Testing the AGB Scenario as the Origin of the Extreme-Helium Population in omega Centauri

Abstract

The most massive Galactic globular cluster, Omega centauri, appears to have multiple populations. Its bluest main sequence and extended horizontal branch stars are suggested to have the common origin, that is, an extremely high helium abundance of Y ~ 0.4. The high helium abundance is most often attributed to asymptotic giant branch (AGB) stars. In this study we test the AGB hypothesis. We simulate the maximum-AGB models where the impact of AGB stars is maximised by assuming that supernova explosions do not affect the chemical evolution of the proto cloud. We compare the enrichment history of helium, metals, carbon and nitrogen to the observed values. Even under the most generous condition, the maximum-AGB models fail to reproduce the large values of helium Y ~ 0.4 and helium enrichment parameter Delta Y / Delta Z ~ 70 which were deduced from the colour-magnitude diagram fits. They also fail to reproduce the C and N contents of the blue population spectroscopically determined. We conclude that the AGB scenario with the canonical stellar evolution theory cannot explain the observational constraints and that the self chemical enrichment does not provide a viable solution. Alternative processes are desperately called for. Comment: 6 pages, 5 figures, Accepted by MNRAS

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arXiv:0804.1598v1 [astro-ph] 10 Apr 2008
Mon. Not. R. Astron. Soc. 000, 1–?? (2007) Printed 10 April 2008(MN LATEX style file v2.2)
Test on the AGB Scenario as the Origin of the
Extreme-Helium Population in ω Centauri
Ena Choi and Sukyoung K. Yi
Department of Astronomy, Centre for Space Astrophysics, Yonsei University, Seoul 120-749, Korea
10 April 2008
ABSTRACT
The most massive Galactic globular cluster, ω Centauri, appears to have mul-
tiple populations. Its bluest main sequence and extreme horizontal branch stars are
suggested to have the common origin, that is, an extremely high helium abundance
of Y ∼ 0.4. The high helium abundance is most often attributed to asymptotic gi-
ant branch (AGB) stars. In this study we test the AGB hypothesis. We simulate the
maximum-AGB models where the impact of AGB stars is maximised by assuming
that supernova explosions do not affect the chemical evolution of the proto cloud.
We compare the enrichment history of helium, metals, carbon and nitrogen to the
observed values. Even under the most generous condition, the maximum-AGB models
fail to reproduce the large values of helium Y ∼ 0.4 and helium enrichment parame-
ter ∆Y/∆Z ∼ 70 which were deduced from the colour-magnitude diagram fits. They
also fail to reproduce the C and N contents of the blue population spectroscopically
determined. We conclude that the AGB scenario with the canonical stellar evolution
theory cannot explain the observational constraints and that the self chemical enrich-
ment does not provide a viable solution. Alternative processes are desperately called
for.
Key words: galaxies: globular clusters — individual (ω Centauri)
1INTRODUCTION
The origin of the blue population in the most massive
Galactic globular cluster (GC), ω Centauri, is at the cen-
tre of debate after the discovery of its multiple popu-
lations (e.g. Anderson 1997; Lee et al. 1999; Bedin et al.
2005). The explanation of the blue main sequence (bMS)
of ω Cen by a huge excess of the primordial helium abun-
dance, ∆Y ∼ 1.2, was implied via the colour-magnitude di-
agram (CMD) fitting (Norris 2004). This bMS, which con-
tains ∼ 30 percent of the cluster stars, is roughly 0.3 dex
more metal-rich than the red main sequence (rMS) popu-
lation (Piotto et al. 2005). Its blue colour despite its high
metallicity is attributed to an extremely high value of he-
lium. This explanation has further been reinforced by the
fact that the same helium excess can reproduce the extended
horizontal branch (EHB) of ω Cen (D’Antona & Caloi 2004;
Lee et al. 2005). Follow-up spectroscopic and photometric
investigations have been performed by many groups (e.g.
Kayser et al. 2005; Sollima et al. 2006; Stanford et al. 2007;
Villanova et al. 2007; van Loon et al. 2007). The extreme
helium scenario appears to provide a successful solution
to another cluster, NGC2808, which also shows multiple
main sequences (Piotto et al. 2007) and a pronounced EHB
(Lee et al. 2005). It has recently been claimed that the
GCs with an EHB are among the most massive in the
Milky Way, and the possible link between the mass of the
cluster and the helium anomaly is heavily investigated on
(Recio-Blanco et al. 2006; Lee et al. 2007). The existence
of helium-rich GCs in the external galaxy, M87, has also
been suggested (Kaviraj et al. 2007), implying that this phe-
nomenon may be universal.
The extreme helium scenario, however, has been crit-
icised. This is mainly because the helium-enrichment pa-
rameter ∆Y/∆Z corresponding to proposed helium abun-
dance ∼ 70 or even higher, which is more than an or-
der of magnitude larger than observational and theoreti-
cal values, ∆Y/∆Z = 1 – 5 (e.g. Fernandes et al. 1996;
Pagel & Portinari 1998; Jimenez et al. 2003). For possi-
ble origins for the extreme helium abundance, asymp-
totic giant branch(AGB) stars,
Type II supernovae (SN II) have been widely discussed
(Norris 2004;D’Antona et al.
2006). Bekki & Norris (2006) however demonstrated that
such candidates cannot produce the amount of helium re-
quired, for ordinary initial mass functions (IMFs) within
the scheme of a closed-box self enrichment. More recently,
Choi & Yi (2007) showed that essentially no population can
massivestars,and
2005;Maeder & Meynet

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2
E. Choi & S. K. Yi
produce such a high value of ∆Y/∆Z via self-enrichment
processes regardless of the shape of IMF.
Supernovae are not helpful for generating a high value
of ∆Y/∆Z because they produce metals as well as helium.
The ejecta from AGB stars is generally believed to show the
largest helium enrichment parameters (e.g., see Izzard et al.
2004; Choi & Yi 2007). However, the AGB hypothesis is
found to be unsuccessful for matching both the high helium
abundance and the CNO properties constrained from obser-
vations even when the supernova effect is removed from the
calculation (Karakas et al. 2006; Bekki et al. 2007).
We further elaborate on the works of Karakas et al.
(2006); Bekki et al. (2007) by testing the maximum-AGB
hypothesis where the impact of AGB stars is maximised by
assuming that massive star ejecta of unknown mass range
escape the small potential wells of proto clouds. In this let-
ter we search for the parameter space that satisfies all the
observational constraints including spectroscopic measure-
ments.
2THE CHEMICAL EVOLUTION MODELS
2.1 Introduction
We adopt the chemical enrichment code described in
Choi & Yi (2007) following the formalism of Tinsley (1980).
The two-component model assuming instant mixing and
cooling traces the net metallicity Z, helium Y , carbon and
nitrogen contents of the gas and stellar components.
The stellar mass, Ms(t), and the cold gas mass, Mg(t),
are normalised to the initial system mass,
µs(t) ≡
Ms(t)
Mtot(0),µg(t) ≡
Mg(t)
Mtot(0). (1)
In this study, we assume that the formation of the for-
mer (rMS) population is essentially instant:
ψ(t ?= 0) = 0. (2)
The evolution of the gas mass is given by
dµg
dt
= E(t) − ψ(t) (3)
where the ejecta gas mass at time t, E(t), is defined as
E(t) =
?mupper
mt
dmφ(m)(m − wm)ψ(t − τm). (4)
where φ(m) denotes the initial mass function (IMF), wm
the remnant mass for a star with main sequence mass m,
τm the lifetime of a star of mass m, and mupper the upper
mass cut in the initial mass function. The Scalo IMF (Scalo
1986) with cutoffs at 0.1 and 100M⊙ is assumed, and the
remnant mass wm and the lifetime of a star τm are adopted
from Ferreras & Silk (2000, 2001).
The equation for the evolution of metallicity in gas is
given by
d(Zgµg)
dt
= −ψ(t) + EZ(t) (5)
where the mass of ejected metal at time t, EZ(t), is defined
as
?mupper
mt
EZ(t) =
dmφ(m)?mpmψ(t − τm) + (m − wm)ψ(t − τm)Zg(t − τm)?
(6)
where pm denotes the newly synthesized and ejected metal
(or helium, C, N) mass fraction to initial stellar mass. We
will discuss this in greater detail in §2.2.
The initial chemical properties of the models are
adopted from the observational values for the rMS popu-
lation of ω Cen. The initial metallicity Z0 = 0.001 and the
initial C, O abundance [C/M]= 0.0, [N/M]= 1.0 are from
the spectroscopic measurements of Piotto et al. (2005), and
the initial helium abundance Y0 = 0.232 is deduced from the
CMD fit in Lee et al. (2005).
2.2 Chemical Yields
The chemical yields (pm), defined as the mass fraction of
a star of mass m that is newly converted to metals or
helium and ejected, are the most important input param-
eter to the chemical evolution of a population. We basi-
cally adopt the helium, carbon and metal pm predictions
of Maeder (1992) for the mass range 9 − 100M⊙. For nitro-
gen, we adopt the pm prediction of Nomoto et al. (1997).
For M⊙ ? 6 we adopt the helium, carbon, nitrogen, and
metal yields from Herwig (2004). We confirm that the use
of different yields (e.g. van den Hoek & Groenewegen 1997;
Ventura et al. 2002) does not make any notable difference to
our conclusion. We use the chemical yields from the hermi-
tian fits to the pm predictions. In Figure 1, we show the the-
oretical ejecta abundance predicted by our fitting functions
from the metal-poor (Z = 0.001) stars of mass 0.1−100M⊙.
The chemical abundances predicted and the resulting he-
lium enrichment parameters are presented. As shown in the
middle panel, the highest peak around 6M⊙ in the helium
enrichment parameter diagram reaches the value proposed
for the bMS population. Indeed, the AGB ejecta appears to
be the most promising candidate. Supernovae on the other
hand produce more metals than helium and hence are not
helpful for generating a high helium-to-metal population.
2.3The Maximum-AGB model
It has already been shown that a closed-box system can-
not achieve such high values of helium and helium enrich-
ment parameter as implied for the blue population of ω Cen
(Choi & Yi 2007). This is mainly because of the ill effect of
supernovae on ∆Y/∆Z.
In realistic models for small potential wells, the rem-
nants of supernovae are believed to escape the system
(Larson 1974). Such explosions would probably remove the
remnant gas in the potential as well after the first star for-
mation episode. But in general, the escape of the supernova
materials is likely to be easier than the escape of the rem-
nant gas. So we set up ad hoc models in which the super-
nova ejecta escape the system without affecting the chemical
properties of the remnant gas, hence maximising the chemi-
cal influence of AGB stars. We call this “the maximum-AGB
models”.
Our prescription has two input parameters. The first
free parameter, mesc, indicates the critical mass above which
the stellar mass ejecta escape the potential well without af-
fecting the chemical abundance of the remaining gas. This
parameter is likely a function of the mass of the system be-
cause the potential well determines whether the supernova-
driven winds can escape the gravitational potential of the

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AGB effect on ω Cen
3
Figure 1. The theoretical ejecta abundance calculated from the
stellar yields of Maeder (1992) and Herwig (2004). Top: The he-
lium and metal abundances of the ejecta from the metal-poor
(Z = 0.001) stars of mass 0.1 − 100M⊙. Middle: The resulting
helium enrichment parameters. Bottom: The carbon and Nitrogen
abundances of the ejecta from the stars with the initial compo-
sitions [C/M] = 0.0, [N/M] = 1.0 following Piotto et al. (2005).
system or not. Karakas et al. (2006) assumed that the sys-
tem can retain the ejecta from the stars with m ? 6.5M⊙.
We explore an expanded parameter space for 5M⊙ ? mesc ?
99M⊙. The scenario of Karakas et al. is equivalent to our sce-
nario with mesc = 6.5M⊙. The model with the largest mesc
represents the ordinary chemical evolution model which
takes account of all the mass ejecta from stars when cal-
culating the metallicity of the next generations. The model
with the smallest mescshows the extreme condition that the
ejecta from AGB stars dominates the chemical properties
of the next generations, hence the maximum-AGB model.
Then we define E(t), the ejecta gas mass at time t as
E(t) =
?mesc
mt
dmφ(m)(m − wm)ψ(t − τm), (7)
and EZ(t), the mass of the ejected metal at time t as
EZ(t) =?mesc
Another free parameter is RrMS which indicates the
mass ratio of the initial starburst i.e., for the former, red
population of ω Cen to the total system mass. We assume
that the formation of the former (red) population is essen-
tially instant and regulate the fraction of the initial star
formation by using the free parameter RrMS. We calculate
models for 0.5 ? RrMS ? 1.0. The model with RrMS = 1.0
means all gas goes into the star formation at time t = 0 and
the metallicity of the gas that forms the next generation
mt
dmφ(m)?mpmψ(t − τm) + (m − wm)ψ(t − τm)Zg(t − τm)?. (8)
Figure 2. The chemical abundances of the second stellar genera-
tion resulting from the maximum-AGB chemical evolution model.
The results are shown for different values of initial starburst mass
fractions, RrMS = 0.5–1.0 with ∆RrMS = 0.05. Dashed/solid
lines show the models that are incompatible/compatible with the
empirical mass fraction of the blue population (30 percent), for
the age difference of 1Gyr. The shaded region shows the results
for the age difference of 3Gyr. The chemical abundances of the
blue population of ω Cen are shown by the black dotted hori-
zontal line in each panel. Top: The helium enrichment parame-
ter. The mass fractions of the blue population are shown for the
models that are incompatible with the empirical requirement (30
percent). Middle: The helium content. Bottom: The metallicity.
of stars is solely influenced by the ejecta from the former
generation. Then we define the star formation rate as
ψ(t) = RrMS δ(t) (9)
where δ(t) is a Dirac delta function.
In effect we are testing a self-enrichment hypothesis
where the helium enrichment of the blue population is solely
due to the ejecta from the former (red) population. We
calculate the gas enrichment history for the predicted age
difference between the two extreme populations of ω Cen,
i.e. 1 − 3 Gyr (Lee et al. 2005; Stanford et al. 2006). We
also consider the observed number fraction of the bMS stars
(∼ 30percent) as an additional constraint. The rMS-to-bMS
ratio, 7:3, may not be a strong constraint if the bMS and rMS
populations formed in geographically different regions. For
example, the bMS stars are observed to be more centrally
concentrated than the rMS stars (Sollima et al. 2007), and
thus if one assumes that the original rMS stars had a bet-
ter chance of escaping from the system potential during the
dynamical encounters with the Milky Way galaxy over the

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E. Choi & S. K. Yi
Figure 3. The same as Figure 2, but for the spectroscopic mea-
surements [C/M] (top) and [N/M] (bottom).
Hubble time, the original mass ratio may have been higher.
We discuss the impact of this uncertainty in §3.
3 RESULTS
Figure 2 shows the helium and metal contents and the he-
lium enrichment parameter of the remaining gas after a 1-
Gyr evolution. The chemical properties of the models are
presented for our mesc – RrMS parameter space. The mod-
els assuming ∆t ∼ 1 Gyr (that is, the age difference be-
tween the old red and the young blue populations) are
shown by lines, while the shaded region shows the results
for ∆t ∼ 3 Gyr which is close to the upper limit on the
age difference between the two populations (Stanford et al.
2006). The solid/dashed lines show the models that are com-
patible/incompatible with the observed mass ratio, 7:3, re-
spectively. As shown in the top panel of Fig 2, the model
with mesc = 7M⊙ and RrMS = 1.0 has the largest value
of ∆Y/∆Z ∼ 10.5. This value is much higher than the
canonical value, ∆Y/∆Z ∼ 2 (Pagel & Portinari 1998) yet
still much lower than the value we are seeking for (i.e.,
∆Y/∆Z ∼ 70). In addition, the maximum helium con-
tent which can be achieved in this model is Y ∼ 0.33 (for
mesc ? 50M⊙ and RrMS = 1.0), also much smaller than
Y ∼ 0.4 estimated by the CMD analysis of ω Cen. Even
when we assume an extreme condition, mesc = 5M⊙, that is
hardly plausible in terms of physics, the extremely high val-
ues of helium and helium enrichment parameter suggested
for the bMS cannot be reproduced.
As mentioned in §2, the mass fraction of the bMS popu-
lation (30 percent) may be an upper limit. As seen in the top
and middle panels of Figure 2, models cannot reach the re-
quired values even when we lower the bMS mass fraction
constraint by a significant factor. The situation becomes
even worse when we compare the models to the spectro-
scopic line strengths. In Figure 3, we present the resulting
carbon and nitrogen contents of the models for the same
Figure 4. The calculated chemical abundance of the ejecta for
the entire (RrMS= 0.5 ∼ 1.0, ∆R = 0.05) parameter spaces of
the maximum-AGB model is represented. Filled circle and cross
represents the resulting value of mesc= 5,15,99M⊙model. Filled
circle indicates that the condition of mass ratio between rMS and
bMS is satisfied while cross denotes the model which do not meet
this condition. Shaded region shows the viable region of the total
parameter space, mesc = 5 − 99M⊙, which satisfies the mass
ratio condition. Reference values of blue population of ω Cen are
marked(filled star) in each panel.
mesc and RrMS parameter space as in Figure 2. This result
is important since the reference chemical properties of the
bMS are directly measured via spectroscopy, while the he-
lium abundance and the helium enrichment parameter are
deduced from CMD fits. The models with mesc ≈ 7M⊙ show
the largest value of ∆Y/∆Z (Figure 2 top panel) but do not
match the observed carbon content of the bMS (Figure 3
top panel). The horizontal, shaded band shows the observed
value for the bMS stars (Piotto et al. 2005). However, the
errors are not given and can be more significant than we esti-
mated from the literature (Piotto et al. 2005; Stanford et al.
2007). In case of the red population, [N/M] is poorly con-
strained; Piotto et al. (2005) mentioned that values of [N/M]
? 1.0 could also be compatible. We set [N/M] = 1 for the
red population. This assumption on the nitrogen abundance
of the rMS population may appear unphysically high con-
sidering the typical nitrogen production of stars, that is, an
order of [N/M]∼ −1 through 0, as shown in Figure 1. The
use of lower values of [N/M]rMS results in a substantially
greater mismatch in [N/M]bMS in this figure.
We present the resulting carbon, nitrogen and helium
abundances simultaneously in Figure 4. The three cases of
mesc = 5,15,99M⊙ are shown. Filled circle (cross) show the
models that are consistent (inconsistent) with the mass ratio
constraint, respectively. The shaded region shows the the
parameter space that satisfies the mass ratio constraint. The
observed chemical properties of the blue population stars of

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AGB effect on ω Cen
5
Figure 5. The same as Figure 4 but for the [C/M] and [N/M]
space.
ω Cen (filled star in each panel) are not reproduced under
any circumstance. Note the logarithmic scale of the axes.
Figure 5 shows that the models fail to match the spec-
troscopic data of Piotto et al. (2005). The empirical value
(star symbol with errors) measured using the VLT is in rea-
sonable agreement with the more recent measurements of
Stanford et al. (2007). As mentioned, the models are based
on the assumption of [C/M] = 0.0 and [N/M] = 1.0 for the
red population. The model values of [N/M]bMS may be con-
sidered upper limits. The mismatch is significant.
4DISCUSSION
We have used a chemical enrichment model to demonstrate
that the AGB ejecta of the red population cannot have pro-
duced the blue population of ω Cen. We tested a hypothesis
in which the massive star ejecta escape the potential well so
that the AGB effect can be maximised. But even in this ad
hoc scenario, models miserably fail to match the chemical
properties of the blue population of ω Cen. We use the bMS
mass fraction (30 percent) and the age difference between
the two populations (1–3Gyr) as constraints, but changing
them does not make the match any better. We as a result
confirm the result of Karakas et al. (2006).
The helium content of the AGB ejecta is basically too
small to be consistent with the value suggested for the
blue population of ω Cen, Y∼ 0.4, as we discussed earlier
(Choi & Yi 2007). Romano et al. (2007) has also confirmed
this using various yields from independent studies (e.g.
van den Hoek & Groenewegen
2002; Hirschi 2006; Meynet, Ekstrom, & Maeder 2006).
Such a high level of helium excess can be achieved only
through massive stars (Norris 2004; D’Antona et al. 2005;
Maeder & Meynet 2006). However, such massive stars also
produce a large amount of metals and thus resulting in a
small value of ∆Y/∆Z (Choi & Yi 2007). In this respect, a
variation in the initial mass function is useless. The escape
of the massive star ejecta through supernova-driven winds
would lead to a larger ∆Y/∆Z roughly up to 10; yet,
1997;Meynet & Maeder
still much lower than suggested by the CMD fits. Even if
we admit that the estimation for the helium abundance
via CMD fits is extremely difficult and so uncertain, the
maximum-AGB scenario cannot reproduce the carbon and
nitrogen properties spectroscopically observed and hence
probably more robust, either.
Foranalternative
tionscenarios(Tsujimoto, Shigeyama, & Suda
Newsham & Terndrop 2007) have been suggested and
deserve attention especially because they demand only
mildly-enhanced helium abundance for the blue popula-
tion. From a different avenue, Chuzhoy (2006) suggested
that the primordial helium may have been concentrated
in stellar-mass scales within minihalos of size roughly
consistent with dwarf galaxies. This aspect is particularly
appealing because ω Cen is often considered as a remnant
of a former dwarf galaxy and the multiple main sequences
are found in the most massive globular clusters in general.
This scenario offers an attractive solution to the helium
variation in first stars. However, it remains unclear how
long the extreme-helium clumps could last. The blue
population of ω Cen appears to be substantially enhanced
in metals as well and hence hardly qualifies as first stars
and younger than the red population by a couple of billion
years. Choi & Yi (2007) proposed the fluctuation in the
chemical properties of the initial starburst clumps during
and after the first star formation epoch. Given the impact
of the issue to the understanding of the galaxy formation,
a more detailed and realistic model calculation is necessary
until such scenarios become convincing.
solution,surfacepollu-
2007;
ACKNOWLEDGMENTS
We are grateful to Ignacio Ferreras, Leonis Chuzhoy, Young-
Wook Lee, Hansung Gim for useful comments.
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