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)

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 !

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

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)

Outline

X-ray binaries – nuclear physics at the extremes

1. Observations2. Model3. Open Questions4. Nuclear Physics – the rp process

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

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

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

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)

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)

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

Mass transfer by Roche Lobe Overflow

Star expands on main sequence.when it fills its Roche Lobe mass transfer happensthrough the L1 Lagrangian point

John Blondin, NC State, http://wonka.physics.ncsu.edu/~blondin/AAS/

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)

Observation of thermonuclear energy:

Unstable, explosive burning in bursts (release over short time)

Burst energythermonuclear

Persistent fluxgravitational energy

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

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

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

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)

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

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

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

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)

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

Visualizing reaction network solutions

27Si

neutron number13

Protonnumber

14

(p,) (,p)

(,)

(,)

Lines = Flow = dtdt

dY

dt

dYF

ij

j

ji

iji

,

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)

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

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

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

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)

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

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

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:

Production of nuclei in the rp process – waiting points

Movie X-ray burst

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)

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

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)