# The origin of the lead-rich stars in the Galactic halo: Investigation of model parameters for the s-process

Article (PDF Available)inMonthly Notices of the Royal Astronomical Society 368(1) · March 2006with18 Reads
DOI: 10.1111/j.1365-2966.2006.10109.x · Source: arXiv
Abstract
Several stars at the low-metallicity extreme of the Galactic halo show large spreads of lead and associated ‘heavy’ s-process elements ([Pb/hs]). Theoretically, an s-process pattern should be obtained from an AGB star with a fixed metallicity and initial mass. For the third dredge-up and the s-process model, several important properties depend primarily on the core mass of AGB stars. Zijlstra reported that the initial-to-final mass relation steepens at low metallicity, due to low mass-loss efficiency. This might affect the model parameters of the AGB stars, e.g. the overlap factor and the neutron irradiation time, in particular at low metallicity. The calculated results do indeed show that the overlap factor and the neutron irradiation time are significantly small at low metallicities, especially for 3.0 M⊙ AGB stars. The scatter of [Pb/hs] found in low metallicities can therefore be explained naturally when varying the initial mass of the low-mass AGB stars.
arXiv:astro-ph/0603039v1 2 Mar 2006
Mon. Not. R. Astron. Soc. 000, 1–5 (2005) Printed 5 February 2008 (MN L
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The origin of the lead-rich stars in Galactic halo: investigation of the
model parameters for the s-process
Wenyuan Cui
1,2
and Bo Zhang
1,2
1
National Astronomical observatories, Chinese Academy of Sciences, Beijing 100012, China
2
Department of Physics, Hebei Normal University, 113 Yuhua Road, Shijiazhuang 050016, China
Received ........; accepted ........
ABSTRACT
Several stars at the low-metallicity extreme of the Galactic halo show large spreads of [Pb/hs].
Theoretically, a s-process pattern should be obtained from an AGB star with ﬁxed metallicity
and initial mass. For the third dredge-up and the s-process model, several important properties
depend primarily on the core mass of AGB stars. Zijlstra (2004) reported that the initial-ﬁnal-
mass relation steepens at low metallicity, due to low mass-loss efﬁciency. This perhaps affects
the model parameters of the AGB stars, e.g. the overlapfactor and the neutron irradiation time,
in particular at low metallicity. The calculated results show indeed that the overlap factor
and the neutron irradiation time are signiﬁcantly small at low metallicities, especially for
3.0M
AGB stars. The scatter of [Pb/hs] found in low metallicities can therefore be explained
naturally when varying the initial mass of the low-mass AGB stars.
Key words: stars: AGB and post-AGB – stars: mass loss
1 INTRODUCTION
The elements heavier than the iron peak are made through
neutron capture via two principal processes: the r-process (for
rapid process) and the s-process (for slow neutron capture
process)(Burbidge et al. 1957). The observations have conﬁrmed
that, indeed, Asymptotic Giant Branch (AGB) stars show over-
abundances of elements heavier than iron at their surface
(Smith & Lambert 1990), which clearly indicate that the s-process
takes place during the AGB phase in the evolution of low- and
intermediate-mass stars (0.86M(M
)68). Low-mass AGB stars
are usually thought as the main nuclear production site of the s-
process elements (Gallino et al. 1998; Lugaro et al. 2003; Herwig
2004). By now, the generally favoured s-process model is as-
sociated with the partial mixing of protons (PMP) into the ra-
diative C-rich layers during thermal pulses (Straniero et al. 1995;
Gallino et al. 1998, 2003; Straniero et al. 2005). PMP activates
the chain of reactions
12
C(p,γ)
13
N(β)
13
C(α,n)
16
O which likely
occurs in a narrow mass region of the He intershell (i.e.
13
C-
pocket) during the interpulse phasesof an AGB star.The s-elements
thus produced in the deep interior by successive neutron captures
are subsequently brought to the surface by the third dredge-up.
Using the primary-like neutron source (
13
C(α,n)
16
O) and start-
ing with a very low initial metallicity, most iron seeds are con-
verted into
208
Pb. When the third dredge-up episodes mix the
neutron capture products into the envelope, the star will appear
s-enhanced and lead-rich. If the standard PMP scenario holds,
E-mail: wenyuancui@126.com.cn
E-mail: zhangbo@mail.hebtu.edu.cn
all s-process-enriched AGB stars with metallicities [Fe/H]
1
6 -1.3
are thus predicted to be lead(Pb) stars ([Pb/hs]> 1, where hs de-
notes the ’heavy’ s-process elements such as Ba, La, Ce), inde-
pendently of their initial mass and metallicity (Gallino et al. 1998;
Goriely & Mowlavi 2000; Goriely & Siess 2001).
The ﬁrst three such lead stars (HD187861, HD224959,
HD196944 ), have been later conﬁrmed by Van Eck et al. (2001).
At the same time, Aoki et al. (2001) found that the slightly more
metal-deﬁcient stars LP 625-44 and LP 706-7 are enriched in
s-elements, but cannot be considered as lead stars ([Pb/Ce]<
0.4), in disagreement with the standard PMP predictions. Re-
cently, more spectroscopic data of s-rich and lead-rich stars are re-
ported (Aoki et al. 2002; Cohen et al. 2003; Lucatello et al. 2003;
Van Eck et al. 2003; Johnson & Bolte 2002, 2004; Sivarani et al.
2004). Thelarge observation data spreads of [Pb/hs] are strong indi-
cation to suspect a large intrinsic spread of integrated neutron irra-
diations. In order to explain the spreads of [Pb/hs], a large spread of
13
C-pocket efﬁcienciesis subsequently proposed by Straniero et al.
(2005). However, it should be stressed here that the predictions of
the standard PMP scenario are rather robust (Goriely & Mowlavi
2000). In the framework of the PMP scenario, there is no obvious
degree of freedom that could be used to reduce the lead production
in low-metallicity AGB stars (Van Eck et al. 2003). At present, the
physical explanation for the different
13
C-pocket strengths, which
perhaps should not be consistent with the primary nature of the
neutron source, is not yet found (Reyniers et al. 2004). Thus the
1
where [X/Y]=log(N
X
/ N
Y
) - log(N
X
/ N
Y
)
, refers to the Solar Sys-
tem abundances.
2 Wenyuan Cui, and Bo Zhang
fundamental problems, such as the formation and the consistency
of the
13
C-pocket, the neutron exposure signature in the interpulse
period, currently exist in the models of AGB stars.
For the third dredge-up and the thermal pulse model, sev-
eral important properties depend primarily on the core mass M
c
,
while the dependence on the other stellar parameters is negligible or
marginal (Iben 1977; Groenewegen & de Jong 1993; Karakas et al.
2002). Zijlstra (2004) reported that the initial-ﬁnal-mass relation
steepens at low metallicity, due to low mass-loss efﬁciency. This
may cause the degenerate cores of low-Z, high-mass AGB stars to
reach the Chandresekhar mass, leading to an Iben & Renzini-type-
1.5 supernova (Iben & Renzini 1983). On the other hand, this can
obviously affect model parameters of the AGB stars, e.g. the over-
lap factor r, which is the fraction of material that remains to ex-
perience subsequent neutron exposures, and the neutron irradiation
time t, in particular at low metallicity.
In this paper we will present a calculation which indicates that
at low metallicity, largecoremass of AGBstars may allowthe over-
lap factor and the duration of neutron irradiation to reach small val-
ues for a ﬁxed initial mass of AGB stars. This will affect the charac-
ters of the s-process nucleosynthesis, and can explain the observed
abundance pattern of lead-rich stars. The next section discusses the
model parameters of AGB stars. In section 3, we discuss the char-
acteristics of the s-process at low metallicity and the possibility of
lead stars. Finally, in section 4 we summarize the main conclusion
that can be drawn from such an analysis.
2 MODEL PARAMETERS OF AGB STARS
There are four parameters in the parametric model of Howard et al.
(1986) on s-process nucleosynthesis. They are the neutron irradia-
tion time t, the neutron number density N
n
, the temperature T
9
(in
units of 10
9
K) at the onset of the s-process, and the overlap factor
r. Combining these quantities, we can obtain the neutron exposure,
τ=N
n
v
T
t, where v
T
is the average thermal velocity of neu-
trons at T
9
. The temperature is ﬁxed at a reasonable value for the
13
C(α,n)
16
O reaction, T
9
=0.1, for these studies. Using the initial-
ﬁnal mass relations as function of metallicity presented by Zijlstra
(2004), the effects on the parameters can be derived.
2.1 The overlap factor
For the AGB model, the overlap factor r is a fundamental parame-
ter. An analytical formula was given by Iben (1977) as a function
of the core mass M
c
in the range 0.66M
c
61.36:
r = 0.43 0.795(M
c
0.96) + 0.346(M
c
0.96)
2
. (1)
We can obtain an initial-ﬁnal mass relation as a function of metal-
licity, by ﬁtting results of Zijlstra (2004):
M
c
= A(Z) + B(Z)M, (2)
where
A(Z) = 0.46449 + 0.03279log
Z
Z
+ 0.00044(log
Z
Z
)
2
, (3)
and
B(Z) = 0.08729 0.04851log
Z
Z
+ 0.00468(log
Z
Z
)
2
, (4)
which is valid for -46log
Z
Z
60. Combing the equations (1), (2),
(3) and (4), we obtain the overlap factor as a function of the ini-
tial mass and metallicity. The overlap factor is shown in Fig. 1,
Figure 1. The overlap factor of different initial mass AGB stars, as function
of metallicity.
which is signiﬁcantly small at low metallicities, especially for 3M
AGB stars. In AGB stars with initial mass in the range M = 1.5
3.0M
, the core mass M
c
lies between 0.6 and 1.4M
at [Fe/H]=
-2.5. According to the equation (1), the corresponding values of r
will range between 0.8 and 0.13. Gallino et al. (1998) have found
an overlap factor of r = 0.4 0.7 in their standard evolution model
of low-mass AGB stars at solar metallicity, which lies in our pre-
dicted range of r. Aoki et al. (2001) have reported an overlap factor
of r 0.1, found for the best t to metal-deﬁcient AGB stars that
produced the abundance patterns of LP 625-44 and LP 706-7. In an
evolution model of AGB stars, a small r may be realized if the third
dredge-up is deep enough for s-processed material to be diluted by
extensive admixture of unprocessed material. Karakas et al. (2002)
have found that the third dredge-up is more efﬁcient for the AGB
stars with larger core mass. Taking account of the core-mass depen-
dence, the wide range of r-values of the lead enhanced stars can be
explained naturally by the wide range of core-mass values of AGB
stars at low metallicity.
2.2 The neutron exposure
Gallino et al. (1998) have pointed out that the neutron density is
relatively low, reaching 10
7
cm
3
at solar metallicity. Since the
13
C neutron source is of primary nature, the typical neutron den-
sity in the nucleosynthesis zone scales roughly as 1/Z
0.6
, from Z
down to 1/50Z
. At lower metallicities, the effect of the primary
poisons prevails (Gallino et al. 1999; Busso et al. 1999).
There is a possibility for the synthesis of s-process elements in
the AGB stars, i.e., with nucleosynthesis taking place during ther-
mal pulses (Aoki et al. 2001). In this case, the neutron irradiation is
derived primarily by the
13
C(α,n)
16
O reaction, with a minor con-
tribution from the marginal burning of
22
Ne.
However, in the s-process scenario that invokes radiative
13
C-
burning, the nucleosynthesis mostly occurs during the relatively
long interpulse period, in a thin radiative layer at the top of the
He intershell (i.e., the
13
C-pocket model). A second neutron burst
giving rise to a small neutron exposure is released by the marginal
activation of the
22
Ne neutron source in the convective thermal
pulse. The neutron irradiation time t should be close to the in-
terpulse period at low metallicity due to the combination of two
reasons. The ﬁrst is that the higher neutron density can lead to
The origin of the lead-richstars in Galactic halo: investigationof the model parametersfor the s-process 3
Figure 2. The neutron exposure of different initial mass AGB stars, as function of metallicity.
longer neutron irradiation time, and the second is that the shorter
interpulse period is expected for larger core-mass of AGB stars
(Groenewegen & de Jong 1993). Therefor, adopting the interpulse
period as the neutron irradiation time will have a smaller effect on
the low-metallicity stars of interest here than that on stars of solar
metallicity.
In our calculation, the neutron irradiation time t is adopted
respectively as follows:
Case A: the duration of the thermal pulse, where the core-mass-
duration of the convective shell relation is adopted from Iben
(1977).
Case B: the interpulse period, where the core-mass-interpulse pe-
riod relation is adopted from Boothroyd & Sackmann (1988).
We choose respectively τ =0.08mb
1
at [Fe/H]= -0.3 in
case A, which corresponds to a mean neutron exposure
τ
0
=0.296(T
9
/0.348)
1/2
mb
1
, and τ=0.2mb
1
for 3.0M
AGB
stars with solar metallicity in case B (Gallino et al. 1998). Using
the initial-ﬁnal mass relations given by Zijlstra (2004) and the neu-
tron irradiation time t, we can obtain the neutron exposure τ
as a function of metallicity and initial mass (see Fig.2). The trend
shown in Fig.2 (Case A and Case B) can be understood as follows:
τ is proportional to the neutron number density N
n
and the neu-
tron irradiation time t, where N
n
is expected to increase with de-
clining metallicity. However, t declines with declining metallicity
due to the increasing of stellar core mass, which directly leads to
a decline of τ at very low metallicity, especially for 3M
AGB
stars.
Based on the primary nature of the
13
C neutron source, the
value of τ will reach about 6.3 mb
1
around [Fe/H] -2.5 for
the case of radiative
13
C-burning (Gallino et al. 1999). Our result
of case B for the 1.5M
AGB stars is close to the above value. Be-
cause the neutron irradiation time t is shorter for the larger AGB
stars, the neutron exposure τ should be smaller too. Aoki et al.
(2001) have reported a neutron exposure, τ 0.7 mb
1
for
metal-deﬁcient stars LP 625-44 and LP 706-7, which is in the range
of our calculated results for the both cases. The results shown in
Fig. 2 imply that the wide range of τ can be obtained naturally
by considering the dependence of the irradiation time on the core
mass . Since the Pb abundance is very sensitive to the neutron ex-
posure (Gallino et al. 2003; Lugaro et al. 2003), large variations of
the [Pb/hs] ratio could be expected.
3 DISCUSSION
3.1 The Case A
The rst model for
13
C-burning in AGB stars assumed that the
neutrons were released in convective conditions (Hollowell & Iben
1988; K¨appeler et al. 1990). In such calculations, a repeated neu-
tron exposure was achieved thanks to partial overlapping of mate-
rial cycled through several thermal pulses. The s-process mecha-
nism could be approximated by an exponential distribution of neu-
tron exposures exp(τ
0
), where the mean neutron exposure is
given by τ
0
= τ /lnr. The ﬁnal abundance distributions depend
mainly upon τ
0
.
In order to investigate the efﬁciency of the s-process site,
[Pb/hs] is particularly useful (Straniero et al. 2005). There have
been many theoretical studies of s-process nucleosynthesis in
low-mass AGB stars (Delaude et al. 2004; Iwamoto et al. 2004;
Straniero et al. 2005). Unfortunately, the precise mechanism for
chemical mixing of protons from the hydrogen-rich envelop
into the
12
C-rich layer to form
13
C-pocket is still unknown
(Reyniers et al. 2004). This makes it even harder to understand a
large spread of [Pb/hs] found in carbon-rich, metal-deﬁcient stars.
It is an interesting exercise to investigate the effect of the pa-
rameters presented above upon the s-process efﬁciency of AGB
stars. For this purpose, we have used the simple analytical formu-
lation (Clayton & Rassbach 1967; Clayton & Ward 1974) without
depending on any speciﬁc stellar model, with many of the neutron-
capture rates updated (Bao et al. 2000), to study what physical con-
ditions are possible to reproduce the observed abundance pattern
found in the metal-poor stars. The variation of the logarithmic ratio
[Pb/hs] with metallicity is shown in Fig. 3a, where solid lines repre-
sent respectively results of different initial mass of AGB stars. As a
comparison, spectroscopic measurements (ﬁlled squares) of C and
s-rich metal-poor stars are reported. Because of the uncertainties
related to the formation mechanism of the
13
C-pocket (Busso et al.
2001), a large spread of
13
C-pocket efﬁciencies has been proposed
by Straniero et al. (2005) in order to explain the spreads of [Pb/hs],
which has proved to be effective for several purposes (Gallino et al.
1998; Travaglio et al. 1999; Busso et al. 2001). The results (plot
lines) predicted by Straniero et al. (2005) for their standard case
(hereafter ST), ST×2 and ST/75 case are also presented respec-
tively. The ST case (Gallino et al. 1998) was shown to reproduce