{\em Herschel}-ATLAS/GAMA: The Environmental Density of Far-Infrared Bright Galaxies at z≤0.5
C. S. Burton, Matt J. Jarvis, D. J. B. Smith, D. G. Bonfield, M. J. Hardcastle, J. A. Stevens, N. Bourne, M. Baes, S. Brough, A. Cava, A. Cooray, A. Dariush, G. De Zotti, L. Dunne, S. Eales, R. Hopwood, E. Ibar, R. J. Ivison, J. Liske, J. Loveday, S. J. Maddox, M. Negrello, M. W. L. Smith, E. Valiante
MMon. Not. R. Astron. Soc. , ?? – ?? (2012) Printed 30 October 2018 (MN L A TEX style file v2.2)
Herschel (cid:63) -ATLAS/GAMA: The Environmental Density ofFar-Infrared Bright Galaxies at z ≤ . C. S. Burton † , Matt J. Jarvis , , D. J. B. Smith , D. G. Bonfield , M. J. Hardcastle ,J.A. Stevens , N. Bourne , M. Baes , S. Brough , A. Cava , A. Cooray , A. Dariush ,G. De Zotti , , L. Dunne , S. Eales , R. Hopwood , , E. Ibar , R. J. Ivison , ,J. Liske , J. Loveday , S. J. Maddox , M. Negrello , M. W. L. Smith and E. Valiante Centre for Astrophysics, Science & Technology Research Institute, University of Hertfordshire, AL10 9AB, UK Oxford Astrophysics, Department of Physics, Keble Road, Oxford, OX1 3RH, UK Physics Department, University of the Western Cape, Bellville 7535, South Africa School of Physics & Astronomy, Nottingham University, University Park Campus, Nottingham, NG7 2RD, UK Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281 S9, B-9000 Gent, Belgium Australian Astronomical Observatory, P.O. Box 915, North Ryde, NSW 1670, Australia Departamento de Astrof´ısica, Facultad de CC. F´ısicas, Universidad Complutense de Madrid, E-28040 Madrid, Spain Department of Physics and Astronomy, University of California, Irvine, CA 92697, USA Physics Department, Imperial College London, Prince Consort Road, London, SW7 2AZ, UK INAF - Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, I-35122 Padova, Italy SISSA, Via Bonomea 265, I-34136 Trieste, Italy Department of Physics and Astronomy, University of Canterbury, Private Bag 4800, Christchurch, 8140, New Zealand School of Physics and Astronomy, Cardiff University, Queens Buildings, The Parade, Cardiff CF24 3AA, UK Department of Physics and Astronomy, The Open University, Walton Hall, Milton Keynes, MK7 6AA, UK UK Astronomy Technology Centre, Royal Observatory, Edinburgh, EH9 3HJ, UK Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748 Garching, Germany Astronomy Centre, University of Sussex, Falmer, Brighton BN1 9QH, UK
30 October 2018
ABSTRACT
We compare the environmental and star formation properties of far-infrared detected and non–far-infrared detected galaxies out to z ∼ . . Using optical spectroscopy and photometryfrom the Galaxy And Mass Assembly (GAMA) and Sloan Digital Sky Survey (SDSS), withfar-infrared observations from the Herschel -ATLAS Science Demonstration Phase (SDP), weapply the technique of Voronoi Tessellations to analyse the environmental densities of individ-ual galaxies. Applying statistical analyses to colour, r − band magnitude and redshift-matchedsamples, we show there to be a significant difference at the 3.5 σ level between the normalizedenvironmental densities of these two populations. This is such that infrared emission (a tracerof star formation activity) favours underdense regions compared to those inhabited by exclu-sively optically observed galaxies selected to be of the same r − band magnitude, colour andredshift. Thus more highly star-forming galaxies are found to reside in the most underdenseenvironments, confirming previous studies that have proposed such a correlation. However,the degeneracy between redshift and far-infrared luminosity in our flux-density limited sam-ple means that we are unable to make a stronger statement in this respect. We then applyour method to synthetic light cones generated from semi-analytic models, finding that overthe whole redshift distribution the same correlations between star-formation rate and environ-mental density are found. Key words: method: data analysis – galaxies: statistics – galaxies: submillimetre– galaxies:star formation. (cid:63)
Herschel is an ESA space observatory with science instruments providedby European-led Principal Investigator consortia and with important partic-ipation from NASA. † E-mail: [email protected]
It is clear that if we are to understand the process by which galaxiesform and evolve, we have to consider the role that their immedi- c (cid:13) a r X i v : . [ a s t r o - ph . C O ] M a y C. S. Burton et al. ate environment plays. Dressler (1980) was the first to show thatthere is a correlation between the morphology of a galaxy pop-ulation and the density of its environment. Further studies havesince shown that disk dominated ‘late-type’ galaxy morphologieswith high star formation rates (SFR) dominate underdense regions,while their elliptical ‘early-type’ counterparts, with low SFR, dom-inate the densest regions (Postman & Geller 1984; Dressler et al.1997; Dom´ınguez et al. 2001; Goto et al. 2003; Kauffmann et al.2004; O’Mill et al. 2008; Lee et al. 2010; Wijesinghe et al. 2012).It has also been shown, with the advent of large area sur-veys such as the Sloan Digital Sky Survey (SDSS; York et al.2000), that these galaxies can be categorised into two distinct op-tical colour populations, ‘
Red ’ and ‘
Blue ’, where the colour of agalaxy is dependent on several internal properties that represent theevolutionary history of the galaxy; metallicity ( Z ), star formationhistory (SFH) and dust attenuation ( A ). These two colour popula-tions show, at a fixed luminosity, a correlation with density suchthat the densest regions are populated by the red, early-type pas-sive galaxies, with blue, star-forming late-types observed in lessdense regions (Poggianti et al. 2006). However, earlier work byBalogh et al. (1997, 1998) compared galaxies with similar lumi-nosities and morphologies from both dense cluster and low den-sity field environments, and found that that the SFR was still lowerin dense cluster regions and thus the SFR-density correlation stillheld regardless of the morphology of the galaxy. This indicates thatthe observed SFR-density relation cannot be exclusively tied to themorphology-density relation; other processes must be influencingthe observed correlations. It is currently believed that this reduc-tion in SFR with increased environmental density is directly linkedto the stripping of cold gas from galaxies via some type of directinteraction, and several mechanisms have been invoked to explainthis observed correlation.For example, major mergers (Barnes & Hernquist 1992) cancause a burst of star-formation activity and feedback from such star-burst events is able to prevent gas cooling, and as a result the gas re-mains out of pressure equilibrium with its environment. Due to thispressure difference the gas expands out of the central regions of thegalaxy sweeping up the inter-stellar medium (ISM). This ejectionof the ISM from the merger remnant can lead to further suppressionof star formation (Mac Low & Ferrara 1999; Gay et al. 2010). Al-ternatively, other processes such as harassment, strangulation andram-pressure stripping may also play an important role (see e.g.Boselli & Gavazzi 2006, for a review). Star formation within a galaxy typically increases the dust contentof the ISM through processes associated with the short-lived mas-sive stars that inhabit these regions, such as supernovae, that re-distribute material into the surrounding ISM (Dunne et al. 2003;Sugerman et al. 2006; Dunne et al. 2009; Gomez et al. 2012). Thisdust then absorbs a significant fraction of the ultra-violet (UV) lightemitted by the young O-B type stars associated with these regionsand is heated to temperatures of around 20-40 K, emitting thermalradiation at far-infrared wavelengths. This makes the use of far-infrared emission from a galaxy a widely used diagnostic for theobscured SFR of a galaxy (Kennicutt 1998; Hirashita et al. 2003;Driver et al. 2007; Cortese et al. 2008; Nordon et al. 2010; Buatet al. 2010; Dunne et al. 2011; Smith et al. 2012a).However, other contributions to the UV radiation field whichheats the dust, such as AGN and older stellar populations withinthe galaxy, may lead to overestimates of the SFR using far-infrared emission (Schmitt et al. 2006; da Cunha et al. 2008; Nardini et al.2008; Bendo et al. 2010, 2012; Groves et al. 2012; Smith et al.2012a; Smith et al. 2012b). Conversely, in galaxies where the ISMis optically thin at UV wavelengths, the measured SFR will emergedirectly from the UV and not in the far-infrared. In these galaxies,deriving the star formation from far-infrared emission may lead toan underestimation of the total SFR (Kennicutt 1998). However,as more than per cent of energy ever radiated from stars hasbeen absorbed by dust and re-radiated into the infrared (Puget et al.1996; Fixsen et al. 1998; Adelberger & Steidel 2000; Finn et al.2010), with the bulk of star formation since z = 1 occurring indust obscured galaxies (Calzetti & Heckman 1999; Le Floc’h et al.2005; Patel et al. 2013), only AGN, low metallicity systems andvery passive but dusty galaxies will lie off the far-infrared to SFRrelation.Initial studies of the relationship between SFR and infraredemission from galaxies focused on shorter wavelengths using the Infrared Astronomical Satellite (IRAS; Neugebauer et al. 1984) andmore recently the
Spitzer Space Observatory (Rieke et al. 2004).
IRAS surveyed the vast majority of the sky between − µ m,providing a large census of dusty galaxies in the local Universe.Using these data, Goto (2005) investigated the optical properties of4248 infrared-selected galaxies by positionally matching data fromthe IRAS with optical data from the SDSS. Using a volume limitedsample at z ≤ . and applying a th-nearest neighbour den-sity estimate, a trend was found such that galaxies with the highestinfrared luminosities reside in relatively low-density local environ-ments, suggesting that star-forming galaxies favour underdense re-gions, in agreement with previous studies at other wavelengths.The environmental densities of IRAS -detected luminous infra-red galaxies (LIRGs; ≤ L FIR < L (cid:12) ) at . ≤ z < . were also studied by Hwang et al. (2010). They found that thefraction of LIRGs was strongly dependent on both the morphologyand the distance to the nearest neighbour galaxy. They concludethat the evolution of the SFR-density relation from high to low red-shifts is consistent with the idea that galaxy-galaxy interactions andmerging play a critical role in triggering star formation in LIRGs.Additionally, Tekola et al. (2012) examined the relationshipbetween star formation and the environments of LIRGs selectedfrom IRAS and compared these with other types of high- and low-redshift galaxies out to z ∼ . They identified that there was aluminosity ( L IR ∼ h − L (cid:12) ) at which infrared selected galax-ies preferentially resided in higher density environments, comparedto “normal” galaxies. Above this luminosity the average densityincreases, whereas below this luminosity, infrared-selected galax-ies reside in environments of equal density, similar to the generalpopulation. They conclude, therefore, that infrared activity for non-LIRGs is not dependent on density and that the SFR-density re-lationship for these galaxies is similar to that of blue galaxies at z ∼ .At higher redshifts, Feruglio et al. (2010) used µ m observa-tions from Spitzer to investigate the environmental effects on starformation in LIRGs and ultra-luminous infrared galaxies (ULIRGs; > L (cid:12) ) in the Cosmic Evolution Survey (COSMOS; Scovilleet al. 2007) at . < z < . . They found the fraction of thesegalaxies to decrease with density out to z ∼ , but that the relation-ship flattens out with increasing redshift.Due to the wavelength coverage of IRAS ( − µ m), themajority of galaxies detected by these studies were found by Breg-man et al. (1998) to be spirals and starbursts in the local universe( z < . ). This restriction resulted in the IRAS providing little in-formation about the cooler dust, which traces the bulk of the dust c (cid:13) , ?? ––
IRAS surveyed the vast majority of the sky between − µ m,providing a large census of dusty galaxies in the local Universe.Using these data, Goto (2005) investigated the optical properties of4248 infrared-selected galaxies by positionally matching data fromthe IRAS with optical data from the SDSS. Using a volume limitedsample at z ≤ . and applying a th-nearest neighbour den-sity estimate, a trend was found such that galaxies with the highestinfrared luminosities reside in relatively low-density local environ-ments, suggesting that star-forming galaxies favour underdense re-gions, in agreement with previous studies at other wavelengths.The environmental densities of IRAS -detected luminous infra-red galaxies (LIRGs; ≤ L FIR < L (cid:12) ) at . ≤ z < . were also studied by Hwang et al. (2010). They found that thefraction of LIRGs was strongly dependent on both the morphologyand the distance to the nearest neighbour galaxy. They concludethat the evolution of the SFR-density relation from high to low red-shifts is consistent with the idea that galaxy-galaxy interactions andmerging play a critical role in triggering star formation in LIRGs.Additionally, Tekola et al. (2012) examined the relationshipbetween star formation and the environments of LIRGs selectedfrom IRAS and compared these with other types of high- and low-redshift galaxies out to z ∼ . They identified that there was aluminosity ( L IR ∼ h − L (cid:12) ) at which infrared selected galax-ies preferentially resided in higher density environments, comparedto “normal” galaxies. Above this luminosity the average densityincreases, whereas below this luminosity, infrared-selected galax-ies reside in environments of equal density, similar to the generalpopulation. They conclude, therefore, that infrared activity for non-LIRGs is not dependent on density and that the SFR-density re-lationship for these galaxies is similar to that of blue galaxies at z ∼ .At higher redshifts, Feruglio et al. (2010) used µ m observa-tions from Spitzer to investigate the environmental effects on starformation in LIRGs and ultra-luminous infrared galaxies (ULIRGs; > L (cid:12) ) in the Cosmic Evolution Survey (COSMOS; Scovilleet al. 2007) at . < z < . . They found the fraction of thesegalaxies to decrease with density out to z ∼ , but that the relation-ship flattens out with increasing redshift.Due to the wavelength coverage of IRAS ( − µ m), themajority of galaxies detected by these studies were found by Breg-man et al. (1998) to be spirals and starbursts in the local universe( z < . ). This restriction resulted in the IRAS providing little in-formation about the cooler dust, which traces the bulk of the dust c (cid:13) , ?? –– ?? he environmental density of far-infrared bright galaxies mass (e.g. Dunne et al. 2011), in other galaxy populations, espe-cially early-type morphologies. In comparison, Spitzer can probelonger wavelengths ( − µ m) and therefore is less susceptibleto this bias, although galaxies with the coldest dust temperatureswould still be missed (Eales et al. 2010; Symeonidis et al. 2011,2013). Considering that cold dust is present across all types ofgalaxies and is a major contributor to infrared luminosity (Willmeret al. 2009), and closely traces the total dust mass, it is crucial thatwe are able to select galaxies at longer wavelengths.With the launch of the Herschel Space Observatory (Pilbrattet al. 2010) we are now able to select galaxies at these longer wave-lengths. A number of studies have begun to investigate how starformation in a galaxy, traced by far-infrared emission at ≥ µ m,is linked to the environment in which the galaxy resides. Dar-iush et al. (2011) used far-infrared data from the Herschel
As-trophysical Terahertz Large Area Survey (H-ATLAS; Eales et al.2010) Science Demonstration Phase (SDP) to examine the ultravi-olet and optical properties and environments of low redshift galax-ies ( . ≤ z ≤ . ) from the SDSS and the Galaxy And MassAssembly survey (GAMA; Driver et al. 2011; Hill et al. 2011;Baldry et al. 2010). They found that H-ATLAS detects predomi-nantly blue/star-forming galaxies, with a minor contribution fromred galaxies (comprising highly obscured and passive systems). Us-ing the 5th-nearest neighbour as an estimate of the environmentaldensity, they found that the fraction of H-ATLAS detected galaxiesis much higher ( ∼ per cent) in low-density environments com-pared to high-density environments, where the fraction was foundto be ∼ per cent. However, the detection rate of red and bluegalaxies appears to be similar for both high- and low-density en-vironments, indicating that it is the colour of a galaxy, rather thanthe density of its local environment, that governs whether it is de-tectable by H-ATLAS.A consistent result was also found by Rowlands et al. (2012),who found that H-ATLAS detected early-type galaxies tend to havebluer (NUV-r) colours, higher SSFRs and younger stellar popula-tions than optically observed early-type morphologies. They com-pare 354 spiral and 30 early-type galaxy morphologies at low red-shift ( z < . ), finding no significant difference between the en-vironmental densities of these populations. However, it is possiblethat they are not sampling a large enough range of environmentswith such small population samples.Coppin et al. (2011) also used far-infrared data from H-ATLAS to examine the centres of optically selected galaxy clus-ters at z ∼ . to search for statistical evidence of obscuredstar formation in the cluster population. Using Voronoi Tessella-tions (described in Section 3.1) to locate cluster members, theyfound an excess in the surface density of far-infrared sources within ∼ . Mpc of the centre of these clusters. They conclude that thefar-infrared emission is associated with dust-obscured star forma-tion in cluster galaxies, translating to a rate of ∼ (cid:12) yr − . ThisSFR, maintained over the 3 Gyr since z = 0 . , would contributeenough mass to construct a typical S0-type bulge that would matchthe observed increase in bulge-dominated galaxies in cores of clus-ters over the same timescale.The effects of environment on the far-infrared properties ofgalaxies are also discussed by Davies et al. (2010), who use datafrom the Herschel
Virgo Cluster Survey (HeViCS; Davies et al.2012), finding that relatively few faint far-infrared sources that canbe associated with confirmed Virgo cluster members. Furthermore,studies by Cortese et al. (2010a,b) present
Herschel observationsof the perturbed galaxy NGC in the Virgo cluster and identifyregions of extra-planar dust up to ∼ − kpc away from the galaxy disk. This dust is found to closely follow the distribution of strippedatomic and molecular hydrogen, supporting the idea that gas anddust are perturbed in a similar way within the cluster environment.In contrast to these results, Geach et al. (2011a), using24 µ m observations from Spitzer , investigated large-scale filamen-tary structure surrounding rich clusters out to z ∼ . , and foundthat the SFRs of individual galaxy members within a cluster arenot significantly different to identically selected field galaxies. Al-though pockets of enhanced star formation were observed, theysuggest that this is the result of some ‘pre-processing’ effect wheresatellite groups have star formation triggered via gravitational tidalinteractions during cluster infall. However, they state that there isno environmental mechanism acting to enhance the star formationwithin individual galaxies.It is evident that the majority of these studies have eitherused density measures that do not detect differences on the small-est scales (i.e. n th-nearest neighbour or aperture gridding) and/orthey have focused entirely on narrow and local redshifts ( z (cid:46) . ).In this paper we use data from H-ATLAS to investigate the envi-ronmental dependence of far-infrared emission using a techniquebased on Voronoi Tessellations. Unlike the n th-nearest neighbourtechnique, Voronoi Tessellations calculate the environmental den-sity of galaxies on individual galaxy scales and hence can probe theenvironmental density to a greater degree of accuracy.In Section 2 we outline the optical and infrared data that weuse. In Section 3 we present how both the spectroscopic and pho-tometric redshifts for our sample of galaxies were measured andsampled and introduce our algorithm to estimate the environmentaldensity. In Section 4 we present the results of our analysis to de-termine whether there are any differences in environmental densitybetween the far-infrared bright and faint sources, and investigatewhether the SFR is linked to the environmental density. In Sec-tion 5 we compare our results to semi-analytic models and discussthe physical mechanisms that may explain our results. In Section 6we discuss our results in the context of the physical mechanismsoutlined above and in Section 7 we summarise our findings. Weadopt a cosmology throughout with Ω m = 0 . , Ω Λ = 0 . and H = 71 kms − Mpc − . We use far-infrared data from the science demonstration phase ofH-ATLAS (Rigby et al. 2011). H-ATLAS provides data across awavelength range of 100-500 µ m using the Photo-detector ArrayCamera and Spectrometer (PACS; Poglitsch et al. 2010) at 100and 160 µ m; and the Spectral and Photometric Imaging REceiver(SPIRE; Griffin et al. 2010) at 250, 350 and 500 µ m. The H-ATLASobservations consist of two scans in parallel mode reaching 5 σ point source sensitivities of 132, 126, 32, 36 and 45 mJy in the 100,160, 250, 350, and 500 µ m channels, respectively, with beam sizesof approximately 9, 13, 18, 25 and 35 arcsec in the same five bands.The SPIRE and PACS map-making procedures are described byPascale et al. (2011) and Ibar et al. (2010) respectively, while thecatalogues are described by Rigby et al. (2011). Smith et al. (2011)used a likelihood ratio (LR) method to associate optical counter-parts with the H-ATLAS galaxies down to a limiting magnitude of r = 22 . within a 10 arcsec radius. This resulted in optical counter-parts for , objects from the H-ATLAS 250 µ m catalogue, eachwith a reliability R > . which ensures not only that the contam-ination rate is low but also that only one r − band source dominates c (cid:13) , ?? – ?? C. S. Burton et al. the far-infrared emission. While the entire H-ATLAS survey aimsto compile a catalogue of ∼ extra-galactic far-infrared sourcesout to z ∼
3, the SDP field covered ∼ ∼ × h m , +0 ◦ r = 21 . . We use spectroscopic redshifts from both the SDSS and the GAMAsurvey Data Release One (DR1). Spectroscopic redshifts are pro-vided for magnitude limits of r < . , K < . and z < . inthe GAMA 9hr (G09) field which includes the H-ATLAS SDP. Thisis combined with photometric redshifts derived from the combina-tion of optical ( ugriz ) SDSS and near-infrared ( YJHK ) UKIDSS-LAS imaging data as detailed in Smith et al. (2011). This completeoptical–near-infrared catalogue, containing photometric and spec-troscopic redshifts (hereafter named the Optical-9hr catalogue),totals 909,985 objects from which we remove all sources with r > . due to the fact that at fainter magnitudes the signal-to-noise ratio deceases to an extent where errors associated with thephotometry become large. In addition, we remove objects classifiedas point-like in the SDSS imaging. This reduced the Optical-9hrcatalogue to , objects, of which , had spectroscopicredshifts across a redshift range of < z < . . In this section we describe our method of determining the environ-mental density of individual galaxies in redshift slices. First, as thevast majority of the galaxies in our sample do not have spectro-scopic redshifts, we are forced to use their photometric redshiftsin order to establish where they reside in three dimensional space.Spectroscopic redshifts have errors of the order of ∆ z ∼ − (Driver et al. 2011) with the average error associated with our pho-tometric redshifts of the order of ∆ z ∼ . . As these photomet-ric redshifts apply to both H-ATLAS and non–H-ATLAS sources,both populations would experience similar biases associated withthese errors. Adopting a single redshift at the peak of the photo-metric redshift probability distribution (z-PDF) would not accu-rately represent our limited knowledge of the redshift of individ-ual galaxies. We therefore use the full photometric z-PDF to carryout Monte-Carlo (MC) simulations which sample each z-PDF 1000times generating 1000 MC cubes for each object. From these sam-ples we ensure that we have a good statistical representation of the3-dimensional distribution of galaxies within the survey area. How-ever, where available, we use spectroscopic redshifts due to theirsmaller uncertainties. In order to calculate the environmental density of individual galax-ies we apply a numerical algorithm called ‘Voronoi Tessellations’(VT; Icke & van de Weygaert 1987; van de Weygaert & Icke 1989)to the Optical-9hr catalogue. The algorithm works by initially treat-ing each object in the field as a single point source (or nucleus). Itthen constructs a convex polygon (or ‘Voronoi cell’) around eachof these nuclei enclosing all points that are closer to that nucleusthan any other. The area of the Voronoi cell is a good representa-tion of the local environment of that object, such that the reciprocalof this area gives a direct measure of the density. The VT technique
Figure 1.
An example of how the VT algorithm works, showing a subset ofobjects placed within the redshift slice 0.09 ≤ z < has been used in many areas of astronomy, initially in the study oflarge-scale structure of the universe (e.g., Icke & van de Weygaert1987; van de Weygaert & Icke 1989; Diehl & Statler 2006) andmore recently in studies of cluster detection (e.g., Kim et al. 2000;Ramella et al. 2001; van Breukelen et al. 2006a; van Breukelenet al. 2006b; van Breukelen & Clewley 2009; Geach et al. 2011b;Soares-Santos et al. 2011).The VT algorithm does not take redshift into account whenlinking each nucleus together as we lack the necessary resolutionin redshift to apply a three-dimensional VT algorithm. Thereforeit is necessary to group galaxies into redshift slices so as to avoidprojection effects. Subsequently each of the 1000 3D MC fieldsare split into redshift slices so that the VT algorithm can be ap-plied to each slice individually; thus only objects within each slicehave the VT algorithm applied to them, maximising the accuracyof the density calculation for each object. The width of each sliceis limited such that, if too wide, projection effects may become aproblem. In addition, if the slice is too small, an overdense regionin terms of the rest of the field may go undetected by the VT al-gorithm if it is spread across multiple slices. The typical velocitydispersion between gravitationally bound group/cluster galaxies iswithin the region of a few hundred kilometres per second (Hayneset al. 1984; Martini et al. 2007), which equates to a spread in red-shift of ∆ z/ (1+ z ) ∼ − at z = 1 . Therefore we adopt a redshiftslice of width ∆ z = 0 . , easily incorporating associated galacticenvironments and resulting in 120 slices across each of the 10003D MC realisations across the full redshift range of our data out to z = 1 . .For each object in each MC cube realisation its Voronoi cellarea ( x i ) is calculated, the mean of which ( ¯ x i ) gives the overallmean area calculated for that object across all of the MC realisa-tions. Taking an inverse of this mean area gives a value for themean environmental density ( ¯ ρ i ) for that object. Figure 1 shows anexample of one VT slice (containing a smaller subset of the datafor illustrative purposes) and it is immediately clear that objects to-wards the outside of the field have overly large Voronoi cell areas.This edge effect is the result of the VT algorithm not finding any c (cid:13) , ?? ––
An example of how the VT algorithm works, showing a subset ofobjects placed within the redshift slice 0.09 ≤ z < has been used in many areas of astronomy, initially in the study oflarge-scale structure of the universe (e.g., Icke & van de Weygaert1987; van de Weygaert & Icke 1989; Diehl & Statler 2006) andmore recently in studies of cluster detection (e.g., Kim et al. 2000;Ramella et al. 2001; van Breukelen et al. 2006a; van Breukelenet al. 2006b; van Breukelen & Clewley 2009; Geach et al. 2011b;Soares-Santos et al. 2011).The VT algorithm does not take redshift into account whenlinking each nucleus together as we lack the necessary resolutionin redshift to apply a three-dimensional VT algorithm. Thereforeit is necessary to group galaxies into redshift slices so as to avoidprojection effects. Subsequently each of the 1000 3D MC fieldsare split into redshift slices so that the VT algorithm can be ap-plied to each slice individually; thus only objects within each slicehave the VT algorithm applied to them, maximising the accuracyof the density calculation for each object. The width of each sliceis limited such that, if too wide, projection effects may become aproblem. In addition, if the slice is too small, an overdense regionin terms of the rest of the field may go undetected by the VT al-gorithm if it is spread across multiple slices. The typical velocitydispersion between gravitationally bound group/cluster galaxies iswithin the region of a few hundred kilometres per second (Hayneset al. 1984; Martini et al. 2007), which equates to a spread in red-shift of ∆ z/ (1+ z ) ∼ − at z = 1 . Therefore we adopt a redshiftslice of width ∆ z = 0 . , easily incorporating associated galacticenvironments and resulting in 120 slices across each of the 10003D MC realisations across the full redshift range of our data out to z = 1 . .For each object in each MC cube realisation its Voronoi cellarea ( x i ) is calculated, the mean of which ( ¯ x i ) gives the overallmean area calculated for that object across all of the MC realisa-tions. Taking an inverse of this mean area gives a value for themean environmental density ( ¯ ρ i ) for that object. Figure 1 shows anexample of one VT slice (containing a smaller subset of the datafor illustrative purposes) and it is immediately clear that objects to-wards the outside of the field have overly large Voronoi cell areas.This edge effect is the result of the VT algorithm not finding any c (cid:13) , ?? –– ?? he environmental density of far-infrared bright galaxies objects outside of this boundary and consequently being unable totriangulate in these areas. In order to prevent this edge effect alter-ing the mean density result, a cut is then made around the outsideof the field to remove the outermost objects (and their overly largecell areas) from the Optical-9hr catalogue. The position of this cutwas calculated by plotting the right ascension (RA) and declina-tion (Dec) values separately against a value that represents a nor-malised value for the mean area, the significance ( S ) (this value isintroduced to account for a peak in the number density of objectsas explained in Section 3.2). The resultant plots showed, unsurpris-ingly, a sharp increase in mean area of the cells towards the outsideof the field and that this edge effect penetrated the field by approxi-mately ± . degrees in both RA and Dec. As the Optical-9hr fieldextends well beyond the H–ATLAS-SDP field on all sides, this cutis not significant in terms of the number of sources lost and doesnot interfere with the accuracy of our analysis.Furthermore, to ensure that the accuracy of the comparisonbetween the two samples is maintained, it is necessary to includeonly Optical-9hr objects that reside within the boundary of the H–ATLAS-SDP field. This ensures that all objects included in thedensity measure are from across the same region and thus havebeen observed by both SDSS and H-ATLAS observations. Thuswhen comparing far-infrared detected and undetected galaxies weare not counting any far-infrared luminous galaxies that would oth-erwise be detected in the H-ATLAS SDP catalogue if it were notfor the boundary limits of the H-ATLAS SDP region. After theseregion cuts are applied, the final Optical-9hr catalogue is reducedto 129,518 objects. In section 4.1, this catalogue is divided accord-ing to whether or not the galaxies have far-infrared emission in or-der that these sub-samples can then be compared. Table 1 showsthe number of galaxies within these sub-samples in addition to thenumber of galaxies with photometric and spectroscopic redshifts. With a value for the mean environmental density calculated foreach object in the Optical-9hr field it is possible to examine the3D density distribution across the entire redshift range. Due to theflux-density limit of the observations and the much larger volumebeing sampled at higher redshift, a peak in the density distributionis found at z ∼ . corresponding to the peak in the galaxy numberdensity. This peak in the detection rate would naturally lead to anincrease in the mean density being returned by the VT algorithmfor redshift slices in this range. Therefore two Voronoi cells fromtwo different redshift slices cannot be accurately compared in termsof their environment. In order to counteract this bias it is necessaryto normalize the Voronoi cell areas across the entire redshift rangeto produce a normalized environmental density for each object.We therefore create a separate random field by applying a ran-dom position to each Optical-9hr object within the H-ATLAS SDPregion within each redshift slice of that MC realisation. We applyour VT algorithm to the random field and determine the mean cellarea ¯ x Slice (defined as the sum of the individual cell areas in thatslice divided by their number) and the standard deviation σ of each random redshift slice. Our density measure is therefore given by, S c = ¯ x slice − x i σ , (1)where x i is the measured VT cell area for each object from the realfield per MC realisation and S c is the normalized density value incomparison to a random distribution for each object. Figure 2.
The relationship between the normalized densities returned by theVT and NN techniques. The Spearman’s Rank Correlation Coefficient ( r s )between both density distributions returns a value of r s = 0 . at a > σ level, indicating a strong correlation. S c therefore shows how the real field compares to a com-pletely random distribution, in terms of the standard deviation σ ofthat random distribution, and thus accounts for differences in uni-formity of the field between slices. This normalisation also allowsfor the comparison of different objects from across redshift sliceswith different population densities. Taking the mean of these valuesacross all MC realisations gives the mean normalized comparisondensity ( ¯ S c ). Using VT to probe galaxy environments on individual galaxy scalesis a relatively new approach to the study of galaxy environmen-tal density. Previous work in the analysis of galactic environmentshas instead predominantly relied on estimating the local densityof galaxies using the projected N th-nearest neighbour technique( Σ N ), which measures the environmental density in terms of thenumber of galaxies within a circular region defined by the radiusto the N th-nearest galaxy (e.g., Dressler 1980; Lewis et al. 2002;Miller et al. 2003; Balogh et al. 2004; Cooper et al. 2005; Silver-man et al. 2009; Cucciati et al. 2010; Hern´andez-Fern´andez et al.2012; Wijesinghe et al. 2012). We therefore test our Voronoi Tes-sellation density measure (VT) against this N th-nearest neighbourtechnique (NN) in order to establish whether there are any signifi-cant differences between the results obtained from both techniques,both in terms of how our overall density correlations are affected aswell as a comparison of the techniques ability to probe detailedstructure.For our comparison we use N = 5 in line with the majorityof recent studies that have used the NN technique to examine localenvironmental densities of galaxies (e.g., Cucciati et al. 2010; Wi-jesinghe et al. 2012 and Hern´andez-Fern´andez et al. 2012). We usethe NN algorithm in exactly the same way as our VT method de-scribed in Section 3.1, with the NN algorithm applied to each red-shift slice within each MC cube, once more normalising the fieldto account for differences in number density and uniformity acrossthe redshift range. The only difference between the methods comesas a result of the fact that, unlike a VT cell, the Σ N parameter rep-resents larger densities with larger values and thus, to reflect this,we reverse the sign of ¯ S c such that positive values once more repre- c (cid:13) , ?? – ?? C. S. Burton et al.
Figure 3.
Colour co-ordinated plots of the field with all redshift slices com-piled to show the whole density distribution. Red and orange colours rep-resent the most overdense regions (positive ¯ S c values) and blue and purplerepresents the most underdense regions (negative ¯ S c values) with the rangeof the normalized density limited to − ≤ ¯ S c ≤ for clarity. Top : TheVT method density output.
Bottom : 5th-nearest neighbour method densityoutput. The plots confirm that the VT and NN methods reproduce the samedensity structure across the field. sent a normalized overdensity. We maintain the boundaries appliedto our VT density calculation to both prevent such edge effects andto maintain comparison accuracy between the two methods.We apply both the Voronoi Tessellation and N th-nearestneighbour techniques independently to our Optical-9hr catalogue;Figure 2 shows the relationship between the initial outputs returnedby both techniques. Calculating the Spearman’s Rank CorrelationCoefficient ( r s ) between both density distributions returns a valueof r s = 0 . at a > σ level, indicating a strong (although non-linear) correlation. In addition, Figure 3 shows the normalized com-parison densities ( ¯ S c ) returned by each technique plotted accordingto RA and Dec positions and coloured according to density. Bothfigures clearly show that each density measure has successfully re-produced the same general density structure across the field, withthe most extreme over- and under-densities located by both meth-ods. However, there are some noticeable differences between themethods indicating that the intensity of the local density in specificregions differs between each method.From the direct comparison between the two methods in Fig-ure 2, it is clear that the NN method has a greater dynamic rangein the densest environments where the VT method saturates. Con- Table 1.
The number of objects within the Optical and FIR sub-samples ofthe initial , objects of the Optical-9hr catalogue. These sub-samplesare also divided according to the number of objects with photometric orspectroscopic redshifts in the density analysis.Sample Total Number Number of Photo-z Number of Spec-zFIR 2,265 1,489 776Optical 127,250 123,730 3,520 versely the VT method appears more suited to distinguishing be-tween less dense environments where the NN method saturates.Figure 3 shows that using the NN method results in larger regions ofpeak overdensities with less defined regions of intermediate densityin comparison with the structure distribution from the VT method.A full investigation of the pros and cons of different density mea-sures has been conducted by Muldrew et al. (2012) and we refer thereader to that paper for more information. But to summarise theyfind that the NN technique is very poorly correlated with the re-spective dark-matter-halo mass, although the NN technique is ableto describe the internal densities of high-mass haloes.It is also clear that the initial value selected for N will deter-mine the accuracy of the NN technique in various environments.Where the value of N remains below the number of associatedsatellites, the measured density will increase with increasing val-ues of N . Subsequently in our comparison with the VT method, thepeak over densities returned from the th-nearest neighbour wouldbe reduced if, for example, only the rd-nearest neighbour wereused. However, with a larger value of N the NN method will loseresolution and become more susceptible to the projected separa-tions between distinct overdense regions, influencing the densityresult.In contrast, the VT method does not suffer from these issues,as essentially the number of neighbours used to define the densityare not fixed. From the methodology of using the VT algorithm(Section 3.1) it is evident that one does not need to necessarily cat-egorise each galaxy into a group or cluster, but can instead simplymeasure the surface density of that galaxy directly from the proper-ties of its Voronoi cell. Consequently the VT method is fully adapt-able to changes in uniformity of the field and calculates densitieson individual galaxy scales. Therefore the VT method represents areliable and accurate alternative to the more well established NNdensity measure. As described in Section 2.1, we use the likelihood-ratio techniqueof Smith et al. (2011) to associate the far-infrared sources with theiroptical counterparts. This cross-matched sample is hereafter named‘FIR’ (consisting of 2,265 objects) while simultaneously remov-ing them from the Optical-9hr catalogue reducing this sample to , objects (hereafter named ‘Optical’). These sub-samplesare shown in Table 1, where they are also divided according to thenumber of galaxies with photometric and spectroscopic redshifts.In order to accurately compare how ¯ S c values differ betweenthe FIR and Optical catalogues it is necessary to ensure that we arecomparing like with like, such that the objects selected for compar-ison should be considered to be from the same population. By se-lecting a matched sample of galaxies based on their colour, SDSS r − band model apparent magnitude and redshift distributions weensure that these properties have no influence on any differences c (cid:13) , ?? ––
The number of objects within the Optical and FIR sub-samples ofthe initial , objects of the Optical-9hr catalogue. These sub-samplesare also divided according to the number of objects with photometric orspectroscopic redshifts in the density analysis.Sample Total Number Number of Photo-z Number of Spec-zFIR 2,265 1,489 776Optical 127,250 123,730 3,520 versely the VT method appears more suited to distinguishing be-tween less dense environments where the NN method saturates.Figure 3 shows that using the NN method results in larger regions ofpeak overdensities with less defined regions of intermediate densityin comparison with the structure distribution from the VT method.A full investigation of the pros and cons of different density mea-sures has been conducted by Muldrew et al. (2012) and we refer thereader to that paper for more information. But to summarise theyfind that the NN technique is very poorly correlated with the re-spective dark-matter-halo mass, although the NN technique is ableto describe the internal densities of high-mass haloes.It is also clear that the initial value selected for N will deter-mine the accuracy of the NN technique in various environments.Where the value of N remains below the number of associatedsatellites, the measured density will increase with increasing val-ues of N . Subsequently in our comparison with the VT method, thepeak over densities returned from the th-nearest neighbour wouldbe reduced if, for example, only the rd-nearest neighbour wereused. However, with a larger value of N the NN method will loseresolution and become more susceptible to the projected separa-tions between distinct overdense regions, influencing the densityresult.In contrast, the VT method does not suffer from these issues,as essentially the number of neighbours used to define the densityare not fixed. From the methodology of using the VT algorithm(Section 3.1) it is evident that one does not need to necessarily cat-egorise each galaxy into a group or cluster, but can instead simplymeasure the surface density of that galaxy directly from the proper-ties of its Voronoi cell. Consequently the VT method is fully adapt-able to changes in uniformity of the field and calculates densitieson individual galaxy scales. Therefore the VT method represents areliable and accurate alternative to the more well established NNdensity measure. As described in Section 2.1, we use the likelihood-ratio techniqueof Smith et al. (2011) to associate the far-infrared sources with theiroptical counterparts. This cross-matched sample is hereafter named‘FIR’ (consisting of 2,265 objects) while simultaneously remov-ing them from the Optical-9hr catalogue reducing this sample to , objects (hereafter named ‘Optical’). These sub-samplesare shown in Table 1, where they are also divided according to thenumber of galaxies with photometric and spectroscopic redshifts.In order to accurately compare how ¯ S c values differ betweenthe FIR and Optical catalogues it is necessary to ensure that we arecomparing like with like, such that the objects selected for compar-ison should be considered to be from the same population. By se-lecting a matched sample of galaxies based on their colour, SDSS r − band model apparent magnitude and redshift distributions weensure that these properties have no influence on any differences c (cid:13) , ?? –– ?? he environmental density of far-infrared bright galaxies Figure 4. g-r vs r-i colour distribution for the ‘matched’ catalogues Optical( red ) and Herschel ( blue ) numbering , and sources respectively. in environmental density found between the two catalogues. Thisis achieved by gridding the field in four dimensions in order to in-corporate all g − r , r − i , m r and z parameter space, selectingmatched objects as only those which share an associated grid spacein all four planes. The choice of g − r and r − i colours are selectedas we limit our Optical catalogue in the r -band apparent magnitude.As explained in Section 2.2 and as shown in Taylor et al. (2011),colours provide a reasonable method of matching sources in termsof their stellar mass over the redshift range under investigation here,although we also investigate this further in Section 4.5. The grid el-ements applied to the total g − r and r − i colour distributionsincorporate . and . magnitudes respectively in colour space.This difference reflects the larger range of the total g − r colour dis-tribution. Simultaneously, the z and m r ranges have grid elementsincorporating . in redshift and . in r − band magnitude.All Optical sources that share an associated grid space with aFIR detection in all four planes are initially grouped as potentialmatches to those FIR objects. Then, within each grid space, a mul-tiple of the potential matches (totalling three times the FIR sourcesin that grid space) are selected as matched objects. Selecting Op-tical matches equal to a multiple of the FIR sources in each gridelement allows for a more robust comparison without sacrificingany similarities between their distributions. Any additional Opticalor FIR sources that are not matched are discarded. The FIR samplecontains considerably fewer objects than the Optical sample ( , against , ), therefore a large proportion of the Optical sam-ple will not have an associated FIR object and thus will be lostfrom the final cross-match. This reduces the sample size to , and for the Optical and FIR samples respectively.In addition, the number-density of galaxies reduces with in-creasing redshift to such an extent as to affect our sampling. There-fore we apply a maximum peak redshift limit onto the samples of z ≤ . . This maximum redshift does not influence the ¯ S c valuesof the remaining sample due to the fact that each ¯ S c value alreadyincorporates the high redshift galaxies via the full z-PDF samplingachieved within the algorithm. Figures 4 & 5 show the colour, red-shift and magnitude distributions for these two matched samples. We use one- and two-dimensional Kolmogorov-Smirnoff tests (KS-tests) to confirm that our matched samples are consistent with hav-
Figure 5.
Redshift vs r − band apparent magnitude ( m r ) for the ‘matched’Optical ( red ) and Herschel ( blue ) catalogues. Only the redshift range of < z ≤ . and m r range of < m r < . was included in the sam-pling, outside of these ranges the completeness of the catalogues reducedsignificantly. ing been drawn from the same underlying distribution in termsof their colour, magnitude and redshift distributions and that thevarious combinations are consistent with each other. These testsdemonstrate that our null hypothesis, such that the ‘Optical’ controlsample is drawn from the same underlying distribution as the FIRsample, cannot be rejected at a significant level. The results of thesetests are presented in Table 2. We then applied the one-dimensionalKS test to the environmental density measurements for the Opticaland FIR samples ( ¯ S c ), which return a probability of just . × − ,rejecting the null hypothesis of them being drawn from the sameunderlying distribution at the . σ level. Therefore we find a sig-nificant difference in the distribution of the galaxy environmentaldensity between far-infrared selected galaxies and a control samplewith no detectable far-infrared emission. To test this result furtherwe applied a two-dimensional KS-test to both Optical and FIR pop-ulations comparing the environmental densities in conjunction withthe optical properties and the redshifts. The two-dimensional KS-test comparing the colours, r − band magnitude and redshift distri-butions to the environmental density values are presented in Table 2and show that the environmental densities of the FIR and Opticalsamples are significantly different in all cases.The extent of this difference is illustrated in Figure 6 wherewe show normalized histograms of the two environmental densitydistributions. It is clear that the Optical population ( red ), with themean of its distribution at ¯ S c = (12 . ± . × − (denotedby the red dashed line), is more overdense (has larger values of ¯ S c )than the FIR population ( blue ), with the mean of its distribution at ¯ S c = (3 . ± . × − (denoted by the blue dashed line). Us-ing the Mann-Whitney U (MWU) test we also test for differencesbetween the median values of the distributions. For the Optical andFIR populations the test returns a probability of × − , indi-cating that the two populations have significantly different medianvalues at the . σ level. In Section 4.6 we show the same result isreturned when the NN method is used to calculate the environmen-tal density, thus showing consistency with our VT result. c (cid:13) , ?? – ?? C. S. Burton et al.
Figure 6.
Normalized histograms showing how the distribution of environmental density ( ¯ S c ) of the total colour matched Optical ( red ) and FIR ( blue )populations compare, with shaded histograms representing the number of spectroscopic redshifts in each sample. Left : Full matched catalogues containing , Optical and
FIR objects. The histograms show error bars depicting the normalized error associated with each bin, where ¯ S c > signifies anoverdensity and ¯ S c < signifies an underdensity in terms of the entire redshift range ( ≤ z < . ). The FIR data are shifted generally to lower ¯ S c values,with the mean of the distribution at ( . ± . ) × − ( blue dashed line ), this is contrasted against the mean of the Optical distribution at ( . ± . ) × − ( red dashed line ). KS and MWU-tests indicate a significant difference to the 3.5 σ level. Centre and
Right : Normalized histograms that show the fullmatched sample binned in redshift ( ≤ z < . ) and ( . ≤ z < . ) respectively, showing a continued separation between the distributions increasingwith redshift from 2.2 σ to 3.3 σ significance. Table 2.
Two sample and two-dimensional KS and MWU-test results overthe full SFR and redshift range ( < z ≤ . ). Where op represents Opti-cal ( , objects) and FIR represents FIR ( objects). The two densitydistributions are significantly different at the 3.5 σ level from KS tests, withthe medians of the distributions different at the 4.5 σ level from MWU tests.Distributions Compared KS Prob. MWU Prob. z op vs z FIR ( g − r ) op vs ( g − r ) FIR ( r − i ) op vs ( r − i ) FIR m r ( op ) vs m r ( FIR ) ( ¯ S c ) op vs ( ¯ S c ) FIR < − < − ( g − r, r − i ) op vs ( g − r, r − i ) FIR ( g − r, z ) op vs ( g − r, z ) FIR ( r − i, z ) op vs ( r − i, z ) FIR ( m r , z ) op vs ( m r , z ) FIR ( g − r, m r ) op vs ( g − r, m r ) FIR ( r − i, m r ) op vs ( r − i, m r ) FIR ( g − r, ¯ S c ) op vs ( g − r, ¯ S c ) FIR ( r − i, ¯ S c ) op vs ( r − i, ¯ S c ) FIR ( m r , ¯ S c ) op vs ( m r , ¯ S c ) FIR ( z, ¯ S c ) op vs ( z, ¯ S c ) FIR
Table 3.
Full SFR range KS-test and MWU-test results for the comparisonof both the Optical and FIR populations ¯ S c distributions within individualredshift slices. From KS results the density distributions are different be-tween the 2.2 σ -3.3 σ level. The number of objects from each population aregiven:Redshift Slice Optical IR KS Prob. MWU Prob. ≤ z < .
680 227 0.028 0.028 . ≤ z < . < − < − Clearly in any flux-density limited sample there is a bias in thesense that the higher-redshift sources are more luminous than thoseat lower redshift. Therefore, to further examine the difference be-tween the Optical and FIR environmental density distributions wesplit the two populations into two redshift slices of < z ≤ . and . < z ≤ . . The ≤ z ≤ . bin contains objectsfrom the Optical population with objects from the FIR popula-tion and the . < z ≤ . bin contains , objects from the Optical population and objects from the FIR population. Theresults of the KS-tests comparing the density measurements withinthese bins are shown in Table 3; these show that the null hypothesiscan be rejected and the two populations can be considered differ-ent in terms of their overall density distributions at the 2.2 σ levelfor the low-redshift bin and . σ level for the high-redshift bin.The MWU test returns probabilities of . and . × − forthe low- and high-redshift bins respectively, also indicating that thetwo distributions have significantly different median values. Thesebinned distributions are shown in Figure 6. Consistent results arefound when the NN method is used to calculate the environmentaldensity, as shown in Section 4.6.These results show that, as with the full redshift range, ob-jects in both redshift bins are significantly different in terms oftheir overall density distributions and their median values. How-ever, it is evident that these statistical differences are higher in thehigher-redshift bin and that this bin contains a larger number of ob-jects in both samples. We investigate the impact of this differencein number density with increasing redshift by matching the numberof galaxies in the higher and lower bins and repeating the samplecomparisons. First, by increasing the redshift boundary between thehigher and lower bins (from z = 0 . to z = 0 . ) to achieve ap-proximate matching in sample sizes above and below this redshift.Second, by reducing the number of objects within the higher red-shift bin to match exactly with the lower bin samples. In both caseswe find that the same trends are found and our results remain thesame.With fewer objects in the lower redshift bin, the signal to noisewill be lower at these redshifts, flattening the density distributionsand affecting the comparison. Furthermore, at higher redshifts, ob-jects with lower IR luminosities are excluded by the flux-densitylimit of the H-ATLAS survey. Thus, the density distribution of theless luminous far-infrared galaxies may actually be similar to theOptical population. In contrast the higher redshift bins contain amuch higher proportion galaxies with higher levels of star forma-tion and therefore exhibit a stronger correlation with density. Theconsequence of this bias is that the statistical differences found be-tween the total Optical and FIR distributions (shown in Table 2)may be being diluted by galaxies with low SFRs at low redshift. In c (cid:13) , ?? ––
680 227 0.028 0.028 . ≤ z < . < − < − Clearly in any flux-density limited sample there is a bias in thesense that the higher-redshift sources are more luminous than thoseat lower redshift. Therefore, to further examine the difference be-tween the Optical and FIR environmental density distributions wesplit the two populations into two redshift slices of < z ≤ . and . < z ≤ . . The ≤ z ≤ . bin contains objectsfrom the Optical population with objects from the FIR popula-tion and the . < z ≤ . bin contains , objects from the Optical population and objects from the FIR population. Theresults of the KS-tests comparing the density measurements withinthese bins are shown in Table 3; these show that the null hypothesiscan be rejected and the two populations can be considered differ-ent in terms of their overall density distributions at the 2.2 σ levelfor the low-redshift bin and . σ level for the high-redshift bin.The MWU test returns probabilities of . and . × − forthe low- and high-redshift bins respectively, also indicating that thetwo distributions have significantly different median values. Thesebinned distributions are shown in Figure 6. Consistent results arefound when the NN method is used to calculate the environmentaldensity, as shown in Section 4.6.These results show that, as with the full redshift range, ob-jects in both redshift bins are significantly different in terms oftheir overall density distributions and their median values. How-ever, it is evident that these statistical differences are higher in thehigher-redshift bin and that this bin contains a larger number of ob-jects in both samples. We investigate the impact of this differencein number density with increasing redshift by matching the numberof galaxies in the higher and lower bins and repeating the samplecomparisons. First, by increasing the redshift boundary between thehigher and lower bins (from z = 0 . to z = 0 . ) to achieve ap-proximate matching in sample sizes above and below this redshift.Second, by reducing the number of objects within the higher red-shift bin to match exactly with the lower bin samples. In both caseswe find that the same trends are found and our results remain thesame.With fewer objects in the lower redshift bin, the signal to noisewill be lower at these redshifts, flattening the density distributionsand affecting the comparison. Furthermore, at higher redshifts, ob-jects with lower IR luminosities are excluded by the flux-densitylimit of the H-ATLAS survey. Thus, the density distribution of theless luminous far-infrared galaxies may actually be similar to theOptical population. In contrast the higher redshift bins contain amuch higher proportion galaxies with higher levels of star forma-tion and therefore exhibit a stronger correlation with density. Theconsequence of this bias is that the statistical differences found be-tween the total Optical and FIR distributions (shown in Table 2)may be being diluted by galaxies with low SFRs at low redshift. In c (cid:13) , ?? –– ?? he environmental density of far-infrared bright galaxies Table 4.
Two sample KS and MWU-test results for each SFR bin, collectively over the full redshift range ( < z ≤ . ) where op represents the Opticaland FIR represents the FIR populations. (A): SFR of 0 to 15 M (cid:12) yr − contains cross-matched Optical objects and cross-matched FIR objects. (B):SFR of 15 to 30 M (cid:12) yr − bin contains , cross-matched Optical objects and cross-matched FIR objects. (C): Minimum SFR of 30 M (cid:12) yr − bincontaining cross-matched Optical objects and cross-matched FIR objects.Distributions Compared KS Prob. (A) MWU Prob. (A) KS Prob. (B) MWU Prob. (B) KS Prob. (C) MWU Prob. (C) z op vs z FIR ( g − r ) op vs ( g − r ) FIR ( r − i ) op vs ( r − i ) FIR m r ( op ) vs m r ( FIR ) ( ¯ S c ) op vs ( ¯ S c ) FIR < − < − < − Figure 7.
Top : The calculated SFR ( M (cid:12) yr − ) against redshift for the totalFIR catalogue. Bottom : The three SFR bins from the FIR catalogue versusredshift. The < SF R <
15 M (cid:12) yr − bin (Solid line) containing objects, the < SF R ≤
30 M (cid:12) yr − bin (Dashed line) containing objects and the SF R >
30 M (cid:12) yr − bin (Dotted line) containing objects z ≤ . . order to examine the full impact of these objects, in Section 4.4, weapply SFR bins to the FIR catalogue and repeat the above analysis. The SFR of a galaxy can be estimated using the relation given inKennicutt (1998) as proportional to the total IR luminosity ( L FIR )over 8-1000 µ m, assuming a Salpeter IMF between . (cid:12) −
100 M (cid:12) (Salpeter 1955), such that:
SF R ( M (cid:12) yr − ) = 4 . × − · L FIR (ergs · s − ) , (2) The thermal emission of far-IR galaxies can be represented by amodified black body emission spectrum from Blain et al. (2003): f ν ∝ ν β exp (cid:0) hνkT − (cid:1) , (3)where h is the Planck constant, k is the Boltzmann constant, and T represents the temperature. The emissivity index, β modifies thePlanck function by assuming that the dust emissivity varies as apower law with frequency, ν β , where β can be between 1-2 as de-scribed in Hildebrand (1983), depending on the frequency of theobservations. We fix the dust emissivity index to β = 1 . with dusttemperature ( T ) equal to 26 K as found by Dye et al. (2010) andJarvis et al. (2010) and integrate the modified blackbody over thewavelength range − µ m to obtain the far-infrared luminos-ity. We then use equation 2 to determine the SFR (in M (cid:12) yr − ) foreach galaxy (see Figure 7).As a check of our L FIR values we compare the galaxies inour sample to the subset of objects with far-infrared luminositiesdetermined from the full energy balance models of da Cunha et al.(2008) by Smith et al. (2012a). We find that our L FIR values areslightly underestimated, and a correction factor of . is neededto produce a 1:1 correlation. This suggests that, as we are assuminga fixed dust temperature of 26 K, our estimate misses ∼ per centof the total dust luminosity, and hence the SFRs are underestimatedin our calculation. We therefore apply this correction factor to our L FIR values to account for this difference in our resultant SFRs.We note that this correction makes very little difference to our over-all results on the relative environmental densities between differentbins in SFR.It is also worth noting that the SFRsestimated from FIR emis-sion may be overestimates of the true SFR. We know that far-infrared emission is a tracer of star formation in an idealised casewhere young stars dominate the radiation field and dust opacity ishigh (Kennicutt et al. 2009). Multi-temperature dust distributionsand emission from dust heated by older ISM stars (da Cunha et al.2008; Smith et al. 2012a) are not be expected to be consistent withequation 2, and this also plays a part in our correction factor of1.25. This must also be balanced against the fact that any unob-scured component of star formation would not be detected in theFIR. Thus, although far-infrared emission is highly correlated withSFR we note that the absolute values of SFR should be used withcaution.We bin the FIR objects in terms of their SFR in bins of − , − and >
30 M (cid:12) yr − in order to compare the impact ofdifferent SFRs on our initial results. Again matching the controlsample to the individual binned SFR samples we perform KS-tests and MWU-tests on all combinations. The results of thesetests are shown in Table 4. From KS and MWU tests the densitydistributions for all our SFR bins are shown to be different; for c (cid:13) , ?? – ?? C. S. Burton et al.
Figure 8.
Histograms of the r − K colours for the Optical (red) and FIR(blue) samples showing that they have significantly different distributionsat a > σ level with the FIR galaxies lying redward of the Optical galaxies. Figure 9.
Normalised histograms of the environmental density ( ¯ S c ) of bothOptical ( red ) and FIR ( blue ) populations, cross-matched in r − K , m K and z parameter space. KS and MWU tests indicate a significant difference tothe > σ level. The FIR data is shifted generally to lower ¯ S c values, withthe mean of its distribution at . ± . ( blue dashed line ), contrastedagainst the mean of the Optical distribution at . ± . ( red dashed line )Shaded histograms represent the number of spectroscopic redshifts in eachsample. SFR > −
15 M (cid:12) yr − the difference in environmental density ispresent at the 2.6 σ level for both the KS-test and the MWU test,for −
30 M (cid:12) yr − the KS and MWU tests shows a differenceat the 2.7 σ and 3.8 σ level, and for the SFR >
30 M (cid:12) yr − the dis-tributions are significantly different at the 3.3 σ and 4.8 σ levels,respectively.This shows that the SFRs derived from the far-infrared emis-sion of galaxies are strongly linked to the environmental densityof the galaxy. Selecting only those galaxies with the highest SFRsresults in an even more pronounced difference between the normal-ized density distributions of the Optical and FIR populations. In our analysis we have only used the most sensitive optical bandsto define our optical and far-infrared selected samples, due to the
Table 5.
Two sample and two-dimensional KS and MWU-test results overthe full SFR and redshift range ( < z ≤ . ). Where op represents Optical( , objects) and FIR represents FIR ( , objects) matched in termsof their K − band magnitude, r − K colour and redshift distribution. Thetwo density distributions are different at the > σ level from KS tests, withthe medians of the distributions different at the > σ level from MWUtests.Distributions Compared KS Prob. MWU Prob. z op vs z FIR ( r − K ) op vs ( r − K ) FIR m K ( op ) vs m K ( FIR ) ( ¯ S c ) op vs ( ¯ S c ) FIR < − < − ( r − K, z ) op vs ( r − K, z ) FIR ( m K , z ) op vs ( m K , z ) FIR ( r − K, m K ) op vs ( r − K, m K ) FIR ( r − K, ¯ S c ) op vs ( r − K, ¯ S c ) FIR < − - ( m K , ¯ S c ) op vs ( m K , ¯ S c ) FIR < − - ( z, ¯ S c ) op vs ( z, ¯ S c ) FIR < − - wealth of such data over the survey region used. However, wewould expect that the galaxies which are detected in H-ATLAS tobe subject to dust reddening effects, as we know that they must havesignificant amounts of dust in them to be detected in the first place.This could cause our Optical and FIR galaxies to be mismatchedin terms of their intrinsic stellar colours and their stellar masses.To investigate this we include the K − band data from the UKIRTInfrared Sky Survey (Lawrence et al. 2007), which is available formany (but not all) of our sources. We did not use this initially asthe number of galaxies with a K − band identification is less thanthe number which are identified in the g , r and i bands. In Fig-ure 8 we show a histogram of the r − K colours of our matchedsample of Optical ( red ) and FIR ( blue ) galaxies where, due to thesmaller number of K -band detections, the size of each sample is re-duced to 2,139 and objects respectively. This shows that thereis indeed a significant difference in the r − K distributions be-tween the Optical and FIR galaxies at a > σ level, suggestingthat dust reddening may well be biasing our results. However, thiswould only strengthen our results due to the fact that, as we cross-match in the r − band, the reddening we see in Figure 8 is caused bythe FIR population having brighter K − band magnitudes than theOptical sample. Therefore, due to this reddening, we are likely tobe overestimating the FIR K − band magnitudes and subsequentlytheir masses. Given that we know more massive galaxies generallytrace denser environments, correcting for this would lead to a largerdifference between the Optical and FIR samples.To test the rigour of our result we repeat our density analysiswith Optical and FIR samples cross-matched in terms of r − K , m K and z parameter space. As this new cross-matching takes into con-sideration only three dimensions, the resultant number of objectsconsidered matched in all three of these parameters is larger thanin our initial four-dimensional cross-matching, with , Opticaland , FIR objects. Applying KS and MWU tests to the datareturn probability values consistent with a significant difference be-tween the environmental density distributions to the > σ level,with the FIR population once more favouring underdense regionscompared to the Optical sample with mean values of . ± . and . ± . respectively. Table 5 gives the results of the statis-tical comparison and the density distributions are plotted in Figure9. We do not extend on this analysis here as new data from theVISTA VIKING Survey (e.g. Findlay et al. 2012) over the full H- c (cid:13) , ?? ––
Two sample and two-dimensional KS and MWU-test results overthe full SFR and redshift range ( < z ≤ . ). Where op represents Optical( , objects) and FIR represents FIR ( , objects) matched in termsof their K − band magnitude, r − K colour and redshift distribution. Thetwo density distributions are different at the > σ level from KS tests, withthe medians of the distributions different at the > σ level from MWUtests.Distributions Compared KS Prob. MWU Prob. z op vs z FIR ( r − K ) op vs ( r − K ) FIR m K ( op ) vs m K ( FIR ) ( ¯ S c ) op vs ( ¯ S c ) FIR < − < − ( r − K, z ) op vs ( r − K, z ) FIR ( m K , z ) op vs ( m K , z ) FIR ( r − K, m K ) op vs ( r − K, m K ) FIR ( r − K, ¯ S c ) op vs ( r − K, ¯ S c ) FIR < − - ( m K , ¯ S c ) op vs ( m K , ¯ S c ) FIR < − - ( z, ¯ S c ) op vs ( z, ¯ S c ) FIR < − - wealth of such data over the survey region used. However, wewould expect that the galaxies which are detected in H-ATLAS tobe subject to dust reddening effects, as we know that they must havesignificant amounts of dust in them to be detected in the first place.This could cause our Optical and FIR galaxies to be mismatchedin terms of their intrinsic stellar colours and their stellar masses.To investigate this we include the K − band data from the UKIRTInfrared Sky Survey (Lawrence et al. 2007), which is available formany (but not all) of our sources. We did not use this initially asthe number of galaxies with a K − band identification is less thanthe number which are identified in the g , r and i bands. In Fig-ure 8 we show a histogram of the r − K colours of our matchedsample of Optical ( red ) and FIR ( blue ) galaxies where, due to thesmaller number of K -band detections, the size of each sample is re-duced to 2,139 and objects respectively. This shows that thereis indeed a significant difference in the r − K distributions be-tween the Optical and FIR galaxies at a > σ level, suggestingthat dust reddening may well be biasing our results. However, thiswould only strengthen our results due to the fact that, as we cross-match in the r − band, the reddening we see in Figure 8 is caused bythe FIR population having brighter K − band magnitudes than theOptical sample. Therefore, due to this reddening, we are likely tobe overestimating the FIR K − band magnitudes and subsequentlytheir masses. Given that we know more massive galaxies generallytrace denser environments, correcting for this would lead to a largerdifference between the Optical and FIR samples.To test the rigour of our result we repeat our density analysiswith Optical and FIR samples cross-matched in terms of r − K , m K and z parameter space. As this new cross-matching takes into con-sideration only three dimensions, the resultant number of objectsconsidered matched in all three of these parameters is larger thanin our initial four-dimensional cross-matching, with , Opticaland , FIR objects. Applying KS and MWU tests to the datareturn probability values consistent with a significant difference be-tween the environmental density distributions to the > σ level,with the FIR population once more favouring underdense regionscompared to the Optical sample with mean values of . ± . and . ± . respectively. Table 5 gives the results of the statis-tical comparison and the density distributions are plotted in Figure9. We do not extend on this analysis here as new data from theVISTA VIKING Survey (e.g. Findlay et al. 2012) over the full H- c (cid:13) , ?? –– ?? he environmental density of far-infrared bright galaxies Table 6.
Two sample and two-dimensional KS and MWU-test results fromthe application of the 5th-nearest neighbour technique to the SDSS and H-ATLAS SDP data from Section 4. Where op represents Optical ( , ob-jects) and FIR represents FIR ( objects). The two density distributionsare significantly different to the 3.9 σ level from KS tests in agreement withour VT technique.Distributions Compared KS Prob. MWU Prob. z op vs z FIR ( g − r ) op vs ( g − r ) FIR ( r − i ) op vs ( r − i ) FIR m r ( op ) vs m r ( FIR ) ( ¯ S c ) op vs ( ¯ S c ) FIR < − < − ( g − r, r − i ) op vs ( g − r, r − i ) FIR ( g − r, z ) op vs ( g − r, z ) FIR ( r − i, z ) op vs ( r − i, z ) FIR ( m r , z ) op vs ( m r , z ) FIR ( g − r, m r ) op vs ( g − r, m r ) FIR ( r − i, m r ) op vs ( r − i, m r ) FIR ( g − r, ¯ S c ) op vs ( g − r, ¯ S c ) FIR ( r − i, ¯ S c ) op vs ( r − i, ¯ S c ) FIR ( m r , ¯ S c ) op vs ( m r , ¯ S c ) FIR ( z, ¯ S c ) op vs ( z, ¯ S c ) FIR
ATLAS fields will mean that the analysis presented here could becarried out with a K − band selected sample in the near future. Applying the same KS and MWU statistical comparisons from Sec-tion 4.2 between our cross-matched FIR and Optical data sets, wefind good agreement between the NN and the VT method; the twoNN defined normalized density distributions ( ¯ S c ) are significantlydifferent, with a KS test probability of . × − indicating asignificant difference at the . σ level. As with our VT methodall other parameter comparisons show no significant difference asshown in Table 6. In further agreement with the results establishedusing the VT method, the mean values of the two density distribu-tions reveal that the cross-matched FIR catalogue contains objectswith lower environmental densities than the Optical catalogue withmean values of . ± . and . ± . respectively. MWUtests reveal a significant difference between the median values atthe 4.6 σ level. In addition, repeating the redshift binning from Sec-tion 4.3 returns consistent results such that differences are found inboth bins increasing from 2 σ in the lowest bin to 3.3 σ in the higherbin. In this section we use the semi-analytic models (SAMs) of Hen-riques et al. (2012), who construct pencil-beam synthetic light-cones for square areas (1.4 deg × h − Mpc which is smaller than the co-moving distance of an object at z ∼ . Therefore periodic replication of the simula-tion can lead to multiples of the same object being included dueto discontinuities in large scale structure at the boundaries betweenreplications (Kitzbichler & White 2007). Here we apply our environmental density measurement to the mockcatalogues of Henriques et al. (2012) in order to establish whetherthe same relationship between environmental density and SFR isfound. Our results from Section 4 have shown there is a statisticallysignificant difference between the density distributions of galaxieswith and without obscured star formation (as traced by far-IR emis-sion). This is such that galaxies with obscured star formation favourunderdense regions while galaxies without star formation favouroverdense regions.We use all mock catalogues from Henriques et al. (2012),with additional data taken from the mock catalogue of Guo et al.(2011). The data are selected to span the same redshift range asour observed data ( < z ≤ . ), however these catalogues donot initially contain any errors on their redshift values. Thereforein order to achieve similar redshift sampling as within our environ-mental density measurement in Section 3, it is necessary to apply aredshift error to each object based on matching the r − band mag-nitude ( m r ) and photometric redshift ( z ) values to the observeddata catalogue. This therefore establishes a likely value for the red-shift error based on these parameters. This is achieved by cross-matching each Henriques & Guo (hereafter HG) object to the totalOptical-9hr catalogue, locating all matches in r − band magnitude( m r ) and photometric redshift ( z ). For each match, the photometricerror from the Optical-9hr catalogue is applied as the redshift errorto the HG object. Where a spectroscopic redshift is located, a stan-dard error for a spectroscopic redshift ( . ) is applied, as in theinitial analysis (Section 3). In addition, as with the observed data inSection 2.2, an apparent r − band magnitude cut was implementedremoving all galaxies with magnitudes fainter than 21.5. The re-sultant number of objects across the HG catalogue totals , objects. Applying our environmental density measure returns nor-malized environmental density values in comparison to a randomfield ( ¯ S c ) for each object, as with our observed data in Section 3.2.However, due to the smaller field size ( − . < RA < . degreesand − . < Dec < . degrees) the edge effect cuts imposed dur-ing the analysis have a greater impact on the number of sources cutfrom our HG catalogue, further reducing the catalogue to , objects.For our analysis it is first necessary to determine which galax-ies in the simulated catalogue would have far-IR emission, and thusbe detectable by the H-ATLAS survey. This is achieved by calcu-lating the µ m flux for each object from the given SFR and red-shift values given by the SAM. This is the direct reverse of thecalculation in Section 4.4 where we calculate the SFR, assuminga temperature and emissivity index, from the µ m flux of eachFIR galaxy. The average 5 σ µ m flux limit of the H-ATLASobservations ( . mJy), taken from Rigby et al. (2011), providesan exact cut-off point for which a galaxy could be considered de-tectable in the survey. From here the HG catalogue could be splitinto IR and non-IR detected objects, equivalent to our FIR and Op-tical catalogues in our observed data analysis from Section 4.1. Ob-jects with a µ m flux density greater than . mJy are there-fore considered detectable by H-ATLAS, hereafter called FIR-HG( , objects), and those with a µ m flux density less than c (cid:13) , ?? – ?? C. S. Burton et al.
Figure 10.
A set of normalized histograms form the SAM output that show how the distribution of environmental density ( ¯ S c ) of the colour matched Optical-HG ( red ) and FIR-HG ( blue ) populations change with redshift. Left : The full SFR range of both environmental density ( ¯ S c ) distributions ( , and objects respectively), along with error bars depicting the normalized error associated with each bin. The two distributions are significantly different to the 4 σ level as determined by KS tests. Centre : The lower redshift bin ( < z ≤ . ) KS and MWU statistical tests reveal that the distributions are statisticallydifferent and that the null hypothesis can be rejected to at least the 2.4 σ level. Right : In the higher redshift bin ( . < z ≤ . ) the distributions are againsignificantly different and the null hypothesis can be rejected to at least the 3.4 σ level. Figure 11.
Normalized histograms showing the comparison between theredshift distributions of both FIR and FIR-HG samples.
Solid line:
The to-tal FIR-HG redshift distribution showing a clear weighting towards lowerredshifts.
Dashed line:
The total FIR redshift distribution which peaks athigher redshifts. . mJy are not considered detectable by H-ATLAS and hereafternamed Optical-HG ( , objects).As with our observed data in Section 4.1, a like with likecross-matching process is applied. We find , objects from theOptical-HG population matched with objects from the FIR-HGpopulation. Both of these cross-matched samples represent approx-imately the same percentage of their parent populations as foundwith our observed cross-matched samples from Section 4.1. Thiswas such that the cross-matched Optical and Optical-HG samplesrepresent ∼ per cent of their parent populations, with the FIR andFIR-HG samples representing ∼ and ∼ per cent respectively. We perform the same statistical analysis, as with our observed datain Section 4.2, i.e. applying one- and two-dimensional KS tests aswell as MWU-tests to the two cross-matched populations, the re-sults of which are given in Table 7. These values show, in agreementwith our observed data in Section 4.2, that the null hypothesis canbe rejected to at least the 4 σ level for the normalized environmental Table 7.
Full SFR range. Two sample and two-dimensional KS and MWU-test results over full redshift range ( < z ≤ . ) where op representsOptical-HG ( , objects) and FIR represents FIR-HG ( objects). Thedensity distributions are significantly different to the 4 σ level from KS tests,with the median values of the distributions different to the 4.7 σ level fromMWU tests:Distributions Compared KS Prob. MWU Prob. z op vs z FIR ( g − r ) op vs ( g − r ) FIR ( r − i ) op vs ( r − i ) FIR m r ( op ) vs m r ( FIR ) ( ¯ S c ) op vs ( ¯ S c ) FIR < − < − ( g − r, r − i ) op vs ( g − r, r − i ) FIR ( g − r, z ) op vs ( g − r, z ) FIR ( r − i, z ) op vs ( r − i, z ) FIR ( m r , z ) op vs ( m r , z ) FIR ( g − r, m r ) op vs ( g − r, m r ) FIR ( r − i, m r ) op vs ( r − i, m r ) FIR ( g − r, ¯ S c ) op vs ( g − r, ¯ S c ) FIR < − - ( r − i, ¯ S c ) op vs ( r − i, ¯ S c ) FIR < − - ( m r , ¯ S c ) op vs ( m r , ¯ S c ) FIR ( z, ¯ S c ) op vs ( z, ¯ S c ) FIR density ( ¯ S c ) of the Optical-HG and FIR-HG populations. All otherparameter comparisons cannot be considered significantly differentat any reliable statistical level (e.g. > σ ).The two density distributions are shown in Figure 10 ( left ). Asexpected, it is the FIR-HG population ( blue ), with the mean of itsdistribution at ¯ S c = ( − . ± . × − ( blue dashed line ), thatis biased towards underdense regions, while the Optical-HG popu-lation ( red ), with the mean of its distribution at ¯ S c = (2 . ± . × − ( red dashed line ), shows a bias towards overdense regions.Errors included on each bin are small and support the differencefound between the distributions. It is worth noting that if we donot include simulated photometric errors and treat the SAM red-shift values as precise, the resultant ¯ S c distributions exhibit a muchlarger spread in values. Inclusion of photometric errors evidentlyreduces this spread by essentially ‘washing out’ the density struc-ture we are trying to recover. However, when precise redshifts val-ues are used we find the same correlations are found between theOptical-HG and FIR-HG populations, despite the increased spread,with both populations exhibiting a significant difference.To further examine the difference found between the Optical- c (cid:13) , ?? ––
Full SFR range. Two sample and two-dimensional KS and MWU-test results over full redshift range ( < z ≤ . ) where op representsOptical-HG ( , objects) and FIR represents FIR-HG ( objects). Thedensity distributions are significantly different to the 4 σ level from KS tests,with the median values of the distributions different to the 4.7 σ level fromMWU tests:Distributions Compared KS Prob. MWU Prob. z op vs z FIR ( g − r ) op vs ( g − r ) FIR ( r − i ) op vs ( r − i ) FIR m r ( op ) vs m r ( FIR ) ( ¯ S c ) op vs ( ¯ S c ) FIR < − < − ( g − r, r − i ) op vs ( g − r, r − i ) FIR ( g − r, z ) op vs ( g − r, z ) FIR ( r − i, z ) op vs ( r − i, z ) FIR ( m r , z ) op vs ( m r , z ) FIR ( g − r, m r ) op vs ( g − r, m r ) FIR ( r − i, m r ) op vs ( r − i, m r ) FIR ( g − r, ¯ S c ) op vs ( g − r, ¯ S c ) FIR < − - ( r − i, ¯ S c ) op vs ( r − i, ¯ S c ) FIR < − - ( m r , ¯ S c ) op vs ( m r , ¯ S c ) FIR ( z, ¯ S c ) op vs ( z, ¯ S c ) FIR density ( ¯ S c ) of the Optical-HG and FIR-HG populations. All otherparameter comparisons cannot be considered significantly differentat any reliable statistical level (e.g. > σ ).The two density distributions are shown in Figure 10 ( left ). Asexpected, it is the FIR-HG population ( blue ), with the mean of itsdistribution at ¯ S c = ( − . ± . × − ( blue dashed line ), thatis biased towards underdense regions, while the Optical-HG popu-lation ( red ), with the mean of its distribution at ¯ S c = (2 . ± . × − ( red dashed line ), shows a bias towards overdense regions.Errors included on each bin are small and support the differencefound between the distributions. It is worth noting that if we donot include simulated photometric errors and treat the SAM red-shift values as precise, the resultant ¯ S c distributions exhibit a muchlarger spread in values. Inclusion of photometric errors evidentlyreduces this spread by essentially ‘washing out’ the density struc-ture we are trying to recover. However, when precise redshifts val-ues are used we find the same correlations are found between theOptical-HG and FIR-HG populations, despite the increased spread,with both populations exhibiting a significant difference.To further examine the difference found between the Optical- c (cid:13) , ?? –– ?? he environmental density of far-infrared bright galaxies Table 9.
Two sample KS and MWU-test results where op represents Optical-HG and FIR represents FIR-HG. (A): SFR of 0 to 5 M (cid:12) yr − containingOptical-HG objects and FIR-HG objects. The difference between the two density distributions in this bin cannot be distinguished. (B): SFR of 5 to10 M (cid:12) yr − containing Optical-HG objects and
FIR-HG objects. The density distributions are different at the 3.3 σ level from KS tests and 3.4 σ from MWU tests. (C): SFR of > M (cid:12) yr − containing Optical-HG objects and
FIR-HG objects. From KS tests the two density distributions aredifferent at the 3 σ level, with the median values of the distributions different at the 3.6 σ level from MWU tests:Distributions Compared KS Prob. (A) MWU Prob. (A) KS Prob. (B) MWU Prob. (B) KS Prob. (C) MWU Prob. (C) z op vs z FIR ( g − r ) op vs ( g − r ) FIR ( r − i ) op vs ( r − i ) FIR m r ( op ) vs m r ( FIR ) ( ¯ S c ) op vs ( ¯ S c ) FIR < − Table 8.
Full SFR range KS-test and MWU-test results for both the Optical-HG and FIR-HG populations for ¯ S c distributions within the individual red-shift slices shown in Figure 10. The null hypothesis is rejected at the 2.4 σ -2.9 σ level for both distributions in the lower redshift bin from KS and MWUtests. The null hypothesis is rejected at the 3.4 σ -3.9 σ level in the higher red-shift bin:Redshift Slice Optical IR KS Prob. MWU Prob. ≤ z < . . ≤ z < .
911 310 < − < − HG and FIR-HG populations we once more split the two popu-lations into redshift bins, repeating the analysis from Section 4.3.Figure 11 shows the redshift distributions of both the FIR (dashedline) and FIR-HG (solid line) data. It is immediately clear that theFIR-HG population is primarily weighted towards lower redshiftswith a mean value of ( . ± . ) × − . Its number density fallsoff beyond z ∼ . reaching a maximum redshift of z = 0 . ,short of the full redshift range of the FIR sample. In comparison theFIR population retains an approximately consistent number densityacross its entire redshift range with a mean value of ( . ± . ) × − . Therefore it is necessary to adjust the redshift binning fromthat applied to the FIR data in Section 4.3 to account for this differ-ence. Reducing the boundary between our higher and lower redshiftbins from z = 0 . to z = 0 . , we bin the Optical-HG and FIR-HG populations, re-plotting histograms to represent the data withinthese redshift bins and reapplying KS-tests and MWU tests to thedata. The redshift bins are plotted into normalized histograms dis-played in Figure 10 and the KS and MWU test results from thisredshift binning are given in Table 8. These statistical tests confirmthat the same SFR-density trend with redshift is found as with ourobservational data analysis in Section 4.3.This trend is found despite the differences between the redshiftdistributions of both observed and simulated FIR data sets (Fig-ure 11). We determine that a galaxy constitutes part of the FIR-HGpopulation by selecting objects based on their µ m flux, which iscalculated from the individual SFR derived from the SAM of Guoet al. (2011). As noted in Section 4.4 our calculation of the SFRfrom the far-infrared luminosity is subject to a range of assump-tions that may or may not be valid. Furthermore, the parametersused within the SAM to calculate SFR may also not accurately in-corporate all of the physical processes that govern SFR. Detailedanalyses of these effects are beyond the scope of this paper, there-fore we adopt a conservative approach and consider that the resultsfrom the observations and the SAMs are in qualitative agreement. Here we repeat the same SFR binning analysis from Section 4.4.Applying this stage of the analysis to the populations derived from SAMs allows us to further probe the differences between the sim-ulated data and the data obtained observationally. The reduction inthe number of FIR-HG objects between the low and high redshiftbins is illustrated in Figure 12. This shows how the number densityof the FIR-HG population falls off beyond z ∼ . , in compari-son with our observed data in Figure 7. It is evident that the FIR-HGpopulation has a higher fraction of sources at higher redshifts thanFIR population. Due to the vast majority of the FIR-HG populationresiding below z ∼ . it is necessary to adjust the SFR binningparameters, from those applied to the FIR population, to narrowerSFR ranges in order to achieve three comparative samples of thispopulation. We therefore bin the FIR-HG objects in terms of theirSFR in bins of − , − and >
10 M (cid:12) yr − . In agreementwith our results in Section 4.4, we find that with higher levels ofstar formation, the statistical difference between the two popula-tions from KS and MWU tests increases. Only in our lowest SFRbin ( − (cid:12) yr − ) is no significant difference found between theOptical-HG and FIR-HG samples. These values are presented inTable 9.Figure 12 shows how at higher SFRs the number density ofobjects reduces to such an extent that it makes further analysis un-feasible. Therefore it was not possible to introduce SFR bins athigher SFRs than 10 M (cid:12) yr − to the analysis. Despite this, somekey conclusions can be made with regards to the Optical-HG/ FIR-HG comparison based on the three SFR bins applied to the data.This analysis has shown that, for galaxies with SFRs higher than5 M (cid:12) yr − , there is a statistically significant difference betweenboth of the ¯ S c distributions and that this statistical difference be-comes more pronounced in these higher SFR bins as a result ofremoving lower star-forming objects from the comparison. Fromfinding no statistical difference between the density distributions ofthe Optical-HG and FIR-HG populations when SFRs are less than5 M (cid:12) yr − to finding a significant difference to at least the 3 σ levelin higher SFR bins. We again test the N th-nearest neighbour against our Voronoi Tes-sellation methods. We apply the NN method to our analysis ofsemi-analytic models. Following the same processes from Sections5.1 and 5.2 we apply our algorithm, changed to incorporate theNN method, to the total HG catalogue, again dividing the outputaccording to the H-ATLAS flux limit and cross-matching in g − r , r − i , z and m r parameter space. This, once more, provides two cat-alogues representative of optical and far-infrared (Optical-HG andFIR-HG) that can be accurately compared to analyse differences indensity.We find that our results match those of Section 5.2, with KSand MWU test results finding a significant difference between the c (cid:13) , ?? – ?? C. S. Burton et al.
Figure 12.
Top : SFR ( M (cid:12) yr − ) versus redshift for the total FIR-HG cat-alogue. This shows that above 10 M (cid:12) yr − the number of objects reducessignificantly. Bottom : Plot of the three SFR bins from the FIR-HG cataloguevs redshift. The < SF R < (cid:12) yr − bin (Solid line) containing objects, the < SF R ≤
10 M (cid:12) yr − bin (Dashed line) containing objects and the SF R >
10 M (cid:12) yr − bin (Dotted line) containing objects. normalized densities of the Optical-HG and FIR-HG populationsonly (Table 10). With a KS-test and MWU-test probabilities of ∼ − indicating a significant difference at the > ∼ σ level in bothcases. The mean values of each distribution lie at ( . ± . ) × − for the Optical-HG and ( . ± . ) × − for the FIR-HG indicating that the Optical-HG population occupy generallymore overdense regions in agreement with our study using VT. The increased statistical separation between the Optical and FIRdensity distributions, found with both increasing redshift and in-creasing SFR, provides a clue to the role of environment in the evo-lution of galaxies over the redshift range ( < z ≤ . ). We finda clear segregation in the galaxy environmental density betweenfar–infrared-detected sources and those galaxies that are matchedin terms of optical colour, magnitude and redshift but devoid of de-tectable far-infrared emission. Moreover, we find that this segrega-tion becomes more pronounced at brighter far-infrared luminosity(or SFR) or at higher redshift. Unfortunately our data precludes us Table 10.
Two sample and two-dimensional KS and MWU-test results fromthe application of the 5th-nearest neighbour technique to our semi-analyticmodel analysis Optical-HG and FIR-HG populations. Where op representsOptical-HG ( , objects) and FIR represents FIR-HG ( objects). Thetwo density distributions are significantly different to the 4.5 σ level fromKS tests in agreement with our VT technique.Distributions Compared KS Prob. MWU Prob. z op vs z FIR ( g − r ) op vs ( g − r ) FIR ( r − i ) op vs ( r − i ) FIR m r ( op ) vs m r ( FIR ) ( ¯ S c ) op vs ( ¯ S c ) FIR < − < − ( g − r, r − i ) op vs ( g − r, r − i ) FIR ( g − r, z ) op vs ( g − r, z ) FIR ( r − i, z ) op vs ( r − i, z ) FIR ( m r , z ) op vs ( m r , z ) FIR ( g − r, m r ) op vs ( g − r, m r ) FIR ( r − i, m r ) op vs ( r − i, m r ) FIR ( g − r, ¯ S c ) op vs ( g − r, ¯ S c ) FIR < − - ( r − i, ¯ S c ) op vs ( r − i, ¯ S c ) FIR < − - ( m r , ¯ S c ) op vs ( m r , ¯ S c ) FIR ( z, ¯ S c ) op vs ( z, ¯ S c ) FIR < − - from distinguishing between an evolutionary effect and one associ-ated with the level of star formation activity.It is important to note that the reliability criterion ( R > . ),that we employ from Smith et al. (2011) to select optical coun-terparts to the FIR data, does not present a bias in our results. Thispotential bias is such that in denser regions, with an increased num-ber of potential optical counterparts to a FIR object, the reliabilityparameter for that FIR object, as defined in Smith et al. (2012a),would reduce. In other words, in denser regions it potentially be-comes more difficult to reliably associate the FIR detection with aunique optical source. Therefore the FIR object may be excludedleaving only the FIR detections in relatively low-density environ-ments. We tested this bias by making a more inclusive cut to the FIRsample based on the minimum likelihood-ratio (LR) rather than thereliability criterion (R). Our FIR sample was therefore increased toinclude these previously missing sources. Upon repeating the anal-ysis we found that we still obtained similarly significant differencesbetween the FIR and Optical samples.These results support previous studies that also suggest thatthe presence of star formation in a galaxy is negatively correlatedwith the density of its environment (e.g., Dressler 1980; Postman& Geller 1984; Dressler et al. 1997; Dom´ınguez et al. 2001; Gotoet al. 2003; Kauffmann et al. 2004; O’Mill et al. 2008; Lee et al.2010). Our analysis has shown that this correlation holds on in-dividual galaxy scales, and thus the processes responsible for thiscorrelation must have influence at this level as well as on largerscales. In addition, our use of far-infrared observations mean ourresults are not affected by uncertainties associated with extinctionor H α to SFR conversions.However, the exact mechanism responsible for the observedreduction of SFR with increase in density remains uncertain. Re-cent studies by Deng et al. (2011) and Wijesinghe et al. (2012)suggest that there is no trend with environment when restricting theSFR-density comparison to purely star-forming objects. They con-clude, therefore, that the observed SFR-density correlation is dueto the increasing fraction of passive galaxies across the total galaxysample since z ∼ . Deng et al. (2011) go further and suggest thatthe SFR-density relation is strongly colour dependent, with bluegalaxies exhibiting a very weak correlation between environmentand SFR. In contrast, they find red galaxies to exhibit strong cor- c (cid:13) , ?? ––
Two sample and two-dimensional KS and MWU-test results fromthe application of the 5th-nearest neighbour technique to our semi-analyticmodel analysis Optical-HG and FIR-HG populations. Where op representsOptical-HG ( , objects) and FIR represents FIR-HG ( objects). Thetwo density distributions are significantly different to the 4.5 σ level fromKS tests in agreement with our VT technique.Distributions Compared KS Prob. MWU Prob. z op vs z FIR ( g − r ) op vs ( g − r ) FIR ( r − i ) op vs ( r − i ) FIR m r ( op ) vs m r ( FIR ) ( ¯ S c ) op vs ( ¯ S c ) FIR < − < − ( g − r, r − i ) op vs ( g − r, r − i ) FIR ( g − r, z ) op vs ( g − r, z ) FIR ( r − i, z ) op vs ( r − i, z ) FIR ( m r , z ) op vs ( m r , z ) FIR ( g − r, m r ) op vs ( g − r, m r ) FIR ( r − i, m r ) op vs ( r − i, m r ) FIR ( g − r, ¯ S c ) op vs ( g − r, ¯ S c ) FIR < − - ( r − i, ¯ S c ) op vs ( r − i, ¯ S c ) FIR < − - ( m r , ¯ S c ) op vs ( m r , ¯ S c ) FIR ( z, ¯ S c ) op vs ( z, ¯ S c ) FIR < − - from distinguishing between an evolutionary effect and one associ-ated with the level of star formation activity.It is important to note that the reliability criterion ( R > . ),that we employ from Smith et al. (2011) to select optical coun-terparts to the FIR data, does not present a bias in our results. Thispotential bias is such that in denser regions, with an increased num-ber of potential optical counterparts to a FIR object, the reliabilityparameter for that FIR object, as defined in Smith et al. (2012a),would reduce. In other words, in denser regions it potentially be-comes more difficult to reliably associate the FIR detection with aunique optical source. Therefore the FIR object may be excludedleaving only the FIR detections in relatively low-density environ-ments. We tested this bias by making a more inclusive cut to the FIRsample based on the minimum likelihood-ratio (LR) rather than thereliability criterion (R). Our FIR sample was therefore increased toinclude these previously missing sources. Upon repeating the anal-ysis we found that we still obtained similarly significant differencesbetween the FIR and Optical samples.These results support previous studies that also suggest thatthe presence of star formation in a galaxy is negatively correlatedwith the density of its environment (e.g., Dressler 1980; Postman& Geller 1984; Dressler et al. 1997; Dom´ınguez et al. 2001; Gotoet al. 2003; Kauffmann et al. 2004; O’Mill et al. 2008; Lee et al.2010). Our analysis has shown that this correlation holds on in-dividual galaxy scales, and thus the processes responsible for thiscorrelation must have influence at this level as well as on largerscales. In addition, our use of far-infrared observations mean ourresults are not affected by uncertainties associated with extinctionor H α to SFR conversions.However, the exact mechanism responsible for the observedreduction of SFR with increase in density remains uncertain. Re-cent studies by Deng et al. (2011) and Wijesinghe et al. (2012)suggest that there is no trend with environment when restricting theSFR-density comparison to purely star-forming objects. They con-clude, therefore, that the observed SFR-density correlation is dueto the increasing fraction of passive galaxies across the total galaxysample since z ∼ . Deng et al. (2011) go further and suggest thatthe SFR-density relation is strongly colour dependent, with bluegalaxies exhibiting a very weak correlation between environmentand SFR. In contrast, they find red galaxies to exhibit strong cor- c (cid:13) , ?? –– ?? he environmental density of far-infrared bright galaxies relation between environmental density and SFR attributing this tothe increasing presence of red late-type morphologies. As our anal-ysis has focused on the direct comparison of star formation prop-erties with the individual environmental densities of each object,we have shown that there is a clear difference between the star-forming and passive population in our colour-matched samples inagreement with earlier work by G´omez et al. (2003) and Welikalaet al. (2008).Furthermore, we have carried out the same analysis on SAMswhere we obtain a similar result, i.e. the environmental density dis-tributions from the total simulated Optical-HG and FIR-HG pop-ulations were found to be significantly different at the 4 σ level.Qualitative agreement is also found when we bin in terms of bothredshift and SFR. We have compared the environmental and star formation propertiesof two populations of galaxies out to z ∼ . . For this analysis wehave used optical spectroscopy and photometry from the GAMA9hr survey (DR1 data) and SDSS, with far-infrared observationsfrom the H-ATLAS SDP. We use Voronoi Tessellations to analysethe environmental densities of these galaxies on individual scalesnormalized to account for differences in the population density anduniformity across the redshift range due to the flux limit of the sur-vey and the increasing volume sampled with increasing redshift.The environmental density of the Optical and far-IR cata-logues were then compared by initially matching the cataloguesin multi-dimensional colour, magnitude and redshift space ( g − r , r − i , m r , z ) selecting a matched population of the Optical sourcesnumbering three times that of the far-IR distribution, in order toobtain a robust comparison over < z ≤ . . Our key results are:(i) Objects with far-IR detected emission, and levels of star for-mation > (cid:12) yr − , reside in less dense environments than galax-ies not detected at far-infrared wavelengths.(ii) The environmental density difference between the two far-IR and non-far-IR luminous galaxies also increases with redshift,with a 2.2 σ difference in the lower bin ( < z ≤ . ) and a3.3 σ difference in the higher bin ( . < z ≤ . ), with thefar-infrared detected galaxies again residing in less dense environ-ments. In relation to this, we find an increasing separation betweenthe density distributions with increasing SFR from 2.6 σ , 2.7 σ and3.3 σ respectively, although we note that we cannot distinguish red-shift effects from luminosity effects in our flux-density limited sam-ple.(iii) We find substantial differences between redshift distribu-tions of both our observed and SAM far-infrared samples. This pro-vides interesting indications on how recipes for star formation needto be modified within SAMs to improve their ability to model theobserved universe.(iv) We also note that VT are a reliable and accurate method ofcalculating the environmental densities for individual galaxies. In-deed, the use of VT for this purpose may surpass the NN technique,as their improved resolution is able to measure more detailed den-sity structure. The
Herschel -ATLAS is a project with
Herschel
REFERENCES
Adelberger, K. L. & Steidel, C. C. 2000, ApJ, 544, 218Baldry, I. K., et al. 2010, MNRAS, 404, 86Balogh, M., et al. 2004, MNRAS, 348, 1355Balogh, M. L., Morris, S. L., Yee, H. K. C., Carlberg, R. G., &Ellingson, E. 1997, ApJL, 488, L75+Balogh, M. L., Schade, D., Morris, S. L., Yee, H. K. C., Carlberg,R. G., & Ellingson, E. 1998, ApJL, 504, L75+Barnes, J. E. & Hernquist, L. 1992, ARA&A, 30, 705Bendo, G. J., et al. 2012, MNRAS, 419, 1833Bendo, G. J., et al. 2010, A&A, 518, L65Blain, A. W., Barnard, V. E., & Chapman, S. C. 2003, MNRAS,338, 733Boselli, A. & Gavazzi, G. 2006, PASP, 118, 517Bregman, J. N., Snider, B. A., Grego, L., & Cox, C. V. 1998, ApJ,499, 670Buat, V., et al. 2010, MNRAS, 409, L1Calzetti, D. & Heckman, T. M. 1999, ApJ, 519, 27Cooper, M. C., Newman, J. A., Madgwick, D. S., Gerke, B. F.,Yan, R., & Davis, M. 2005, ApJ, 634, 833Coppin, K. E. K., et al. 2011, MNRAS, 416, 680Cortese, L., et al. 2010a, A&A, 518, L63Cortese, L., Boselli, A., Franzetti, P., Decarli, R., Gavazzi, G.,Boissier, S., & Buat, V. 2008, MNRAS, 386, 1157Cortese, L., et al. 2010b, A&A, 518, L49Croton, D. J., et al. 2006, MNRAS, 365, 11Cucciati, O., et al. 2010, A&A, 524, A2da Cunha, E., Charlot, S., & Elbaz, D. 2008, MNRAS, 388, 1595Dariush, A., et al. 2011, MNRAS, 418, 64Davies, J. I., et al. 2010, A&A, 518, L48Davies, J. I., et al. 2012, MNRAS, 419, 3505Deng, X.-F., Chen, Y.-Q., & Jiang, P. 2011, MNRAS, 417, 453Diehl, S. & Statler, T. S. 2006, MNRAS, 368, 497Dom´ınguez, M., Muriel, H., & Lambas, D. G. 2001, AJ, 121, 1266Dressler, A. 1980, ApJ, 236, 351Dressler, A., et al. 1997, ApJ, 490, 577Driver, S. P., Allen, P. D., Liske, J., & Graham, A. W. 2007, ApJL,657, L85Driver, S. P., et al. 2011, MNRAS, 413, 971Dunne, L., Eales, S., Ivison, R., Morgan, H., & Edmunds, M.2003, Nature, 424, 285Dunne, L., et al. 2011, MNRAS, 417, 1510Dunne, L., et al. 2009, MNRAS, 394, 1307Dye, S., et al. 2010, A&A, 518, L10Eales, S., et al. 2010, PASP, 122, 499 c (cid:13) , ?? – ?? C. S. Burton et al.
Feruglio, C., et al. 2010, ApJ, 721, 607Findlay, J. R., Sutherland, W. J., Venemans, B. P., Reyl´e, C.,Robin, A. C., Bonfield, D. G., Bruce, V. A., & Jarvis, M. J. 2012,MNRAS, 419, 3354Finn, R. A., et al. 2010, ApJ, 720, 87Fixsen, D. J., Dwek, E., Mather, J. C., Bennett, C. L., & Shafer,R. A. 1998, ApJ, 508, 123Gay, C., Pichon, C., Le Borgne, D., Teyssier, R., Sousbie, T., &Devriendt, J. 2010, MNRAS, 404, 1801Geach, J. E., Ellis, R. S., Smail, I., Rawle, T. D., & Moran, S. M.2011a, MNRAS, 413, 177Geach, J. E., Murphy, D. N. A., & Bower, R. G. 2011b, MNRAS,413, 3059Gomez, H. L., et al. 2012, ApJ, 760, 96G´omez, P. L., et al. 2003, ApJ, 584, 210Goto, T. 2005, MNRAS, 360, 322Goto, T., Yamauchi, C., Fujita, Y., Okamura, S., Sekiguchi, M.,Smail, I., Bernardi, M., & Gomez, P. L. 2003, MNRAS, 346,601Griffin, M. J., et al. 2010, A&A, 518, L3+Groves, B., et al. 2012, MNRAS, 426, 892Guo, Q., et al. 2011, MNRAS, 413, 101Haynes, M. P., Giovanelli, R., & Chincarini, G. L. 1984, ARA&A,22, 445Henriques, B. M. B., White, S. D. M., Lemson, G., Thomas, P. A.,Guo, Q., Marleau, G.-D., & Overzier, R. A. 2012, MNRAS,2442Hern´andez-Fern´andez, J. D., Iglesias-P´aramo, J., & V´ılchez, J. M.2012, ApJS, 199, 22Hildebrand, R. H. 1983, QJRAS, 24, 267Hill, D. T., et al. 2011, MNRAS, 412, 765Hirashita, H., Buat, V., & Inoue, A. K. 2003, A&A, 410, 83Hwang, H. S., Elbaz, D., Lee, J. C., Jeong, W.-S., Park, C., Lee,M. G., & Lee, H. M. 2010, A&A, 522, A33Ibar, E., et al. 2010, MNRAS, 409, 38Icke, V. & van de Weygaert, R. 1987, A&A, 184, 16Jarvis, M. J., et al. 2010, MNRAS, 409, 92Kauffmann, G., White, S. D. M., Heckman, T. M., M´enard, B.,Brinchmann, J., Charlot, S., Tremonti, C., & Brinkmann, J. 2004,MNRAS, 353, 713Kennicutt, Jr., R. C. 1998, ARA&A, 36, 189Kennicutt, Jr., R. C., et al. 2009, ApJ, 703, 1672Kim, R., Strauss, M., Bahcall, N., Gunn, J. E., Lupton, R. H.,Vogeley, M. S., Schlegel, D., & the SDSS Collaboration. 2000,in Astronomical Society of the Pacific Conference Series, Vol.200, Clustering at High Redshift, ed. A. Mazure, O. Le F`evre, &V. Le Brun, 422–+Kitzbichler, M. G. & White, S. D. M. 2007, MNRAS, 376, 2Lawrence, A., et al. 2007, MNRAS, 379, 1599Le Floc’h, E., et al. 2005, ApJ, 632, 169Lee, J. H., Lee, M. G., Park, C., & Choi, Y.-Y. 2010, MNRAS,403, 1930Lewis, I., et al. 2002, MNRAS, 334, 673Mac Low, M. & Ferrara, A. 1999, ApJ, 513, 142Martini, P., Mulchaey, J. S., & Kelson, D. D. 2007, ApJ, 664, 761Miller, C. J., Nichol, R. C., G´omez, P. L., Hopkins, A. M., &Bernardi, M. 2003, ApJ, 597, 142Muldrew, S. I., et al. 2012, MNRAS, 419, 2670Nardini, E., Risaliti, G., Salvati, M., Sani, E., Imanishi, M., Mar-coni, A., & Maiolino, R. 2008, MNRAS, 385, L130Neugebauer, G., et al. 1984, ApJL, 278, L1Nordon, R., et al. 2010, A&A, 518, L24 O’Mill, A. L., Padilla, N., & Garc´ıa Lambas, D. 2008, MNRAS,389, 1763Pascale, E., et al. 2011, MNRAS, 415, 911Patel, H., Clements, D. L., Vaccari, M., Mortlock, D. J., Rowan-Robinson, M., P´erez-Fournon, I., & Afonso-Luis, A. 2013, MN-RAS, 428, 291Pilbratt, G. L., et al. 2010, A&A, 518, L1Poggianti, B. M., et al. 2006, ApJ, 642, 188Poglitsch, A., et al. 2010, A&A, 518, L2+Postman, M. & Geller, M. J. 1984, ApJ, 281, 95Puget, J.-L., Abergel, A., Bernard, J.-P., Boulanger, F., Burton,W. B., Desert, F.-X., & Hartmann, D. 1996, A&A, 308, L5Ramella, M., Boschin, W., Fadda, D., & Nonino, M. 2001, A&A,368, 776Rieke, G. H., et al. 2004, ApJS, 154, 25Rigby, E. E., et al. 2011, MNRAS, 415, 2336Rowlands, K., et al. 2012, MNRAS, 419, 2545Salpeter, E. E. 1955, ApJ, 121, 161Schmitt, H. R., Calzetti, D., Armus, L., Giavalisco, M., Heckman,T. M., Kennicutt, Jr., R. C., Leitherer, C., & Meurer, G. R. 2006,ApJ, 643, 173Scoville, N., et al. 2007, ApJS, 172, 1Silverman, J. D., et al. 2009, ApJ, 695, 171Smith, D. J. B., et al. 2012a, MNRAS, 427, 703Smith, D. J. B., et al. 2011, MNRAS, 416, 857Smith, M. W. L., et al. 2012b, ApJ, 756, 40Soares-Santos, M., et al. 2011, ApJ, 727, 45Sugerman, B. E. K., et al. 2006, Science, 313, 196Symeonidis, M., Page, M. J., & Seymour, N. 2011, MNRAS, 411,983Symeonidis, M., et al. 2013, MNRASTaylor, E. N., et al. 2011, MNRAS, 418, 1587Tekola, A. G., V¨ais¨anen, P., & Berlind, A. 2012, MNRAS, 419,1176van Breukelen, C. & Clewley, L. 2009, MNRAS, 395, 1845van Breukelen, C., Clewley, L., & Bonfield, D. 2006a, ArXiv As-trophysics e-printsvan Breukelen, C., et al. 2006b, MNRAS, 373, L26van de Weygaert, R. & Icke, V. 1989, A&A, 213, 1Welikala, N., Connolly, A. J., Hopkins, A. M., Scranton, R., &Conti, A. 2008, ApJ, 677, 970Wijesinghe, D. B., et al. 2012, MNRAS, 3150Willmer, C. N. A., Rieke, G. H., Le Floc’h, E., Hinz, J. L., En-gelbracht, C. W., Marcillac, D., & Gordon, K. D. 2009, AJ, 138,146York, D. G., et al. 2000, AJ, 120, 1579 c (cid:13) , ?? ––