Very Massive Stars in High-Redshift Galaxies
Mon. Not. R. Astron. Soc. 000, 1–11 (2006) Printed 11 November 2021 (MN LaTEX style file v2.2)
Very Massive Stars in High-Redshift Galaxies
Mark Dijkstra1⋆ and J. Stuart B. Wyithe1†
1School of Physics, University of Melbourne, Parkville, Victoria, 3010, Australia
11 November 2021
ABSTRACT
A significant fraction of Lyα emitting galaxies (LAEs) at z > 5.7 have rest-frame
equivalent widths (EW) greater than∼ 100Å. However only a small fraction of the Lyα
flux produced by a galaxy is transmitted through the IGM, which implies intrinsic Lyα
EWs that are in excess of the maximum allowed for a population-II stellar population
having a Salpeter mass function. In this paper we study characteristics of the sources
powering Lyα emission in high redshift galaxies. We propose a simple model for Lyα
emitters in which galaxies undergo a burst of very massive star formation that results
in a large intrinsic EW, followed by a phase of population-II star formation with a
lower EW. We confront this model with a range of high redshift observations and
find that the model is able to simultaneously describe the following eight properties
of the high redshift galaxy population with plausible values for parameters like the
efficiency and duration of star formation: i-iv) the UV and Lyα luminosity functions
of LAEs at z=5.7 and 6.5, v-vi) the mean and variance of the EW distribution of Lyα
selected galaxies at z=5.7, vii) the EW distribution of i-drop galaxies at z∼6, and
viii) the observed correlation of stellar age with EW. Our modeling suggests that the
observed anomalously large intrinsic equivalent widths require a burst of very massive
star formation lasting no more than a few to ten percent of the galaxies star forming
lifetime. This very massive star formation may indicate the presence of population-
III star formation in a few per cent of i-drop galaxies, and in about half of the Lyα
selected galaxies.
Key words: cosmology–theory–galaxies–high redshift
1 INTRODUCTION
Narrow band searches for redshifted Lyα lines have
discovered a large number of Lyα emitting galaxies
with redshifts between z = 4.5 and z = 7.0 (e.g.
Hu & McMahon 1996; Hu et al. 2002; Malhotra & Rhoads
2002; Kodaira et al. 2003; Dawson et al. 2004; Hu et al.
2004; Stanway et al. 2004; Taniguchi et al. 2005;
Westra et al. 2006; Kashikawa et al. 2006; Shimasaku et al.
2006; Iye et al. 2006; Stanway et al. 2007; Tapken et al.
2007). The Lyα line emitted by these galaxies is very
prominent, often being the only observed feature. The
prominence of the Lyα line is quantified by its equivalent
width (EW), defined as the total flux of the Lyα line, FLyα
divided by the flux density of the continuum at 1216 Å:
EW≡ FLyα/f1216 . Throughout this paper we refer to the
rest-frame EW of the Lyα line (which a factor of (1 + z)
lower than the EW in the observers frame).
Approximately 50% of Lyα emitters (hereafter LAEs)
at z = 4.5 and z = 5.7 have lines with EW∼ 100 − 500 Å
⋆ E-mail:dijkstra@physics.unimelb.edu.au
† E-mail:swyithe@physics.unimelb.edu.au
(Dawson et al. 2004; Hu et al. 2004; Shimasaku et al. 2006).
For comparison, theoretical studies conclude that the maxi-
mum EW which can be produced by a conventional popula-
tion of stars is 200-300 Å. Moreover, this maximum EW can
only be produced during the first few million years of a star-
burst, while at later times the luminous phase of Lyα EW
gradually fades (Charlot & Fall 1993; Malhotra & Rhoads
2002). Therefore, observed EWs lie near the upper envelope
of values allowed by a normal stellar population.
The quoted value for the upper envelope of EW∼ 200−
300 Å corresponds to the emitted Lyα flux. However not
all Lyα photons are transmitted through the IGM, and we
expect some attenuation. Within the framework of a Cold
Dark Matter cosmology, gas surrounding galaxies is signifi-
cantly overdense, and possesses an infall velocity relative to
the mean IGM (Barkana 2004). As a net result, the IGM
surrounding high redshift galaxies is significantly opaque to
Lyα photons. Indeed it can be shown that for reasonable
model assumptions, only ∼ 10− 30% of all Lyα photons are
transmitted through the IGM (Dijkstra et al. 2007). As a
result, the intrinsic Lyα EW emitted by high redshift LAEs
is systematically larger than observed. Indeed, this observa-
tion suggests that a significant fraction of LAEs at z > 4.5
c© 2006 RAS
http://arxiv.org/abs/0704.1671v2
2 Mark Dijkstra & J. Stuart B. Wyithe
have intrinsic EWs that are much larger than can possibly
be produced by a conventional population of young stars.
One possible origin for this large EW population is pro-
vided by active galactic nuclei (AGN), which can have much
larger EWs due to their harder spectra (e.g. Charlot & Fall
1993). However, large EW LAEs are not AGN for several
reasons: (1) the Lyα lines are too narrow (Dawson et al.
2004) (2) these objects typically lack high–ionisation state
UV emission lines, which are symptomatic of AGN activity
(Dawson et al. 2004), and (3) deep X-Ray observations of
101 Lyα emitters by Wang et al. (2004, also see Malhotra et
al. 2003, Lai et al, 2007) revealed no X-ray emission neither
from any individual source, nor from their stacked X-Ray
images.
Several recent papers have investigated the stel-
lar content of high-redshift LAEs by comparing stellar
synthesis models with the observed broad band colors
(Finkelstein et al. 2007). These comparisons are often aided
by deep IRAC observations on Spitzer (Lai et al. 2007;
Pirzkal et al. 2007). In this paper we take a different ap-
proach. Instead of focusing on individual galaxies, our goal
is to provide a simple model that describes the population
of Lyα emitting galaxies as a whole. This population is de-
scribed by the rest-frame ultraviolet (UV) and Lyα lumi-
nosity functions (LFs) at z = 5.7 and z = 6.5 , and the
Lyα EW distribution at z = 5.7 (Shimasaku et al. 2006;
Kashikawa et al. 2006). The sample of high-redshift LAEs
is becoming large enough that meaningful constraints can
now be placed on simple models of galaxy formation.
The outline of this paper is as follows: In § 2 -§ 5
we describe our models. In § 6 we discuss our results,
and compare with results from stellar synthesis models, be-
fore presenting our conclusions in § 7. The parameters for
the background cosmology used throughout this paper are
Ωm = 0.24, ΩΛ = 0.76, Ωb = 0.044, h = 0.73 and σ8 = 0.74
(Spergel et al. 2007).
2 THE MODEL
Dijkstra et al. (2007b) found that the observed Lyα LFs at
z = 5.7 and z = 6.5 are well described by a model in which
the Lyα luminosity of a galaxy increases in proportion to
the mass of its host dark matter Mtot. One can constrain
quantities related to the star formation efficiency from such
a model (also see Mao et al. 2007; Stark et al. 2007).
However, it is also possible to obtain constraints from
the rest-frame UV-LFs. In contrast to the Lyα LF, the UV-
LF is not affected by attenuation by the IGM, which allows
for more reliable constraints on quantities related to the star
formation efficiency. In the first part of this paper (§ 3-§ 4)
we present limited modeling to illustrate parameter depen-
dences, using the UV-LF to constrain model parameters re-
lated to star formation efficiency and lifetime. These model
parameters may then be kept fixed, and the Lyα LFs and
EW distributions used to constrain properties of high red-
shift LAEs such as their intrinsic Lyα EW and the fraction
of Lyα that is transmitted through the IGM. Later, in § 5,
we present our most general model, and fit to both the UV
and Lyα LFs, as well as the EW distribution, simultane-
ously, treating all model parameters as free.
3 MODELING THE UV AND LYα
LUMINOSITY FUNCTIONS.
3.1 Constraints from the UV-LF.
We begin by presenting a simple model for the UV-LF
(Wyithe & Loeb 2007; Stark et al. 2007). In Figure 1 we
show the rest-frame UV-LFs of LAEs at z = 5.7 and
z = 6.5 (Shimasaku et al. 2006; Kashikawa et al. 2006). We
use the following simple prescription to relate the ultravi-
olet flux density emitted by a galaxy, f1350, to the mass
of its host dark matter Mtot. The total mass of baryons
within a galaxy is (Ωb/Ωm)Mtot, of which a fraction f∗
is assumed to be converted into stars over a time scale of
tsys = ǫDCthub. Here, ǫDC is the duty cycle and thub(z), the
Hubble time at redshift z. This prescription yields a star
formation rate of Ṁ∗ = f∗(Ωb/Ωm)M/tsys. The star forma-
tion rate can then be converted into f1350 using the relation
f1350 = 7 × 1027(Ṁ∗/[M⊙/yr]) erg s−1 Hz−1 (Kennicutt
1998). The precise relation is uncertain but differs by a fac-
tor of less than 2 between a normal and a metal-free stel-
lar population (see e.g. Loeb et al. 2005). Uncertainty in
this conversion factor does not affect our main conclusions.
The presence of dust would lower the ratio of f1350 and Ṁ∗,
which could be compensated for by increasing f∗. However,
Bouwens et al. (2006) found that dust in z = 6.0 Lyman
Break Galaxies (LBGs) attenuates the UV-flux by an aver-
age factor of only 1.4 (and dust obscuration may be even
less important in LAEs, see § 6.3). Since this is within the
uncertainty of the constraint we obtain on f∗, we ignore ex-
tinction by dust. The number density of LAEs with UV-flux
densities exceeding f1350 is then given by
N(> f1350) = ǫDC
, (1)
where MUV is the mass that corresponds to the flux den-
sity, f1350 (through the relations given above). The func-
tion dn/dM is the Press-Schechter (1974) mass function
(with the modification of Sheth et al. 2001), which gives the
number density of halos of mass M (in units of comoving
Mpc−3)1. The free parameters in our model are the duty
cycle, ǫDC, of the galaxy, and the fraction of baryons that
are converted into stars, f∗. We calculated the UV-LF for
a grid of models in the (ǫDC, f∗)-plane, and generated like-
lihoods L[P ] = exp[−0.5χ2], where χ2 =
PNdata
(modeli −
datai)
2/σ2i , in which datai and σi are the i
th UV-LF data
point and its error, and modeli is the model evaluated at the
ith luminosity bin. The sum is over Ndata = 8 data points.
The inset in Figure 1 shows the resulting likelihood contours
1 Our model effectively states that the star formation rate in a
galaxy increases linearly with halo mass. This is probably not cor-
rect. To account for a different mass dependence we could write
the star formation rate as Ṁ∗ ∝ M
β , where β is left as a free pa-
rameter. However, the range of observed luminosities span only 1
order of magnitude, and we will show that the choice β = 1 pro-
vides a model that describes the observations well. Furthermore,
the duty cycle ǫDC may be viewed as the fraction of dark mat-
ter halos that are currently forming stars. The remaining fraction
(1− ǫDC) of halos either have not formed stars yet, or are evolv-
ing passively. In either case, the contribution of these halos to the
UV-LF is set to be negligible.
c© 2006 RAS, MNRAS 000, 1–11
Very Massive Stars in High-z Galaxies 3
Figure 1. Constraints on the star formation efficiency from the
observed rest-frame UV-luminosity functions of LAEs at z = 5.7
(red squares) and z = 6.5 (blue circles) (Shimasaku et al. 2006;
Kashikawa et al. 2006). In our best-fit model, a faction f∗ ∼
0.06 of all baryons is converted into stars over a time-scale of
ǫDCthub ∼ 0.03 Gyr (see text). The inset shows likelihood con-
tours in the (ǫDC, f∗)-plane at 64%, 26% and 10% of the peak
likelihood. Also shown on the upper horizontal axis is the mass
corresponding to MAB,1350 in the best-fit model.
in the (ǫDC, f∗)-plane at 64%, 26% and 10% of the peak like-
lihood. The best fit model has (ǫDC, f∗) = (0.03, 0.06) and is
plotted as the solid line. In the following sections we assume
this combination of f∗ and ǫDC.
3.2 Constraints from the Lyα LF.
We next model the Lyα LF, beginning with the best-fit
model of the previous section. The number density of LAEs
at redshift z with Lyα luminosities exceeding Tα × Lα is
given by (Dijkstra et al. 2007b)
N(> Tα × Lα, z) = ǫDC
(z), (2)
where the Lyα luminosity and host halo mass, Mα are re-
lated by
Tα × Lα = Lα
Mα(M⊙)
tsys(yr)
Tα. (3)
In this relation, Tα is the IGM transmission multiplied by
the escape fraction of Lyα photons from the galaxy, and
Lα = 2.0 × 1042 erg s−1/(M⊙ yr−1), is the Lyα luminos-
ity emitted per unit of star formation rate (in M⊙ yr
Throughout, Lα,42 denotes Lα in units of 1042 erg s−1/(M⊙
yr−1). We have taken Lα,42 = 2.0, which is appropriate for
a metallicity of Z = 0.05Z⊙ and a Salpeter IMF (Dijkstra
et al, 2007). Note that when comparing to observed lumi-
nosities (Shimasaku et al. 2006; Kashikawa et al. 2006), we
have replaced Lα with Tα×Lα. This is because the observed
luminosities have been derived from the observed fluxes by
assuming that all Lyα emerging from the galaxy was trans-
mitted by the IGM, whereas there is substantial absorption
(e.g. Dijkstra et al. 2007). The product Tα×Lα may be writ-
ten as Tα×Lα = 4πd2L(z)Sα, where Sα is the total Lyα flux
Figure 2. Joint constraints on the IGM transmission from the
observed Lyα and rest-frame UV LFs of LAEs at z = 5.7
(Shimasaku et al. 2006) and z = 6.5 (Kashikawa et al. 2006). The
red squares and blue circles represent the data at z = 5.7 and
z = 6.5. Using the model that best describes the UV-LFs with
(fstar, ǫDC) = (0.06, 0.03) we fit to the observed Lyα LF. The
only free parameter of our model was the fraction of Lyα that
was transmitted through the IGM at z = 5.7, Tα,57 (see text).
Shown in the inset is the likelihood for Tα,57, normalised to a
peak of unity. The figure shows that in order to simultaneously
fit the Lyα and UV-LFs, only ∼ 30% of Lyα photons are trans-
mitted through the IGM. The best fit models are overplotted as
the solid lines.
detected on earth and dL(z) is the luminosity distance to
redshift z. The product Tα × Lα may therefore be viewed
as an effective luminosity inferred at earth. Furthermore,
the selection criteria used by Shimasaku et al. (2006) and
Kashikawa et al. (2006) limits these surveys to be sensitive
to LAEs with EW >∼10Å. In the reminder of this paper, the
EW of model LAEs is always larger than this EWmin, and
we need not worry about selection effects when comparing
our model to the data.
In this section, we set the transmission at z = 6.5 (de-
noted by Tα,65) to be a factor of ∼ 1.2 lower2 than at z = 5.7
(denoted by Tα,57). This ratio is the median of the range
found by Dijkstra et al. (2007). We then calculated the Lyα
LF for a range of Tα,57, and generated likelihoods L[P ] =
exp[−0.5χ2], where χ2 =
Ndata
(modeli − datai)2/σ2i , for
each model. Here, datai and σi are the i
th data point and its
error, and modeli is the model evaluated at the i
th luminos-
ity bin. The sum is over Ndata = 6 points at each redshift.
In Figure 2 we show the Lyα luminosity functions at z = 5.7
and z = 6.5. The red squares and blue circles represent data
from Shimasaku et al. (2006, z = 5.7) and Kashikawa et al.
(2006, z = 6.5), respectively.
The likelihood for Tα,57 (normalised to a peak of unity)
is shown in the inset. The best fit model is overplotted
as the solid lines, for which the value of the transmission
is Tα,57 = 0.30. The modeling presented in this and the
2 For our primary results in § 5 we allow this ratio to be a free
parameter. The results presented in this section is not sensitive
to the precise choice of the ratio of IGM transmission at z = 5.7
and z = 6.5.
c© 2006 RAS, MNRAS 000, 1–11
4 Mark Dijkstra & J. Stuart B. Wyithe
previous section therefore suggests that, in order to simul-
taneously fit the Lyα and UV luminosity functions, only
∼ 30% of the Lyα can be transmitted through the IGM. This
transmission is in good agreement with the results obtained
by Dijkstra et al. (2007), who modeled the transmission di-
rectly and found that for reasonable model parameters the
transmission must lie in the range 0.1 <∼Tα <∼0.3.
3.3 The Predicted Equivalent Width
While in agreement with the observed LFs, the model de-
scribed in § 3.2 does not reproduce the very large ob-
served equivalent widths. The Lyα luminosity can be rewrit-
ten in terms of the star formation rate (Ṁ∗) and EW as
Lα = 2.0 × 1042 erg s−1Ṁ∗(M⊙/yr)(EW/160 Å). Here we
have used the relation Lα =EW×[ναf(να)/λα], where f(να)
is the flux density in erg s−1 Hz−1 at να, and where we
denoted the Lyα frequency and wavelength by να and λα
respectively. Furthermore, we assumed the spectrum to be
constant between 1216 Å and 1350 Å. For Lα,42 = 2.0, we
find a best fit model that predicts LAEs to have an observed
EW of Tα × 160 Å ∼ 50 Å. This value compares unfavor-
ably with the observed sample that includes EWs exceed-
ing ∼ 100 Å in ∼ 50% of cases for Lyα selected galaxies
(Shimasaku et al. 2006).
Thus although our simple model can successfully repro-
duce the observed Lyα and UV luminosity functions, the
model fails to reproduce the observed large EW LAEs. This
discrepancy cannot be remedied by changing the intrinsic
Lyα emissivity of a given galaxy, Lα: increasing Lα would
be simply be compensated for by a lower Tα and vice versa.
In the next section we discuss a simple modification of this
model that aims to alleviate this discrepancy.
4 THE FLUCTUATING IGM MODEL
The model described in § 3 assumed that the Lyα flux of
galaxies was subject to uniform attenuation by the IGM.
In this section we relax this assumption and investigate the
predicted EWs in a more realistic IGM where transmission
fluctuates between galaxies. We refer to this model as the
’fluctuating IGM’ model. In this model, a larger transmis-
sion translates to a larger observed equivalent width. As a
result, galaxies with large Tα are more easily detected, and
the existence of these galaxies may therefore affect the ob-
served EW-distribution for Lyα selected galaxies, even in
cases where they comprise only a small fraction of the in-
trinsic population. In this section we investigate whether
this bias could explain the anomalously large observed EW.
We assume a log-normal distribution for Tα,57,
P (u)du =
× exp
“−(u− 〈u〉)2
du, (4)
where 〈u〉 = log〈Tα,57〉 is the log (base 10) of the mean
transmission and σu is the standard deviation in log-space.
Throughout this section we drop the subscript ’57’. Eq (4)
may be rewritten in the form
f(> u) =
u− 〈u〉√
, (5)
Figure 3. Same as Figure 2. However, instead of assuming a
single value of IGM transmission Tα,57, we assumed a log-normal
distribution of IGM transmission with a mean of log Tα,57 and
standard deviation of (in the log) σu (see text). This reflects the
possibility that the IGM transmission fluctuates between galaxies.
The inset shows likelihood contours for (log Tα,57, σu). Increasing
σu flattens the luminosity function (and moves it upward), which
is illustrated by the model LFs shown as solid lines, for which
we used (Tα,57, σu) = (0.27, 0.2) (shown as the thick black dot
in the inset). The best-fit model to the data has σu ∼ 0 (which
corresponds to the model shown in Figure 2).
which gives the fraction of LAEs with log Tα > u. The num-
ber density of LAEs is then given by
N(> Tα ×Lα) = ǫDC
f(> u(Tα ×Lα,M)) (6)
where
u(Tα × Lα,M) = log
“Tα × Lα
LαṀ∗
. (7)
Eq (6) differs from Eq (2) in two ways: (1) there is no lower
integration limit, and (2) there is an additional term f(>
u). These two differences reflect the facts that all masses
contribute to the number density of LAEs brighter than Tα×
Lα, and that lower mass systems require larger transmissions
(Eq 7) which are less common (Eq 5). In the limit σu → 0,
the function f(> u) ’jumps’ from 0 to 1 at Mmin (Eq 3),
which corresponds to the original Eq (2).
In this formalism we may also write the number density
of LAEs with transmission in the range u±du/2 ≡ log Tα ±
d log Tα
, which is given by
N(u)du = P (u)du
Mmin(u)
. (8)
Here Mmin(u) is the minimum mass of galaxies that can
be detected with a transmission in the range u± du/2 (for
Mtot < Mmin the total flux falls below the detection thresh-
old). The number density of LAEs with transmission in the
range u ± du/2 may be used to find the number density of
LAEs with equivalent widths in the range log EW± d log EW
via the relation EW= 160Tα Å (for the choice Lα,42 = 2.0,
see § 3.2). Eq (8) shows that the observed equivalent width
distribution takes the shape of the original transmission dis-
tribution, modulo a boost which increases towards larger
As in § 3.2 we assume the best-fit model parameters
c© 2006 RAS, MNRAS 000, 1–11
Very Massive Stars in High-z Galaxies 5
for ǫDC and f∗ derived from the UV-LFs determined in
§ 3.1. We calculate model Lyα LFs on a grid of models in
the (σu, 〈Tα〉)-plane, and generate likelihoods following the
procedure outlined in § 3.2. The results of this calculation
are shown in Figure 3 where we plot the Lyα LFs together
with likelihood contours in the (σu, 〈Tα〉)-plane (inset). The
best-fit models favor no scatter in Tα (σu ∼ 0). The reason
for this is that for any given model, a scatter in Tα serves
to flatten the model LF. However, the observed Lyα LF is
quite steep, and as a result the data prefers a model with no
scatter. Furthermore, a scatter in Tα results in a model LF
that lies above the original (constant transmission) LF at
all Tα × Lα. This also explains the shape of the contours in
the (σu, 〈Tα〉)-plane; increasing σu must be compensated for
by lowering 〈Tα〉). To illustrate the impact of a fluctuating
Tα, the model LFs shown in Figure 3 are not those of the
best-fit model, but of a model with (〈Tα〉, σu) = (0.27, 0.2).
Figure 4 shows the observed EW-distribution (solid
line) at z = 5.7 associated with the Lyα LFs shown in Fig-
ure 3. This model may be compared to the observed distri-
bution (shown as the histogram, data from Shimasaku et al,
2006). The upper horizontal axis shows the transmission cor-
responding to each equivalent width. The dotted line shows
the distribution of transmission (given by Eq 4). Note that
the range of transmissions shown in Figure 4 extends to
Tα > 1, which of course is not physical. The model EW-
distribution has a tail towards larger EWs. However, the
model distribution peaks at EW∼ 50 Å. As was seen in
the constant transmission model, this is clearly inconsistent
with the observations, which favor values of EW∼ 100 Å.
Shimasaku et al. (2006) also show a probability distribution
of EW, which is probably closer to the actual distribution.
Although this distribution does peak closer to EW∼ 50 Å,
it is still significantly broader than that of the model (see
§ 6 for more arguments against the fluctuating IGM model).
We point out that the model distribution shown in Figure 4
is independent of the assumed value of Lα,42.
5 LYα EMITTERS POWERED BY VERY
MASSIVE STARS.
In § 3 we demonstrated that a simple model where Lα and
LUV were linearly related to halo mass can reproduce the
UV and Lyα LFs, but not the observed EW distribution.
In § 4 we showed that this situation is not remedied by a
variable IGM transmission, and that favored models have a
constant transmission. In this section we discuss an alternate
model, which leads to consistency with both the observed
Lyα LFs, UV-LFs, and the EW-distribution. In this model,
galaxies are assumed to have a bright Lyα phase (hereafter
the ’population III’-phase) which lasts a fraction fIII of the
galaxies’ life-time. After this the galaxy’s Lyα luminosity
drops to the ’normal’ value for population II star formation.
This model may be viewed as an extension of the idea
originally described by Malhotra & Rhoads (2002), that
large EW LAEs are young galaxies in the early stages of
their lives. In this picture, the sudden drop in Lyα luminos-
ity could represent i) a sudden drop in the ionising lumi-
nosity when the first O-stars died, or ii) an enhanced dust-
opacity after enrichment by the first type-II supernovae. Al-
ternatively, our parametrisation could represent a scenario
Figure 4. Comparison of the observed equivalent width distribu-
tion (EW, histogram), with the model prediction for a model in
which we assumed a log-normal distribution of IGM transmission
with (Tα,57, σu) = (0.27, 0.2) (see Fig 3). The EW is related to Tα
via EW= 160Tα Å. The dotted line shows the fraction, f(> Tα)
(shown on the right vertical axis), of galaxies with a transmission
greater than Tα (Eq 5). Galaxies with large Tα are more easily
detected, hence the large Tα (EW) end is boosted considerably,
resulting in closer agreement (but not close enough) to the data.
in which the population III phase ended after the first pop-
ulation III stars enriched the surrounding interstellar gas
from which subsequent generations of stars formed. Hence,
we refer to this model as the ’population III’ model. We will
show that to be consistent with the large values of the ob-
served EW, a very massive population of stars is required
during the early stages of star formation.
To minimise the number of free parameters we modeled
the time dependence of the Lyα EW as a step-function. The
number density of LAEs is then given by
N(> Tα × Lα, z) = fIII × ǫDC
Mα,III
(z) + (9)
(1− fIII)× ǫDC
Mα,II
Here,Mα,II is the mass related to Tα×Lα through Tα×Lα =
Lα×Tα×Ṁ∗, while Mα,III is the population III mass, which
is calculated with Lα replaced by Lα = (EWIII/160 Å)×2×
1042 erg s−1.
Whereas in previous sections we chose fiducial or best
fit parameters for illustration, for the model described in this
section we take the most general approach. We fit the model
simultaneously to the UV-LF and Lyα LFs, as well as to
the observed EW-distribution of Lyα selected galaxies. This
model predicts two observed equivalent widths (Tα×EWIII
and Tα×EWII) in various abundances. The associated mean
and variance from the model are compared to the observed
EW-distribution, which has a mean of 〈EW〉 = 120± 25 Å,
and a standard deviation of σEW = 50± 10 Å.
Our model has 6 free parameters
(ǫDC, f∗, Tα,57, Tα,65, fIII,EWIII). We produce likelihoods
for each parameter by marginalising over the others in
this space. The lower set of panels in Figure 5 show
likelihood contours for our model parameters at 64%,
26% and 10% of the peak likelihood. The best-fit models
have EWIII ∼ 600 − 800 Å and fIII = 0.04 − 0.1 which
c© 2006 RAS, MNRAS 000, 1–11
6 Mark Dijkstra & J. Stuart B. Wyithe
Figure 5. Marginalised constraints on the 6 population-III model parameters, (ǫDC, f∗,Tα,57,Tα,65, fIII,EWIII), are shown in the lower
three panels. In the best-fit population-III model, each galaxy goes through a luminous Lyα phase during which the equivalent width
is EWIII = 600 − 800 Å for a fraction fIII = 0.04 − 0.1 of the galaxies life time. Although the bright phase only lasts a few to ten per
cent of their life-time, galaxies in the bright phase are more easily detectable, and the number of galaxies detected in Lyα surveys in the
bright phase is equal to that detected in the faint phase. This is also demonstrated by the thick solid line (with label ’1.0’) in the lower
left panel, which shows the combination of fIII and EWIII that produces equal numbers of galaxies in the population III and II phase
(the dashed lines are defined similarly, also see Fig 6). The best-fit intrinsic equivalent widths are in excess of the maximum allowed for
a population-II stellar population having a Salpeter mass function. Therefore, this model requires a burst of very massive star formation
lasting no more than a few to ten percent of the galaxies star forming lifetime, and may indicate the presence of population-III star
formation in a large number of high-redshift LAEs.
corresponds to a physical timescale for the population-III
phase of fIII× ǫDC × thub ∼ 4−50 Myr (for 0.1 <∼ǫDC <∼0.5).
The model Lyα luminosity functions at z=5.7 and
z=6.5 described by (ǫDC, f∗, Tα,57, Tα,65, fIII,EWIII) =
(0.2, 0.14, 0.22, 0.19, 0.08, 650 Å) are shown as solid lines
and provide good fits to the data. The model produces
two observed EWs, namely Tα×EWII = 35 Å and Tα×
EWIII = 143 Å . It is worth emphasising that the emitted
EW of the bright phase depends on the choice Lα,42 via
EWIII = 650(Lα,42/2.0) Å. Hence, a lower/higher value
of Lα,42 would decrease/increase the intrinsic brightness
of the ’population III’ phase. Note that Lα,42 = 1.0 when
LAEs formed out of gas of solar metallicity, which is
unreasonable given the universe was only ∼ 1 Gyr old at
z = 6. Furthermore, Lα,42 = 1 would have yielded a best-fit
Tα,57 = 0.5, which is well outside the range calculated by
Dijkstra et al. (2007). We there conclude that Lα,42 is in
excess of unity.
In performing fits we have fixed the value of EWII to
correspond to a standard stellar population, and then ex-
plored the possibility that there might be a second phase of
SF producing a larger EW. Our modeling finds strong sta-
tistical evidence for this early phase and rules out the null-
hypothesis that properties can be described by population-II
stars alone at high confidence (grey region in the lower left
panel inset of Fig 5). Despite the fact that the best fit model
has a bright phase which lasts only a few per cent of the total
star formation lifetime, the two populations of LAEs are sim-
ilarly abundant in model realisations of the observed sample
in Lyα selected galaxies (see § 5.1 for a more detailed com-
parison to the observed EW distributions). This is shown
in the lower left panel in Figure 5 in which the solid line
(with label ’1.0’) shows the combination of fIII and EWIII
for which the observed number of galaxies in the popula-
tion III phase (NIII) equals that in the population II phase
(NII). The dashed lines show the cases NIII/NII = 0.3 and
NIII/NII = 3.0. The duration of the bright Lyα phase meets
theoretical expectations for a burst of star formation, while
the large EW requires a very massive stellar population (e.g
Schaerer 2003; Tumlinson et al. 2003). In summary, in order
to reproduce both the UV and Lyα LFs, and the observed
population of large EW galaxies, we require a burst of very
massive star formation lasting <∼10 per cent of the galaxies
lifetime.
c© 2006 RAS, MNRAS 000, 1–11
Very Massive Stars in High-z Galaxies 7
5.1 EW Distribution of UV and Lyα Selected
Galaxies
Stanway et al. (2007) show that 11 out of 14 LAE candidates
among i-drop galaxies in the Hubble Ultra Deep Field have
EW< 100 Å. If galaxies are included for which only upper or
lower limits on the EW are available, then this fraction be-
comes 21 out of 26. Thus the distribution of EWs for i-drop
selected galaxies differs strongly from the EW-distribution
observed by Shimasaku et al. (2006). We next describe why
this strong dependence of the observed Lyα EW distribu-
tion on the precise galaxy selection criteria arises naturally
in our population III model.
We first assume that the Lyα selected and UV-selected
galaxies were drawn from the same population (this assump-
tion is discussed further in § 6.3). In our model a galaxy that
is selected based on it’s rest-frame UV-continuum emission
has a probability fIII of being observed in the Lyα bright
phase, while the probability of finding a galaxies in the
Lyα faint phase is 1 − fIII. In § 5 we found fIII ∼ 0.1,
hence an i-drop galaxy is ∼ 10 times more likely to have
a low than a high observed EW. If we denote the number
of galaxies with EW> 100 Å by NIII, and the number of
galaxies with EW< 100 Å by NII, then the model predicts
NIII/NII =fIII/(1 − fIII) ∼ 0.1, while the observed fraction
including the galaxies for which the EW is known as upper
or lower limit is NIII/NII = 0.19± 0.05. Therefore the quali-
tative difference in observed Lyα EW distribution among i-
drop galaxies in the HUDF and among Lyα selected galaxies
follows naturally from our two-phase star formation model.
Note that our model predicts population III star formation
to be observed in fIII/(1 − fIII) ∼ 10% of the z = 6.0 LBG
population.
The dependence of the observed EW distribution on the
selection criteria used to construct the sample of galaxies is
illustrated in Figure 6. To construct this figure, we have
taken the best-fit population III model of § 5. For the pur-
pose of presentation, we let the IGM fluctuate according to
the prescription of § 4 with σu = 0.1, so that the model pre-
dicts a finite range of EWs in each phase. The left and right
panels show the predicted EW distribution for Lyα selected
(left panel) and UV-selected (right panel) galaxies as the
solid lines, respectively. For a UV-selected galaxy the prob-
ability of being in the bright phase and having an observed
EW in the range EWIII×(Tα±dTα/2) is fIIIP (Tα)dTα. Here
P (Tα)dTα is the probability that the IGM transmission is in
the range Tα±dTα/2, which is derived from Eq 4. The units
on the vertical axis are arbitrary, and chosen to illustrate
the different predicted and observed Lyα EW distribtions
for the two samples at large EWs. The observed distribu-
tions for Lyα and UV selected galaxies, shown as histograms,
are taken from Shimasaku et al. (2006) and Stanway et al.
(2007), respectively. Figure 6 clearly shows that both the
predicted and observed Lyα selected samples contain signif-
icantly more large EW LAEs than the UV-selected sample.
Our model naturally explains the qualitative shape of these
distributions and their differences.
Before proceeding we mention a caveat to the distribu-
tions shown in Figure 6. In our model all galaxies have an
EW of Tα×EWII ∼ 25−35 Å during the population II phase,
while in contrast Stanway et al. (2007) do not detect 10 out
of 26 LBGs, which implies that ∼ 40% of LBGs have an
Figure 6. Comparison of the predicted EW distribution for UV
and Lyα selected galaxies. The best-fit population-III model (see
§ 5) was used. In order to get a finite range of observed EWs (in-
stead of only two values at Tα×EWII and Tα×EWIII, we assumed
the IGM transmission to fluctuate. The units on the vertical axis
are arbitrary. The figure shows that in our population III model,
the Lyα selected sample contains a larger relative fraction of large
EW LAEs than the UV-selected (i-drop) sample, which is quali-
tatively in good agreement with the observations (shown by the
histograms).
EW <∼6 Å. Thus there is a descrepancy between our model
and the observations with respect to the value of EW in the
population II phase. The resolution of this discrepancy lies
in the fact that the very low EW emitters are drawn from
the UV (i-drop) sample and not the Lyα selected sample
our model was set up to describe. This issue is discussed in
more detail in § 6.3.
An EW distribution of dropout sources was also pre-
sented by Dow-Hygelund et al. (2007). These authors per-
formed an analysis similar to Stanway et al. (2007) and
found 1 LAE with EW= 150 Å among 22 candidate
z=6.0 LBGs. When interpreted in reference to our model,
this translates to NIII/NII ∼ 5%, which is consistent
with the model predictions. Therefore, when interpreted
in light of a two-phase star formation history and differ-
ent selection methods, the EW distribution observed by
Dow-Hygelund et al. (2007) is consistent with that found
by Shimasaku et al. (2006).
If population III star formation does provide the ex-
planation for the very large EW Lyα emitters, then we
would expect the large EW emitters to become less common
with time as the mean metallicity of the Universe increased.
To test this idea, we can compare the EW-distribution at
z = 5.7 with the results at lower redshift from Shapley et al.
(2003) who found that <∼0.5% of z = 3 LBGs have Lyα
EW> 150 Å , and that <∼2% of z = 3 LBGs to have Lyα
EW> 100 Å. Dow-Hygelund et al. (2007) argue that the
fraction of large EW Lyα lines at z = 6 is consistent with
that observed at z = 3 (Shapley et al. 2003). However, if
the EW distribution did not evolve with redshift, then the
probability that a sample of 22 LBGs will contain at least
1 LAE with EW >∼150 Å is <∼10%. Thus the hypothesis
that the observed EW distribution remains constant is ruled
out at the ∼ 90% level. On the other hand, in a similar
analysis Stanway et al. (2007) found 5 out of 26 LBGs to
have an EW >∼100 Å. If the EW distribution did not evolve
c© 2006 RAS, MNRAS 000, 1–11
8 Mark Dijkstra & J. Stuart B. Wyithe
with redshift, then the probability of finding 5 EW >∼100
Å in this sample is only ∼ 10−4. Furthermore, Nagao et al.
(2007) recently found at least 5 LAEs with EW> 100 Å at
6.0 <∼z <∼6.5, and conclude that 8% of i’-drop galaxies in
the Subaru Deep Field have EW> 100 Å, which is signifi-
cantly larger than the fraction of large EW LBGs at z = 3.
Therefore, the observed EW distribution of LBGs at z = 6 is
skewed more toward large EWs than at z = 3. The strength
of this result is increased by the fact that the IGM is more
opaque to Lyα photons at z = 6 than at z = 3. Thus we con-
clude that the intrinsic EW distribution must have evolved
with redshift.
6 DISCUSSION
6.1 Comparison with Population Synthesis
Models
Population synthesis models have suggested that the broad
band colors of observed LAEs are best described with young
stellar populations (Gawiser et al. 2006; Pirzkal et al. 2007;
Finkelstein et al. 2007). Lai et al. (2007) found the stellar
populations in three LAEs to be 5−100 Myr old, and possi-
bly as old as 700 Myr (where the precise age upper limit de-
pends on the assumed star formation history of the galaxies).
However as was argued by Pirzkal et al. (2007), since these
galaxies were selected based on their detection in IRAC,
a selection bias towards older stellar populations may ex-
ist (also see Lai et al. 2007). Furthermore, Finkelstein et al.
(2007) found that LAEs with EW> 110 Å have ages <∼4
Myr, while LAEs with EW< 40 Å have ages between 20-
400 Myr. This latter result in particular agrees well with
our population III model. On the other hand, in a fluctu-
ating IGM model for example, the EW of LAEs should be
uncorrelated with age.
In models presented in this paper, on average f∗ ∼ 0.15
of all baryons are converted into stars within halos of mass
Mtot ∼ 1010 − 1011M⊙, yielding stellar masses in the range
M∗ = 10
8−109M⊙ (Dijkstra et al. 2007b; Stark et al. 2007).
This compares unfavorably with the typical stellar masses
found observationally in LAEs which can be as low as
M∗ = 10
6 − 107M⊙ (Finkelstein et al. 2007; Pirzkal et al.
2007). However, the lowest stellar masses are found (natu-
rally) for the younger galaxies. Indeed, the LAEs with the
oldest stellar populations can have stellar masses as large
as 1010M⊙. Thus, we do not find the derived stellar masses
in LAEs to be at odds with the results of this paper. If
significant very massive (or population III) star formation
indeed occurred in high redshift LAEs, then one may ex-
pect these stars to reveal themselves in unusual broad-band
colors (e.g. Stanway et al. 2005). However, Tumlinson et al.
(2003) have shown that the most distinctive feature in the
spectrum of population III stars is the number of H and He
ionising photons (also see Bromm et al. 2001). Since these
are (mostly) absorbed in the IGM, the broad band spec-
trum of population III stars is in practice difficult to dis-
tinguish from a normal stellar population (Tumlinson et al.
2003), especially when nebular continuum emission is taken
into account (Schaerer & Pelló 2005, see their Fig 1). Hence,
population III stars would not necessarily be accompanied
by unusually blue broad band colors.
6.2 Alternative Explanations for Large EW LAEs
We have shown that a simple model in which high-redshift
galaxies go through a population-III phase lasting <∼15
Myr can simultaneously explain the observed Lyα LFs at
z = 5.7 and z = 6.5 (Kashikawa et al. 2006), and the ob-
served EW-distribution of Lyα selected galaxies at z = 5.7
(Shimasaku et al. 2006). In addition, this model predicts the
much lower EWs found in the population of UV selected
galaxies (Stanway et al, 2007, see § 5.1). Moreover the con-
straints on the population-III model parameters such as the
duration and the equivalent width of the bright phase are
physically plausible, and consistent with existing population
synthesis work (see § 6.1).
Are there other interpretations of the large observed
EWs? One possibility was discussed in § 4, where we showed
that the simple model in which the IGM transmission fluc-
tuates between galaxies reproduces the LFs, but fails to
simultaneously reproduce the Lyα LFs and the observed
EW-distribution. In addition, this model fails to reproduce
other observations. Dijkstra et al. (2007) calculated the im-
pact of the high-redshift reionised IGM on Lyα emission
lines and found the range of plausible transmissions to lie
in the range 0.1 < Tα < 0.3. This work showed that it is
possible to boost the transmission to (much) larger values
but not without increasing the observed width of the Lyα
line. Absorption in the IGM typically erases all flux blue-
ward of the Lyα resonance, and when infall is accounted
for, part of the Lyα redward of the Lyα resonance as well.
This implies that Lyα lines that are affected by absorption
in the IGM are systematically narrower than they would
have been if no absorption in the IGM had taken place. It
follows that in the fluctuating IGM model, Lyα EW should
be strongly correlated with the observed Lyα line width (or
FHWM). This correlation is not observed. In fact, observa-
tions suggest that an anti-correlation exists between EW
and FWHM (Shimasaku et al. 2006; Tapken et al. 2007).
This anti-correlation provides strong evidence against the
anomalously large EWs being produced by a fluctuating
IGM transmission.
A second possibility is the presence of galaxies with
strong superwinds. The models of Dijkstra et al. (2007) did
not study the impact of superwinds on the Lyα line pro-
file. The presence of superwinds can cause the Lyα line to
emerge with a systematic redshift relative to the Lyα reso-
nance through back scattering of Lyα photons off the far side
of the shell that surrounds the galaxy (Ahn et al. 2003; Ahn
2004; Hansen & Oh 2006; Verhamme et al. 2006). However,
superwinds tend not only to redshift the Lyα line, they also
make the Lyα line appear broader than when this scatter-
ing does not occur. As in the case of the fluctuating IGM
model, this results in a predicted correlation between EW
and FWHM, which is not observed. Furthermore in wind-
models, the overall redshift of the Lyα line, and thus Tα,
increases with wind velocity, vw. This predicts that EW in-
creases with wind velocity. However, observations of z = 3
LBGs by Shapley et al. (2003) show that EW correlates with
v−1w (Ferrara & Ricotti 2006). We therefore conclude that
the large EW in LAEs cannot be produced by superwind
galaxies.
A third possibility might be that within the Lyα emit-
ting galaxy, cold, dusty clouds lie embedded in a hot inter-
c© 2006 RAS, MNRAS 000, 1–11
Very Massive Stars in High-z Galaxies 9
Figure 7. Comparison of the best-fit population III model
(shown in Figure 5) with the UV-LF constructed by
Bouwens et al. (2006) using ∼ 300 LBGs in the Hubble Deep
Fields. This good agreement is likely a coincidence since in our
model all LBGs have an observed EW >
30 Å, while the obser-
vations show that ∼ 40% of all LBGs are not detected in Lyα
(EW <
6 Å). This overlap could possibly be (partly) due to a
lower dust content of LAEs relative to their Lyα quiet counter-
parts (see text).
cloud medium of negligible Lyα opacity. Under such condi-
tions, the continuum photons can suffer more attenuation
than Lyα photons which bounce from cloud to cloud and
mainly propagate through the hot, transparent inter-cloud
medium (Neufeld 1991; Hansen & Oh 2006). This attenua-
tion of continuum leads to a large EW. We point out that in
this scenario, large EW LAEs are not intrinsically brighter
in Lyα. At fixed Lyα flux, one is therefore equally likely
to detect a low EW LAE. In other words, to produce the
observed EW distribution one requires preferential destruc-
tion of continuum flux by dust in ∼ 50% of the galaxies.
Currently there is no evidence that this mechanism is at
work even in one galaxy. Furthermore, the rest-frame UV
colors of galaxies in the Hubble Ultra Deep Field imply that
dust in high-redshift galaxies suppresses the continuum flux
by only a factor of ∼ 1.4 (Bouwens et al. 2006). The maxi-
mum boost of the EW in a multi-phase ISM is therefore 1.4,
which is not nearly enough to produce intrinsic equivalent
widths of EW∼ 600 − 800 Å. In summary, the only model
able to simultaneously explain all observations calls for a
short burst of very massive star formation.
6.3 Comparison with the LBG Population
In § 5.1 we have shown that the observed EW distributions
of Lyα selected and i-drop galaxies and their differences can
be reproduced qualitatively with our population III model.
However, in our model all high-redshift galaxies have an ob-
served EW of at least Tα×EWII ∼ 30 Å, whereas many
i-drop galaxies are not detected in Lyα. Kashikawa et al.
(2006) show that the UV-LFs of LAEs at z = 6.5 and
z = 5.7 overlap with that constructed by Bouwens et al.
(2006) from a sample of ∼ 300 z = 6 LBGs discovered in
the Hubble Deep Fields. Naively, this overlap implies that
LBGs and LAEs are the same population and therefore that
all LBGs should be detected by Lyα surveys. Since Lyα sur-
veys only detect galaxies with EW >∼20 Å, this suggests all
LBGs should have a Lyα EW >∼20 Å contrary to observa-
tion. To illustrate this point further, we have taken the best-
fit population III model shown in Figure 5 and compared the
model predictions for the rest-frame UV-LF with that of
Bouwens et al. (2006) in Figure 7. Clearly, our best-fit pop-
ulation III model fits the data well. However, Stanway et al.
(2007) found ∼ 40% of i-drop galaxies in the HUDF to have
an observed EW <∼6 Å, and a similar result was presented
by Dow-Hygelund et al. (2007).
Two effects may help reconcile these two apparently
conflicting sets of observations: (i) Dow-Hygelund et al.
(2007) found Lyα emitting LBGs to be systematically
smaller. That is, for a fixed angular size, the z850-band flux
of LAEs is systematically higher with ∆z850 ∼ −1. If we
assume that the angular scale of a galaxy is determined by
the mass of its host halo, then this implies that for a fixed
mass the z850-band flux of LAEs is systematically higher,
and (ii) only a fraction of LBGS are LAEs. The drop-out
technique used to select high redshift galaxies is known to
introduce a bias against strong LAEs, as a strong Lyα line
can affect the broad band colors of high-redshift galaxies.
This may cause ∼ 10−46% of large EW LAEs to be missed
using the i-drop technique (Dow-Hygelund et al. 2007).
If only a fraction fα of all LBGs are detected in Lyα,
then effect (i) would explain why the UV-LF of LAEs lies
less than a factor of 1/fα below the observed UV-LF of
the general population of LBGs. This is because a more
abundant lower mass halo is required to produce the same
UV-flux in LAEs, which would shift the LF upwards. In
addition, effect (ii) may reduce this difference even further.
It follows that these two effects combined may cause the LFs
to overlap. Thus the overlap of the UV and Lyα selected UV-
LFs appears to be a coincidence, and not evidence of their
being the same population of galaxies. This implies that our
model is valid for Lyα selected galaxies, but not the high-
redshift population as a whole and explains the lack of very
low EWs in UV selected samples discussed in § 5.1.
The reason why LAEs may be brighter in the UV for
a fixed halo mass is unclear. It is possibly related to dust
content. Bouwens et al. (2006) found the average amount
of UV exctinction to be 0.4 mag in the total sample of
z = 6 LBGs. This value is close to the average excess z850-
band flux detected from LAEs for a given angular scale
(Dow-Hygelund et al. 2007). If LAEs contain less (or no)
dust, then this would explain why they are brighter in the
UV and thus why they appear more compact. The possi-
bility that ’Lyα quiet’ LBG contain more dust than their
Lyα emitting counterparts is not very surprising, as a low
dust abundance has the potential to eliminate the Lyα line.
Thus LAEs could be high redshift galaxies with a lower dust
content.
Shimasaku et al. (2006) and Ando et al. (2006) found
that luminous LBGs, MUV <∼ − 21.0, typically do not con-
tain large EW Lyα emission lines. This deficiency of large
EW LAEs among UV-bright sources is not expected in
our model, and may reflect that UV-bright sources are
more massive, mature, galaxies that cannot go through a
population-III phase anymore. It should be pointed out
though that the absence of large EW LAEs among galax-
c© 2006 RAS, MNRAS 000, 1–11
10 Mark Dijkstra & J. Stuart B. Wyithe
ies with MUV <∼ − 21.0 in the survey of Shimasaku et al.
(2006) is consistent with our model: The observed num-
ber density of sources with MUV <∼ − 21.0 is ∼ 5 × 10
cMpc−3 (see Fig 1). In our best-fit pop-III model (shown in
Fig 5), a fraction fIII ∼ 0.08 of these galaxies would be in the
bright phase. This translates to a number density of large
EW LAEs of ∼ 4× 10−6 cMpc−3. Given the survey volume
of ∼ 2×105 cMpc3, the expected number of large EW LAEs
with MUV <∼ − 21.0 is ∼ 0.8, and the absence of large EW
LAE among UV bright sources is thus not surprising.
6.4 Clustering Properties of the LAEs
In our model large EW LAEs are less massive by a factor
of EWIII/EWII ∼ 4 at fixed Lyα luminosity. Since clus-
tering of dark matter halos increases with mass, it follows
that our model predicts large EW LAEs to be clustered less
than their low EW counterparts (at a fixed Lyα luminos-
ity). The clustering of LAEs is typically quantified by their
angular correlation function (ACF), w(θ), which gives the
excess (over random) probability of finding a pair of LAEs
separated by an angle θ on the sky. The ACF depends on
the square of the bias parameter (w(θ) ∝ b2(m)), which for
galaxies in the population II phase is ∼ 1.24 − 1.4 times
larger than for galaxies in the population III phase, for the
mass range of interest. This implies that the clustering of low
EW LAEs at fixed Lyα luminosity is enhanced by a factor
of ∼ 1.5− 2.0. Existing determinations of the ACF of LAEs
by Shimasaku et al. (2006) and Kashikawa et al. (2006) are
still too uncertain to test this prediction.
7 CONCLUSIONS
Observations of high redshift Lyα emitting galaxies (LAEs)
have shown the typical equivalent width (EW) of the Lyα
line to increase dramatically with redshift, with a signifi-
cant fraction of the galaxies lying at z > 5.7 having an
EW >∼100 Å. Recent calculations by Dijkstra et al. (2007)
show that the IGM at z > 4.5 transmits only 10 − 30%
of the Lyα photons emitted by galaxies. In this paper we
have investigated the transmission using a model that re-
produces the observed Lyα and UV LFs. This model re-
sults in an empirically determined transmission of Tα ∼
0.30(Lα,42/2.0)−1, where Lα,42 denotes the Lyα luminos-
ity per unit star formation rate (in M⊙ yr
−1) Lα in units
of 1042 erg s−1 (§ 3). This value is in good agreement with
earlier theoretical results.
If only ∼ 30% of all Lyα that was emitted by high
redshift galaxies reaches the observer, then this impies that
the intrinsic EWs are systematically (much) larger than ob-
served in many cases. To investigate the origin of these very
high EWs, we have developed semi-analytic models for the
Lyα and UV luminosity functions and the distribution of
equivalent widths. In this model Lyα emitters undergo a
burst of very massive star formation that results in a large
intrinsic EW, followed by a phase of population-II star for-
mation that produces a lower EW3. This model is referred
3 Technically, the model discussed in § 5 only specifies that galax-
ies go through a ’population-III phase for a fraction fIII ∼ 0.1 of
to as the ’population III model’ and is an extension of the
idea originally described by Malhotra & Rhoads (2002), who
proposed large EW Lyα emitters to be young galaxies.
The population III model in which the Lyα equivalent
width is EWIII ∼ 650(Lα,42/2.0) Å for <∼50 Myr, is able
to simultaneously describe the following eight properties of
the high redshift galaxy population: i-iv) the UV and Lyα
luminosity functions of LAEs at z=5.7 and 6.5, v-vi) the
mean and variance of the EW distribution of Lyα selected
galaxies at z=5.7, vii) the EW distribution of UV- selected
galaxies at z∼6 (§ 5), and viii) the observed correlation of
stellar age and mass with EW (§ 6.1). Our modeling sug-
gests that the anomalously large intrinsic equivalent widths
observed in about half of the high redshift Lyα emitters
require a burst of very massive star formation lasting no
more than a few to ten percent of the galaxies star forming
lifetime. This very massive star formation may indicate the
presence of population-III star formation in a large number
of high-redshift LAEs. The model parameters for the best-fit
model are physically plausible where not previously known
(e.g. those related to the efficiency and duration of star for-
mation), and agree with estimates where those have been
calculated directly (e.g the IGM transmission, EWIII, and
fIII).
In addition, we argued that the observed overlap of the
UV-LFs of LAEs with that of z∼ 6 LBGs appears to be at
odds the observed Lyα detection rate in high-redshift LBGs,
suggesting that LAEs and LBGs are not the same popula-
tion. A lower dust content of LAEs relative to their ‘Lyα
quiet’ counterparts would partly remedy this discrepancy,
and could also explain why LAEs appear to be typically
more compact (§ 6.3).
Semi-analytic modeling of the coupled reionisation and
star formation histories of the universe suggests that popu-
lation III star formation could still occur after the bulk of
reionisation had been completed (Scannapieco et al. 2003;
Schneider et al. 2006; Wyithe & Cen 2007). The observa-
tion of anomalously large EWs in Lyα emitting galaxies at
high redshift may therefore provide observational evidence
for such a scenario. In the future, the He 1640 Å may be
used as a complementary probe (e.g Tumlinson et al. 2001,
2003). The EW of this line is smaller by a factor of >∼20 for
population III (Schaerer 2003). However, the He 1640Å will
not be subject to a small transmission of ∼ 10− 30%, mak-
ing it accessible to the next generation of space telescopes.
On the other hand, it may also be possible to observe the
He 1640 Å in a composite spectra of z = 6 LBGs. Indeed,
the He 1640 Å line has already been observed in the com-
posite spectrum of z= 3 LBGs (Shapley et al. 2003), which
led Jimenez & Haiman (2006) to argue for population III
star formation at redshifts as low as z = 3−4. If population
III star formation was more widespread at higher redshifts,
as predicted by our model, then the composite spectrum
their lifetimes. Our model does not specify when this population-
III phase occurs. Hypothetically, the population III phase could
occur at an arbitrary moment in the galaxies’ lifetime when it
is triggered by a merger of a regular star forming galaxy and a
dark matter halo containing gas of primordial composition. Note
however that such a model would probably have difficulties ex-
plaining the apparent observed correlation between Lyα EW and
the age of a stellar population (§ 6.1).
c© 2006 RAS, MNRAS 000, 1–11
Very Massive Stars in High-z Galaxies 11
of LBGs at higher redshifts should exhibit an increasingly
prominent He 1640 Å line. In particular, this line should be
most prominent in the subset of LBGs that have large EW
Lyα emission lines.
Acknowledgments JSBW and MD thank the Aus-
tralian Research Counsel for support. We thank Avi Loeb
for useful discussions, and an anonymous referee for a helpful
report that improved the content of this paper.
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c© 2006 RAS, MNRAS 000, 1–11
http://arxiv.org/abs/astro-ph/0611799
http://arxiv.org/abs/astro-ph/0702377
http://arxiv.org/abs/astro-ph/0612513
http://arxiv.org/abs/astro-ph/0701882
	Introduction
	The Model
	Modeling the UV and Ly Luminosity Functions.
	Constraints from the UV-LF.
	Constraints from the Ly LF.
	The Predicted Equivalent Width
	The Fluctuating IGM Model
	Ly Emitters Powered by Very massive Stars.
	EW Distribution of UV and Ly Selected Galaxies
	Discussion
	Comparison with Population Synthesis Models
	Alternative Explanations for Large EW LAEs
	Comparison with the LBG Population
	Clustering Properties of the LAEs
	Conclusions
