Transition From Population III to Population II Stars

0.17 MB·English

by  Taotao Fang

Draftversion February2,2008
PreprinttypesetusingLATEXstyleemulateapjv.6/22/04
TRANSITION FROM POPULATION III TO POPULATION II STARS
Taotao Fang1 and Renyue Cen2
(Received;Revised; Accepted)
Draft versionFebruary 2, 2008
ABSTRACT
ThetransitionfromPopulationIIItoPopulationIIstarsisdeterminedbythepresenceofasufficient
amountofmetals,inparticular,oxygenandcarbon. Thevastlydifferentyieldsoftheserelevantmetals
betweendifferentinitialstellarmassfunctionswouldthencausesuchatransitiontooccuratdifferent
times. We show that the transition from Pop III to Pop II stars is likely to occur before the universe
5 can be reionized, if the IMF is entirely very massive stars (M ≥140M⊙). A factor of about 10 more
0 ionizingphotonswouldbeproducedinthecasewithnormaltop-heavyIMF(e.g.,M ∼10−100M⊙),
0
when such a transition occurs. Thus, a high Thomson optical depth (τ ≥ 0.11− 0.14) may be
2 e
indication that the Population III stars possess a more conventionaltop-heavy IMF.

n Subject headings: stars: abundances — supernovae: general — galaxies: formation — intergalactic
a medium — cosmology: theory — early universe
J

1
3 1. INTRODUCTION 2003; Mackey, Bromm, & Hernquist 2003). How-
ever, how massive Pop III stars are remains un-
Recentobservationsofthehighredshift(z >6)quasar
2 clear. While simulations have suggested that Pop
spectra from the Sloan Digital Sky Survey (SDSS) and
v the cosmic microwave background fluctuations from III stars may be more massive than 100M⊙ (“vary
5 the Wilkinson Microwave Anisotropy Probe (WMAP) massive star”, VMS; Abel, Bryan, & Norman 2000;
6
Bromm, Ferrara,Coppi, & Larson 2001), Tan & McKee
5 combine to paint a complicated reionization picture
(2004)arguethattakingintoaccountfeedbackprocesses
5 (Fan et al. 2001; Kogut et al. 2003). While it seems rel-
would likely limit the mass of the Pop III stars to the
0 atively secure to claim that the reionization process has
4 begunatz ≥10andends atz ∼6 (e.g., Fan et al.2001; range 30−100M⊙. Observationally, the VMS picture
is advocated by Oh, Nollett, Madau, & Wasserburg
0 Becker et al. 2001; Barkana 2002; Cen & McDonald
/ 2002), exactly when it starts and how it evolves are (2001) and Qian & Wasserburg (2002), based on
h the argument that the metal yield patterns from
yet unclear, although the overall picture is consistent
p
pair-instability supernova (PISN) explosion of VMS
- with a physically motivated double reionization model
o (Cen 2003; Wyithe & Loeb 2003) that was proposed progenitors (Heger & Woosley 2002) are consistent with
r before WMAP released its reionization measurement. observations (see also Wasserburg & Qian 2000; 2001).
t On the other hand, Tumlinson, Venkatesan,& Shull
s The conventional wisdom is that stars are primarily
a (2004)arguethatthe generalpatterninmetal-poorhalo
responsible for producing most of the ionizing pho-
: stars, especially the Fe-peak and r-process elements,
v tons. Unavoidably, there is a transition epoch from
favors the yield pattern of Type II supernovae (SNII)
i metal-free Population III (Pop III) to metal-poor
X Population II (Pop II) stars at some high redshift (see, with an initial mass function (IMF) above 10 M⊙ and
r e.g., Omukai 2000; Bromm, Ferrara,Coppi, & Larson without VMS (see also Daigne et al. 2004). Other
a arguments based on observations such as metallicities of
2001; Schneider, Ferrara, Natarajan,& Omukai 2002;
the intergalactic (IGM) at z ∼ 3−4 in the Lyα forest
Mackey, Bromm, & Hernquist 2003; Schneider et al.
(Venkatesan & Truran 2003) and cosmic star formation
2003; Bromm & Loeb 2003).
history (Daigne et al. 2004) also favor a SNII type
It is thought that Pop III stars may be much more
IMF. Umeda & Nomoto (2003) and Umeda & Nomoto
massive than Pop II stars. This expectation is based
(2003)arguethattheobservedmetalabundancepattern
on the physics of metal cooling. Lack of metals in
are better matched by core-collapsed supernova with
the gas at early times results in an absolute floor
temperature of gas at ∼ 100K, whereas a small but M⋆ = 10 − 50M⊙ through pair-instability supernova
explosion (Heger & Woosley 2002).
significant amount of metals would enable gas to
cool down to ∼ 10K. Consequently, Pop III stars It thus seems beneficial to explore possible differences
between different IMFs. In this Letter, we investigate
are expected to be much more massive than Pop
theissueofthetransitionfromPopIII toPopII.Specif-
II stars (Carr, Bond, & Arnett 1984; Larson 1998;
ically,followingBromm & Loeb(2003),wenotethatthe
Abel, Bryan, & Norman 2000; Hernandez & Ferrara
transitionfromPopIIItoPopIIisdictatedbyefficiency
2001; Bromm, Ferrara,Coppi, & Larson
of cooling by a limited number of species, in particu-
2001; Bromm, Kudritzki, & Loeb
lar, C and O. Thus, it is the amount of C and O, not
2001; Nakamura & Umemura 2001;
necessarily the total amount of “metals”, that deter-
Bromm, Coppi, & Larson 2002; Omukai & Palla
mines the transition. While the ionizing photon produc-
1 Department of Astronomy, UniversityofCalifornia,Berkeley, tion efficiency turns out to be quite comparable in both
CA94720; ChandraFellow cases, either with a VMS IMF or a more normal top-
2 Department of Astrophysical Sciences, Princeton University, heavy IMF (e.g., Tumlinson, Venkatesan,& Shull 2004),
PeytonHall,IvyLane,Princeton,NJ08544
2 Fang & Cen
they have very different metal patterns in the exploded
final products. In PISN case the supernova ejecta is en-
riched by α-elements, whereas the major products of
SNII are hydrogen and helium with a small amount
of heavy elements (see, e.g., Woosley & Weaver 1995;
Heger & Woosley 2002). Consequently, the transition
from Pop III to Pop II stars should occur at different
times. We show that a normal top-heavy IMF is pre-
ferred to VMS and probably required if Pop III stars
were to reionize the universe at high enough redshift.
2. TRANSITIONFROMPOPIIITOPOPII
We firstdefine f asthe baryonfractionthathas been
⋆
processed through Pop III stars, f ≡ M /M , where
⋆ III b
M and M are total baryonic mass and the baryonic
b III
massinPopIIIstars,respectively. Wealsodefinetheto-
tal ionization photons (hν ≥ 13.6eV) produced per unit
mass of Pop III stars as < N > photonsM−1. For
ph ⊙
completeness we show in Figure 1 the time-integrated
ionization photons per solar mass emitted during the
lifetime of a Pop III star vs. its initial mass M ,
⋆
adoptedfromSchaerer(2002). Theverticaldottedlineat Fig. 1.— Ionization photons produced during the lifetime of
a zero-metallicity Pop III star as a function of its initial mass
M⋆ =140M⊙ is to distinguish between PISN and SNII. M⋆, adopted from Schaerer (2002). The dotted vertical line in-
Clearly,formostofthemassrange(80.M⋆ <260M⊙), dicatesM⋆=140M⊙. Evidently,theproducedionizationphotons
the ionizing photons produced during the lifetime of the isnearlyaconstant forbothPISNandSNIIcases.
star is ∼ 1062photonsM−1. This lifetime-integrated
⊙
number of ionizing photons varies only about a factor
of less than 2 when the initial mass is ∼ 20M⊙. It is metallicity of element i, Zi :
IGM
because the total ionizing photon production of a short-
µy
lifetime VMS is boosted by its higher production rate. Zi = i N . (2)
However, we should keep in mind that photon produc- IGM <Nph >mH ion
tionratecouldbeimportantifthetypicalrecombination Zero-metallicity Pop III stars with different initial
time scale is shorter than the lifetime of Pop III stars. masseshavedistinctivepatternoffinalmetalproductions
The typical lifetimes of a 200 and 25 M⊙ Pop III stars (see, e.g., Heger & Woosley 2002). For stars with initial
caorem∼bin2a.2t×ion10t6imanedsc6a.l5e×is1r0o6uygrhsly(Stcrhecae∼re1r0270(C02H).IIT/1h0e)r−e1- mtharsosuegsh1t0yp.e IMI⋆su.per4n0oMva⊙e,xnpeloustiroonn. sTtahres maraejofroirtmyeodf
yrs at redshift z ∼ 17, where CHII is the clumping fac- the ejecta are hydrogen and helium, with small amount
tor of H II regions (Ricotti & Ostriker 2004). While in of heavy metals. Between 40 . M⋆ . 100M⊙, black
generaltrec islongerthanthelifetimeofPopIIIstars,at holes form through direct collapse of the star. At M⋆ ∼
some overdense regions when CHII > 20 the lifetime of 100M⊙, the electron-positron pair instability starts to
a small mass star could be longer than trec, and in this dominate, but if M⋆ .140M⊙, an iron core will still be
case more than 1 ionizing photon are necessary to ion- formed and eventually collapse to a black hole without
ize the entire IGM. Having this caution in mind, in the any metal productions. When 140.M⋆ . 260M⊙, the
following we assume that all the Pop III stars produce pulsationinducedbythepairinstabilityissoviolentthat
about the same amount of ionizing photons in their life- one single pulse disrupts the entire star and eject abun-
time and roughly 1 ionizing photon per atom is needed dant α-elements. At above 260M⊙ again black holes
to reionize the universe. Using relevantnumbers andas- will form. An upper limit of 500M⊙ of a Pop III star
suming a mean atom weight of µ = 0.76, we find that that can be formed from accretion into primordial pro-
the number of the ionizing photons per hydrogen atom tostar was recently found by Bromm & Loeb (2004) via
produced, denoted as Nion, is three-dimensional numerical simulation. It is important
to note that essentially all metals are produced for mass
N =11 µ −1 f⋆ <Nph > . ranges of 10 – 40 M⊙ and/or 140 – 260 M⊙. Pop III
ion (cid:16)0.76(cid:17) (cid:18)10−4(cid:19) 1062photonsM−⊙1! sptaatrtserwnitohfinmethtaelsse, twwhoicmhawsisllrhanavgeesgpreraotduimcepadcisttionncttihvee
(1)
Letus define y as the yield ofelement i,y ≡M /M , important metal cooling agents, namely, C and O.
i i i ⋆
We study four types of IMFs: two types for PISN and
where M is the mass of element i produced by the ini-
i twotypes forType II SN.AnIMFisdefinedasΨ(M)≡
tial stellar mass M . Assuming metals produced by su-
pernova explosion c⋆an be effectively transported out of Ψ0M−Γ with Ψ0
the host halos and uniformly pollute the intergalactic m2
medium (IGM), then the IGM metallicity of element i, Ψ0M−ΓdM =1. (3)
Zi = f y , where f is the baryon fraction defined Zm1
IGM ⋆ i ⋆
above. Substituting f from Eq. 1, we can then relate Thefour typesare: (1)PISNmodel1,with140.M .
⋆ ⋆
the ionization photon per H atom, Nion, to the IGM 260M⊙; (2) PISN model 2, 100 . M⋆ . 260M⊙; (3)
Transtition from Pop III to Pop II 3
Type II Supernova model 1, with 10 . M⋆ . 140M⊙;
and (4) Type II Supernova model 2, with 30 . M .
⋆
140M⊙. Model (2) is introduced to see how sensitive
the metal yield of PISN model depends on various mass
limits. Model (4) is motivated by the suggestion of
Tan & McKee (2004) that the first stars should have
masses between 30−100M⊙. To avoid the degeneracy
between the IMF index and mass limits we adopted a
consistentIMFindexofΓ=1.5amongallthefourmod-
els.
ForeachIMFwe compute the metalyield. As pointed
out by Bromm & Loeb (2003) metal cooling at low tem-
perature (T ≤100K) is dominated by fine-structure line
coolingofCIIandOI,weconcentrateonthemetalyield
of C and O. The yield can be calculated through
m2
y = Ψ(M)Y (M)dM, (4)
i i
Zm1
where the subscript i represents C or O, and Y (M) is
i
defined as the ratio of the mass fraction of the element
i in solar units, in this way Y (M) is one half of the
i
production factors defined in Heger & Woosley (2002).
For the PISN type IMF we use the production factors
of Heger & Woosley (2002). For SNII type IMF model
1 and 2 we adoptthe production factorscalculated from
Woosley & Weaver (1995) model Z12A, Z15A, ... and
Z30B, Z35B, .... series, respectively.
With metal yield y and ionizing photon produc-
i
tion rate < N >, we can now compute the ele-
ph
ment metallicity Zi as a function of ionizing pho- Fig. 2.—Oxygen(toppanel)andCarbon(bottompanel)metal-
tons per hydrogenIaGtMom through Eq. 2. The results licities as a function of the ionizing photons per H atom. The
solidand dotted lines represent PISN model 1 and 2, dashed and
are shown in Figure 2. The top and bottom pan-
dot-dashed lines are for SNII model 1 and 2, respectively. The
els show the oxygen and carbon metallicities, respec- horizontalshadowedareasshowthecriticaltransitionmetallicities
tively. The metal abundance in this definition is rel- andtheirerrorsfromBromm&Loeb(2003).
ative to the solar value, i.e., [O/H] = log (n /n ) −
10 O H
log10(nO/nH)⊙. The solid and dotted lines represent
PISN model 1 and 2, dashed and dot-dashed lines are
for SNII model 1 and 2, respectively. The horizontal
shadowed areas show the critical transition metallici- Pop III stars will be able to ionize the universe alone,
ties Zcrit and their errors from Bromm & Loeb (2003), unless ionizing photon escape fraction is ≥ 20% and/or
[C/H]crit ≃ −3.5 ± 0.1 and [O/H]crit ≃ −3.05 ± 0.2, metal enrichment is very inefficient.
respectively. The free-fall time scale for gas clump
is t ≈ 5 × 105(n /104cm−3)−1/2yrs, and the crit- 3. CONCLUSIONS
ff H
ical transition metallicities are obtained by equating Based on the consideration of cooling due to C and O
the cooling time at temperature T = 100K (below atlowtemperatures(T <100K),wenotethatitmaybe
which metal cooling dominates) to tff for a gas den- expectedthatthe transitionfromPopIII toPopII stars
sity of n = 104cm−3 (Abel, Bryan, & Norman 2000; should occur when ∼ 1 ionizing photon per H atom is
H
Bromm, Coppi, & Larson 2002). produced, if the IMF is entirely VMS. A factor of about
Immediately, we see that the transition from Pop III 10 more ionizing photons would be produced in the case
to Pop II occurs much earlier in Model 1 and 2 than with normal top-heavy IMF (e.g., M ∼ 10−100M⊙),
in Models 3 and 4. We see that about 1.0−3.1 ioniz- when such a transition occurs. Thus, it will be much
ing photons per H atom are produced in PISN Model 1, more difficult, if not impossible, to achieve an earlier
3−6 photons in PISN model 2, whereas 8.6−14 ion- (z ≫ 10) reionization in the former case. Therefore, if
izing photons per H atom is produced in SN II Model future WMAP data firm up the Thomson optical depth
1 and 2. Not all ionizing photons can escape into the to τ ≥ 0.11−0.14, one may be forced to adopt a more
IGM, nor do the metals. Metal enrichment of the IGM conventional top-heavy IMF. If minihalos were largely
may be expected to be inhomogeneous, which perhaps responsible for producing ionizing photons at high red-
would yield a higher effective metal enrichment in star shift, then an IMF with VMS may be still viable, as
formationregionsifgalaxyformationisbiased. The fact the ionizing photon escape fraction from minihalos may
supernovaexplosionsinthePISN(Model1)maybemore well exceed 50%, shown by the recent radiation hydro-
energeticthaninthe othertwomodels maysuggestthat dynamic simulations (Whalen, Abel, & Norman 2004;
perhaps more metals could be transported to the IGM Kitayama,Yoshida, Susa, & Umemura 2004).
in the former case. It thus seems improbable that PISN We assume that metals can efficiently get mixed
4 Fang & Cen
with the general IGM and adopted a simplified Yoshida, Bromm, & Hernquist 2004). The exact
picture that metals produced by Pop III stars are effect is, however, unclear, when coupled with spatially
uniformly distributed in the IGM. In the PISN case non-uniform galaxy and star formation.
Bromm, Yoshida, & Hernquist (2003) found for a WeemphasizethataconventionalIMFmaynotbethe
supernova explosion with an energy of ∼ 1053 ergs, onlywaytoalleviatetheconflictbetweenthemetalyield
at least 90% of metals can be effectively transported ofthePopIIIstarsandthenumberofionizationphotons
into surrounding IGM. Yoshida, Bromm, & Hernquist they produced. Ricotti & Ostriker (2004) argued that
(2004) discussed a simplified VMS IMF (all Pop III most Pop III stars should collapse into black holes to
stars have mass of 200 M⊙ and explode as PISN): avoidproducing too much metals with added benefits of
they trace the star formation history and calculate additional accretion produced energy.
the mean number of ionization photons per atom and
the mean metalicity of the IGM. Their results are
consistent with results from our PISN model 1 and We thanks the anonymous referee for many helpful
2. The derived τ falls short of WMAP result when comments. We gratefully acknowledge financial support
e
constrained by a critical metalicity of [Z/H] = −3.3, bygrantsAST-0206299,AST-0407176andNAG5-13381.
this is consistent with our conclusion that a VMS T. Fang was supported by the NASA through Chandra
IMF may not be favored by recent WMAP result. Postdoctoral Fellowship Award Number PF3-40030 is-
However, metal mixing is most likely inhomogeneous, suedbytheChandraX-rayObservatoryCenter,whichis
that could affect the transition from Pop III to Pop II operatedby the Smithsonian AstrophysicalObservatory
stars (see, e.g., Scannapieco, Schneider, & Ferrara for and on behalf of the NASA under contract NAS8-
2003; Mackey, Bromm, & Hernquist 2003; 39073.
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