![Abundance ratios [Sr/Fe] of the metal-poor stars as a function of [Fe/H]. The triangles (black) and down triangles (blue) indicate the ratios of the weak r-process stars and the main r-process stars, respectively. The red squares indicate low-Sr stars and gray symbols represent other EMP stars.](https://www.researchgate.net/profile/Wy-Cui/publication/352387345/figure/fig1/AS:11431281170981086@1687973530638/Abundance-ratios-Sr-Fe-of-the-metal-poor-stars-as-a-function-of-Fe-H-The-triangles_Q320.jpg)
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Pollution tracks of r-process material in [Sr/Ba] vs.
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Pollution tracks of r-process material in [Sr/Ba] vs. [Ba/Fe] space for the early
Galaxy
Wan-Qiang Han1,2, Guo-Chao Yang3, Lu Zhang4, Wen-Yuan Cui1, Ping Niu2, Fang Wen1and Bo Zhang1
1Department of Physics, Hebei Normal University, Shijiazhuang 050024, China; zhangbo@hebtu.edu.cn
2Department of Physics, Shijiazhuang University, Shijiazhuang 050035, China
3School of Sciences, Hebei University of Science and Technology, Shijiazhuang 050018, China
4College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, China
Received 2020 June 26, accepted 2020 November 20
Abstract In the early Galaxy, elemental abundances of the extremely metal-poor (EMP) stars contain
abundant information about the neutron-capture nucleosynthesis and the chemical enrichment history. In
this work, we study the abundance characteristics of Sr and Ba for the EMP stars in the [Sr/Ba] vs. [Ba/Fe]
space. We find that there are three boundaries for the distribution region of the EMP stars. The weak r-
process star CS 22897–008 lies on the upper end and the main r-process stars lie on the right end of the
region. Near the right boundary of the distribution region, there is an Fe-normal belt. For the EMP stars in
the belt, element Fe dominantly originates from the normal massive stars. The low-Sr stars ([Sr/Fe]6−0.3)
distribute in the region of the lower left of the Fe-normal belt and their Fe should originate partly from the
prompt inventory.We find that the formation of the lower boundary of the distribution region is due to the
pollution of the main r-process material and the formation of the right boundary could be explained by the
combination of the weak r- and main r-process material. Furthermore, the formation of the left boundary is
due to the pollution of the weak r-process material. Although the [Sr/Ba] ratios are related to the relative
importance of the weak r-process material, the scatter of [Sr/Ba] ratios for the EMP stars mainly depends
on the abundance ratio of the weak r-process.
Key words: stars: abundances — stars: formation — stars: massive
1 INTRODUCTION
Elemental abundance ratios of the extremely metal-poor
(EMP) stars ([Fe/H]6−2.5) are used to probe the
nucleosynthetic characteristics, since the stars are formed
in the early Galaxy and the gas clouds in which the stars
formed were polluted by only a few nucleosynthetic events
(McWilliam et al. 1995;Ryan et al. 1996;Frebel & Norris
2015). Elements beyond zinc are believed to be created
mainly by the slow (s) and rapid (r) neutron-capture (n-
capture) processes. The r-process, building up about a
half heavy elements in the universe, is divided into two
subcomponents. The weak r-process, which is also called
“lighter element primary process” (Travaglio et al. 2004)
or “limited r-process” (Cain et al. 2018;Frebel 2018), can
create the lighter n-capture elements within 38 6Z <
56. The determinate astrophysical site (or sites) of the
weak r-process remains (or remain) unclear (Frebel 2018).
The main r-process can create both light and heavy n-
capture elements. The site of the main r-process had long
been debated (Sneden et al. 2008;Thielemann et al. 2011).
Recently, neutron star mergers (NSMs) are believed to
be the most promising site for the main r-process nucle-
osynthesis (Cowperthwaite et al. 2017;Drout et al. 2017;
Thielemann et al. 2017;Ji & Frebel 2018;Cˆot´e et al.
2018). Based on the study of the r-process nucleosynthesis
yields from the dynamical ejecta mass produced by
NSMs GW170817, Abbott et al. (2017) reported that, if
more than 10%of the ejecta is changed into the r-
process elements, NSMs could fully explain the r-process
abundances in the Galaxy. Furthermore, the identification
of strontium in the spectra of AT2017gfo from the mergers
GW170817 (Watson et al. 2019) could be an evidence
that the origin of the r-process elements is the NSMs.
It is significant to note that the Sr abundances of the
EMP stars are related to both the main r-process and
the weak r-process, so the Sr abundance ratios contain
the abundant information about n-capture nucleosynthesis
and enrichment history of the early Galaxy. Furthermore,
111–2 W. Q. Han et al.: Pollution Tracks of r-process Material
[Sr/Fe] ratios also contain the information about the
astrophysical origin of the element Fe.
Because the metal-poor stars CS 31082-001 and
CS 22892-052 are largely enhanced with the r-process
elements (e.g., [Sr/Fe]≃0.8, [Eu/Fe]&1.6) (Hill et al.
2002;Sneden et al. 2003) and exhibit a distinct r-process
abundance pattern, they are considered as the main r-
process stars (Sneden et al. 2008). On the other hand, the
metal-poor stars HD 122563 and HD 88609 show low
abundances of the n-capture elements (e.g., [Sr/Fe]≃0,
[Eu/Fe]<0) (Honda et al. 2006,2007) and are treated as
the weak r-process stars (Honda et al. 2007;Montes et al.
2007). In order to investigate the astrophysical origins of
the n-capture elements, the abundance characteristics of
the EMP stars should contain the abundant information
(McWilliam 1998;Honda et al. 2004). Because the lower
limit of [Sr/Fe] ratios of the weak r-process stars is about
−0.3±0.2dex (Honda et al. 2004,2007) and the upper
limit of [Sr/Fe] ratios of the main r-process stars is about
0.8±0.2dex (Aoki et al. 2010), considering the observed
uncertainties, the Sr abundances of the very metal-poor
stars within the range of -0.3<[Sr/Fe].1.0 should be
explained by the combined contributions of the weak r-
process and main r-process (Spite et al. 2018). On the
other hand, some metal-poor stars show low Sr abundances
with [Sr/Fe]6−0.3(Honda et al. 2004;Barklem et al.
2005;Franc¸ois et al. 2007;Hollek et al. 2011;Cohen et al.
2013;Roederer et al. 2014;Li et al. 2015a;Jacobson et al.
2015;Hansen et al. 2015;Mardini et al. 2019), which are
lower than the observed [Sr/Fe] ratios of the weak r-
process stars and are named as low-Sr stars in this
work. Obviously, an additional Fe inventory is needed
for explaining the low [Sr/Fe] ratios of the low-Sr stars.
Qian & Wasserburg (2001) have suggested that, in the
early Galaxy, there should exist another nucleosynthetic
component originated from the first very massive stars.
This component is called as the initial or prompt(p-
) inventory and only produces Fe and light elements.
However, the effect of the p-inventory on the abundances
of the EMP stars has not been studied in detail. Using
a three-component model with HNe, H and L∗sources,
Qian & Wasserburg (2008) quantitatively explained the
great shortfall of the abundance ratios [Sr, Y, Zr/Fe] in
some metal-poor stars with [Fe/H].−3. In recent years,
much more abundance data of new detected EMP stars
are presented (Lai et al. 2008;Mashonkina et al. 2010;
Hollek et al. 2011;Cohen et al. 2013;Roederer et al.
2014;Mashonkina et al. 2014;Siqueira Mello et al. 2014;
Li et al. 2015b,a;Jacobson et al. 2015;Hansen et al. 2015;
Aoki et al. 2017;Cain et al. 2018;Spite et al. 2018;
Mardini et al. 2019).
Recently, based on the abundance analysis of the
EMP stars, Spite et al. (2018) reported that, within the
first peak elements, the abundances are well correlated,
which is similar to the correlation inside the abundances
of the second-peak elements. However, they found that
there is no correlation between any first peak element
with any second peak element and the distribution of
the EMP stars in [Sr/Ba] vs. [Ba/Fe] space shows a
very complex enrichment picture. Spite et al. (2018) also
pointed that the star CS 22897–008 is a r-poor star with
high [Sr/Ba] ratio (1.59±0.28) which is higher than the
ratio of HD 122563. Although there have been many
theoretical and observational studies of the r-process
nucleosynthesis, the astrophysical information emerged
from the abundance distribution of the n-capture elements
of the EMP stars have not been revealed in detail. In
this case, it is of the upmost importance to collect a
large number of first and second peak elements in the
metallicity range −4.56[Fe/H]6−2.5, to explore
the nucleosynthesis processes and enrichment history in
early Galaxy (Andrievsky et al. 2011;Siqueira Mello et al.
2014;Spite et al. 2018;Cowan et al. 2019). In order
to better understand the abundance distribution of the
n-capture elements, more detailed studies about the
enrichment history of the EMP stars are still needed. This
motivates us to study the abundance relations between Sr
and other elements (Ba and Fe). In Section 2, we study the
abundance relation of the EMP stars between the first peak
element Sr and the second peak element Ba. The relation
of Fe produced in the normal massive stars and the weak
r-process elements, the effect of the p-inventory on the
abundances of the low-Sr stars, the relation of the pollution
tracks and the abundance boundaries, the relation of the
scatter trend and the ratios of the r-process are studied in
[Sr/Ba] vs. [Ba/Fe] space. Section 3 gives our conclusions.
2 THE ABUNDANCE DISTRIBUTION OF THE
EMP STARS IN THE [SR/BA] VS. [BA/FE] SPACE
The elemental abundances of the very metal-poor stars
can provide crucial clues in exploring the r-process
nucleosynthesis in the early universe. Element Eu is
believed to be the r-process element since Eu is dominantly
produced by the r-process. On the other hand, Ba is
believed to mainly originate from the s-process of the
low and intermediate mass AGB stars in the solar system
(Arlandini et al. 1999). However, for the lowest metallici-
ties, Ba dominantly comes from the main r-process, since
the long time-scale for the evolution of the AGB stars
(Truran et al. 2002). Because the abundances of Ba have
been measured for almost all stars with lower metallicity,
as in many previous studies (Honda et al. 2004;Roederer
2013), we take Ba (instead of Eu) as the representative
element of the main r-process. In this section, we will
explore the abundance relation between the elements
Sr and Ba. The observational and theoretical results of
W. Q. Han et al.: Pollution Tracks of r-process Material 111–3
the previous studies (Honda et al. 2004;Franc¸ois et al.
2007;Andrievsky et al. 2011;Siqueira Mello et al. 2014;
Spite & Spite 2014;Roederer 2017;Spite et al. 2018)
imply that the [Sr/Ba] scatter should not be ascribed to one
nucleosynthetic process. The distribution of [Sr/Ba] for
the metal-poor stars could present important clues about
the pollution of r-process material in the early Galaxy. So
the quantitative study of the distribution of [Sr/Ba] for the
more metal-poor stars is necessary.
Figure 1shows the abundance ratios [Sr/Fe] of
EMP stars as a function of [Fe/H]. The weak r-
process stars HD 122563 (Honda et al. 2007) and
CS 22897–008 (Spite et al. 2018) are indicated as
black triangles. The abundance ratios of four main
r-process stars CS 31082–001, CS 22892–052, CS
29497–004, and SDSS J2357–0052 are adopted
from Hill et al. (2002,2017); Sneden et al. (2003);
Aoki et al. (2010) and plotted as blue down triangles.
For the other EMP stars, the abundances are taken from
Westin et al. (2000); Cowan et al. (2002); Depagne et al.
(2002); Johnson & Bolte (2002); Honda et al. (2004);
Barklem et al. (2005); Franc¸ois et al. (2007); Lai et al.
(2008); Mashonkina et al. (2010); Roederer et al. (2010);
Hollek et al. (2011); Cohen et al. (2013); Roederer et al.
(2014); Mashonkina et al. (2014); Siqueira Mello et al.
(2014); Li et al. (2015b,a); Jacobson et al. (2015);
Hansen et al. (2015); Aoki et al. (2017); Cain et al.
(2018); Spite et al. (2018); Mardini et al. (2019). Note
that, the carbon-enhance metal-poor (CEMP) stars with
s-process enhancement (e.g. [Ba/Fe]>1,[Ba/Eu]>0) are
excluded from the collected observational data because we
focus on the r-process nucleosynthesis. From the figure we
can see that, for the EMP stars with [Sr/Fe]>−0.3(gray
symbols), the [Sr/Fe] ratios are higher than that of HD
122563 and lower than those of the main r-process stars,
which means that their Sr abundances should be explained
by the mixture of the main r-process and the weak
r-process material. On the other hand, the low-Sr stars
([Sr/Fe]6−0.3) are indicated as the red squares. Because
the [Sr/Fe] ratios of the low-Sr stars are lower than those
of the weak r-process stars, an additional Fe inventory
is needed for explaining the low [Sr/Fe] ratios. Figure 2
shows the [Ba/Fe] as a function of [Fe/H]. The symbols
are the same as in Figure 1. We can see that, although
most low-Sr stars are r-poor stars ([Ba/Fe]6−0.5),
the differences of Ba abundances of two groups are not
distinct in the range −4.0.[Fe/H].−2.5. However, the
sample stars with [Fe/H].−4.0or with [Ba/H]∼−5.5
(dotted line: [Ba/H]=−5.5) are the low-Sr stars.
Because Ba is produced by the main r-process and Sr
can be produced by both the main r-process and the weak
r-process, in order to reveal the abundance characteristics
of the EMP stars in detail, in Figure 3, we present the
[Sr/Ba] ratios as a function of [Ba/Fe] ratios. The data
are the same as in Figure 1. The black horizontal dashed
lines represent the ratios of HD 122563 (lower) and CS
22897–008 (upper), and their averaged ratio is indicated
as a black horizontal solid line. The blue horizontal solid
line represents the minimum ratios of [Sr/Ba] for the
main r-process stars, and the blue horizontal dashed lines
represent the typical uncertainties. Spite et al. (2018) have
reported that there is no clear correlation between the
abundance of a first peak element Sr and the abundance
of a second peak element Ba. They pointed out that there
is a minimum of [Sr/Ba] corresponding to its value in
the r-rich stars and characteristics of the main r-process,
and an upper limit of [Sr/Ba] corresponding to the line
of [Sr/Ba]=−[Ba/Fe]+0.7. From the figure we can see
that there are three boundaries for the distribution region
of the EMP stars and the right boundary is near the line
of [Sr/Ba]=−[Ba/Fe]+0.7. The higher ratios of the weak
r-process star CS 22897–008 are [Ba/Fe]∼−1.0±0.2and
[Sr/Ba]∼1.59 ±0.28 which are close to the upper vertex
of the triangle. On the other hand, the main r-process stars
lie on the right end of the lower boundary and the low-Sr
star CS 30325–094 (red empty star) is close to the left end
of the lower boundary of the region. For a given [Sr/Fe]
ratio, the relation of [Sr/Ba] and [Ba/Fe] can be presented
by a straight line with the slope of −1. In the figure, each
of these lines is characterized by a value of [Sr/Fe].
Taking the averaged abundance ratio ([Sr/Fe]= 0.1) of
the weak r-process stars HD 122563 and CS 22897–008,
in the figure, the weak r-process ratio is indicated by the
inclined solid line with [Sr/Ba]>−0.27 which is the upper
limit of the main r-process ratio. After considering the
upper ratio ([Sr/Fe]= 0.46) and the lower ratio ([Sr/Fe]=
−0.27), the weak r-process ratio can be indicated by a belt
(gray squares). We can see that the right boundary of the
region is close to the line through CS 22897–008, which
means that the formation of the right boundary is mainly
due to the weak r-process ratio. For the weak r-process
stars HD 122563 and CS 22897–008, the averaged ratio
[Sr/Fe]∼0.1means that the production of the weak r-
process elements is coupled with that of Fe and the weak
r-process event should occur in Fe core-collapse SNe with
the progenitors of ∼11 −25M⊙, since Fe is produced in
the massive stars of ∼11 −25M⊙(Woosley & Weaver
1995;Qian & Wasserburg 2007). On the other hand, the
[Sr/Ba] ratios of the stars indicted by the green squares
are close to those of the main r-process stars, although
their [Sr/Fe] ratios lie in the range of the weak r-process
stars. Because the [Sr/Fe] ratios in the belt are close to the
weak r-process ratio, the astrophysical origin of elements
Sr and Fe of the EMP stars should be similar to those of
the weak r-process stars. So the belt could be named as
the Fe-normal belt and the stars in the belt could be named
111–4 W. Q. Han et al.: Pollution Tracks of r-process Material
[Fe/H]
[Sr/Fe]
Fig.1 Abundance ratios [Sr/Fe] of the metal-poor stars as a function of [Fe/H]. The triangles (black) and down triangles
(blue) indicate the ratios of the weak r-process stars and the main r-process stars, respectively. The red squares indicate
low-Sr stars and gray symbols represent other EMP stars.
[Ba/Fe]
[Fe/H]
observational limit
Fig.2 Abundance ratios [Ba/Fe] of the metal-poor stars as a function of [Fe/H]. The data and symbols are the same as in
Fig. 1. The dotted line indicates the observed limit.
as Fe-normal stars. From the figure we can also see that
the low-Sr stars (red symbols) distribute in the region of
the lower left of the Fe-normal belt, which means that
an additional Fe inventory is needed for explaining the
phenomenon of the low-Sr stars. The belt and the low-
Sr stars were not mentioned in Spite et al. (2018) for the
reason of the small number of samples. Note that, based
on the abundance analysis of four stars in ultra-faint dwarf
galaxies (UFDs), Ji et al. (2019) discussed the most viable
candidates for the sources of low Sr and Ba abundances at
low metallicity and reported that the variations of [Sr/Ba]
in UFDs cannot be explained by just a single r-process,
and the astrophysical origin of low Sr and Ba abundances
is still an open question.
Qian & Wasserburg (2001) have suggested that, in the
early Galaxy, there should exist another nucleosynthetic
component, i.e., p-inventory, originated from the first very
massive stars. It is interesting to explore the effect of the
p-inventory on the abundances of the low-Sr stars. In this
case, for elements Fe, there are two possible astrophysical
origins: normal Fe and prompt Fe. Taking the abundance
ratio of the weak r-process as Fe-normal dominant ratio
([Sr/Fe]∼0.1), in the figure, each of the straight dashed
lines with a slope of −1is also characterized by the
contributed fractions of the p-inventory for the element
Fe (green line: Fe-normal dominant, magenta line: 83.2%,
cyan line: 95.0%, wine line: 98.7%, red line: 99.7%). We
can see that, for a given [Sr/Ba] ratio, the [Ba/Fe] ratios
decrease with increasing the contributed fraction of the p-
inventory. For star CS 30325-094 which is indicated by the
empty star, element Fe originates dominantly from the p-
inventory.
Note that the right boundary of the distribution region
decreases with increasing [Ba/Fe]. The weak r-process
stars and the main r-process stars lie on the left end and
the right end of the boundary, respectively. Obviously, the
W. Q. Han et al.: Pollution Tracks of r-process Material 111–5
[Ba/Fe]
[Sr/Ba]
-1.9 -1.4 -0.9
0.1
-0.27
0.46
-2.4
Fig.3 The straight lines with various [Sr/Fe] ratios and Fe-normal belt in [Sr/Ba] vs. [Ba/Fe] space. The black horizontal
dashed lines represent the ratios of HD 122563 (lower) and CS 22897-008 (upper), and their averaged ratio is indicated
as a black horizontal solid line. The blue horizontal solid line represents the minimum ratios of [Sr/Ba] for the main
r-process stars, and the blue horizontal dashed lines represent the typical uncertainties. The straight dashed lines with
the slope of −1characterized by various values of [Sr/Fe] represent various relations of [Sr/Ba] and [Ba/Fe]. The red
empty star represents CS 30325-094. The solid line with the slope of −1is the relation of [Sr/Ba]=−[Ba/Fe]+0.7from
Spite et al. (2018).
[Ba/Fe]
[Sr/Ba]
Fig.4 The pollution track of the main r-process material in a gas cloud with initial weak r-process abundances. The
symbols are indicated as in Fig. 1. The curves (dashed line is from CS 22897–008, short dashed line is from HD 122563,
and the solid line is from the averaged abundance of them) indicate the polluted results by the main r-process material.
boundary could provide useful clue about the chemical
enrichment of the gas clouds in which the stars formed.
For a gas cloud polluted by the r-process material, the mass
abundance of the ith element could be expressed as:
Xi=Mini ∗Xi,ini
Mini +Mr
+Mr∗Xi,r
Mini +Mr
= (1 −f)∗Xi,ini +f∗Xi,r ,
(1)
where fis the mass fraction of the r-process material.
Mini and Mrare the initial mass of the cloud and the
mass of the r-process material, respectively. Xi,ini and
Xi,r are the initial mass abundance and the r-process
abundance of the ith element, respectively. In order to
explore the astrophysical reason of the right boundary
formation, the initial abundance Xi,ini is taken from
the abundances of the weak r-process star HD 122563
(Honda et al. 2007), CS 22897–008 (Spite et al. 2018) and
the averaged abundance of them, respectively. The r-
process abundance Xi,r (i.e., Xi,r =Xi,r,m) is taken from
the abundance of the main r-process star CS 31082-001
(Hill et al. 2002). Figure 4shows the calculated results.
The curves with arrows represent the pollution track when
increasing the main r-process material. We can see that
the track calculated from Equation (1) is consistent with
the right boundary of the distribution region of the EMP
stars within the uncertainties. The calculated result means
that the formation of the right boundary is related to the
pollution of the main r-process material.
111–6 W. Q. Han et al.: Pollution Tracks of r-process Material
[Ba/Fe]
[Sr/Ba]
Fig.5 Pollution from the main r-process material in [Sr/Ba] vs. [Ba/Fe] space. The curved lines indicate calculated
pollution tracks with various [Sr/Fe] ratios (black line: [Sr/Fe]= 0.1, magenta line: [Sr/Fe]=−0.9, cyan line: [Sr/Fe]=
−1.4, wine line: [Sr/Fe]=−1.9, red line: [Sr/Fe]=−2.4).
[Ba/Fe]
[Sr/Ba]
Fig.6 The pollution of the weak r-process material in [Sr/Ba] vs. [Ba/Fe] space. The short dashed curves indicate
calculated pollution tracks with various initial [Ba/Fe] ratios (wine for −2.0, royal blue for −1.5, dark yellow for −1.0,
olive for −0.5, orange for 0, and black for 1.17). The violet horizontal line with arrow indicates the pollution track of the
main r-process material.
Because the p-inventory only produces Fe and light
elements and barely produces n-capture elements, the gas
cloud in which the low-Sr stars formed had been polluted
by the r-process material. Based on the [Sr/Fe] ratio of
the straight line with a slope of −1and the [Sr/Ba] ratio
of HD 122563, the initial abundances of Sr and Ba of
the gas cloud in which the low-Sr star formed can be
derived. In this case, the abundances of the gas cloud
polluted by the main r-process material can be calculated
from Equation (1). In Figure 5, the curved lines indicate
calculated pollution tracks with various initial [Sr/Fe]
ratios (black line: [Sr/Fe]= 0.1, magenta line: [Sr/Fe]=
−0.9, cyan line: [Sr/Fe]=−1.4, wine line: [Sr/Fe]=−1.9,
red line: [Sr/Fe]=−2.4). We can see that the distribution
region of the low-Sr stars can be explained by the pollution
of the main r-process material after considering the effect
of the p-inventory. Furthermore, the horizontal line of the
main r-process ratio is the asymptotic line of pollution
tracks with various [Sr/Fe] ratios.
Based on the abundance analysis of the EMP stars,
Spite et al. (2018) have reported that the scatter of [Sr/Ba]
strongly increases when [Ba/Fe] decreases. On the other
hand, below [Ba/Fe].−1.0, the scatter of [Sr/Ba] does
not continue to increase. These characteristics of the
abundance distribution can also be seen from Figure 6.
It is interesting to note that the observed left boundary is
explicit: it is close to a straight line with [Ba/Fe]⋍−2.0for
[Sr/Ba].0, while [Sr/Ba] ratio increase with increasing
[Ba/Fe] ratio for [Sr/Ba]>0. From the figure we can see
that, for the left boundary, the lower end is close to the
main r-process line (blue horizontal line) and the upper
end is close to the abundances of the weak r-process stars.
W. Q. Han et al.: Pollution Tracks of r-process Material 111–7
HD 122563
CS 30325-094
CS 31082-001
[Ba/Fe]
[Sr/Ba]
low Sr stars
CS 22897-008
Fe normal belt
Fig.7 Formation of the abundance boundary in [Sr/Ba] vs. [Ba/Fe] space for the early Galaxy. The blue dashed line
represents the lower boundary which is due to the pollution of the main r-process material. The wine dashed curve
represents the left boundary. The black dashed curve is right boundary which is the mixture of the weak r- and the main
r-processes. The red short dashed line is the boundary of the Fe-normal belt (or Fe-normal stars) and the low Sr stars. The
solid curves represent results of the chemical evolution model by Famiano et al. (2016) which is dependent on various
equation of state (EOS)(O’Connor & Ott 2011) about the scatter of [Sr/Ba] in metal-poor stars (Orange is for LS180,
magenta is for LS220, green is for LS375 and royal is for Shen). The solid line with the slope of −1is the relation of
[Sr/Ba]=−[Ba/Fe]+0.7.
-1.6 -1.2 -0.8 -0.4 0.0 0.4 0.8 1.2 1.6
-1.6
-1.2
-0.8
-0.4
0.0
0.4
[Ba/Eu]
[Ba/Fe]
Fig.8 [Ba/Eu] vs. [Ba/Fe] in the early Galaxy. The horizontal solid line is the averaged value of the [Ba/Eu] ratios for the
sample stars. The horizontal dashed line represents the r-process ratio of the solar system (Li et al. 2013).
Taking the abundances of the lower end as the initial
abundances, the abundances of the gas cloud polluted by
the weak r-process material (i.e., Xi,r =Xi,r,w ) can also
be calculated from Equation (1). In Figure 6, the wine short
dashed curve indicates the pollution track of the weak r-
process material. We can see that the left boundary of the
EMP stars can be explained by the pollution of the weak
r-process material. In another word, the formation of the
left boundary is due to the pollution of the weak r-process
material.
Spite et al. (2018) suggested that the distribution of
[Sr/Ba] of the EMP stars should be explained by two
independent steps: the first enrichment by the main r-
process material and the second enrichment mainly by the
weak r-process material. Taking the [Sr/Ba] ratio of the
main r-process and various [Ba/Fe] ratios as the initial
abundances, the abundances of the gas cloud polluted
by the weak r-process material can also be calculated
from Equation (1). In Figure 6, the short dashed curves
indicate calculated pollution tracks with various initial
111–8 W. Q. Han et al.: Pollution Tracks of r-process Material
[Ba/Fe] ratios (wine line: [Ba/Fe]=−2.0, royal blue line:
[Ba/Fe]=−1.5, dark yellow line: [Ba/Fe]=−1.0, olive
line: [Ba/Fe]=−0.5, orange line: [Ba/Fe]= 0, black line:
[Ba/Fe]= 1.17). We can see that the distribution region
of the EMP stars can be explained by the pollution of the
weak r-process material, which is in agreement with the
suggestion of Spite et al. (2018). Note that the pollution
track with the highest initial [Ba/Fe] being close to the Fe-
normal belt reach the position of the weak r-process star
CS 22897–008, which means that, although the [Sr/Ba]
ratios are related to the relative importance of the weak
r-process material (Spite et al. 2018), the spread trend of
[Sr/Ba] ratios for [Ba/Fe]&−1.0is mainly constrained by
the abundance ratio of the weak r-process. From the figure
we can see that, although the pollution tracks converge
at the position of the weak r-process star CS 22897–008,
the pollution track with the highest initial [Ba/Fe] shows
a flat trend (black short dashed line). The pollution tracks
with lower initial [Ba/Fe] ratios are steeper for [Sr/Ba].0,
since the effect of pollution by the weak r-process material
is higher for the gas cloud with lower initial [Ba/Fe] ratios.
In order to explain the position of left vertex of the
region, we explore the abundance characteristics of the
natal cloud polluted by the r-process material. Taking
Xi,ini = 0 for n-capture elements, the abundances of
the gas cloud polluted by the weak r-process and main r-
process material can also be calculated. In Equation (1),
adopting f=0.0007 and Xi,r =Xi,r,w +Xi,r,m, we can
derive [Ba/Fe]=−2.0and [Sr/Ba]=−0.46. In Figure 6,
the calculated abundances are plotted by a filled star which
is close to the left vertex of the distribution region of
the EMP stars. The result means that, for the natal cloud
polluted by the r-process, the effect of the main r-process
is higher than that of the weak r-process, which should be
the astrophysical reason that the abundance ratio of the
left vertex of the region is close to the ratio of the main
r-process.
Based on a chemical evolution model which is
dependent on the nuclear equation of state (EOS),
Famiano et al. (2016) studied the light r-process element
enrichment and the scatter of [Sr/Ba] ratio in the metal-
poor stars. In Figure 7, for comparison, we present their
GCE results for various assumptions. For simplicity, we
only show the special pollution lines at the boundaries
and the line of [Sr/Ba]=C[Ba/Fe]+0.7. From the figure,
we can see that the lines of the GCE model are near the
Fe-normal belt when [Ba/Fe]<−0.5, then concentrate
and become horizontal when [Ba/Fe]>0. This means
that our results are consistent with the GCE results.
The line of [Sr/Ba]=C[Ba/Fe]+0.7is near the right
boundary, which means the astrophysical reason of the
formation for the line (or right boundary) is due to the
pollution of combination of the weak r- and main r-process
material. The extremely metal-poor fast rotation massive
star (FRMS) may be a possible site for the first peak
elements (Chiappini et al. 2011;Frischknecht et al. 2016;
Prantzos et al. 2018). Using the weak s-process production
of FRMS, Cescutti et al. (2013) explained the spread of
[Sr/Ba] in the EMP stars. However, they reported that the
FRMS does not produce Eu. Figure 8shows [Ba/Eu] vs.
[Ba/Fe] for the EMP stars. From the figure we can see
that, for the sample stars, the [Ba/Eu] ratios are lower
than zero and their averaged ratio is near the solar main
r-process ratio (Li et al. 2013). This implies that Ba and
other neutron-capture elements in the sample stars should
mainly come from the r-process (e.g., Montes et al. 2007;
Famiano et al. 2016).
3 DISCUSSIONS AND CONCLUSIONS
In early Galaxy, nearly all the n-capture nucleosynthesis
and chemical enrichment information are contained in the
abundances of the EMP stars with various r-enhancement
levels. In order to understand the chemical enrichment
history of the n-capture elements in the early Galaxy,
we study the abundance relations between the first peak
element Sr and the second peak element Ba in the [Sr/Ba]
vs. [Ba/Fe] space for the EMP stars. The results are
summarized as follows:
1. Distribution region and three vertices
There are three boundaries and three vertices for
the distribution region of the EMP stars. The lower
boundary of the region is close to the main r-process
ratio. The weak r-process star CS 22897–008 lies
on the upper vertex and the main r-process stars lie
on the right end of the lower boundary. There are
three distinct abundance characteristics for the weak
r-process stars, i.e., [Sr/Fe]∼0.1, [Sr/Ba]∼1.2, and
[Ba/Fe]∼−1.0. For a gas cloud polluted by a weak
r-process event, the observed ratios of [Sr/Fe]∼0.1
for the weak r-process stars means that the weak r-
process elements are ejected from an SN II coupled
with element Fe (i.e., normal Fe) and the ratio of
the yield of weak r-process element to the yield of
normal Fe is about a constant. In this case, element
Fe in the gas cloud dominantly originates from the
normal massive stars and the abundances of the main
r-process elements are reduced because of the dilution
by the weak r-process material. The pollution of weak
r-process material directly leads to the higher weak
r-process ratios ([Sr/Ba]∼1.6) and the lower main
r-process ratios ([Ba/Fe]∼−1.0, [Eu/Fe]∼−0.5).
There are two distinct abundance characteristics for
the main r-process stars, i.e., [Ba/Fe]&1.0and
[Sr/Ba]∼−0.5. [Ba/Fe]&1.0means that the
production of main r-process elements does not couple
with the iron group elements, which implies that the
W. Q. Han et al.: Pollution Tracks of r-process Material 111–9
sites of the main r-process and the weak r-process are
different. The two abundance characteristics lead to
the main r-process stars lie on the right side of right
vertex of the region.
Because the abundances of CS 30325-094
(Franc¸ois et al. 2007) are close to the left vertex
of the region, we take the abundances of the star
as a representative. There are three abundance
characteristics, i.e., [Sr/Fe]∼−2.4, [Ba/Fe]∼−2.0,
and [Sr/Ba]∼−0.5. For the star, [Sr/H]∼−5.5and
[Ba/H]∼−5.5which are close to the observational
limits. [Sr/Fe]∼−2.4means that element Fe in this
star dominantly originates from p-inventory, since the
ratio of [Sr/Fe] is lower than that of the Fe-normal
stars about 2.4 dex. [Sr/Ba]∼−0.5means that the
natal cloud had been polluted by the main r-process
material, which is in agreement with the suggestion
by Spite et al. (2018). Because of the abundance
characteristics of low-Sr and low-Ba, the abundances
of CS 30325-094 can be treated as the start point of
the pollution tracks of the main r-process material
and the weak r-process material. The position of the
left vertex can be explained by that, for the natal
cloud polluted by the r-process, the effect of the main
r-process is higher than that of the weak r-process.
2. Fe-normal belt
From the distribution of the EMP stars, we find that
there are barely any sample stars lying on the weak r-
process ratio ([Sr/Ba]∼1.6), which implies that, for a
gas cloud polluted by a weak r-process event, the weak
r-process elements are ejected from an SN II coupled
with element Fe (i.e., normal Fe) and the ratio of the
yield of weak r-process element to the yield of normal
Fe is about a constant. In another word, element Fe
in the weak r-process stars dominantly originates from
the normal massive stars. Although [Sr/Ba]∼1.2is
a characteristic of the weak r-process, [Sr/Fe]∼0.1
has constrained the position of the weak r-process
stars, which is the astrophysical reason that the weak
r-process stars lie on top vertex of the region. There is
a belt which is close to the weak r-process ratio, i.e.,
[Sr/Fe]= 0.1±0.3. The sample stars in the belt could
be named as Fe-normal stars, since the astrophysical
origin of element Fe is similar to those of the weak
r-process stars. The right boundary of the distribution
region for the EMP stars is close to the right side of
the belt for [Ba/Fe].0.5.
3. Low-Sr stars and p-inventory
The low-Sr stars distribute in the region of the lower
left of the Fe-normal belt and the additional Fe
inventory is needed for explaining the phenomenon
of the low-Sr stars. For the low-Sr stars, element Fe
should originate partly from the p-inventory and the
observed scatter of [Sr/Fe] is about 2.0 dex. For a
given [Sr/Ba] ratio, the [Ba/Fe] ratios decrease with
increasing the contributed fraction of the p-inventory.
4. Three boundaries of the distribution region and
pollution tracks of the r-process material
The formation of the left boundary of the distribution
region is due to the pollution of the weak r-process
material and the formation of the lower boundary is
due to the pollution of the main r-process material. It
is interesting to note that the formation of the right
boundary could be explained by the combination of
the weak r- and main r-process material. In this case,
the weak r-process star CS 22897–008 lie on the
top end of the pollution track (e.g., the short dashed
curve in Fig. 6), which implies that the main r-process
elements, such as Ba and Eu, had already existed in the
gas cloud which the weak r-process star formed. This
is consistent with the suggestion that the enrichment of
the heavy elements should undergo two independent
steps: a first main r-process event and a second weak
r-process event.
5. Scatter trend of [Sr/Ba] ratios and the abundance ratios
of the r-process
The right boundary could be treated as the track when
increasing the pollution of the weak r-process material
in the extremely enriched main r-process material. For
[Ba/Fe]&0.5, the flat trend of the pollution track is
in agreement with the predictions of the highest initial
[Ba/Fe] by Spite et al. (2018). In this case, the scatter
of [Sr/Ba] ratios increases with decreasing [Ba/Fe]
weakly. On the other hand, for [Ba/Fe]<0.5, the
pollution track is close to the upper limit of the Fe-
normal belt. Consequently, the scatter of [Sr/Ba] ratios
increases with decreasing [Ba/Fe] strongly. Spite et al.
(2018) found that the scatter of [Sr/Ba] strongly
increases when [Ba/Fe] decreases and suggested that
the scatter depends on the relative importance of the
weak r-process material. Our calculation implies that,
although the [Sr/Ba] ratios are related to the relative
importance of the weak r-process material, the scatter
of [Sr/Ba] ratios mainly depends on the abundance
ratio of the weak r-process.
In the past several decades, many researchers have per-
formed investigations about the abundance characteristics
and astrophysical sites of the r-process. The results of this
work could present more information for understanding
the abundance distributions of the n-capture elements in
the EMP stars. Obviously, more detailed studies of the
elemental abundances of the r-process enhanced stars are
required.
Acknowledgements We thank the referee for the help-
ful and constructive suggestions, which improved this
paper greatly. This work has been supported by the
111–10 W. Q. Han et al.: Pollution Tracks of r-process Material
National Natural Science Foundation of China under
grants 11673007, 11547041, 11643007, and 11773009,
the Natural Science Foundation of Hebei Province under
grants A2018106014 and A2019208194.
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