The Astrophysical Journal, 757:54 (22pp), 2012 September 20 doi:10.1088/0004-637X/757/1/54
C
2012. The American Astronomical Society. All rights reserved. Printed in the U.S.A.
A CENSUS OF OXYGEN IN STAR-FORMING GALAXIES: AN EMPIRICAL MODEL LINKING
METALLICITIES, STAR FORMATION RATES, AND OUTFLOWS
H. J. Zahid
1
,G.I.Dima
1
, L. J. Kewley
1,2
,D.K.Erb
3
, and R. Dav
´
e
4
1
Institute for Astronomy, University of Hawaii at Manoa, 2680 Woodlawn Drive, Honolulu, HI 96822, USA
2
Research School of Astronomy & Astrophysics, Mount Stromlo Observatory, Cotter Road Weston Creek, ACT 2611, Australia
3
Department of Physics, University of Wisconsin–Milwaukee, 1900 E. Kenwood Boulevard, Milwaukee, Wisconsin, WI 53211, USA
4
Department of Astronomy, University of Arizona, 933 North Cherry Avenue, Rm. N204 Tucson, AZ 85721, USA
Received 2012 May 11; accepted 2012 July 18; published 2012 September 5
ABSTRACT
In this contribution, we present the first census of oxygen in star-forming galaxies in the local universe. We examine
three samples of galaxies with metallicities and star formation rates (SFRs) at z = 0.07, 0.8, and 2.26, including
the Sloan Digital Sky Survey (SDSS) and DEEP2 survey. We infer the total mass of oxygen produced and mass of
oxygen found in the gas-phase from our local SDSS sample. The star formation history is determined by requiring
that galaxies evolve along the relation between stellar mass and SFR observed in our three samples. We show that
the observed relation between stellar mass and SFR for our three samples is consistent with other samples in the
literature. The mass–metallicity relation is well established for our three samples, and from this we empirically
determine the chemical evolution of star-forming galaxies. Thus, we are able to simultaneously constrain the SFRs
and metallicities of galaxies over cosmic time, allowing us to estimate the mass of oxygen locked up in stars.
Combining this work with independent measurements reported in the literature, we conclude that the loss of oxygen
from the interstellar medium of local star-forming galaxies is likely to be a ubiquitous process with the oxygen
mass loss scaling (almost) linearly with stellar mass. We estimate the total baryonic mass loss and argue that only
a small fraction of the baryons inferred from cosmological observations accrete onto galaxies.
Key words: galaxies: abundances – galaxies: evolution – galaxies: formation – galaxies: high-redshift – galaxies:
ISM
Online-only material: color figures
1. INTRODUCTION
A complete theory of galaxy formation and evolution will
have to be able to self-consistently account for, among other
physical processes, the star formation and chemical evolution
of galaxies. Our understanding of galaxy evolution is rooted in
the currently accepted cosmological model in which large-scale
structure in the universe traces out the cosmic web of dark mat-
ter and growth of the universe is accelerated by dark energy. In
this theoretical framework, a hierarchical formation of galaxies
is favored in which larger galaxies form as the dark matter halos
within which they are embedded merge over time. It is not well
established in which epoch in cosmic history this is the dominant
mode of growth. However, recent observations of strong corre-
lations observed between fundamental galaxy parameters (e.g.,
mass, age, size, luminosity, baryonic content, and angular mo-
mentum) have led some to question the stochastic nature of the
hierarchical formation scenario (Disney et al. 2008;Nairetal.
2010). One possible resolution is that galaxies and groups of
galaxies gather matter early on followed by quiescent, isolated
evolution (Peebles & Nusser 2010). The evolution of galaxies
may be simpler than a hierarchical formation model suggests.
A large number of studies have recently revealed that there
exists a tight relation between stellar mass and star formation
rates (SFRs) out to z ∼ 2 (Noeske et al. 2007b; Salim et al.
2007; Daddi et al. 2007; Elbaz et al. 2007; Pannella et al. 2009;
Elbaz et al. 2011, among others). We refer to this as the MS
relation. All these studies find the slope of the relation to be
near unity and a 1σ scatter of 0.3 dex. The relation and
its small scatter are taken as evidence that secular processes,
such as gas accretion, are the dominant mechanism for star
formation, with mergers playing a minor role. In particular,
Noeske et al. (2007b) suggest that the presence of an MS relation
with constant scatter at several epochs implies that star formation
is gradually declining, with galaxies spending 67% (95%) of
their star formation lifetime within a factor of ∼2 (4) of their
average SFR.
Several studies have applied the observational constraints
imposed by the MS relation and its evolution to uncover star
formation histories of galaxies. Noeske et al. (2007a)show
that their model of “staged” galaxy evolution accounts for the
observed relation. In their model, less massive galaxies have
later onset of initial star formation with longer timescales of
exponential decay. Similar models result if star-forminggalaxies
are assumed to lie on the MS relation at all epochs. Several
studies have focused on this simpler approach of continuity
of star formation along the MS relation. Conroy & Wechsler
(2009) combine this approach with abundance matching to dark
matter halos, concluding that mergers play a minor role in mass
growth of galaxies. Using this approach, Peng et al. (2010)are
able to explain the shape and evolution of the observed stellar
mass function for star-forming galaxies. Papovich et al. (2011)
apply this technique to understand the gas accretion process at
high redshifts. Leitner & Kravtsov (2011) use this technique
to show that gas recycling is sufficient to fuel the observed
star formation in the local universe, and Leitner (2012) argue
that most star-forming galaxies in the local universe formed at
1 <z<2.
The chemical evolution of the gas phase of star-forming
galaxies is largely constrained by observations of the
mass–metallicity (MZ) relation. Lequeux et al. (1979) were the
first to show that the metallicities of galaxies increase with stellar
1
The Astrophysical Journal, 757:54 (22pp), 2012 September 20 Zahid et al.
mass. The MZ relation is well established in the local universe
(Tremonti et al. 2004) and has been observed for intermediate-
(Savaglio et al. 2005; Cowie & Barger 2008; Zahid et al. 2011;
Moustakas et al. 2011) and high-redshift galaxies (Erb et al.
2006a; Mannucci et al. 2009). The shape of the MZ relation
is observed to be relatively constant with evolution in the zero
point such that galaxies at earlier redshifts are found to have
lower gas-phase abundance.
The metal content of galaxies is governed by the processes
of star formation and large-scale gas flows. Outflowing gas
has directly been observed in starburst galaxies (Rupke et al.
2005; Martin 2006; Tremonti et al. 2007; Rich et al. 2010;
Tripp et al. 2011) and is found to be a ubiquitous phenomenon
in higher redshift star-forming galaxies (Shapley et al. 2003;
Weiner et al. 2009; Steidel et al. 2010). A recent survey of
the halos of galaxies conducted by Tumlinson et al. (2011)
reveals that large reservoirs of oxygen are found to exist in
the circumgalactic medium (CGM) of all star-forming galaxies.
They conclude that the CGM of star-forming galaxies contains
a substantial amount of gas and metals, perhaps far exceeding
the gas within the galaxies themselves. In this study, we use our
census of oxygen to quantify the loss of metals and gas from the
interstellar medium (ISM) of normal local star-forming galaxies.
Census techniques have proven to be crucial in our under-
standing of cosmological evolution. A well-constrained inven-
tory of the energy content of the universe is one of the greatest
triumphs of modern cosmology. By comparing a census of the
observed baryons in the local universe to the expected cosmo-
logical density, Fukugita et al. (1998, among others) showed
that the vast majority of baryons are not observed. This is one of
the missing baryon problems. A second related problem is that
the amount of baryons within galaxies is not in accord with ex-
pectations inferred from the properties of the dark matter halos
within which they are embedded (e.g., Bell et al. 2003b). The-
oretical cosmological models suggest that the missing baryons
are to be found in the warm-hot intergalactic medium (WHIM;
Cen & Ostriker 1999;Dav
´
eetal.2001). Baryons in this phase
may or may not be associated with galaxies, and it remains un-
clear what fraction of the baryons accreted onto galaxies and
were later ejected.
In this study we present a self-consistent, empirically con-
strained census model of oxygen in star-forming galaxies. The
data used in this study are presented in Section 2, and the meth-
ods used in deriving the stellar masses, metallicities, and SFRs
of galaxies are discussed in Section 3. We parameterize the
SFRs of galaxies as a function of stellar mass and redshift in
Section 4 by examining the MS relation at several redshifts.
We describe the various components of our oxygen census in
Section 5. We develop our self-consistent empirical models for
the star formation and chemical history of galaxies in Sections 6
and 7, respectively, by imposing the continuity condition that
galaxies build up their stellar mass by evolving along the empir-
ical relation between stellar mass and SFR with the metallicity
inferred from the MZ relation at several redshifts. In Section 8
we present the results of our census, and in Section 9 we discuss
systematics and uncertainties in our approach. We provide a dis-
cussion of our results in Section 10 and a summary of our results
in Section 11. For this study, we adopt the standard cosmology
(H
0
, Ω
m
, Ω
Λ
) = (70 km s
−1
Mpc
−1
, 0.3, 0.7).
2. THE DATA AND SAMPLE SELECTION
In this section, we describe the local sample of galaxies from
Sloan Digital Sky Survey (SDSS; Section 3.1), our intermediate-
redshift sample from DEEP2 (Section 3.2), and a high-redshift
sample from Erb et al. (2006a; Section 3.3). Galaxies are
primarily selected such that the chemical properties can be
determined from their spectra. The binned data are given in
Table 1.
2.1. The SDSS Sample
We draw our local sample from the SDSS DR7, which
consists of ∼900,000 galaxies spanning a redshift range of
0 <z<0.7 (Abazajian et al. 2009). The survey has a Petrosian
limiting magnitude of r
P
= 17.8 covering 8200 deg
2
.The
spectra have a nominal spectral range of 3900–9100 Å and a
spectral resolution of R ∼ 2000. We make use of the ugri z-
band photometry available for each object (Stoughton et al.
2002) and the publicly released emission-line fluxes measured
by the MPA-JHU group.
5
We refer to the sample presented here
as the “metallicity-selected SDSS sample.”
We correct for dust extinction in the emission lines by
inferring a reddening correction from the Balmer decrement. For
case B recombination with electron temperature T
e
= 10
4
K and
electron density n
e
= 10
2
cm
−3
, the intrinsic Hα/Hβ ratio is
expected to be 2.86 (Osterbrock 1989). We get the intrinsic color
excess, E(B −V ), and the correction for dust attenuation using
the extinction law of Cardelli et al. (1989) and a corresponding
R
v
= 3.1. We note that the results of this study are not dependent
on our choice of a particular extinction law.
We select a pure star-forming sample of local emission-line
galaxies from the SDSS DR7. We first distinguish star-forming
galaxies from active galactic nuclei (AGNs) by constraining the
ionizing radiation source using the [O iii] λ5007, [N ii] λ6584,
Hβ, and Hα emission lines (Baldwin et al. 1981; Veilleux &
Osterbrock 1987; Kauffmann et al. 2003; Kewley et al. 2006).
In particular, we remove galaxies using the equation given in
Kewley et al. (2006) where
log([O iii]/Hβ) > 0.61/(log([N ii]/Hα) −0.05) + 1.3. (1)
In order to avoid aperture effects, we require a g-band fiber
aperture covering fraction >30% in addition to imposing a lower
redshift limit of 0.04 (Kewley et al. 2004). The median covering
fraction for the metallicity-selected SDSS sample is 38%.
Kewley et al. (2006) find that the SDSS sample is incomplete at
higher redshifts, and in order to minimize evolutionary effects,
we also impose an upper limit redshift cutoff of z = 0.1.
In order to establish comparable samples, galaxies in the
local sample are selected from SDSS using the same selection
criteria as the DEEP2 sample. In particular, galaxies are selected
to have signal-to-noise ratio (S/N) of Hβ>3, σ
R23
< 2, and
equivalent width of Hβ>4 Å. Here, σ
R23
is the error in the R23
parameter, which is the ratio of the oxygen nebular emission
([O ii] λ3727 doublet and [O iii] λλ4959, 5007) to Hβ. These
particular selection criteria give us a sample of ∼20,000 star-
forming galaxies in the limited redshift range of 0.04 <z<0.1.
2.2. The DEEP2 Sample
Our sample of intermediate-redshift star-forming galaxies
is taken from the DEEP2 survey (Davis et al. 2003). Details
of sample selection and properties are given in Zahid et al.
(2011); here we summarize the data selection. The survey
consists of ∼45,000 galaxies targeted mostly in the redshift
range of 0.7 >z>1.4 by applying a color preselection using
5
http://www.mpa-garching.mpg.de/SDSS/DR7/
2
The Astrophysical Journal, 757:54 (22pp), 2012 September 20 Zahid et al.
Tab le 1
Data
log(M
∗
/M
) 12 + log(O/H) E(B −V ) log(Ψ)
SDSS
8.51 8.707 ± 0.004 0.11 ± 0.02 −0.20 ± 0.02
8.82 8.736 ± 0.006 0.13 ± 0.02 −0.12 ± 0.02
8.97 8.787 ± 0.007 0.15 ± 0.02 −0.19 ± 0.02
9.08 8.819 ± 0.008 0.16 ± 0.02 −0.20 ± 0.02
9.17 8.859 ± 0.007 0.18 ± 0.02 −0.19 ± 0.02
9.23 8.875 ± 0.006 0.19 ± 0.01 −0.14 ± 0.01
9.30 8.900 ± 0.006 0.20 ± 0.01 −0.12 ± 0.01
9.36 8.920 ± 0.006 0.22 ± 0.01 −0.10 ± 0.01
9.41 8.923 ± 0.006 0.23 ± 0.01 −0.07 ± 0.01
9.45 8.946 ± 0.006 0.24 ± 0.01 −0.06 ± 0.01
9.49 8.947 ± 0.006 0.24 ± 0.01 −0.03 ± 0.01
9.54 8.969 ±
0.006 0.27 ± 0.01 −0.02 ± 0.01
9.57 8.977 ± 0.004 0.26 ± 0.01 −0.01 ± 0.01
9.61 8.993 ± 0.006 0.27 ± 0.01 0.03 ± 0.01
9.64 8.989 ± 0.005 0.28 ± 0.01 0.05 ± 0.01
9.68 9.007 ± 0.004 0.28 ± 0.01 0.07 ± 0.01
9.71 9.010 ± 0.004 0.30 ± 0.01 0.09 ± 0.01
9.75 9.022 ± 0.004 0.30 ± 0.01 0.11 ± 0.01
9.78 9.035 ± 0.003 0.32 ± 0.01 0.13 ± 0.01
9.81 9.037 ± 0.004 0.33 ± 0.01 0.16 ± 0.01
9.85 9.048 ± 0.003 0.33 ± 0.01 0.17 ± 0.01
9.88 9.056 ± 0.003 0.36 ± 0.01 0.22 ± 0.01
9.92 9.059 ± 0.003 0.36 ± 0.01 0.24 ± 0.01
9.95 9.068 ± 0.003 0.38 ± 0.01 0.27 ± 0.01
10.00 9.061 ± 0.003 0.39 ± 0.01 0.32 ± 0.01
10.04 9.081
± 0.002 0.40 ± 0.01 0.34 ± 0.01
10.09 9.084 ± 0.003 0.43 ± 0.01 0.40 ± 0.01
10.15 9.088 ± 0.002 0.44 ± 0.01 0.47 ± 0.01
10.24 9.086 ± 0.003 0.47 ± 0.01 0.53 ± 0.01
10.39 9.095 ± 0.002 0.52 ± 0.01 0.73 ± 0.01
DEEP2
9.25 8.69 ± 0.02 0.17 ± 0.03 0.35 ± 0.03
9.32 8.76 ± 0.02 0.19 ± 0.02 0.32 ± 0.02
9.39 8.78 ± 0.02 0.20 ± 0.03 0.37 ± 0.03
9.44 8.77 ± 0.02 0.21 ± 0.03 0.39 ± 0.03
9.49 8.74 ± 0.01 0.21 ± 0.03 0.43 ± 0.03
9.56 8.80 ± 0.02 0.23 ± 0.03 0.49 ± 0.03
9.64 8.83 ± 0.02 0.24 ± 0.04 0.54 ± 0.04
9.72 8.84 ± 0.02 0.26 ± 0.03 0.60 ± 0.03
9.79 8.86 ± 0.02 0.27 ± 0.05 0.60 ± 0.05
9.87 8.92 ± 0.02 0.31 ± 0.05 0.72 ± 0.05
9.97 8.94 ± 0.02 0.33 ± 0.03 0.77 ± 0.03
10.07 8.93 ± 0.02 0.35 ± 0.03 0.82 ± 0.03
10.18 8.96 ± 0.01 0.38 ± 0.03 0.92 ± 0.03
10.33 9.00 ± 0.01 0.43 ± 0.02 0.98 ± 0.02
10.59 9.04 ± 0.01 0.53
± 0.04 1.29 ± 0.04
E06
9.14 <8.55 0.14 ± 0.09 1.40 ± 0.14
9.56 8.72 ± 0.07 0.21 ± 0.07 1.41 ± 0.05
9.89 8.82 ± 0.06 0.28 ± 0.08 1.60 ± 0.06
10.12 8.86 ± 0.06 0.33 ± 0.07 1.52 ± 0.08
10.32 8.92 ± 0.06 0.39 ± 0.09 1.78 ± 0.06
10.73 8.97 ± 0.05 0.52 ± 0.06 1.96 ± 0.06
Notes. The stellar mass (Column 1), metallicity determined from the diagnostic
of Kobulnicky & Kewley (2004, Column 2), fitted E(B − V ) from Equation (6)
(Column 3), and SFR (Column 4) for the SDSS, DEEP2, and E06 samples. For the E06
sample the metallicity has been converted from Pettini & Pagel (2004) to Kobulnicky
&Kewley(2004) using the conversion constants in Kewley & Ellison (2008). DEEP2
and E06 samples we have corrected for dust extinction when determining SFRs from
the Balmer lines using the E(B − V ) values given in Column 3. For the DEEP2
and SDSS data, the values are the median in bins of stellar mass. The errors are
determined from bootstrapping and are analogous to the standard error on the mean.
For the E06 sample, the errors are the standard error of the mean. Each data bin is
equally populated such that the SDSS, DEEP2, and E06 samples contain ∼700, ∼90,
and ∼15 galaxies in each bin, respectively. Electronic version available upon request.
BRI-band photometry (Coil et al. 2004). The survey has a
limiting magnitude of R
AB
= 24.1 and covers 3.5 deg
2
.The
spectra have a nominal spectral range of 6500–9100 Å and a
resolution of R ∼ 5000. The emission-line equivalent widths
are measured in Zahid et al. (2011), and we adopt the same
values here.
The sample selection is based on the spectral and photometric
properties of the galaxies. We reduce AGN contamination by
first requiring that log(R23) < 1 (L. J. Kewley et al. 2012,
in preparation). Using the color separation for blue and red
galaxies parameterized by Willmer et al. (2006), Weiner et al.
(2007) conclude that only a small fraction of blue galaxies in
DEEP2 appear to harbor AGNs, whereas a large fraction of red
emission-line galaxies show evidence of AGN emission. We
further limit AGN contamination by removing 48 galaxies in
the sample that are classified as red galaxies using the color
division of Willmer et al. (2006).
Given the nominal spectral coverage, the redshift range of
galaxies in our sample is limited by the necessity to simultane-
ously observe both the [O ii] λ3727 doublet and the [O iii] λ5007
emission lines, which are required for chemical analysis. We
further require that the S/NHβ>3, the error of the R23
emission-line ratio, σ
R23
, be less than 2, and the equivalent
width of Hβ>4 Å. Finally, due to ambiguity in the metallic-
ity determination of DEEP2 galaxies at low stellar masses (see
Section 3.2), we also remove all galaxies with M
∗
< 10
9.2
M
.
This selection criterion gives us a sample of 1348 star-forming
galaxies in the limited redshift range of 0.75 <z<0.82.
2.3. The E06 Sample
Erb et al. (2006a, E06 hereafter) determine the MZ relation
from 87 star-forming galaxies at z ∼ 2.2 selected from a larger
sample of 114 galaxies described in Erb et al. (2006b). The
galaxies are selected on the basis of their rest-frame UV colors,
and redshifts are determined from their UV spectra. All galaxies
in the sample have UGRK-band photometry. Most also have
J-band photometry, and 32 galaxies have been observed at 3.6,
4.5, 5.4, and 8.0 μm with IRAC on board the Spitzer Space
Telescope.Hα spectra were obtained using NIRSPEC on the
Keck II telescope.
The metallicity for these galaxies is determined from the
emission-line ratio of [N ii] λ6584 to Hα.The[Nii] λ6584 line
is sensitive to metallicity, with the strength of the line decreasing
with decreasing metallicity. The S/N of the individual galaxy
spectra is insufficient to measure the weak [N ii] λ6584 line. In
order to increase the S/N of their spectra and to increase the
chance of detecting [N ii] emission line at low metallicities, E06
stack 14 or 15 individual galaxy spectra binned by stellar mass
into 6 composite spectra. The [N ii] λ6584 and Hα emission-
line fluxes and metallicities are measured from these composite
spectra.
3. METHODS
In this section, we discuss our methods for determining stellar
masses (Section 3.1), metallicities (Section 3.2), and SFRs
(Section 3.3).
3.1. Stellar Mass
We use the Le Phare
6
code developed by S. Arnouts and O.
Ilbert to estimate the galactic stellar mass. This code estimates
6
http://www.cfht.hawaii.edu/-arnouts/LEPHARE/cfht_lephare/lephare.html
3
The Astrophysical Journal, 757:54 (22pp), 2012 September 20 Zahid et al.
Figure 1. Stellar mass determined by Erb et al. (2006c) plotted against our
determination using Le Phare. The dashed line is the one-to-one agreement, and
the solid line is offset by 0.29 dex. In the five higher mass bins, the stellar mass
estimates used in E06 are greater by a factor of two (0.29 dex).
the stellar masses of galaxies by comparing photometry with
stellar population synthesis models in order to determine the
mass-to-light ratio, which is then used to scale the observed
luminosity (Bell et al. 2003b; Fontana et al. 2004). We syn-
thesize magnitudes from the stellar templates of Bruzual &
Charlot (2003) and use a Chabrier (2003) initial mass func-
tion (IMF). The 27 models have two metallicities and seven
exponentially decreasing star formation models (SFR ∝ e
−t/τ
)
with τ = 0.1, 0.3, 1, 2, 3, 5, 10, 15, and 30 Gyr. We apply the
extinction law of Calzetti et al. (2000) allowing E(B − V )to
range from 0 to 0.6, and the stellar population ages range from
0 to 13 Gyr. The median statistical error for the derived stel-
lar masses, determined from propagating the uncertainty in the
photometry, is 0.15 dex. Though systematic effects may be large
(Drory et al. 2004; Conroy et al. 2009), we have consistently
measured the stellar masses for our different samples, giving us
a robust relative measure (Swindle et al. 2011; R. Swindle 2012,
private communication).
We account for emission-line contributions by taking the
Kennicutt (1998a) relation between the synthesized UV lumi-
nosity and SFR and the emission lines. This treatment accounts
for Hα,Hβ, [O ii] λ3727, and [O iii] λλ4959, 5007 (Ilbert et al.
2009). In our sample, making no correction for the emission-line
contributions does not significantly alter our mass determina-
tions. We adopt the median of the mass distribution and take
the 68% confidence interval as a measure of the error. In Zahid
et al. (2011), we compare this method with the method used by
the MPA/JHU group to determine stellar masses of the SDSS
galaxies. We find that the two estimates differ by a constant off-
set of ∼0.2 dex and that the dispersion between the two methods
is 0.14 dex.
E06 measure stellar masses using a similar method of com-
paring photometry with stellar population synthesis models (Erb
et al. 2006c). However, an important difference is that they mea-
sure the “total” stellar mass, which is the integral of the SFR
over the lifetime of the galaxy. They find that this stellar mass
is ∼10%–40% higher than the instantaneous (or what they term
“current living”) stellar mass. However, most mass estimates
found in the literature are generally the instantaneous and not
“total” stellar mass. We recalculate the stellar masses for their
individual galaxies and bin the data according to their original
binning. In Figure 1, we compare the mass estimates for each
of their six bins. The x-axis shows our mass estimate, and the
y-axis is the original mass estimate from E06. The error bar
represents the rms dispersion of stellar masses in each mass bin.
For the five higher mass bins, we find that there is a constant
offset such that the E06 estimates are 0.29 dex higher than our
estimate. For the lowest mass bin, there appears to be a near one-
to-one agreement, though the 0.29 dex offset is within the errors.
This is most likely due to the fact that the lowest mass galax-
ies are younger and therefore have a much closer agreement
between their instantaneous and “total” stellar mass. Moreover,
we do not concern ourselves too much with the lowest mass bin
as the metallicity measure is only an upper limit for this bin.
Since we do not rebin the E06 data in determining the metallic-
ity, we adopt their stellar mass values but subtract 0.29 dex to
make them consistent with our estimates.
Figure 2(a) shows the distribution of the stellar masses for all
three samples.
3.2. Metallicity
We use two strong-line methods to determine the metallicity
of galaxies in our sample. In this section, we only present
the parameterization of the calibration and defer a detailed
discussion of the methods until Section 8.3. For the SDSS and
DEEP2 sample, we determine metallicities using the calibration
of Kobulnicky & Kewley (2004). This method relies on the R23
and O32 parameters, which are defined as
R23 =
[O ii] λ3727 + [O iii] λλ4959, 5007
Hβ
(2)
Figure 2. Histogram of the (a) stellar mass, (b) metallicity, (c) SFR (M
yr
−1
), and (d) fitted E(B −V ) for the DEEP2 (solid black) and SDSS (dashed blue) samples.
The values for the six binned data points of E06 are shown by the red ticks.
(A color version of this figure is available in the online journal.)
4
The Astrophysical Journal, 757:54 (22pp), 2012 September 20 Zahid et al.
and
O32 =
[O iii] λλ4959, 5007
[O ii] λ3727
. (3)
Here, the ratio implies the ratio of the measured line intensities.
We have used the assumption that the ratio of the fluxes of
[O iii]λ5007 to [O iii]λ4959 is 3 (Osterbrock 1989). Due to
the higher S/Nofthe[Oiii]λ5007 line, for the sum of the
[O iii]λ4959 and [O iii]λ5007 flux we adopt a value of 1.33 times
the [O iii]λ5007 flux.
The R23 strong-line method is known to be sensitive to the
ionization parameter. The ionization parameter characterizes
the ionization state of the gas and quantitatively represents the
number of ionizing photons per second per unit area divided
by the hydrogen density. The ionization parameter can be
constrained by measuring the ratio of the line intensity of
the same element at two ionization stages. The method of
Kobulnicky & Kewley (2004) does this explicitly by using
the O32 line ratio. Because both the metallicity and ionization
parameter are interdependent, an iterative scheme is used, the
details of which are provided in the Appendix of Kewley &
Ellison (2008). In particular, we use Equations (A4) and (A6).
The DEEP2 data are not flux calibrated, so we use the
line equivalent widths with a correction applied for Balmer
absorption (Zahid et al. 2011). For consistency, we determine
the SDSS metallicities using line equivalent widths as well.
Several studies have established that line equivalent widths can
be substituted for line fluxes when measuring metallicities if
data are not flux calibrated or a reliable reddening estimate
is unavailable (Kobulnicky & Phillips 2003; Moustakas et al.
2010; Zahid et al. 2011). In particular, we test this on our SDSS
sample and find that the dispersion between the metallicities
measured using equivalent widths and dereddened line fluxes
is ∼0.05 dex, which is less than intrinsic uncertainties of the
strong-line method. The average difference in the MZ relation
derived using the two methods is <0.01 dex.
One issue with using the R23 method is that metallicity is
not a monotonic function of R23. For a particular value of
the R23 parameter there are two possible values of metallicity
known as the upper and the lower branch metallicity. This
degeneracy is generally alleviated by employing a second
metallicity diagnostic that relies on line ratios that are monotonic
with metallicity. For our SDSS sample of galaxies, the use of
[N ii]/Hα
reveals that the vast majority (∼99%) of galaxies
are on the upper branch. For our DEEP2 sample, the nominal
wavelength coverage of the spectra does not allow us to
simultaneously observe the R23 lines and [N ii]/Hα. We assume
that all galaxies with M
∗
> 10
9.2
M
lie on the upper metallicity
branch (for more details see Figure 5 in Zahid et al. 2011).
The calibration of Kobulnicky & Kewley (2004) is based on
theoretical photoionization models. Empirical methods rely on
calibrating strong-line ratios to metallicities determined using
temperature-sensitive auroral lines. E06 determine metallicities
using the empirical calibration of Pettini & Pagel (2004). The
metallicity is given by
12 + log(O/H) = 8.90 + 0.57 × N2, (4)
where N2 = log([N ii]λ6584/Hα). Using ∼28,000 galaxies
from the SDSS DR4, Kewley & Ellison (2008) derive constants
for converting between various diagnostics. We use these
conversion constants to consistently determine metallicities
for all three samples using both the theoretical and empirical
calibrations of Kobulnicky & Kewley (2004) and Pettini & Pagel
(2004).
The metallicity of a galaxy is traditionally defined as a number
density of oxygen relative to hydrogen and is given as 12 +
log(O/H). For this study, we require the mass density of oxygen
relative to hydrogen. We convert number density to mass density
using the relation
log(Z
g
) = 12 + log(O/H) − 12 −log
M
O
/M
H
XM
H
+ YM
He
= log(O/H) − log
15.999/1.0079
0.75 × 1.0079 + 0.25 × 4.0026
.
(5)
For the remainder of the paper, Z
g
refers to the gas-phase mass
density of oxygen relative to hydrogen. Also, when referring to
metallicity or gas-phase oxygen abundance, we mean to refer
to Z
g
.
Figure 2(b) shows the distribution of the metallicities for all
three samples.
3.3. Star Formation Rate
The SFRs for the SDSS sample are derived by the MPA/
JHU group using the technique of Brinchmann et al. (2004)
with additional improvements given by Salim et al. (2007). The
strong emission lines of each galaxy are fit using the nebular
emission models of Charlot & Longhetti (2001). All emission
lines contribute to constraining the dust attenuation, though the
largest contribution comes from the Hα/Hβ ratio. At the median
redshift of the SDSS, about 1/3 of the galaxy light is contained
within the 3
fiber. In order to account for losses, Brinchmann
et al. (2004) derive an aperture correction, which was improved
upon by Salim et al. (2007). We convert from a Kroupa to
Chabrier IMF by dividing by 1.06.
We estimate the SFRs for the DEEP2 and E06 sample from
the Hβ and Hα emission lines, respectively. In order to reliably
estimate the SFR, it is necessary to make a correction to the
Balmer line flux due to dust extinction. Since the nominal
wavelength coverage of both the DEEP2 and E06 spectra does
not allow us to observe multiple order Balmer lines, we are not
able to derive a correction from the Balmer decrement. Garn
&Best(2010) have shown that for a sample of star-forming
galaxies from the SDSS the extinction determined from the
Hα/Hβ ratio can be predicted from the stellar mass, Hα
luminosity, or metallicity of the galaxy with a dispersion of
∼0.1 dex. The relation between stellar mass and dust extinction
found by Garn & Best (2010) is shown to be valid out to z ∼ 1.5
(Sobral et al. 2012), and a relation between dust extinction,
stellar mass, and metallicity is also observed in galaxies at z ∼ 2
(Reddy et al. 2010).
Xiao et al. (2012) obtain a slightly better fit (dispersion
of 0.07 dex) by incorporating galaxy inclination and using a
different parameterization. We determine E(B − V ) for our
sample of SDSS galaxies from the Balmer decrement assuming
the Cardelli et al. (1989) extinction law and parameterize
E(B − V ) as a function of stellar mass and metallicity using
a similar formulation to Xiao et al. (2012). The color excess is
given by
E(B − V ) = (p
0
+ p
1
Z
p
2
) × M
p
3
, (6)
where Z = 10
(12+log(O/H)−8)
and M = M
∗
/10
10
. The metallici-
ties are derived using the calibration of Kobulnicky & Kewley
(2004). We perform a nonlinear least-squares fit using the
MPFIT
7
set of routines (Markwardt 2009). The data are
7
http://purl.com/net/mpfit
5
