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Wright, A. H. and Robotham, A. S. G. and Driver, S. P. and Alpaslan, M. and Andrews, S. K. and Baldry, I.
K. and Bland-Hawthorn, J. and Brough, S. and Brown, M. J. I. and Colless, M. and da Cunha, E. and Davies,
L. J. M. and Graham, A. W. and Holwerda, B. W. and Hopkins, A. M. and Kae, P. R. and Kelvin, L. S. and
Loveday, J. and Maddox, S. J. and Meyer, M. J. and Moett, A. J. and Norberg, P. and Phillipps, S. and
Rowlands, K. and Taylor, E. N. and Wang, L. and Wilkins, S. M. (2017) 'Galaxy And Mass Assembly
(GAMA): the galaxy stellar mass function to z = 0.1 from the r-band selected equatorial regions.', Monthly
notices of the Royal Astronomical Society., 470 (1). pp. 283-302.
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https://doi.org/10.1093/mnras/stx1149
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MNRAS 470, 283–302 (2017) doi:10.1093/mnras/stx1149
Advance Access publication 2017 May 11
Galaxy And Mass Assembly (GAMA): the galaxy stellar mass function
to z = 0.1 from the r-band selected equatorial regions
A. H. Wright,
1,2‹
A. S. G. Robotham,
1
S. P. Driver,
1,3
M. Alpaslan,
4
S. K. Andrews,
1
I. K. Baldry,
5
J. Bland-Hawthorn,
6
S. Brough,
7
M. J. I. Brown,
8
M. Colless,
9
E. da Cunha,
9
L. J. M. Davies,
1
Alister W. Graham,
10
B. W. Holwerda,
11
A. M. Hopkins,
6
P. R. Kafl e ,
1
L. S. Kelvin,
5
J. Loveday,
11
S. J. Maddox,
12,13
M. J. Meyer,
1
A. J. Moffett,
6
P. Norberg,
14
S. Phillipps,
15
K. Rowlands,
3
E. N. Taylor,
10
L. Wang
16,17
and S. M. Wilkins
18
Affiliations are listed at the end of the paper
Accepted 2017 May 9. Received 2017 April 24; in original form 2017 January 18
ABSTRACT
We derive the low-redshift galaxy stellar mass function (GSMF), inclusive of dust corrections,
for the equatorial Galaxy And Mass Assembly (GAMA) data set covering 180 deg
2
.We
construct the mass function using a density-corrected maximum volume method, using masses
corrected for the impact of optically thick and thin dust. We explore the galactic bivariate
brightness plane (M
–μ), demonstrating that surface brightness effects do not systematically
bias our mass function measurement above 10
7.5
M
. The galaxy distribution in the M–μ plane
appears well bounded, indicating that no substantial population of massive but diffuse or highly
compact galaxies are systematically missed due to the GAMA selection criteria. The GSMF
is fitted with a double Schechter function, with M
= 10
10.78±0.01±0.20
M
, φ
1
= (2.93 ±
0.40) × 10
−3
h
3
70
Mpc
−3
, α
1
=−0.62 ± 0.03 ± 0.15, φ
2
= (0.63 ± 0.10) × 10
−3
h
3
70
Mpc
−3
and α
2
=−1.50 ± 0.01 ± 0.15. We find the equivalent faint end slope as previously estimated
using the GAMA-I sample, although we find a higher value of M
. Using the full GAMA-II
sample, we are able to fit the mass function to masses as low as 10
7.5
M
, and assess limits
to 10
6.5
M
. Combining GAMA-II with data from G10-COSMOS, we are able to comment
qualitatively on the shape of the GSMF down to masses as low as 10
6
M
. Beyond the
well-known upturn seen in the GSMF at 10
9.5
, the distribution appears to maintain a single
power-law slope from 10
9
to 10
6.5
. We calculate the stellar mass density parameter given
our best-estimate GSMF, finding
= 1.66
+0.24
−0.23
± 0.97 h
−1
70
× 10
−3
, inclusive of random and
systematic uncertainties.
Key words: galaxies: evolution – galaxies: fundamental parameters – galaxies: general –
galaxies: luminosity function, mass function – galaxies: stellar content.
1 INTRODUCTION
The galaxy stellar mass function (GSMF; Bell et al. 2003;Baldry,
Glazebrook & Driver 2008;Baldryetal.2012) is arguably one
of the most fundamental measurements in extragalactic astronomy.
Its integral returns the density of baryonic mass currently bound
in stars (and hence the global efficiency of star formation) while
the shape of the distribution describes the evolutionary pathways
that have shuffled matter from atomic to stellar form – essentially
E-mail: awright@uni-bonn.de
mergers building the high-mass end of the GSMF (M
≥ 10
10.8
)
while in situ star formation fuelled by gas accretion has built the
low-mass end (Robotham et al. 2014). Not surprisingly the GSMF
is also the key calibration for most galaxy formation models that
are carefully tuned to best reproduce the latest GSMF measurement
(Genel et al. 2014; Gonzalez-Perez et al. 2014; Crain et al. 2015;
Schaye et al. 2015;Laceyetal.2016). In particular, the comparison
between observations of the GSMF and numerical simulations of
the dark-matter halo mass function have led directly to the notion
of feedback – both AGN feedback at high mass (see e.g. Bower
et al. 2006; Croton et al. 2006) and supernova feedback at low mass
(Efstathiou 2000). These are now core elements of semi-analytic
C
2017 The Authors
Published by Oxford University Press on behalf of the Royal Astronomical Society
284 A. H. Wright et al.
prescriptions used to populate the haloes formed in purely dark-
matter N-body simulations (Gonzalez-Perez et al. 2014;Laceyetal.
2016).
Observationally, the measurement of the GSMF has superseded
the earlier focus on the measurements of the galaxy luminosity
function. Initially these were undertaken in the optical and later
at near-IR (NIR) wavelengths, where the NIR light was shown to
more closely trace the low-mass stellar populations that dominate
the stellar mass repository. NIR is the best single-band proxy for
stellar mass because NIR colours contain little information about
mass-to-light variations. This conspires to mean there is less scatter
in NIR single-band mass-to-light estimates compared to the same
proxies measured in the optical. Once multiband optical and NIR
data became ubiquitous; however, better estimates could be obtained
by making use of full spectral energy distribution (SED) colour in-
formation. Ultimately a lot of information on optical mass-to-light
is contained in the rest-frame g − r − i colours, so surveys such
as the Sloan Digital Sky Survey (SDSS) and Galaxy And Mass
Assembly (GAMA) could make estimates of stellar mass content
that are accurate within <0.2 dex (Taylor et al. 2011). Over the past
two decades the ability to estimate stellar mass has also become
more established (see e.g. Kauffmann et al. 2003;Belletal.2007;
Taylor et al. 2011). As a consequence, effort has now shifted from
measuring galaxy luminosity functions to the GSMF. The most no-
table measurements are those deriving from large redshift surveys,
in particular the 2dF Galaxy Redshift Survey (2dFGRS; Cole et al.
2001), SDSS (Bell et al. 2003;Baldryetal.2008), the Millennium
Galaxy Catalogue (MGC; Driver et al. 2007) and GAMA (Baldry
et al. 2012). In general there is a reasonable consensus with the latest
measurement from the GAMA team (Baldry et al. 2012), probing
to a stellar mass limit of 10
8
M
.
However three key observational concerns remain: susceptibility
to surface brightness selection effects, the impact of dust attenuation
and the prospect of a sharp upturn in the space density at very low
stellar masses (i.e. below the current observational mass limits). All
three effects could potentially lead to underestimating the GSMF
and the corresponding stellar mass density. This is particularly sig-
nificant when looking to reconcile the current stellar mass density
with the integral of the cosmic star formation history (CSFH; see
Baldry & Glazebrook 2003; Wilkins, Trentham & Hopkins 2008a),
where a significant discrepancy was seen. In an attempt to explain
this discrepancy, some studies have invoked either a top-heavy ini-
tial mass function (IMF) (which produces more luminosity per unit
mass of stars; Baldry & Glazebrook 2003), a time varying IMF
(Wilkins et al. 2008b; Gunawardhana et al. 2011; Ferreras et al.
2015), distinct IMFs for bulge (closed-box star formation with a
top-heavy IMF) and disc formation (infall star formation with a
standard Chabrier-like IMF) as proposed by Lacey et al. (2016),
or an IMF with a larger fraction of returned mass (e.g. Maraston
2005; see also Madau & Dickinson 2014). Additionally, the inte-
grated cosmic star formation history will tend to capture all star
formation events without consideration of dynamical interactions
that deposit formed stars into the intra-halo medium. This means
that the integrated cosmic star formation history naturally includes
stellar material not currently bound to observed galaxies. The com-
bination of the CSFH and the GSMF measured across a broad
redshift range is therefore a powerful tool to constrain the IMF,
feedback and extraneous material stripped from galaxies.
The first comprehensive measurements of the GSMF were made
by Cole et al. (2001). This was based on the combination of spec-
troscopic measurements from the 2dFGRS combined with photo-
metric NIR measurements from 2MASS. Concurrently, Kochanek
et al. (2001) also used 2MASS to estimate the value of
from
K-band luminosity function, although did not calculate the GSMF
explicitly. Andreon (2002) subsequently demonstrated that the shal-
low 2MASS survey misses dim galaxies entirely and significantly
underestimated the fluxes of late-type systems. Similarly the later
and larger studies based on SDSS and GAMA are both reliant
on the completeness of the spectroscopic input catalogues derived
from (relatively) shallow drift-scan SDSS imaging. Blanton et al.
(2005) demonstrated, via adding simulated galaxies to SDSS data,
that incompleteness in the imaging and spectroscopy can become
severe for systems with average surface brightnesses of μ
50, r
≈
23.5 mag arcsec
−2
(see fig. 2 of Blanton et al. 2005,andfig.11of
Baldry et al. 2012). However, one indication that the surface bright-
ness problem may not be overly severe comes from deep field studies
(see e.g. Driver 1999), novel analysis methods designed to search
for low surface brightness galaxies in wide-field imaging (Williams
et al. 2016) and dedicated low surface brightness studies (see e.g.
Geller et al. 2012; Davies, Davies & Keenan 2016), which generally
found that large populations of low surface brightness systems do
not contribute significantly to the stellar mass density. Furthermore,
attempts to correct galaxy luminosity function estimates via a bi-
variate brightness analysis also failed to find extensive populations
of low surface brightness giant galaxies (see e.g. Cross et al. 2001;
Driver et al. 2005).
Dust attenuation has perhaps a more subtle effect. Generally dust
will both diminish and redden a galaxy’s emission, and these two
effects arguably cancel – the reduction in total light is compensated
for by an increase in the estimated mass-to-light ratio (see e.g. the
vector shown in fig. 6 of Bell et al. 2003,andfig.11ofTaylor
et al. 2011). Strictly this is only true in the optically thin case, as
if no light from a particular region is able to escape then the loss
of flux cannot be recovered. The MGC team (Driver et al. 2007)
attempted to quantify the impact of dust attenuation on galaxy mass
estimates by measuring the shift in the recovered M
-parameter of
the optical B-band luminosity function with systemic inclination.
The implicit assumption was that, if dust attenuation is signifi-
cant, edge-on systems should be more attenuated than their face-on
counterparts. A significant M
− cos(i) effect was seen (Driver et al.
2007) which, following extensive modelling using radiative transfer
codes (Popescu et al. 2000; Tuffs et al. 2004), suggested that the
average face-on central opacity of galaxy discs was τ
v
= 3.8; i.e. the
centres of galaxies are optically thick. The resulting impact, based
on corrections using the radiative transfer models, was to increase
the estimate of the present day integrated stellar mass density from
∼5 per cent (Baldry et al. 2008)to∼8 per cent (Driver et al. 2007).
However, significant concerns remain as to the validity of adopting
a constant central face-on opacity for all galaxy types. Indeed, di-
rect observations of galaxies have indicated that the intrinsic nature
of dust in galaxies is highly variable, depending on multiple fac-
tors such as morphology and environment (see e.g. White, Keel &
Conselice 2000; Keel & White 2001; Holwerda 2005; Holwerda
et al. 2013a,b).
Measurements of the GSMF to date reliably extend only to
10
8
M
whereas we have proof-of-existence of galaxies with
masses as low as 10
3
M
in the Local Group (McConnachie 2012).
Hence, there is also some uncertainty as to whether an extrapolation
of the GSMF from 10
8
to 10
3
M
is valid. Recently the study by
Moffett et al. (2016), where the stellar mass functions was divided
by galaxy type, showed two populations with very rapidly rising
slopes at the mass-limit boundary.
All three areas (surface brightness, dust attenuation and low-mass
systems) have the potential to bring into question the robustness of
MNRAS 470, 283–302 (2017)
GAMA: GSMF to z = 0.1 285
our current estimates of the GSMF and the integrated cosmic stellar
mass density. In this paper we provide an updated GSMF, defined
using the SDSS r band, for the completed GAMA (Driver et al.
2011; Liske et al. 2015) survey equatorial fields.
In Section 2, we introduce the GAMA-II sample that is approx-
imately double the size of the GAMA-I sample used in Baldry
et al. (2012), extending 0.4 mag deeper (to r = 19.8 mag) and
over an expanded area of 180 deg
2
. We also utilize the full GAMA
panchromatic imaging data set (Driver et al. 2016b), and photom-
etry measured consistently in all bandpasses from far-UV (FUV)
to far-IR (FIR) (Wright et al. 2016). The FIR data from Herschel
ATLAS (Eales et al. 2010) in particular allow for full SED mod-
elling using codes such as
MAGPHYS (da Cunha, Charlot & Elbaz
2008; da Cunha & Charlot 2011), which accounts for dust attenua-
tion and re-emission when calculating stellar masses. In Section 3,
we compare the stellar masses derived from optical data using stel-
lar template modelling (Taylor et al. 2011) to those derived via the
full SED modelling from
MAGPHYS. In Section 4, we derive our base
GSMF, incorporating density modelling of the GAMA volumes. In
Section 5, we revert to a simpler empirical 1/V
max
method applied
in the bivariate brightness plane to specifically explore the possible
impact of surface brightness selection bias. Finally, in Section 6, we
include similar photometric data from the G10-COSMOS regions
(Davies et al. 2015a; Andrews et al. 2017), fitted with
MAGPHYS
(Driver et al. 2016b) using high precision photometric redshifts
from Laigle et al. (2016), to provide an indication as to the pos-
sible form of the stellar mass function to very low stellar masses
(10
6
M
). We discuss our results in Section 7. T hroughout this
work, we use a standard concordance cosmology of
M
= 0.3,
= 0.7, H
o
= 70 km s
−1
Mpc
−1
,andh
70
= H
o
/70 km s
−1
Mpc
−1
.
We implement a standard Chabrier (2003) IMF, and all magnitudes
are presented in the AB system.
2 DATA AND SAMPLE DEFINITION
The GAMA (Baldry et al. 2010;Driveretal.2011; Hopkins et al.
2013; Liske et al. 2015) survey is a large multiwavelength data
set built upon a spectroscopic campaign aimed at measuring red-
shifts for galaxies with r < 19.8 mag at >98 per cent completeness
(Robotham et al. 2010). The survey’s complementary multiwave-
length imaging is in 21 broad-band photometric filters (Driver et al.
2016b) spanning from the FUV to the FIR. Given this wealth of
broad-band imaging, we are able to calculate matched photometry
for the purposes of estimating galaxy stellar masses. We use 21-
band photometry contained in the GAMA
LAMBDAR Data Release
(LDR), presented in Wright et al. (2016). The LDR photometry is
deblended matched aperture photometry accounting for each im-
age’s pixel resolution and point spread function. Apertures used in
LAMBDAR are defined using a mixture of source extractions on the
SDSS r band, source extractions on the VISTA Z band and by-hand
definitions using VISTA Z-band images. Measurements are made
for all images in the GAMA Panchromatic Data Release (Driver
et al. 2016b).
This photometric data set is designed specifically for use in cal-
culating SEDs, as the photometry and uncertainties are consistently
measured across all passbands. Furthermore, as the photometry is
matched aperture, there exists an estimate in every band for every
object in the sample, with a corresponding uncertainty (except, of
course, where there is no imaging data available due to coverage
gaps). For the calculation of relevant cosmological distance param-
eters and redshift limits, fluxes have been appropriately k-corrected
using KCorrect (Blanton & Roweis 2007), and redshifts have
been flow-corrected using the models of Tonry et al. (2000)as
described in Baldry et al. (2012).
We calculate stellar masses for the LDR photometry using two
independent methods. First, we fit panchromatic SEDs to the full
21-band data set using the energy balance program
MAGPHYS (da
Cunha et al. 2008; da Cunha & Charlot 2011). A full description
of the
MAGPHYS fits to the GAMA LDR is provided in Driver et al.
(2017).
MAGPHYS utilizes information from the UV to the FIR to
estimate the total stellar mass of each galaxy from both visible
and obscured stars, assuming Bruzual & Charlot (2003)(BC03)
models, a Chabrier (2003) IMF, and the Charlot & Fall (2000) dust
obscuration law. Secondly, we use the measurement of Taylor et al.
(2011) who estimated stellar masses by fitting a comprehensive
grid of SED templates to photometry from the SDSS u band to
the VIKING K
s
-band, applied to our updated LDR photometry.
Their technique uses stellar population synthesis (SPS) models with
exponentially declining star formation histories, without bursts, and
the same BC03 models and Chabrier (2003)IMFas
MAGPHYS,but
uses a Calzetti et al. (2000) dust obscuration law. In addition to this
difference in implemented dust obscuration law, the predominant
differences between these two methods are:
(i) the wider range of photometric filters (and energy balance)
used in
MAGPHYS;
(ii) the incorporation of bursty star formation histories in
MAG-
PHYS;
(iii) a sparser grid of star formation histories in
MAGPHYS.
For clarity, throughout this work we refer to stellar mass estimates
from
MAGPHYS, which utilize the full FUV to FIR bandpass, as
‘bolometric’ masses, and stellar masses from our SPS templates,
which are fit across the near-UV to NIR passbands, as ‘optical’
masses.
Using these two methods, we check for systematic differences
in our estimated stellar masses. By comparing the two sets of mass
estimates, we can explore how our subsequent fits are systematically
affected by our choice of stellar mass estimation. In particular, an
observed difference in the mass estimates (and GSMF fits) can
indicate the impact of optically thick dust on our masses (as
MAGPHYS
includes consideration of optically thick dust, whereas our optically
estimated masses do not).
Fig. 1 shows a compendium of the four main comparison planes
that demonstrate systematic differences; namely variations as a
function of stellar mass (upper left), dust-to-stellar mass ratio (up-
per right), galaxy inclination (lower left) and
MAGPHYS burst fraction
over the last 2 Gyr (lower right). We note that there are two pop-
ulations that separate out in the upper panels, most notably in the
dust-to-stellar mass ratio comparison. The most systematically dif-
ferent stellar masses are localized at small stellar masses, high dust-
to-stellar mass ratios, and at higher
MAGPHYS burst fraction. Each of
these properties is consistent with belonging to the predominantly
young and disc-dominated portion of the sample, where bursts and
variations in the dust obscuration prescription are likely to have
the most impact. As a result, we postulate that the differences seen
in the mass estimates stem predominantly from the differences in
libraries, models and burst prescriptions implemented in our fitting
procedures. However despite these visible differences, we find that
94.8 per cent of the sample are contained within |log
10
M|≤0.2
for the entire sample. This fraction increases to 97.8 per cent if we
select only masses with
MAGPHYS goodness-of-fit 0.5 ≤ χ
2
ν
≤ 1.5.
For the low redshift portion of the data (0.002 < z < 0.1), there are
86.0 per cent of masses within |log
10
M|≤0.2, and 88.8 per cent
when selecting 0.5 ≤ χ
2
ν
≤ 1.5. In general, the optically derived
MNRAS 470, 283–302 (2017)
286 A. H. Wright et al.
Figure 1. Comparison of bolometric stellar masses returned by MAGPHYS to those measured using the optical-only method presented in Taylor et al. (2011),
as a function of
MAGPHYS stellar mass (panel ‘a’), MAGPHYS dust mass (panel ‘b’), galaxy inclination (panel ‘c’) and MAGPHYS burst fraction over the last 2 Gyr
(panel ‘d’). While all of these figures show typical agreement within ±0.2 dex, there are systematic trends visible in each distribution which we attribute to the
difference in chosen dust attenuation and burst models between the codes.
masses return slightly higher stellar masses (median offset log
10
M = log
10
M
OPT
− M
BOL
= 0.03) than the bolometrically mod-
elled masses, and (as there is no obvious trend in inclination) there
appears to be no indication of significant quantities of optically
thick dust. All of these systematic shifts in masses are well within
both the typical quoted mass uncertainty (median mass uncertainty
δlog
10
M = 0.10), and within the width of the central 68th per cent
range (i.e. 1σ ) of the distribution (σ
M
= 0.14).
Finally, we implement a correction to account for flux/mass
missed by the matched aperture photometry described in Wright
et al. (2016). To correct for systematically missed flux/mass, we
utilize the GAMA S
´
ersic profile fits to our sample. We calculate
the linear ratio between the measured S
´
ersic flux and aperture flux
for each source (this is the same aperture correction described in
Taylor et al. (2011), and is often referred to as the ‘fluxscale’ fac-
tor in GAMA data products and publications). This correction has
the effect of preferentially boosting high-mass sources, as stellar
mass is loosely correlated with galaxy S
´
ersic index n and (in a
fixed finite aperture) galaxies will increasingly miss flux with in-
creasing n. However, as this correction is based on the empirically
estimated S
´
ersic fits (which are themselves possibly subjected to
random and systematic biases), we provide the results for the un-
corrected masses in Appendix A. These fits provide lower limits for
the various parameters estimated in this work.
2.1 Additional systematic biases
By estimating our stellar masses using our ‘optical’ and ‘bolomet-
ric’ methods, we attempt to explore how the stellar mass function
is affected by some of the choices and assumptions that have been
made in this work (such as the impact of dust and the allowed
burstiness). However, these tests certainly do not encompass the full
gambit of assumptions implicit to stellar mass estimation using SPS
models. Such assumptions are required because of our uncertainty
of, for example, the stellar IMF (Driver et al. 2012), the contribu-
tion of thermally pulsing asymptotic giant branch (TP-AGB) stars
(Maraston 2005; B ruzual 2007; Conroy, Gunn & White 2009), the
choice of parametrization of star formation histories (Fontana et al.
2004;Pacificietal.2015), modelling of bursts (Pozzetti et al. 2007)
and more. Here we briefly discuss the effect of some of these as-
sumptions, and derive an estimate of the systematic uncertainty
required to be added to our estimates of stellar masses and their
derived quantities.
Systematic effects originating from our uncertainty in the stellar
IMF are well documented in the literature, and there is an ongoing
debate as to whether the shape of the IMF is well described by
something akin to the Chabrier (2003) IMF, or whether it is better
described by a top-heavy (Baldry & Glazebrook 2003) or bottom-
heavy (Kroupa, Tout & Gilmore 1993) function, or whether there is
a single valid description for the IMF over all times (Wilkins et al.
2008a). Generally, variation of the IMF manifests itself as a shift in
the stellar population mass-to-light ratio, and thus as a scaling of the
estimated mass of each galaxy, as the IMFs typically differ in their
treatment of only the most and least massive stars (Bell et al. 2003;
Driver 2013). This, in turn, means that a change in the IMF will
cause a multiplicative scaling of estimated quantities such as M
and
. Driver et al. (2012) provided a prescription for converting
between some of the various popular IMFs in the literature, which
MNRAS 470, 283–302 (2017)
