We have used large samples of GAMA and SDSS galaxies covering a wide range in SFR to construct the Hα LFs in several redshift bins. Owing to the deep spectroscopic observations of GAMA combined with the area of the survey, both the faint and bright ends of the low redshift (z < 0.1) star forming LF are explored in detail in this study.
The key results are:
• The Saunders et al. (1990) functional form, which is used to fit the observed radio and far–infrared LFs for star forming galaxies in the literature, now proves to be a good representation of the Hα LF. This is an important result demonstrating that a consistent functional form reproduces the LF of the star forming galaxies at a variety of different SFR–sensitive wavelengths.
• Using GAMA data we extend the observed Hα LF by ∼ 1 order of magnitude in luminosity towards both fainter and brighter luminosities than other published results. The low–z GAMA and SDSS LFs indicate an increasing number density of star forming galaxies at faint luminosities. While this result is qualitatively in agreement with the LFs of Westra et al. (2010) and James et al. (2008), we observe this effect at fainter luminosities than they reach. The nature of this faint population has been examined further in Brough et al. (2011).
• We investigate the effects of bivariate selection and find that it introduces an incompleteness that is difficult to account for, excluding optically faint but Hα bright systems. We find that the SFR density estimates from emission line measures are affected strongly by bivariate selection, leading to the large scatter seen in the SFH.
• We have investigated the comic (sample) variance effects on GAMA LFs by dividing two GAMA regions (GAMA–09h and GAMA–12h) into12 square degree regions, and calculating LFs and SFR densities for each sub–region. We find that the dispersion in SFR densities due to cosmic (sample) variance can be between factors of two to three.
• We exhaustively test a number of potential biases, systematics and limitations such as the assumption of a constant stellar absorption and completeness corrections, the empirical estimation of Balmer decrements, cosmic (sample) variance issues etc., on the calculation of the LFs, and find that our results are robust to all of these.
• The bivariate Mr/Hα selection imposed on the GAMA and SDSS emission line galaxies make the star
forming samples somewhat incomplete. As a consequence, the SFR densities we derive can only be lower limits. Nonetheless our measurements are the best estimates to date of the low redshift Hα LFs, and the corresponding luminosity density arising from Hα.
3
Bivariate distribution functions of Hα star forming galaxies
Abstract
We present the bivariate LHα–Mr and LHα–M, where M is the stellar mass, distribution functions of Galaxy And Mass
Assembly (GAMA) survey Hα star forming (SF) galaxies. While GAMA provides optically deep spectroscopic observations
over a wide sky area enabling the detection of a large number star forming galaxies covering0.001 < SF RHα < 100, the
requirement for an Hα detection in targets selected from an r–band magnitude limited survey leads to an incompleteness
due to missing optically faint star forming galaxies. To correct for this incompleteness, we use the lowest redshift LHα–Mr
and LHα–M distributions as a reference to model the higher–z bivariate LFs, thereby approximating the contribution from
the missing optically faint star forming galaxies to the local star formation rate and stellar mass densities. Furthermore, we
present the univariate MrandM LFs of Hα SF galaxies obtained by integrating the bivariate LFs along the LHαaxis. As our
sample is selected on the basis of detected Hα emission, a direct tracer of on–going star formation in galaxies, this sample represents a true star forming galaxy sample, and is drawn from both photometrically classified blue and red sub–populations, though mostly from the blue population. We find that not all members of the GAMA blue population, conventionally called star formers, have detected Hα emission, and approximately 20–30% at all stellar masses of the GAMA red population, conventionally called passive galaxies, are in fact star forming. This would mean blue galaxies, although may not have current star formation, have undergone a recent burst of star formation, while the red galaxies may be dominated by old stars but still have some on–going star formation, or they may be dusty star forming systems.
Gunawardhana M. L. P. et. al., MNRAS (submitted)
3.1
Introduction
The observed univariate luminosity function (LF) is one of the fundamental measures of galaxy properties. It is usually one of the first results to be measured from galaxy surveys (e.g. Loveday et al. 2012; Croom et al. 2009; Blanton et al. 2003c; Liske et al. 2003; Norberg et al. 2002). The importance of the LF, defined as the co–moving source density with luminosity (or magnitude)L + ∆L, extends to all areas of astronomy. In an observational context, it is used to quantify the mean space density of galaxies per unit luminosity and the evolution of statistical properties of a galaxy sample across cosmic time (Gunawardhana et al. 2013; Westra et al. 2010; Shioya et al. 2008). In theoretical modelling, the LF is a key ingredient needed to constrain the dark matter halo formation (Bower et al. 2008; Croton et al. 2006). In an era of multi–wavelength legacy surveys with intrinsically complicated multi–band selections (e.g. Driver et al. 2011, Galaxy And Mass Assembly survey), understanding the effects of selection and systematic biases on the shape of the LF is imperative in obtaining reliable LF measures to facilitate advances in galaxy formation and evolution research.
Simply due to the existence of detection limits, no single survey can directly detect all sources to provide a com- plete and unbiased galaxy sample. The detection probability of an object is a function of a number of parameters,
64 BIVARIATE DISTRIBUTION FUNCTIONS OFHαSTAR FORMING GALAXIES
both external (e.g. survey selection, area and depth, star–galaxy separation, observing conditions and redshift, spectroscopic and target completeness) and intrinsic to the object (e.g. surface brightness, size and colour). As luminosity is strongly correlated with both sets of factors, the least luminous objects in any magnitude–limited survey have the poorest detection probabilities (Geller et al. 2012), thus occupying a relatively small volume. The low luminosity galaxies, although they do not dominate the luminosity budget of the universe, greatly outnumber the luminous giants. As other studies have empasised (Petrosian 1998), measuring the evolution of the slope of the faint end of the LF is a challenge. This arises because of the preferential bias against faint galaxies due to surface brightness limits (Geller et al. 2012; Dalcanton et al. 1997; Sprayberry et al. 1996), galaxy morphologies (Tempel et al. 2011; Marzke et al. 1998), spectral types (Madgwick et al. 2002; Folkes et al. 1999), environment (Zandivarez & Mart´ınez 2011; Tempel et al. 2009; Xia et al. 2006) and colour (Blanton et al. 2001) as well as external issues (Loveday et al. 2012; Driver et al. 2005).
Any galaxy sample selected based on a parameter other than the primary survey selection criteria is biased as a result of the dual sample and survey selection. Gunawardhana et al. (2013) and Westra et al. (2010) present the Hα univariate LFs and determine the evolution of Hα star formation rate density (SFRD) in the local universe using Hα star forming (SF) galaxy samples drawn respectively from the r–band magnitude–limited Galaxy And Mass Assembly (GAMA) and Smithsonian Hectospec Lensing surveys. These studies show that their lowest redshift (z < 0.1) samples are in fact the most complete and span the largest range in both intrinsic Hα luminosity (LHα) andr–band absolute magnitude (Mr), e.g. the GAMAz < 0.1 sample probes 30.5. log LHα(W ) . 36
and−24 . Mr . −10 (Gunawardhana et al. 2013). With increasing redshift, however, the sample completeness
drops in the sense that a fraction of optically faint star forming galaxies are missing from the higher–z sub–samples and this fraction increases with increasing redshift. As a consequence, the final SFRDs based on bivariately selected samples are underestimated, manifesting as an apparent lack of evolution with redshift in contrast to current observations (P´erez-Gonz´alez et al. 2008; Hopkins & Beacom 2006; Madau et al. 1996). To recover the missing contribution from optically faint star forming galaxies requires studying how the selection biases influence the LF.
The bivariate LF (Phillipps & Disney 1986) provides a powerful method of studying the luminosity density in different epochs inclusive of selection biases (e.g. bivariate brightness distributions, bivariate luminosity and size distribution). There is a rich collection of literature on using bivariate LFs to explore the space density of galaxies as a function of both survey selection wavelength and surface brightness limits (Driver et al. 2005; Cross et al. 2001; Blanton et al. 2001; Driver 1999), galaxy size (Cameron & Driver 2007; de Jong et al. 2004; de Jong & Lacey 2000; Sodre & Lahav 1993), radio luminosity (Mauch & Sadler 2007; Ledlow & Owen 1996; Sadler et al. 1989), S´ersic index, stellar mass and spectral type (Ball et al. 2006a), colour (Baldry et al. 2004) and in pairs of various galaxy properties (Driver et al. 2006; Blanton et al. 2003a) as well as bivariate ultraviolet/infrared LFs (Takeuchi et al. 2012; Saunders et al. 1990).
In this followup paper to Gunawardhana et al. (2013), hereafter paper I (Chapter 2 of this thesis), we explore the GAMA bivariate LHα–Mrand LHα–M LFs. The primary aims of this investigation are to model the low redshift
bivariate LFs to use as a reference to account for the missing optically faint star forming galaxies at higher–z. We further present the univariate Mr LFs and stellar mass functions (SMF) of Hα SF galaxies. We also explore the
characteristics of photometrically classified blue and red star forming sub–populations in GAMA.
The layout of this paper is as follows. We briefly describe sample selection and the GAMA survey in§ 3.2. A summary of the measurement of the univariate Hα LF is presented in§ 3.3. In § 3.4, we describe the details of the derivation of the bivariate LFs, taking into account different survey selection criteria. The bivariate LF results are presented in§ 3.5 and § 3.8, which also include the univariate LF results obtained from integrating the bivariate LFs along the LHαaxis.§ 3.6 describes the details of the functional forms used to fit the bivariate LFs, and in § 3.7
and§ 3.9, we infer corrected SFR and M densities for our GAMA bivariate LFs.
The assumed cosmological parameters are H0 = 70 km s−1Mpc−1,ΩM = 0.3, and ΩΛ = 0.7. All magnitudes
are presented in the AB system. A Chabrier (2003) IMF is used to derive the stellar mass measurements used in this study and a Baldry & Glazebrook (2003a) IMF is used in the calculation of SFRs. To avoid confusion we state in the figure caption which IMF is used to obtain the results shown.