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Ba Eu Ag Ba: s-process Ag, Eu: r-process Nucleosynthesis Process

Ba: s-process Ag, Eu: r-process - web.pa.msu.edu · Gallino Annu. Rev. Astro. Astrophys. 2008.46:241-288. Downloaded from arjournals.annualreviews.org by Michigan State University

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Ba

Eu

Ag

Ba: s-process Ag, Eu: r-process

Nucleosynthesis Process

Ba

Eu

Ag

Ba: s-process Ag, Eu: r-process

Nucleosynthesis Process

Ba

Eu

Ag

Ba: s-process Ag, Eu: r-process

Nucleosynthesis Process

Metal-poor stars

[Ba/Eu] < 0R-process rich

[Fe/H] < -2.5Metal poor (old stars)

ANRV352-AA46-08 ARI 15 July 2008 11:46

Atomic number

a

b

c

lo

g

Rel

ativ

e lo

g

lo

g

–1

0

1

–12

–10

–8

–6

– 4

2

0

30 40 50 60 70 80 90

–1

0

1

Average abundance offsets with respect to Arlandini et al. (1999) ‘‘stellar model’’

CS 22892-052: Sneden et al. (2003)

HD 115444: Westin et al. (2000)

BD+17°324817: Cowan et al. (2002)

CS 31082-001: Hill et al. (2002)

HD 221170: Ivans et al. (2006)

HE 1523-0901: Frebel et al. (2007)

Individual stellar abundance offsets with respect to Simmerer et al. (2004)

Figure 11(a) Comparisons of n-capture abundances in six r-process-rich Galactic halo stars with the Solar-system r-only abundance distribution.The abundance data of all stars except CS 22892-052 have been vertically displaced downward for display purposes. The solid lightblue lines are the scaled r-only Solar-system elemental abundance curves (Simmerer et al. 2004, Cowan et al. 2006), normalized to theEu abundance of each star. (b) Difference plot showing the individual elemental abundance offsets; abundance differences arenormalized to zero at Eu (see Table 1 and Table 2) for each of the six stars with respect to the Solar-system r-process-only abundances.Zero offset is indicated by the dashed horizontal line. Symbols for the stars are the same as in panel a. (c) Average stellar abundanceoffsets. For individual stars all elemental abundances were first scaled to their Eu values, then averaged for all six stars, and finallycompared to the Solar-system r-only distribution.

262 Sneden · Cowan · Gallino

Ann

u. R

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46:2

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onl

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ANRV352-AA46-08 ARI 15 July 2008 11:46

Atomic number

a

b

c

lo

g

Rel

ativ

e lo

g

lo

g

–1

0

1

–12

–10

–8

–6

– 4

2

0

30 40 50 60 70 80 90

–1

0

1

Average abundance offsets with respect to Arlandini et al. (1999) ‘‘stellar model’’

CS 22892-052: Sneden et al. (2003)

HD 115444: Westin et al. (2000)

BD+17°324817: Cowan et al. (2002)

CS 31082-001: Hill et al. (2002)

HD 221170: Ivans et al. (2006)

HE 1523-0901: Frebel et al. (2007)

Individual stellar abundance offsets with respect to Simmerer et al. (2004)

Figure 11(a) Comparisons of n-capture abundances in six r-process-rich Galactic halo stars with the Solar-system r-only abundance distribution.The abundance data of all stars except CS 22892-052 have been vertically displaced downward for display purposes. The solid lightblue lines are the scaled r-only Solar-system elemental abundance curves (Simmerer et al. 2004, Cowan et al. 2006), normalized to theEu abundance of each star. (b) Difference plot showing the individual elemental abundance offsets; abundance differences arenormalized to zero at Eu (see Table 1 and Table 2) for each of the six stars with respect to the Solar-system r-process-only abundances.Zero offset is indicated by the dashed horizontal line. Symbols for the stars are the same as in panel a. (c) Average stellar abundanceoffsets. For individual stars all elemental abundances were first scaled to their Eu values, then averaged for all six stars, and finallycompared to the Solar-system r-only distribution.

262 Sneden · Cowan · Gallino

Ann

u. R

ev. A

stro

. Ast

roph

ys. 2

008.

46:2

41-2

88. D

ownl

oade

d fr

om a

rjour

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.ann

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s.org

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ichi

gan

Stat

e U

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Lib

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on

06/2

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per

sona

l use

onl

y.

ANRV352-AA46-08 ARI 15 July 2008 11:46

Atomic number

a

b

c

lo

g

Rel

ativ

e lo

g

lo

g

–1

0

1

–12

–10

–8

–6

– 4

2

0

30 40 50 60 70 80 90

–1

0

1

Average abundance offsets with respect to Arlandini et al. (1999) ‘‘stellar model’’

CS 22892-052: Sneden et al. (2003)

HD 115444: Westin et al. (2000)

BD+17°324817: Cowan et al. (2002)

CS 31082-001: Hill et al. (2002)

HD 221170: Ivans et al. (2006)

HE 1523-0901: Frebel et al. (2007)

Individual stellar abundance offsets with respect to Simmerer et al. (2004)

Figure 11(a) Comparisons of n-capture abundances in six r-process-rich Galactic halo stars with the Solar-system r-only abundance distribution.The abundance data of all stars except CS 22892-052 have been vertically displaced downward for display purposes. The solid lightblue lines are the scaled r-only Solar-system elemental abundance curves (Simmerer et al. 2004, Cowan et al. 2006), normalized to theEu abundance of each star. (b) Difference plot showing the individual elemental abundance offsets; abundance differences arenormalized to zero at Eu (see Table 1 and Table 2) for each of the six stars with respect to the Solar-system r-process-only abundances.Zero offset is indicated by the dashed horizontal line. Symbols for the stars are the same as in panel a. (c) Average stellar abundanceoffsets. For individual stars all elemental abundances were first scaled to their Eu values, then averaged for all six stars, and finallycompared to the Solar-system r-only distribution.

262 Sneden · Cowan · Gallino

Ann

u. R

ev. A

stro

. Ast

roph

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008.

46:2

41-2

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d fr

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Stat

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Atomic number

Δ lo

g ε

Rel

ativ

e lo

g ε

-1.5

-1

-0.5

0

0.5

[Nd

/Eu

]

-1.5

-1

-0.5

0

0.5

[Ce

/Eu

]

-1.5

-1

-0.5

0

0.5

[Zr/

Eu

]

-1.5

-1

-0.5

0

0.5

[Y/E

u]

-1.5

-1

-0.5

0

0.5

1

[Sr/

Eu

]

-1.5

-1

-0.5

0

0.5

1

[Ba

/Eu

]

-1.5

-1

-0.5

0

0.5

[La

/Eu

]

-1 -0.5 0 0.5 1 1.5 2[Eu/Fe]

-2

-1.5

-1

-0.5

0

0.5

[Ag

/Eu

]

-1 -0.5 0 0.5 1 1.5 2[Eu/Fe]

-2

-1.5

-1

-0.5

0

0.5

[Sm

/Eu

]

HD122563

CS22892-052

CS31082-001

BD+17 3248

HD221170

HD115444

-1.5

-1

-0.5

0

0.5

[Pd

/Eu

]

-1.5

-1

-0.5

0

0.5

[Nd

/Eu

]

-1.5

-1

-0.5

0

0.5

[Ce

/Eu

]

-1.5

-1

-0.5

0

0.5

[Zr/

Eu]

-1.5

-1

-0.5

0

0.5

[Y/E

u]

-1.5

-1

-0.5

0

0.5

1

[Sr/

Eu

]

-1.5

-1

-0.5

0

0.5

1

[Ba

/Eu

]

-1.5

-1

-0.5

0

0.5

[La

/Eu

]

-1 -0.5 0 0.5 1 1.5 2[Eu/Fe]

-2

-1.5

-1

-0.5

0

0.5

[Ag/E

u]

-1 -0.5 0 0.5 1 1.5 2[Eu/Fe]

-2

-1.5

-1

-0.5

0

0.5

[Sm

/Eu

]

HD122563

CS22892-052

CS31082-001

BD+17 3248

HD221170

HD115444

-1.5

-1

-0.5

0

0.5

[Pd

/Eu

][S

r/Eu]

[Eu/Fe]

Sneden et al., Annu. Rev. Astro. 2008, 46, 241

Montes et al. ApJ 2007, 671, 1685

Solar r-process ratio

Z=38

Z=39

Z=40

Z=46

Z=47

Z=56

Z=57

Z=58

Z=60

Z=62

[Ba/Eu] < 0 R-process rich

[Fe/H] < -1 Metal poor (old stars)

[A/B] = log10(YA/YB)-log10(YA/YB)solar

[Fe/H] = -2.8[Ba/Eu] = -0.5

Light Element Primary Process LEPP abundance pattern

Y.-Z. Qian, G.J. Wasserburg / Physics Reports 442 (2007) 237– 268 249

40 50 60 70 80

Atomic Number (Z)

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

log !

(Z)

EuHD 122563 (Honda et al. 2006)

translated pattern of CS 22892-052 (Sneden et al. 2003)

Ag

Y

PdMo

Ru

Nb

Sr Zr

40 50 60 70 80

Atomic Number (Z)

-3

-2

-1

0

log !

(Z)

Eu

HD 122563 ([Fe/H] = -2.77, Honda et al. 2006)

translated solar r-pattern (Arlandini et al. 1999)

Ag

YPd

Mo

Ru

Nb Ce

Pr

Fig. 8. (a) Data on HD 122563 [squares (Honda et al., 2006)] compared with the solar “r”-pattern translated to pass through the Eu data (red curves).The squares are connected with blue line segments as a guide. Squares with downward arrows indicate upper limits. The abundance pattern of heavyr-elements [Ba (Z = 56) and above] in HD 122563 shown in (a) is similar to the corresponding part of the solar “r”-pattern but with substantialdifferences, especially for Ce and Pr. Note that (Ba/Eu)HD122563 ! (Ba/Eu)",r . There are also gross differences between the data and the translatedsolar “r”-pattern for the CPR elements. Specifically, HD 122563 has much larger proportions of CPR elements relative to heavy r-nuclei as comparedto the solar “r”-pattern. (b) Comparison of the data on HD 122563 [squares (Honda et al., 2006)] with those on CS 22892-052 [red curves (Snedenet al. (2003b))] normalized to the same log !(Y) as for HD 122563. The large difference (by a factor of # 20) in the production of heavy r-nucleirelative to CPR elements shown in (b) suggests that only some sources for CPR elements can also produce heavy r-nuclei.

identical for the three stars with very different enrichments of heavy r-elements shown in Fig. 6. This suggests that theheavy r-nuclei cannot be produced by massive stars of > 11 M", which result in Fe core-collapse SNe and are sourcesfor the elements from O to Ge [see the review by Woosley et al. (2002) and Section 4.4].

4.2. Regularity and variability of the yield pattern of heavy r-nuclei

It appears that the heavy r-elements Ba and above exhibit an abundance pattern close to the corresponding part ofthe solar r-pattern. This was recognized in all of the observational studies cited above. Two stars discussed above,CS 22892-052 and CS 31082-001, have [Fe/H] # $ 3 but extremely high enrichments of heavy r-elements [(Eu/H)

# (1/30.1/20)(Eu/H)"]. These stars must represent contributions from single r-process sources. However, there isno observational basis for believing that there is a single universal yield pattern even for the heavy r-nuclei. In fact,observations show that CS 22892-052 and CS 31082-001 have log(Th/Eu)=$0.62 (Sneden et al. (2003b)) and $0.22(Hill et al., 2002), respectively. This difference of 0.4 dex is much larger than the observational error of # 0.05 dex(Hill et al., 2002). Further, it cannot be attributed to the possible difference in age between the two stars as 232Th(the only long-lived isotope of Th) has an extremely long lifetime of !232 = 20.3 Gyr—even if the two stars were born13.5 Gyr (age of the universe) apart, this would only give a difference of 0.3 dex in log(Th/Eu). Therefore, there isgood reason to believe that the yields of Th and U relative to those of heavy r-elements (e.g., Eu) below A # 195 shouldbe variable. This variation renders calculations of stellar ages from (Th/Eu) rather uncertain. Even a 30% shift in theyield ratio of Th to Eu would give a shift of 6.1 Gyr in age due to the long lifetime of 232Th.

Further evidence for variations in the yield pattern of heavy r-nuclei has been found in HD 122563 with [Fe/H] =$2.77 (Honda et al., 2006). The data on this star (squares) are compared with the solar “r”-pattern (red curves) translatedto pass through the Eu data in Fig. 8a. It can be seen that there is approximate accord between the data and the solarr-pattern for the heavy r-elements (Z!56), but there are also large discrepancies, especially for Ce and Pr (see alsothe comparison between the squares and the dashed curve in Fig. 6b). Clearly, it is important for future measurementsto determine whether such discrepancies extend to other heavy r-elements in HD 122563, particularly Os, Ir, and Ptin the peak at A # 195 of the solar r-pattern. Discovery of other stars of this kind would help establish the range ofvariations in the yield pattern of heavy r-nuclei.

Metal-poor not r-process enriched stars

Qian&Wasserburg Phys. Rep. 2007, 442, 237

HD122563 – r Solar – s – p – r

Fe Co Ni

Rb

Ga Ge

Zn Cu

Se Br

As

Zr Y

Sr

Kr (n,!)

("-)

("+)

neutron number

prot

on n

umbe

r

+ light element primary process

prot

ons

neutrons

Mass knownHalf-life knownnothing known

Big Bang

Cosmic Rays

stellar burning

rp process

p process

s process

r process

Most of the heavy elements (Z>30) are formed in neutron capture processes, either the slow (s) or rapid (r) process

νp process

Light element primary processLEPP

Nucleosynthesis processes

Frohlich et al. 2006,Pruet et al. 2006,

Wanajo et al. 2006

Travaglio et al. 2004Montes et al. 2007

Solar = s-process + r-process

Nucleosynthesis in ν-driven winds

Electron fraction Ye

Lνe/Lνe=1.1

νe+n↔p+e

νe+p↔n+e+Almudena Arcones (Uni Basel) ACP seminar, IPMU (June 22, 2010)

Neutrino-driven winds

Necessary conditions for the production of heavy elements (A>130) by the r-process (Yn/Yseed !):

•fast expansion inhibits the alpha-process and thus the formation of seed nuclei

•Ye = np/(nn+np) < 0.5 (neutron rich)

•high entropy is equivalent to high photon-to-baryon ratio. Photons dissociate seed nuclei into nucleons.

0.5

R [km]

e!

e!

1.00.5

Si

M(r) [M ]

e!

e!

e!

M(r) [M ]

e!

e!

e!

e!

e!

Fe, Ni

M(r) [M ]

R ~ 3000

e!

e!

e!

!e

ChM(r) [M ]~ M

Fe, Ni

Si

0.5 1.0

R [km]

Si

R [km]

M(r) [M ]

Fe, Ni

0.5 1.0

Si

R [km]

R [km]

R [km]

Si

1.0M(r) [M ]

Si!burning shell Si!burning shell

Si!burning shellSi!burning shell

!e,µ," ,!e,µ,"

R ~ 100g

Fe

,µ,"e,!,µ,"e!

#,n

,µ,"e,!,µ,"e!

RFe

RFe

( $>%

$

&)

RFe

$

c o)2%

$<

formationshock

radius of

gR ~ 100

#,n#,n,

seed12

9Be,C,

e!RFe

position ofshock

formation

RFe

!

Neutrino Trapping

Shock Stagnation and Heating,

,µ,"e,!,µ,"e!

~ 10

free n, p

!!e

e

1.3 1.5

R ~ 50!

p

n

sR ~ 200

FeR

10

10

10

10

2

3

4

5

R ~ 10ns

R31.4

!

He

Ni

#

Si

PNS

r!process?

n, p

O

pfree n,

Fe

Ni

R!

hcM

~ 100

Bounce and Shock Formation

nuclear matter

~ 10

nuclei

(t ~ 0.11s,

1.3 1.5

R ~ 50!

Explosion (t ~ 0.2s)sR ~ 200

PNS gain layercooling layer

R ~ 10ns

R1.4

!

Neutrino Cooling and Neutrino!

PNS

Driven Wind (t ~ 10s)

n, p

nuclear matter nuclei

Shock Propagation and Burst

R ~ 100 kms

R!

(t ~ 0.12s)

heavy nucleihcM

$

c(t ~ 0.1s, ~10"# g/cm$)(t ~ 0)Initial Phase of Collapse

Figure 2. Schematic representation of the processes that occur in a collapsing stellar iron core on the way to thesupernova explosion. The diagrams (from top left to bottom right) visualize the physical conditions at the onset ofcore collapse, neutrino trapping, shock formation, propagation of the prompt shock, shock stagnation and revivalby neutrino heating, and r-process nucleosynthesis in the neutrino-driven wind of the newly formed neutron star,respectively, as suggested by current computer simulations. In the upper parts of the figures the dynamical stateis shown, with arrows indicating the flow of the stellar fluid. The lower parts of the figures contain informationabout the nuclear composition of the stellar plasma and the role of neutrinos during the different phases.

41

Lνe/Lνe=1

Entropy

Expansion timescale

S ∼ L-1/6 ϵ-1/3 Rns-2/3 Mns

τ ∼ L-1 ϵ-2 Rns Mns

Woosley et al. 1994Arcones et al. 2007

Hüdepohl et al. 2009

Fischer et al. 2009

Qian&Woosley 1996

Rad

ius

[cm

]

time [s]

neutron star

shock

ν-driven wind simulation

reverse shock

Entr

opy

[kB/

nuc]

Arcones et al. 2007

Rad

ius

[cm

]

time [s]

neutron star

shock

ν-driven wind simulation

reverse shock

– 8 –

duces the results of Boltzmann transport simulations qualitatively. The neutrino spectra

are assumed to follow Fermi-Dirac distributions with spectral temperatures di!erent fromthe local matter temperature in general. The central part (! ! 1013 g/cm3) of the proto-neutron star is replaced by a Lagrangian inner boundary placed below the neutrinosphere.

This reduces the computational time and is justified in part due to the uncertainties in thehigh-density EoS. Models M10-l1-r1 for a 10M! progenitor star, M15-l1-r1 and M15-l1-r6

both for a 15M!, and M25-l5-r4 for a 25M! case (Arcones et al. 2007). Hereafter, thesemodels are referred as 10M, 15M, 15M(s), and 25M, respectively. Note that these models

were selected to cover a wide range of wind entropies and timescales.

Fig. 2.— Evolution of radius, entropy, temperature, and density of a mass element ejected

5s after the explosion for the models 10M, 15M, 15M(s), and 25M.

The evolution of radius, entropy, temperature, and density is shown in Fig. 2 for amass elements ejected at 5 s after the explosion. The proto-neutron start in 10M, 15M,

and 25M follows a very similar contraction and neutrino cooling evolution. As discussedin Sect. 2.1, these models show almost identical evolution of density and temperature in

the wind, although their progenitor stars are rather di!erent. Their wind profiles di!er

– 8 –

duces the results of Boltzmann transport simulations qualitatively. The neutrino spectra

are assumed to follow Fermi-Dirac distributions with spectral temperatures di!erent fromthe local matter temperature in general. The central part (! ! 1013 g/cm3) of the proto-neutron star is replaced by a Lagrangian inner boundary placed below the neutrinosphere.

This reduces the computational time and is justified in part due to the uncertainties in thehigh-density EoS. Models M10-l1-r1 for a 10M! progenitor star, M15-l1-r1 and M15-l1-r6

both for a 15M!, and M25-l5-r4 for a 25M! case (Arcones et al. 2007). Hereafter, thesemodels are referred as 10M, 15M, 15M(s), and 25M, respectively. Note that these models

were selected to cover a wide range of wind entropies and timescales.

Fig. 2.— Evolution of radius, entropy, temperature, and density of a mass element ejected

5s after the explosion for the models 10M, 15M, 15M(s), and 25M.

The evolution of radius, entropy, temperature, and density is shown in Fig. 2 for amass elements ejected at 5 s after the explosion. The proto-neutron start in 10M, 15M,

and 25M follows a very similar contraction and neutrino cooling evolution. As discussedin Sect. 2.1, these models show almost identical evolution of density and temperature in

the wind, although their progenitor stars are rather di!erent. Their wind profiles di!er

15M (slow contraction)

15M (slow contraction)

10M

10M

15M

15M

25M

25M

Nucleosynthesis in ν-driven winds

Integrated abundances based on the neutrino-driven wind simulations

no heavy r-process nucleisome LEPP nuclei produced

(slow contraction)

Arcones&Montes, arXiv:1007.1275

Light element primary process pattern

No major difference as a function of mass progenitor for same neutron

star contraction evolution

Sr-Y-Zr-Nb produced

Roberts et al. NIC_XI_165

Nucleosynthesis and electron fraction

Initial composition determined by

nuclear statistical equilibrium

At high temperatures only n, p,

alphas exist

seed

neutronsprotons

proton-richneutron-rich

T9=8

alphas

Nucleosynthesis and electron fraction

Initial composition determined by

nuclear statistical equilibrium

At high temperatures only n, p,

alphas exist

Seed nuclei created by the time

T9≃5

alphas

neutrons

protonsseed

proton-richneutron-rich

T9=5

Nucleosynthesis and electron fraction

Initial composition determined by

nuclear statistical equilibrium

At high temperatures only n, p,

alphas exist

Seed nuclei created by the time

T9≃5

Charged-particle freeze-out occurs

between T9≃2-3

Formation of heavier nuclei depends

on neutron-to-seed ratio and on

proton-to-seed ratio after freeze-out

neutrons

protons

seed

produced by the νp-process

proton-richneutron-rich

T9=2

alphas

Nucleosynthesis and electron fraction

– 14 –

Fig. 6.— Seed nuclei (i.e., nuclei heavier than 4He), neutron, proton and alpha abundancesas a function of Ye based on the mass element ejected at 5s after the explosion in model 15M.

Dotted, solid and dashed lines correspond to temperatures of 8, 5 and 2 GK, respectively.

Fig. 7.— Dependence of the abundances of representative elements (Sr, Y, Zr, Cd, Ba andEu) on the electron fraction. These abundances result from a mass element ejected at 5s

after the explosion in model 15M.

Abundance pattern is “robust” to local variations of the electron fraction

Production of heavy elements

CdY

Ba

SrZr

proton-richneutron-rich

r-process elements can only be created with extreme Ye values

Nucleosynthesis in proton-rich ν-driven winds

The LEPP component of Travaglio et al. 2004 requires “s-only” isotopes

Superposition of trajectories 0.5 < Ye < 0.65 following Hüdepohl et al. (2009)

Limit assuming that every supernova ejects the same amount of matter with the same

isotopic composition

Abundance pattern is “robust” to local variations of the electron fractionLEPP pattern observed in old metal-poor star can be explained but ....

p-nuclei createdArcones&Montes, arXiv:1007.1275

Nucleosynthesis in neutron-rich ν-driven winds

Superposition of trajectories with 0.5 > Ye > 0.45

Overproduction of A=90 nuclei (Hoffman et al. 1996)

LEPP pattern observed in old metal-poor stars can be explained but ....

Elemental pattern is rather sensitive to electron fraction evolution

Conclusions

First comparison of the light element primary process pattern observed in metal-poor stars

and nucleosynthesis in realistic neutrino driven-wind simulations

Electron fraction has an important effect on final abundances and depends on the uncertain

composition and interaction in the outer layers of the proton-neutron star

Abundance pattern can be reproduced by neutron and proton -rich winds

Proton-rich winds show a rather robust pattern but produce p-nuclei and not in enough

quantities

Neutron-rich winds overproduce A=90 nuclei

A combination of both types of winds is likely and may be able to explain the LEPP solar

system contribution

Nucleosynthesis and neutrino luminosity

– 20 –

Fig. 11.— Same as Fig. 8 but varying the neutrino luminosities. The luminosity of the

simulation is given by the solid black line labeled as “L”. For the other cases this luminosityhas been dived by di!erent factors as indicated by the labels.

3.2.2. Neutron-rich winds

In neutron-rich winds (0.45 ! Ye < 0.5) the amount of ejected LEPP elements is higherthan for the proton-rich case (Fig. 7). However, we do not find a robust LEPP pattern for

neutron-rich winds. In Fig. 12, the abundances and production factors are shown for twopossible evolutions of the electron fraction, which decreases almost linearly with time. Inthe upper panels, the ejecta become only slightly neutron rich with the electron fraction

decreasing from Ye = 0.5 at 1s to Ye = 0.486 at 10s. In this case only the light part of theLEPP (Sr, Y, Zr) can be synthesized. The bottom panels correspond to an initial electron

fraction that evolves from Ye = 0.5 down to Ye = 0.45 at 10s. These more neutron-richconditions lead to elements up to around Silver (Z=47).

The abundances of Sr, Y, and Zr depend on the electron fraction in a non-linear way asshown in Fig. 13. Therefore, slightly di!erent evolutions of the electron fraction are found to

lead to significant changes in this pattern. Moreover, small variations of the entropy and theexpansion timescales have a substantial impact on the neutron-to-seed ratio and thereforeon the abundances, making it even more di"cult to get a robust pattern. This sensitivity in

the final abundances is due to the abrupt drop of the neutron abundances towards Ye = 0.5as shown in Fig. 6.