
ce
1H
4He
abu
ndan
ce56Ni
72Kr
104Sn64Ge 68Se
time (s)
X-ray burst:
• Luminosity:
• Abundances of waiting points
• H, He abundance
![Page 40: Hydrogen burning under extreme conditions Scenarios: Hot bottom burning in massive AGB stars (> 4 solar masses) (T 9 ~ 0.08) Nova explosions on accreting](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649d005503460f949d2278/html5/thumbnails/40.jpg)
0 1 2
3 45 6
7 8
9 10
11 12 13
14
15 16
17 18 19 20
21 22
23 24
25 26 27 28
29 30
31 32
33 34 35 36
37 38 39 4041
42 43 44
45 46 47 48
49 5051 52
5354 55
56
57 58
59
H (1)H e (2)L i (3)
Be (4) B (5) C (6) N (7)
O (8) F (9)
N e (10)N a (11)
M g (12)A l (13)S i (14) P (15)
S (16)C l (17)
A r (18) K (19)
C a (20)Sc (21)
Ti (22) V (23)
C r (24)M n (25)
Fe (26)C o (27)
N i (28)C u (29)
Zn (30)G a (31)
G e (32)As (33)
Se (34)B r (35)K r (36)R b (37)
S r (38) Y (39)
Zr (40)N b (41)
M o (42)Tc (43)
R u (44)R h (45)Pd (46)Ag (47)
C d (48)In (49)
Sn (50)Sb (51)
Te (52) I (53)
Xe (54)
Nuclear data needs:
Masses (proton separation energies)-decay rates
Reaction rates (p-capture and ,p)
Direct reaction rate measurementswith radioactive beams have begun(for example at ANL,LLN,ORNL,ISAC)
Indirect information about ratesfrom radioactive and stable beam experiments(Transfer reactions, Coulomb breakup, …)
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)
Separation energiesExperimentally known up to here
Some recent mass measurenents-endpoint at ISOLDE and ANLIon trap (ISOLTRAP)