A&A 598, A120 (2017) DOI: 10.1051/0004-6361/201628953 Astronomy & cESO 2017 Astrophysics
The VIMOS Public Extragalactic Redshift Survey (VIPERS)?,??
The coevolution of galaxy morphology and colour to z ∼ 1 J. Krywult1,L.A.M.Tasca2,A. Pollo3, 4,D.Vergani5,M. Bolzonella6,I.Davidzon2, 6, A. Iovino7, A. Gargiulo8, C.P. Haines7,M. Scodeggio8,L. Guzzo7, 9,G. Zamorani6,B. Garilli8,B.R. Granett7,S.delaTorre2,U. Abbas10, C. Adami2,D. Bottini8,A. Cappi6,O. Cucciati6,P. Franzetti8,A. Fritz8,V.Le Brun2,O.Le Fèvre2,D. Maccagni8, K. Ma ek16,F. Marulli17, 18, 6, M. Polletta8, 23,R.Tojeiro21,A. Zanichelli22,S. Arnouts2,J. Bel11,E. Branchini12, 13, 14, J. Coupon24, G. De Lucia15, O. Ilbert2, H. J. McCracken19, L. Moscardini17, 18, 6, andT.T.Takeuchi20 (Aﬃliations can be found after the references) Received 17 May 2016 / Accepted 12 October 2016 ABSTRACT Context. The studyof the separationofgalaxy types intodiﬀerent classes that share the same characteristics, and of the evolution of the specifc parameters usedin the classifcation are fundamental for understandinggalaxyevolution. Aims. Weexplore theevolutionof the statistical distributionofgalaxy morphological properties and colours combining high-quality imaging data from the CFHT LegacySurveywith the large number of redshifts and extended photometry from the VIPERS survey. Methods. Galaxy structural parameters were combined with absolute magnitudes, colours and redshifts in order to trace evolution in a multiparameter space. Using a new method we analysed the combination of colours and structural parameters of early-and late-type galaxies in luminosity-redshift space. Results. We fnd that both the rest-frame colour distributions in the(U − B)vs.(B − V)plane and the Sérsic index distributions are well fttedbya sumoftwo Gaussians,witha remarkable consistencyof red-spheroidaland blue-diskygalaxy populations,overtheexplored redshift(0.5< z < 1) and luminosity(−1.5< B − B∗ < 1.0) ranges. The combination of the rest-frame colour and Sérsic index as a function of redshift and luminosity allowsusto presentthe structureofbothgalaxytypesandtheirevolution.Wefndthat early-typegalaxiesdisplayonlyaslowchangeintheir concentrations after z = 1. Their high concentrations were already established at z ∼ 1and depend much more strongly on their luminosity than redshift.In contrast, late-typegalaxies clearly become more concentrated with cosmic time with only littleevolutionin colour, which remains dependent mainly on their luminosity. Conclusions. The combinationof rest-frame coloursand Sérsicindexasa functionof redshiftand luminosity leadstoa precise statistical descriptionofthe structureofgalaxiesand theirevolution. Additionally,the proposed methodprovidesarobustwaytosplitgalaxiesintoearlyandlate types. Key words. cosmology: observations –galaxies: general –galaxies: structure–galaxies:evolution–galaxies: statistics 1. Introduction The humaneyeand brainhaveevolvedtobe ableto rapidlypick up underlying similarities and subtle diﬀerences amongst a set of objects (even unconsciously) allowing them to be eﬃciently and reliably identifedand ordered into categories.Asforgalaxy studies it is common practice to divide sources into populations according to specifcgalaxy properties. Hubble(1926)provides the frst statistical classifcation of extragalactic nebulae based ? Based on observations collected at the European Southern Observatory, Cerro Paranal, Chile, using the Very Large Telescope under programs 182.A-0886 and partly 070.A-9007. Also based on observations obtained with MegaPrime/MegaCam, a joint project of CFHT and CEA/DAPNIA, at the Canada-France-HawaiiTelescope (CFHT), which is operated by the National Research Council (NRC) of Canada, the Institut National des Sciences de l’Univers of the Centre National de la Recherche Scientifque (CNRS) of France, and the University of Hawaii. This work is based in part on data products produced at TERAPIX and the Canadian Astronomy Data Centre as part of the Canada-France-Hawaii Telescope Legacy Survey, a collaborative project of NRC and CNRS. The VIPERS web site is http://vipers.inaf.it/
?? Atable of the ftted parameters is only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr
(130.79.128.5)or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/598/A120
on their shapes. Since then the Hubble tuning fork has been used to divide galaxies into ellipticals, spirals and irregulars, withvariousdegreesof complexityand detail.The original classifcation scheme underwent various modifcations and found one of its most used expositions in Sandage(1961). Recently, a more physical and complete picture of the morphology of nearbygalaxies, based ongalaxy kinematics,was proposedby Cappellari et al. (2011). Still, the well-defnedgalaxy segrega
tion observed in the local Universe starts to lose its discrimina-tory power when moving to higher redshifts(z > 1.5) where galaxies have more irregular and diverse shapes, and new classifcation schemesneedtobe introduced(e.g. vanderWeletal. 2007;Kartaltepe et al. 2015). Due to the impressive amount of photometric data produced by large galaxy surveys (Euclid mission, Large Synoptic Survey Telescope (LSST), among others), it is nec-essary to move from human classifers to automatic tech-niques such as visual-like, machine learning classifcations (Huertas-Companyet al. 2015). Still, citizen-based science projects such as GalaxyZoo(Lintott et al. 2008) allow us to obtain, in the local Universe, the morphologies of millions of galaxies by direct visual inspection. Simplifcations associated with proxies for morphology, such as colour, concentration or Article publishedby EDP Sciences A120, page1of 21 structural parameters, are thusavoided. Hubble SpaceTelescope (HST) based GalaxyZoo projects have proven to be success-ful in classifyinggalaxies up to z ∼ 1.5(Simmons et al. 2014; Melvin et al. 2014;Cheung et al. 2014;Galloway et al. 2015). The standard approach is to identify a series of parameters which correlate with the visual morphology of a galaxy and to defne the parameter-space which best identifes a specifc morphological type (e.g. Abraham et al. 1996; Conselice et al. 2000;Lotz et al. 2008). Amongthe non-parametric diagnostics ofgalaxy structure, the more traditionally used aregalaxy asym-metry, concentration, Gini coeﬃcient (CAS, Conselice 2003), the 2nd-order moment of the brightest 20% of galaxy pixels, clumpiness (or smoothness) and ellipticity(Abraham et al. 2003;Lotzetal.2004).Awidelyused parametric descriptionof thegalactic light profleis based on theexponentof the Sérsic lawfttothegalaxysurface brightness distribution(Sérsic1963). The Sérsic index n, that quantifes how centrally peaked the galaxy light distribution is, has been commonly used as a se-lection criterion to divide early and late-typegalaxies in many investigations (e.g. Driver et al. 2006 applied n = 2to thegalaxies from Millennium Galaxy Catalogue; Cassata et al. 2011 used n = 2 on the high-z HSTgalaxies). Ravindranath et al. (2004) analysed a sample of nearby galaxies with visual morphologies determinedby Freietal. (1996)and artifcially redshifted to z = 0.5and1.0, and found that the single Sérsic profle index n = 2eﬃciently separates early-and late-typegalaxies,evenin the presence of dust or star-forming regions. Alongside the rather qualitative classifcation criteria at the basis of the Hubble-Sandage system, a more quantitative interpretation related to how physical parameters (e.g. stel-lar mass, specifc angular momentum, ages, cold gas fraction, etc.) vary along the Hubble sequence, can be developed (see Roberts&Haynes 1994, for an extensive review). Hubble’s early-typegalaxies (ellipticals and lenticulars) are usually red-der in optical colours, more luminous and massive, have older stellar populations and have smaller reservoirs ofgas and dust. Conversely,late-typegalaxies (spirals and irregulargalaxies) are generally less massive, show younger stellar populations and havebluer colours (e.g. deVaucouleurs 1961;Roberts&Haynes 1994;Kennicutt 1998;Bell et al. 2004;Bundy et al. 2005, 2006; Haynes&Giovanelli 1984; Noordermeer et al. 2005). Many studies suggest that these correlations hold, at least up to z
∼
1 (Fritz et al. 2009; Fritz&Ziegler 2009; Pozzetti et al. 2010; Bolzonella et al. 2010;Kovaˇc et al. 2010;Tasca et al. 2009). In particular,the morphology-colour correlation is traced back to at least (up to) z
∼
2(e.g.Bassett et al. 2013). Similarly to what is seen in the distribution of morphological types,galaxy rest-frame colours tendtosegregate intoa bimodal distribution. This is best evidenced by the colour–magnitude (or colour–stellar mass) diagram, in whichtwo clear loci are preferentially occupiedbythe blue and red populations, known respectively as the blue cloud (or sometimes blue sequence) and the red sequence. Galaxy colours refect the ages and star formation his-tories of the meangalaxy stellar population. Understanding the origin of the observed colour bimodality would therefore help to shedlightonthemaingalaxyevolution mechanismsatplayand their relative timescales. It is now commonly accepted that the total stellar mass within the blue cloud shows very little growth between z = 1andz = 0.5, while the red sequence has grownby at leastafactor ∼2(e.g.Cimatti et al. 2006;Arnouts et al. 2007). The most popular scenario invoked to explain the growth of red galaxies is a migration of a signifcant fraction of star-forming systems from the blue cloud to the red sequence, due to diﬀerent quenching processes and a reflling of the blue cloud due to star-forminggalaxies growing steadilyin stellar mass. Observational studies of high-mass (central) galaxies prefer a self-regulated mass quenching, while quenching in low-mass (satellite)galaxies has likely been mainly due to environmental and/or merging infuences (e.g. Peng et al. 2010, 2012; Wetzel et al. 2014). When a narrow luminosity bin is considered, the resulting distribution of colours can be described relatively well as a sum of two Gauss functions, although it has also been shown that an additional, intermediate population, inhabiting the so-called green valley between the two main sequences, may also be required(Wyder et al. 2007; Mendez et al. 2011; Schawinski et al. 2009; Coppa et al. 2011; Loh et al. 2010; Lackner&Gunn 2012;Brammer et al. 2009). These objects are commonly thought to represent a transition phase from the blue cloud to the red sequence, showing the star formation quenching mechanismatwork(Pozzettietal. 2010). Arnoutsetal. (2013) found that actively star–forming and quiescent galaxies segregate themselves particularly well in the NUV − r versus r − K plane. More recently Moutard et al. (2016), using the multi
wavelength information collected in the VIPERS region, re-ported a locus in the NUVrK diagram inhabited by massive galaxies withavarietyof morphologies probably transiting from the star-forming to the quiescent populations.Asimilar behavior is observed out to z = 1.3(Coppa et al. 2011)and the green valleypopulation is still present when using diﬀerent rest-frame colours, such as U − B (Nandra et al. 2007; Yan et al. 2011), U − V (Brammer et al. 2009;Moresco et al. 2010)andNUV − r (Wyder et al. 2007;Fritz et al. 2014). Understanding the physical processes responsible for the observed bimodality in morphology and colour and its de-pendence on the galaxy environment is a major challenge in the feld of galaxy evolution (e.g. Tasca et al. 2009). To shed some light on how the progenitors of galaxies in the local Universe have acquired their shapes and physical properties, large surveys, as well as the classifcation ofgalaxies at diﬀerent epochs, are needed. The VIMOS Public Extragalactic Red-shift Survey (VIPERS; Guzzo&TheVipersTeam 2013) ful-flls these requirements over the redshift range 0.5 < z < 1.2. VIPERS is a spectroscopic redshift surveywhich provides, on one hand, a unique combination of volume and density and, on the other hand, excellent 5-band photometric coverage with the Canada-France-HawaiiTelescopeLegacySurveyWide (CFHTLS-Wide), suitable for obtaining galaxy morphologies, colours and rest-frame spectral energy distributions (SEDs) from which physical properties such as stellar mass can be derived (e.g. Fritz et al. 2014). The purpose of this work is to develop a robust method for classifyinggalaxies from intermediate redshift rangein orderto analyse their colour and morphological observational parameters from ground-based observations. This paperis organized as follows.In Sect. 2we summarise the data used. In Sect. 3, we describe the method of bimodal
ity analysis using galaxy colour and redshift and discuss the evolutionary trends in colour bimodality. In Sect. 4 we present the methodology of measurement of Sérsic parameters of the VIPERS galaxies from the CFHTLS images, discuss the bi-modality of the Sérsic index distribution and present evolutionaryeﬀectsonthe Sérsic index.In Sect. 5we compare our results with the published relations involving the measurement of the Sérsic index.In Sect. 6we introducea new method for classifyinggalaxies, fullyexploiting the2D distributionin the colourshape plane as a function of rest-frame magnitude and redshift. A120, page2of 21 J. Krywult et al.: VIPERS: evolution of shape and colour bimodalities In Sect. 7we discuss the implications of this new classifcation scheme on theevolutionof early-and late-typegalaxies and we summarise our results in Sect. 8. In Appendices A and B we show the tests of reliability of the Sérsic function profle-ftting procedure. For clarity, for the remainder of this article, when describing the two maingalaxy populations, we will call them red and blue when theyhave been selected simply according to their colours, spheroid-likeand disc-likewhen selected solely basedupon their Sérsic index, and early-type and late-type when the populations are selected for both colour and morphology. In our analysis, all magnitudes are given in the AB photometric system. Throughout the cosmological model with a matter density parameter Ωm = 0.3, we assume cosmologi-cal constant density parameter ΩΛ = 0.7 and Hubble constant H0 = 70 kms−1Mpc−1. 2. Data 2.1. The VIPERS project VIPERS is an ESO Large Programme aimed at measuring red-shifts for ∼105 galaxies at 0.5 < z . 1.2, to accurately and robustly measure clustering, the growth of structure (through redshift-space distortions), and galaxy properties at an epoch when the Universewas approximately half its current age. Spec-troscopic targets were frst selected to a limit of i < 22.5 in two felds (namely W1 and W4) of the Canada-France-Hawaii Telescope Legacy Survey Wide (CFHTLS T0005 re-lease, Mellier et al. 2008), further applying a simple and robust gri colour pre-selectiontoeﬀectively removegalaxiesat z < 0.5. Spectra have been observed with the VIMOS multi-object spec-trograph(Le Fèvre et al. 2003)at moderate resolution(R = 210) usingtheLRRed grism.Thisprovidesawavelengthcoverageof 5500−9500Åanda typical radialvelocity errorof 141kms−1. Coupled to the “short-slits” observing strategy described in Scodeggio et al. (2009), the colour pre-selection allows us to double the galaxy sampling rate (which is ∼40% in the red-shift range of interest) with respect to a pure magnitude-limited sample. At the same time, the total area (approximately24deg2)and the depthof VIPERS resultina largevolume,5 × 107h−3Mpc3, analogous to that of the local 2dFGRS. Such a combination of sampling and depth is unique among current redshift surveys at z > 0.5. Further details on the design of VIPERS, along with its data products, can be found in Guzzo et al. (2014). In the present paper, we investigate the morphological propertiesofgalaxiesin the VIPERS Public Data Release1(PDR-1, see Garilli et al. 2014), and their interplay with rest-frame colours. This catalogue1 includes55358galaxies with spectroscopic redshifts(zspec)over approximately10deg2. Besides the spectroscopic redshift, each galaxy in the PDR-1 catalogue is provided with u, g, r, i, z apparent magnitudes, as estimated by the Terapix team using SExtractor (Bertin&Arnouts 1996). These (MAG_AUTO) magnitudes are part of the CFHTLS-T0005 data release and were derived in double image mode in order to match the same aperture in all bands. The PDR-1 catalogue is fully available to the public through the of-fcial website http://vipers.inaf.it
2.2. Photometric data From the PDR-1 catalogue we selected onlygalaxies with red-shifts measured with the highest reliability, that is, with quality fag zfag = [2, 3, 4, 9] according to the classifcation presented in Guzzo et al. (2014). The same fag scheme was used in previ
ous spectroscopic surveys as VVDS(Le Fèvre et al. 2013)and zCOSMOS(Lilly et al. 2007). Moreover, due to small numbers of high-redshiftgalaxies we restrict our analysis to zspec ≤ 0.95, reducingthe samplesto20208and18299galaxiesintheW1 and W4 felds, respectively. All spectrophotometric rest-frame properties of the VIPERSgalaxies were derived using the SED ftting program Hyperzmass (Bolzonella et al. 2010). Absolute magnitudes were derived using the apparent magnitude that most closely resembled the observed photometric passband, shifted to the redshift of the galaxy under consideration, before applying colour and k-corrections derived from the best-ft SED (see details in Fritz et al. 2014). To investigate the dependence of morphology and colour of galaxies on their redshift, we corrected their absolute magnitudes to account for their intrinsic evolution, as derived from the characteristic luminosity parame-ter(L∗ or M∗ in absolute magnitudes) of the luminosity function (LF) in the Schechter(1976)’s equation.For this purpose, we used the global B-band LF in the redshift range from z = 0.5to 1.3 presented inTable3 of Fritz et al. (2014). These data have been used to compute the linear approximation of evolution with redshift of the characteristic magnitude Bev and to defne the ΔBev luminosityby the equation: ΔBev = MB − Bev(z)= MB + 19.90 + 1.59z. (1) Considering theevolutionof the wholegalaxy population, with-out division into the blue and red populations, we found a slightly steeper Bev evolution than reported in other studies (e.g. Faber et al. 2007). They found that in the redshift range 0 < z < 1 the characteristic magnitude Bev evolves in z with a slope −1.23 ± 0.29; our study, in a diﬀerent redshift range, gives −1.59 ± 0.20, nonetheless consistent with other authors’ results within1σ uncertainties (e.g. Faber et al. 2007). Despite thefact that the linear model adopted in Eq.(1)accurately reproduces the evolution of the global value of Bev in the redshift range of VIPERS, the diﬀerences of diﬀerentgalaxy types in LF param-eters and evolution could, in principle, aﬀect our results.For in-stance, Zucca et al. (2006)measured the evolution of the LFs of four spectrophotometric classes of galaxies up to z = 1.5 in VVDS. They found (see their Fig. 3 and Table 3) that the evolution of M∗ with redshift is linear, consistent for all types B with dM∗(z)/dz = −1.49. In the case of the VIPERS galaxies, Fritzetal. (2014), considering redgalaxies only, found a relation in B-band rest-frame very similar to our Eq.(1), with dM∗(z)/dz = −1.58. Diﬀerences amonggalaxy classes are in-stead larger in the value of the oﬀset, corresponding to the value of the characteristic magnitude of the LF at redshift z = 0. From the linear interpolation of data from Zucca et al. (2006)we ob-tain values equal to –20.25, –20.11, –19.75 and –19.56 mag for the irregular, late spiral, early spiral andE/S0galaxies, respectively. Accordingtoour tests,andgiventhefactthattheevolution of MB ∗ for diﬀerent types is negligible, at least in the con-sidered redshift range, and that the values of the intercept diﬀers by a value of the order of our binning in ΔBev, this additional uncertainty does not signifcantly aﬀect our results. In Fig. 1we present the distribution of rest-frame ΔBev asa functionof redshiftforthe VIPERSgalaxies.The left-sideverti-cal axis shows the ΔBev value, whereas the right-side axis gives A120, page3of 21 Fig.
1.
Distribution of ΔBev,as defnedinEq.(1),asa functionof red-shift z forgalaxies in the VIPERS sample. The red lines enclose the selected sub-samplesofgalaxies. The right-sidevertical axis shows the values of the absolute magnitude MB for a fxed redshift z = 0.7. the absolute magnitude MB at the mean VIPERS redshift z = 0.7. As expected, due to selection eﬀects, we progressively lose the faint population to higher redshifts, leaving only the brighter ob-jects.Inthe presentstudywe considered12volume-limitedsubsamples representedby the red boxesin Fig. 1. Each subsample is statistically complete, spans ΔBev = 0.5magnitudes and has a redshift range Δz = 0.15. 2.3. CFHTLS imaging The morphological analysis was based on the study of the 2D surface brightness profle of the VIPERS galaxies. To model the light profle of galaxies in the VIPERS PDR-1 we used CCD images in the i-band from eighteen W1 and eleven W4 CFHTLS felds covering 28deg2 of the VIPERS project. While the VIPERS PDR-1 catalogueis basedontheTerapix T0005 re-lease,forthe analysisofthe structural parameterswe usea more recent version of the CFHTLS data (i.e. T0006, Goranova et al. 2009). A full description of the CFHTLS data processing including calibration, stacking and mosaicing is provided in Mellier et al. (2008)andGoranova et al. (2009). The public data fromTerapix T0006 are organised in1◦× 1◦ felds and have a pixel scaleof0.18600. The mean seeing, as parameterised by the Full Width at Half Maximum (FWHM) of stellar sources, de-pendsonthe flterofthe CFHTLSimagesandisequalto0.8500 , 0.7800,0.7200,0.6400,0.6800 in the u, g, r, i/y (the flter i broke in 2006 and it was replaced by a similar, but not identical flter, called y)andz-bands, respectively(Goranova et al. 2009). To secure the quality of the derived morphological param-eters, we used CCD tiles in the i photometric band where the mean FWHM is smallest. Objects were extracted by independently running SExtractor on the CFHTLS tiles in the T0006 release. This means that the centroid of photometric sources can be slightly diﬀerent from the coordinates of the corresponding VIPERS spectroscopic objects.We associated spectroscopic and photometric sources on the basis of their relative (projected) dis-tance, assuming a maximum matching radius equal to 100. For 98.6% of the objects, the distance between the VIPERSgalaxy (i.e. its position according to T0005) and the one in the T0006 release is less than0.300, and is larger than0.500 for only0.3% Fig.
2.
Density of the VIPERSgalaxies in the rest-frame(U − B)ver-sus(B − V)colour–colour diagram. The contour lines show thegalaxy density distribution in fve equally spaced levels from 10% to 99% of the maximumvalue. The histogram shows thegalaxy number density distribution projected along the line A − A connecting the two maxima of this distribution. The colours show the median sSFR1/yr values of galaxies derived from SED ftting in seven equally spaced logarithmic bins. of objects. Objects with distances larger than100 were excluded from the present analysis. 3. Rest-frame colours 3.1. Colour-based classifcation of galaxies To probe the colour distributionof VIPERSgalaxies we use the rest-frame(U − B)versus(B − V)colour-colour plot, based on the absolute magnitudes derived in Fritz et al. (2014). The isodensity contour lines presented in Fig. 2 show an evident bimodality in the rest-frame colours, with two wellseparated peaks.We defne the combined colour UBV by pro-jecting thegalaxy rest-frame colours along the A − A dashed line that connectsthetwo densitypeaksofFig. 2.Inthiswaythesep
aration of the red and blue populations is even more prominent than using the one-dimensional analysis, that is, based only on (U − B)or(B − V)rest-frame colours. The dashed line that de-fnes the combined UBV rest-frame colour is described by the following equation: UBV = (B − V)× cos(θ)− (U − B)× sin(θ), (2) where U, B and V are absolute rest-frame magnitudes in the corresponding pass-bands. The angle θ = 58.08◦ is the slope of the A − A line crossing two maxima of the rest-frame colour density distribution,as showninFig. 2.The UBV colour thus allows for a better separation of two maingalaxy populations. The UBV rest-frame colour separation of the two peaks along the UBV line is equal to 0.71, compared to 0.61 and 0.37 when it is pro-jected on the(U − B)and(B − V)axes, respectively. Figure 2 is colour coded by the median specifc Star For-mation Rate (sSFR is defned as the star formation rate per unit A120, page4of 21 J. Krywult et al.: VIPERS: evolution of shape and colour bimodalities stellar massofagalaxy)ofgalaxies insideagiven small range of(U − V)and(B − V)colours. The sSFRs are derived via SED ftting.Values of constant sSFR are almost perpendicular to the line connecting the two colour peaks(A − A line), withvaluesof sSFR steadily decreasing with UBV rest-frame colour along the line A − A. The correlation between the UBV colours and sSFR is therefore clearly evident, with blue colours corresponding to highervaluesof sSFRandredgalaxies beingmostly quiescent. It is also noticeable how this correlation is stronger than the one with(U − B)or(B − V)colours used independently. The lo-cal minimum of the UBV probability distribution corresponds to log(sSFR)≈ 10−10−10−9.5yr−1, which is in a broad agreement withthe characteristicvaluefor greenvalleygalaxies selectedin the NUVrK diagram(Davidzonetal. 2016). Therefore,evenif in the following analysis we use the colour UBV, we note that this parameter can be considered a good proxy of sSFR. 3.2. Galaxy colour bimodality To investigate the dependence of theUBV rest-frame bimodality on galaxy luminosity and redshift we have computed the distribution of the combined rest-frame colour UBV defned in Eq.(2) in each of the subsamples shown in Fig. 1, that is, fve equally-sized bins in ΔBev of width 0.5 mag and three bins in redshift, each of width 0.15 in z (0.50 < z ≤ 0.65, 0.65 < z ≤ 0.80 and0.80 < z ≤ 0.95). The results are presentedin Fig. 3. The bimodalityisa persistent featureover the whole luminosity-redshift rangeexplored.TheshapeofthePDF changes, however. The red population (the red line) is dominant at bright luminosities, whereas the blue population (blue line) becomes increasingly signifcant in thefaintest magnitude bins. As already mentioned in Sect. 1, many studies have re-ported and described this colour bimodality in galaxies out to z ∼ 2(e.g.Strateva et al. 2001;Blanton et al. 2003;Baldry et al. 2004; Bell et al. 2004; Willmer et al. 2006; Faber et al. 2007; Blanton&Berlind 2007;Fritz et al. 2014). The optical colour distribution is, in general, well mod-elled by the sum of two Gauss functions(Strateva et al. 2001; Baldry et al. 2004; Ball et al. 2008). Figure 3 also shows that the UBV rest-frame colour distribution is well approximated by the sum of two Gaussians (the brown curves), in agreement with previous results (e.g. Baldry et al. 2004).Similar results are also found in Ball et al. (2008)and González et al. (2009), for example. The mean and the dispersion of each Gaussian component (the blue and red curves) depend on magnitude and redshift. The blue objects are characterised by a larger dispersion in colour than the red ones, which justifes the terms “blue cloud” and “red sequence”, generally used to characterise the two populations. The local minimum is thought to be populated by objects that are evolving from star-forming to quiescent galaxies. We did not fnd a signifcant excess of objects between the two main galaxy populations with respect to the sum of the two Gauss functions, meaning that there is no statistical evidence of a third population of objects. This is at opposition with the results of other analyses which claim to fnd an excess of ob-jectsintheregion betweenthetwopeaks(e.g. Wyderetal.2007; Mendez et al. 2011; Schawinski et al. 2009; Coppa et al. 2011; Loh et al. 2010; Lackner&Gunn 2012; Brammer et al. 2009). Thisexcessofgalaxiesis usually foundinthe distributionofseveral colour indices, such as U − B (Nandra et al. 2007;Yan et al. 2011), U − V (Brammer et al. 2009; Moresco et al. 2010)and NUV − r (Wyder et al. 2007; Fritz et al. 2014). In particular, Wyder et al. (2007)show that theNUV − r colour distribution is not strictly the sum of two Gaussians, and Coppa et al. (2011), using zCOSMOS data in the redshift range0.5 < z < 1.3, re-porteda thirdgalaxy population located between the blue and red populations. The lack of the thirdgalaxy population located between two Gaussians peaks is possibly related to the narrow luminosity and redshift bins used in this study. The excess of galaxies with respect to the sum of the two Gaussians appears when using a coarser grid redshift or luminosity. Moreover, the UBV rest-frame colour, being an excellent proxy to sSFR, is moreeﬃcient at separating diﬀerentgalaxy populations and less prone to contaminating objects that could populate the intermediate colours. While in the local Universe the colour–magnitude diagram is eﬀective at dividinggalaxies into diﬀerent populations (e.g. Strateva et al. 2001; Baldry et al. 2004; Wyder et al. 2007), to study distant galaxies, it becomes important to consider how the selection depends also on galaxy luminosity and redshift (Bell et al. 2004). Exploring the eﬀects of the luminosity and redshifts in the VIPERS sample, we reveal the systematic blue-ingofboththeblueandred populationsmovingtowardsfainter magnitudesatfxed redshift(blueandredverticallinesinFig. 3). Quantitatively, the blue cloud moves from UBV = 1.07 to 0.73 and the red sequence from UBV = 1.50 to1.37 at z = [0.50, 0.65] for values of ΔBev increasing from −1.5to1.0. Sim-ilar trends in the analysis of the u − r rest-frame colour have beenfoundinthelow redshiftUniverseby Balletal. (2008)and Mendez et al. (2011)using the SDSSgalaxy sample. Moreover, both populations in Fig. 3 evolve toward bluer colours when moving to higher redshifts. The positions of the Gaussian maxima of the red and blue populations can be described by the following formalism: UBVb = 1.06(±0.02) − 0.36(±0.03)z − 0.18(±0.01)ΔBev, (3) UBVr = 1.56(±0.02) − 0.26(±0.02)z − 0.06(±0.01)ΔBev, (4) where z is the redshift, ΔBev is the distance from the evolving characteristic luminosity as defned in Eq.(1), and UBVb and UBVr are the central positions of the blue and redgalaxy distributions, respectively. The quoted errors on the coeﬃcients were estimated through a bootstrap procedure using 1000 resamplings. 4. Sérsic index 4.1. Estimation of Sérsic parameters Toderivethesurface brightness parametersof VIPERSgalaxies, wehave performeda2Dftofthe observedgalaxy i-band light distribution with a PSF-convolved Sérsic model. We used the single component Sérsic(1963)proflegivenby the equation: ⎧⎡ ⎤⎫ ⎪ !1/n ⎪ ⎨ r ⎬ I(r)= Ieexp −bn ⎢ − 1 ⎥ , (5) ⎪ ⎣ ⎦⎪ ⎩⎭ re where re is the radius enclosing half of the total light of the galaxy, Ie is the mean surface brightness at re, and bn isa normalization factor, which is chosen in such a way that re corresponds to the half-light radius(Graham&Driver 2005). This parametrisation well describes the light distributions of elliptical, spiral and irregular galaxies (see e.g. Trujillo et al. 2001a). The detailed analytical properties of Eq.(5)are dis-cussedby Ciotti&Bertin (1999),Trujilloetal. (2001b), and Graham&Driver (2005)forexample. There are many codes in common usage that model the observedgalaxy shapes, such as GIM2D(Simardetal. 2002), A120, page5of 21 Fig.
3.
UBV
rest-frame colour distributions (black histograms) of VIPERSgalaxies in diﬀerent redshift (increasing from left to right)and luminosity(from top to bottom)bins. The blue and red curves represent the Gaussian components ftting the colour distribution of the twogalaxy populations, and the vertical dashed lines mark the maxima of the Gauss functions. The solid brown line shows the sum of the two Gaussians. The centralvalues and1σ widths of the Gaussians for the blue and redgalaxy populations are labeled in each panel, in the top left and right respectively. The numberofgalaxies consideredin each binis also shownin the bottom rightof each panel. BUDDA (de Souza et al. 2004), GASPHOT (Pignatelli et al. 2006), GALFIT(Peng et al. 2002)and GAMA-Sigma (Kelvin et al. 2012), for example. We used the code GALFIT(Peng et al. 2002)to perform the ft. The ftting procedure of GALFIT provides the value of the semi-major axis(ae), the axial ratio(b/a)of the profle, from √ which the circularised eﬀective radius(re = ae b/a), a standard parameter used in the studies of thegalaxy morphology is derived, the Sérsic index n, and the apparent magnitude of the modeledgalaxy. Many GALFIT wrappers to automatise galaxy ftting procedures are publicly available, such as GALAPAGOS (Häußler et al. 2011), PyMorph (Vikram et al. 2010) and GAMA-Sigma(Kelvinetal. 2012).We decided,however, to develop dedicated software combininggalaxy profle ftting by GALFIT and the PSF determination to have the parameters usedin thegalaxy profle estimation fully under control. Weused the CFHTLS-T0006 images of VIPERS targets, and divided each 1◦× 1◦ tile into postage stamps centred on each VIPERSgalaxy(see someexamplesinFig. 4).Todefnethesize of the postage stamps, we rely on the SExtractor parameters, which describe the ellipse associated toagiven i-band detection, namely RK (KRON_RADIUS), A, B (A_IMAGE, B_IMAGE) and θ (THETA_IMAGE). The centre of each postage stamp co-incides with the centroid of the SExtractor ellipse, while its sides(Δx and Δy)are four times larger than the projected total dimension of the ellipse on the x and y axis, that is, p Δx = 8RK(A cos θ)2 + (B sin θ)2 , p Δy = 8RK(A sin θ)2 + (B cos θ)2 . (6) These sizes ensure that each postage stamp has suﬃcient object-free pixels to estimate the background emission, which plays an important role in galaxy image ftting. Similar image sizes are usedby other authors (e.g. Häussler et al. 2007;Kelvin et al. 2012). There are two main approaches to estimating the level of background emission. In the frst procedure the background is characterised independently of the analysis of the target ob-ject, computed a priori, from an annular region surrounding the galaxy, for example(Barden et al. 2005; Häussler et al. 2007; Guo et al. 2009;Fritz et al. 2009; Fritz&Ziegler 2009). In the second method the background is a free parameter that can vary during the GALFIT ftting(Mosleh et al. 2013; Cassata et al. 2011). The Sérsic parameters presented in this paper were ob-tained using this second approach, that is, when the background is a free parameter. When the area of the postage stamp is A120, page6of 21 J. Krywult et al.: VIPERS: evolution of shape and colour bimodalities Fig.
4.
Four examples of the GALFIT image approximation proce-dure. Left column: postage stamps with observedgalaxies; middle col-umn:best-ft PSF-convolved Sérsic modelto eachgalaxy;right column: residual images. The small horizontal bars in the left column correspond to100 . approximately 10 times larger than the target galaxy and the sky-background variance is uniform, the two methodologies to estimate the background are equivalent(Cassata et al. 2011; Mosleh et al. 2013). These conditions are satisfed in our data. Postage stamps centred on eachgalaxy wereextracted from the CFHTLS tiles,and SExtractorwas runto detectalloftheobjects contained therein. In the ftting procedure, all of the other objects within the postage stamp are masked, unless the aperture ellipseofa secondary object, increasedbyafactor1.5, overlaps with that of the main target. In that case, the two (or more) photometric sources are ftted simultaneously to get the best values of the Sérsic profle parameters. The propervaluesofthe initial parametersplayan important role in the non-linear approximation. The values MAG_AUTO, FLUX_RADIUS, A_IMAGE, B_IMAGE, THETA_IMAGE ob-tained by SExtractor were used as a frst guess of re, position angle, ellipticity, and magnitude in GALFIT. In the absence of an estimate of the Sérsic index n in the SExtractor output, the initial value of this parameter in GALFIT ft was set to n = 1.7 for allgalaxies.Asimilar methodology has also been appliedin other studies (e.g. Häussler et al. 2007;Kelvin et al. 2012) Toconvolvethe Sérsic model, GALFIT requiresalocal point spread function (PSF) for each postage stamp. In our analysis we used the Moﬀat function (Moﬀat 1969), that combines simplicity, accuracyand allows us to easily reconstruct the anisotropy of the CFHT feld of view. In the frst step, the isolated stars were selected from the SExtractor output from each1◦× 1◦ CFHTLS tile and the Moﬀat(1969)functionwas ftted to each star. Then, the values of the estimated Moﬀat function parameters were approximated as a function of the star position in each CFHTLS tile.To ensure numerical stability we applied the 2D Chebyshev base: cos(n arccos(x)) instead of the algebraic polynomial one: xn,wheren = 0, 1, 2, etc. The procedure allows us to generate the PSF at the central position of each studiedgalaxy. A detailed description of the PSF construction is given in Ap-pendixB. Figure4shows someexamplesoftheft performedbyGAL-FIT for VIPERS galaxies. The original image of the galaxy, the best-ft PSF-convolved Sérsic modelof eachgalaxy, and the residual map are shown. More details about our morphological analysis and the reliability of GALFIT results are presented in Appendix A. Briefy, we added 4000 artifcial galaxies to the CFHTLS images with structural parameters generated from the Sérsic indices, magnitudes and eﬀective radii obtained by GAL-FITfora randomly-selected subsetofthe VIPERSgalaxiesused in this analysis. From these tests, we estimate uncertainties in our measurements in the magnitude range from 19 to 22.5 mag, of n of |Δn|/n = 0.16 at the 68% level, and 0.33 at the 95% level (i.e. for 95%ofgalaxiesin our sample), while theeﬀective radii are accurate to within 4.4% and 12% for 68% and 95% of our sample, respectively. Our tests also confrm that anybias in the n measurements is negligible. The angular size of the VIPERSgalaxies at z = [0.5, 1] is of the order of a few arcseconds and even in the best quality CFHTLS i-bandimagesusedinthisstudy,wherethe meanvalue of the FWHM is as small as ∼0.600, it is diﬃcult to detect the internal structure of these objects. Almost all of them exhibit a smooth light profle. When discussing the uncertainties of the ftted Sérsic profle parameters it should be noted that the χ2 criterion is not opti-mal to compare diﬀerent models of the light distribution of noisy galaxy images (Peng et al. 2002). Nevertheless, the χ2 criterion is commonly used in similar studies (e.g. Morishita et al. 2014). During the ftting procedure, GALFIT reported a converge problem for somegalaxies: for this reason 5707 (12%) of them were removed from the present work. Moreover, to analyse the galaxies with the best quality Sérsic function parameters, we se-lected only the objects with reduced χ2(χ2 )values smaller DoF than 1.2. Even though the χ2 is not the optimal criterion to com-pare diﬀerent models of the light distribution of noisy galaxy images(Peng et al. 2002), it has been used in similar studies (e.g. Morishita et al. 2014). In fact, from the simulations pre
sented in AppendixA we detected an increase of the fractional error on the Sérsic index n for increasing values of χ2 .We DoF preferredto removethe4%ofgalaxiesinthe high-endtailofthe χ2 DoF distributionin ordertohaveaveryhigh quality sample,the vast majority of fts producingχ2 valuesinthe range0.9−1.15. DoF We also discarded 261 objects with n < 0.2: low values of the Sérsic index imply a lower accuracyin the approximation of the Sérsic bn normalisationfactor(Ciotti&Bertin 1999)and intro-duce a small bias on the distribution of the disk-like profles, but are negligible when compared to the error bars of the ftted Sersic index. Moreover, small values of n < 0.2 are unphysi-cal. Similar low-n cuts are commonly used in other studies. Fi-nally we obtained our sample, constituting38620galaxies. The A120, page7of 21 Fig.
5.
Sérsic index distribution (black histograms) for diﬀerent redshift(from left to right)andΔBev luminosity bins(from top to bottom). The blue and red solid lines show the Gaussian fts to the disc-like and spheroid-like populations, respectively. The vertical dashed lines mark the central values of each Gaussian. The sum of the two Gaussian fts is shown as a solid brown line. The central values hni of the Gauss functions, their1σ widths, and the total numberofgalaxiesin each bin are shownin each panel. volume-limited sampleof objects presentedin Fig. 1consistsof 22 131galaxies. 4.2. Sérsic index bimodality Figure5shows the Sérsic index distribution of VIPERSgalaxies in the same luminosity and redshift bins as used in Sect. 3.2 for the UBV colour. Since the Sérsic index, n, appears as an ex-ponent in Eq.(5)defning the Sérsic profle(Driver et al. 2006, 2011), a logarithmic-spaced x-axis is used to optimise the analysis and visualisation of the wide range of n values. Similarly to the UBV histograms shownin Fig.3, the Sérsic index distribution is bimodal in manyof the redshift-luminosity bins.We thus ft each Sérsic index distribution asa sumoftwo Gauss functions in log n, with one Gaussian component con-sidered to represent the disk-like population (blue curves), and a second to represent the spheroid-likegalaxy population (red curves). The sum of the two Gaussian fts (solid brown curves) well describes the Sérsic indexdistribution at all redshifts and lu-minositiesexplored here.Even though,forgalaxiesfainter than the characteristic luminosity of the LF, that is, ΔBev > 0.0, the global distributionis notevidently bimodal,itis well reproduced by the sum of the two Gauss functions. The vertical blue and red dashed lines in Fig. 5 show the central values of the two Gaussian components for each red-shift and luminosity bin. Comparing the locations of these lines from panel to panel, we see that the mean Sérsic in-dices of both disk-like and spheroid-like galaxy populations vary systematically with luminosity and redshift. In particular, both disk-like and spheroid-like populations become increasingly concentrated with increasing luminosity and decreasing redshift. We fnd that the best two-dimensional linear ft of these po-sitions in the redshift z versus ΔBev luminosity plane is well de-scribed by the following equations: log nd = 0.04(±0.01) − 0.16(±0.01)z − 0.07(±0.01)ΔBev, (7) log ns = 0.47(±0.01) − 0.03(±0.01)z − 0.09(±0.01)ΔBev, (8) where ΔBev isthe luminositygivenbyEq.(1)andnd and ns are the mean Sérsic indicesofthe disc-likeand spheroid-likegalaxy populations. The errors of the best-ft coeﬃcients were estimated by a bootstrap procedure using 1000 resamplings. In principle, the Sérsic index can vary with rest-frame wavelength. The analysis presented in this paper is based on the op-tical i-band images, which correspond to rest-frame 510 nm at z ∼ 0.5 and to 348 nm at z ∼ 1.2. One way to account for this rest-frame change would be to use images obtained through A120, page8of 21 J. Krywult et al.: VIPERS: evolution of shape and colour bimodalities diﬀerent flters for galaxies at diﬀerent redshift ranges. However, the CFHTLS images made in flters u, g, r, z are of lower quality than i-band images which introduces additional noise, higher than a possible eﬀect of the expected correcting factor. Taking this into account, we try to examine a possible eﬀect of this morphological K-correction based on the measurements of localgalaxies. Kelvin et al.(2012)andVulcani et al.(2014)in
vestigated this property in the nearbygalaxies of GAMA sur-vey at z < 0.25. Using diﬀerentgalaxy selection criteria, both based on log(n)andu −r colour, theyfound that the Sérsic index value increases with wavelength, and that, for disk-likegalaxies, this relation is steeper than for spheroidal ones. One might then ask if the redshift evolution of the Sérsic index given by Eqs.(7)and(8)couldbeexplainedby the changein the rest-frame wavelength. The centre of the i-band flter is positioned at λz=0 = 765 nm and is shifted in the observed redshift range from λz=0.5 = 510 nm to λz=1.0 = 383 nm. According to Eqs. (10) and (11) from Kelvinetal. (2012),in sucha rangeofwave
length the value of the Sérsic index of the disk-like galaxies might change from nz=1.0 = 0.89 to nz=0.5 = 1.10, whereas for the spheroidalgalaxies it would change from nz=1.0 = 2.79 to nz=0.5 = 3.03. However, the evolution of the Sérsic index both for disk-like and spheroidal VIPERSgalaxies,givenby Eqs.(7) and(8),isfaster thanexpected from the changeof the observed rest-framewavelength only.For late-typegalaxies the slopeof this relation is equal to −0.82, whereas Kelvin et al.(2012)pre
dictiongives –0.42.For the early-type objects our slope and the slopegivenby Kelvin et al.(2012)are equal to –1.26 and –0.52, respectively.Thus,thechangeofthe rest-framewavelengthwith redshift can only partially explain the observed changes of the Sérsic index. Thus, a large part can be attributed to the genuine galaxy evolution in the redshift rangez = [0.5, 1.0]. The Sérsic index n = 1, commonly used to model the light profle of the disk-like galaxies, is well inside the range [0.81, 1.11] spanned by the average Sérsic indexes mea-sured within the analysed redshift-luminosity space limits. For spheroid-like galaxies we fnd mean values in the range [2.42, 3.69],lowerthanthetypicalvalueusedto describenearby ellipticalgalaxies (i.e. n = 4, see deVaucouleurs 1948). Other authorshave reported similar Sérsic indicesfor early-typegalaxies; hni = 3.0(D’Onofrio 2001), hni = 3.3(Padmanabhan et al. 2004), and n > 2.5(Eales et al. 2015; Griﬃth et al. 2012), for example. Moreover, the tests presented in Appendix A ensure that the Sérsic parameters we obtained are reliable and that the bias in the estimate of n is negligible for all the redshift and lu-minosity bins considered in this analysis. 5. Comparison with the literature Previous studies have shown that the Sérsic index of galaxies depends on both their absolute magnitude and red-shift (e.g. Graham&Guzmán 2003; Tamm&Tenjes 2006; van Dokkum et al. 2010, 2013;Patel et al. 2013;Buitrago et al. 2013).To compare our results with otherworks, Eqs.(7)and(8) are combined with Eq.(1)to obtain the following relations: log nd = −(MB + 19.30 + 3.74z)/13.75, (9) log ns = −(MB + 14.87 + 1.87z)/10.68, (10) where the dependence on absolute magnitude is made explicit. The relation between galaxy luminosity and Sérsic index has been reported in many studies for spheroid-like galaxies (e.g. Young&Currie 1994;Graham&Guzmán 2003;Ferrarese et al. 2006). Moreover, a link between structural parameters and lu-minosityhas also been studiedby Crossetal. (2004)forE/S0 Fig.
6.
Sérsic index – redshift relation: VIPERS results are presented as red and blue solid lines for spheroid-and disc-like galaxies, respectively, for three values of B-band absolute magnitude. Patel et al.(2013)’s results for quiescent and star-forming objects with log(M/M)> 10.5are shown as red flled and empty circles and dashed magenta and blue lines. The relation foundby van Dokkum et al.(2010) for a constant co-moving number density sample is plotted in brown (short-dashed lineand triangles). Buitragoetal. (2013)’s resultsfora sample visually classifed into early-and late-type galaxies is shown as orange flled and empty diamonds, while disc-galaxies measured byTamm&Tenjes(2006)are representedby green squares. The dot-dashed lines show n(z) relation corresponding to the disk-like and spheroidal galaxies, only for MB = −21 mag, obtained from the 2D analysis presentedin Sect. 6. galaxies in the redshift range from z = 0.5 to 1. Equations(9) and(10) show thatfainter disc and spheroidalgalaxies have lower values of the Sérsic index than the luminous ones and that this relation depends on redshift. The dependence of Sérsic index on redshift has been analysed in many studies (e.g. Tamm&Tenjes 2006; van Dokkum et al. 2010, 2013;Patel et al. 2013;Buitrago et al. 2013). Figure 6 shows the Sérsic index-redshift relations for both disc-like and spheroid-like populations within VIPERS for three absolute magnitude values and the comparisons with previous studies. In the following sections we analyse the comparisonforthetwo classesofgalaxiesin detail. 5.1. Spheroid-like galaxies Patel et al. (2013) computed structural parameters of massive galaxies in high-resolution HST imaging from the CANDELS and COSMOS surveys, and measured the evolution of the Sér-sic index ofgalaxies in the redshift range0.25 < z < 3, after splitting them into quiescent and star-forming populations on the basis of their rest-frame UVJ colours. The solid red lines show the Sérsic index-redshift relations for spheroid-like populations described by Eq.(10) for three values of B-band absolute magnitude. The solid red circles in Fig.6showthe median Sérsic indices for quiescentgalaxies with log(M/M)> 10.5in four redshift bins, while the orange dashed line indicates their best-ft Sérsic index-redshift relation over the redshift range0 < z < 2.5of the formn ∝ (1 + z)−0.50(±0.18). The exponent of this relation is consistent with our ft,n ∝ (1+z)−0.64, that we obtain for our brightest(MB = −22) spheroid-likegalaxies, which also fulfll their criterion log(M/M)> 10.5. A120, page9of 21 van Dokkum et al. (2010)measured the Sérsic index param-eter from stacked rest-frame R-band (observed J, H-band) im-ages from NEWFIRM Medium Band Survey. They selected a sample at a given constant cumulative number density, which results in their use of a stellar mass limit which evolves with redshift. The stellar mass limit of their selection at our mean redshift z ∼ 0.7is log(M/M)> 11.35 and does not vary considerably(<0.07dex) in the redshift range we are exploring, 0.5< z < 0.95. At these large stellar masses thegalaxy populationis dominatedby quiescent objects. Rather than ftting Sérsic profles to each individual galaxy and measuring the mean of the distribution, van Dokkumetal. (2010)created deconvolved, stacked images of massivegalaxies within bins of redshift, and ftted Sérsic functions to the stacked radial surface density profle,the resultsof which areshownasbrown trianglesinFig. 6. Theymeasureabest-ftevolutionforthe Sérsicindexoftheform n = 6.0× (1+ z)−0.95over the range0 < z < 20 11galaxies was then subdivided into early-and late-type galaxies on the basis of the visual classifcation. The mean Sérsic indices of visually-selected early-types in bins of redshift are displayed as orange diamonds, and show the same gradual increase in n with time, albeit systematically shifted to higher Sérsic index values by Δn ∼ 1.5. Despite the diﬀerent selection criteria, the evolutionofthe Sérsicindexforbright spheroid-likegalaxiesis in good agreement with the relations found in the literature for massive quiescentgalaxies. 5.2. Disk-like galaxies The Sérsic index-redshift relation for disc-like galaxies given by Eq. 9 is represented in Fig. 6 with dark blue lines, and for MB = −22 mag can be written as nd = 1.65(1 + z)−0.98. The dependence of the n-redshift relation on absolute magnitude is smaller for disc-like-than for spheroid-likegalaxies, while its evolution with cosmic time isfaster for disc-likegalaxies than for spheroid-like ones. Patel et al. (2013) and Buitrago et al. (2013) found simi-lar, decreasing trends. However, their relations are signifcantly oﬀset from our results by Δn ∼ 1, probably refecting the fact that they used selection criteria very diﬀerent from ours (i.e. star-forminggalaxiesin Pateletal.2013andvery massive visually classifed late-type galaxies in Buitrago et al. 2013). In particular, we found that the characteristic stellar mass of our disc-like sample, estimated from the mass-luminosity relation, corresponds to a selection of stellar masses smaller than log(M/M)= 10.5. For a much more meaningful comparison we turned to theTamm&Tenjes(2006)sample who measured the Sérsic pro
fleof22galaxiesinthe HDF-Susinga selection similarto ours, as theyhave only considered disk-likegalaxies (with n < 2) in absolute magnitude range −17 < MB < −22. It is therefore re-assuring that theirs results are consistent with ours, as shown in Fig.6, although their sample contains only22galaxies. Comparing our results with previous work, we fnd, in gen-eral, a good agreement of the evolution of the Sérsic index for A120, page 10 of 21 spheroid-likegalaxies with the ones for quiescent and early-type galaxies. Instead, galaxies defned as star-forming are characterised by larger values of Sérsic index when compared to disk-like ones. 6. Sérsic index-colour distribution In Sects. 3.2 and 4.2 we independently analysed the UBV rest-frame colour and the logarithm of the Sérsic index n of the VIPERS galaxies as a function of the redshift z and ΔBev lu-minosity. Both parameters show a bimodal distribution. Using the local galaxy sample of the Millennium Galaxy Catalogue, Driver et al. (2006)showed not only that both colour and Sérsic index are characterised by bimodal distributions, but that two well-separated populations exist on the u − r rest-frame colour versus log(n)plane. A similar method has been proposed by Kelvin et al. (2012) to study the morphological properties of galaxies in the GAMA survey. To investigate whether this is still true at high redshift we have repeated the Driver et al. (2006)analysis in each of our subsamples.The resultsareshowninFig. 7.The coloursineach surface density map of this plot are normalised to have values in the range 0–1, so that 1 (dark red colour) is the peak den-sity in each bin. The joint probability distribution of UBV rest-frame colour and Sérsic index n is clearly bimodal in all panels, with two well-separated peaks and indicates the presence of two diﬀerent populations that we identify with early-and late-type galaxies. The plot shows that the distributionof the late-typegalaxies are centred at the Sérsic index value n ≈ 1 and the rest-frame colour UBV ≈ 0.8, while those of the early-typegalaxies are centred at UBV ∼ 1.4 and 2.5 < n < 4. The latter peak ap-pears somewhat elongated along the n-axis and moves towards largervaluesof the Sérsic index (from n ∼ 2.5to4) with cosmic time, that is,galaxies become more concentrated at lower red-shift. The two peaks are separatedby the local minimum located at UBV ∼ 1.2, corresponding to sSFR 10−10 yr−1 (see Fig. 2); a value that is often used to separate active from passive ob-jects (e.g. Davidzon et al. 2016). From these plots we see that a moreeﬀectiveseparation can be made using the combined Sérsic index n and UBV rest-frame colour information. We ftted the joint probability distribution of Sérsic index and UBV colour in each redshift-luminosity bin with the sum of two 2D-Gaussians. The iso-density contour lines are separated in steps of 0.2 times the maximum surface density value. The dashed circle around each peak shows the 0.5σ level of each 2D-Gaussian. We do not include a covariance term for the Gauss functions in order to avoid artifcially creating apparent correlations be-tween UBV and n within the single populations due to the presence of the second population. In addition to the dominant populations of early-and late-typegalaxies,Fig. 7shows thata fractionof bluegalaxieshave largevaluesof the Sérsic index(n >∼ 2), while, conversely, some redgalaxieshavea Sérsic index n ≈ 1, typical of disc-like ob-jects.We postponea thoroughinvestigationof these peculiarobjects to a future analysis. Moreover, Fig. 7 gives us information on the galaxy mor-phological type fraction in each luminosity/redshift bin. It shows that the most luminous bins are dominatedby early-typegalaxies, whereas the late-like galaxies dominate the less luminous sub-samples. J. Krywult et al.: VIPERS: evolution of shape and colour bimodalities Fig.
7.
UBV
rest-frame colour vs. Sérsic index n distribution. Each panel shows the colour–codedgalaxy surface density distribution mapof the VIPERSgalaxiesineach redshiftand ΔBev luminositybin.The colourbar presentedinthe bottomright cornergivesthe normalisedgalaxysurface density. The contour lines show the density values in steps of 0.2 obtained from the two Gaussians bivariate ftting procedure. Blue and red dashed lines show the 2-dimensional modelgivenby Eqs.(11)–(14). Crosses identify the positionsof the centre maximal surface density distributionof thegivengalaxy population. The dashed lines around the peaks show thevalueof0.5σ of the Gaussian ft. The histograms present thegalaxy distributions projected on the Sérsic index and UBV colour axes, at the bin z = [0.65, 0.80] and ΔBev = [0.5, 0.0]. A120, page 11 of 21 6.1. Early-type galaxies in the n-UBV plane Thegalaxy surface distributions presented in Fig. 7 show that the positions of early-and late-typegalaxy populations change with both redshift and luminosity. Fitting the sum of two 2D Gauss functions to the distributions in each bin we obtain the positions of the population centres (log(n), UBV). Using these positions we determined the empirical relation connecting thegalaxy population centre with ΔBev and redshift. Our results in Sects. 3.2 and 4.2 showed that the UBV rest-frame colour and the Sérsic index log(n)are well re-producedbya linear dependence on redshift and luminosity.We thus ft the position of the early-typegalaxy population centre (log(ne), UBVe)inFig.7withatwo-dimensional linear function, obtaining the following set of equations describing the central positionof thisgalaxy population asa functionof redshift and luminosity: UBVe = 1.58(±0.02) − 0.27(±0.03)z − 0.04(±0.01)ΔBev , (11) log(ne)= 0.57(±0.03) − 0.18(±0.04)z − 0.10(±0.01)ΔBev, (12) where ΔBev isgivenbyEq.(1).The errors ofthe ftted coeﬃcients were estimated via a bootstrap procedure using 1000 re-samples. The relationsgivenbyEqs.(11)and(12)wereusedto com-pute the central UBVe and ne values for the early-typegalaxy populations as a function of redshift and luminosity, shown in Fig.7asreddashed lines.Thecrossingpointsoftheselinescorrespondtothe positionofthe maxima describedbytheEqs.(11) and(12), whereas the crosses show the surface density maxima of early-typegalaxy populationin each bin. Comparing these positions with the shape of the higher den-sity contour lines and the0.5σ widths of the 2D Gaussian fts (marked as dashed ellipses) we fnd that the simple linear ap-proximation given above accurately predicts the observed peak positionof the early-typegalaxy population. The mean distance between the maxima positions from data and the linear model is smaller than0.1σ. 6.2. Late-type galaxies in the n-UBV plane The same procedurewas also applied to the late-typegalaxy dis-tributions. The following set of equations describes the central position(UBVl, log(nl)of the late-typegalaxy population asa function of redshift and luminosity: UBVl = 1.02(±0.03) − 0.31(±0.05)z − 0.15(±0.01)ΔBev, (13) log(nl)= 0.18(±0.03) − 0.34(±0.04)z − 0.08(±0.01)ΔBev, (14) where ΔBev isgivenbyEq.(1).The UBVl and nl positions of the late-typegalaxy population asa functionof redshift and luminosity are derived similarly to early-typegalaxies and presented as blue dashed linesin Fig. 7. The crossing pointsof these lines determine the maxima position describedby Eqs.(13)and(14). The plot shows that our linear model accurately reproduces the positions ofgalaxy density maxima, with the distance from the maxima computed from data being smaller than0.1σ. 6.3. Comparison of 1D to 2D approximation In Sects. 3.2 and 4.2 we focused our attention on the 1D distributions of the Sérsic index and UBV rest-frame colour. It is worth comparing those results with the ones obtained from the 2D ap-proximation.We fnd that both approachesgive almost the same A120, page 12 of 21 results for the UBV rest-frame colour positionofthegalaxypopulation centres. The1D relationsgivenby Eqs.(3)and(4)and the2D ones presentedby Eqs.(11)and(13)are consistent with each other within ±1σ of the ftted parameters. Some signifcant diﬀerences occur, however, in the approximation of the Sérsic index log(n)positions. The coeﬃcients rep-resenting the redshift dependence in the 1D relations given by Eqs.(7)and(8)and the2D relations presentedby Eqs.(12)and (14)are diﬀerent, with the redshift dependence in the 1D rep-resentation being signifcantly shallower than that obtained with the 2D analysis. The origin of this diﬀerence is evident when comparing Figs. 7 and5: the2Dgalaxy distributioneﬃciently separates both galaxy populations for all ΔBev luminosity and redshift bins. In contrast, in the 1D projection of the Sérsic index log(n), these distributions partially overlap each other, especially for the less luminous disc-and spheroid-likegalaxy popu-lations,as clearly seeninthe histograms presentedinFig. 5.Be
cause of this, the results obtained with the 2D approach are much better determined and more robust than those obtained with the 1D analysis. The Sérsic index evolution obtained from the 1D and 2D analyses canbe compared, making useof Fig. 6again. The dot-dashed black lines located in the regions of the disk-like and spheroidal galaxies show the n(z)relation at MB = −21 mag from the2D approachgivenby Eqs.(12)and(14), respectively. Comparing these results with those obtained from the 1D analysis shown in the same plot as the solid blue and red lines, we fnd a steeper Sérsic index evolution in the 2D approach for bothgalaxy populations. In the 2D approach, the Sérsic index-redshift relation is well approximated by n ∝ (1 + z)−1.08 for late-typegalaxies andby n ∝ (1 + z)−1.47 for early-typegalaxies. The values of the exponents indicate a faster Sérsic index evolution with cosmic time than reported in previous works based only on the Sérsic index or rest-frame colourgalaxy selection(e.g. Tamm&Tenjes2006;van Dokkumetal.2010,2013; Patel et al. 2013;Buitrago et al. 2013). Thegalaxy type classi
fcation based on the 2D distribution of the Sérsic index versus UBV rest-frame colour allows us to better select galaxies be-longingtotheearlyand late-typegalaxy population.Inthisway the method presented in this paper allows us to study in detail the morphological properties ofgalaxies belonging to the early and late-typegalaxy populations. 7. Sersic index-UBV colour coevolution The analysis presented in the previous sections provides a quantitative description of the Sérsic index-UBV colour relation and its dependence on redshift andgalaxy luminosity. Figure 8 makes use of Eqs.(11)–(14)to present these dependencies on the Sérsic indexversus UBV colour plane. Dots representvalues given by the equations presented in the previous sections, for redshift from z = 0.5to 1.0 in steps of 0.1, and black lines con-nect points corresponding to the fxed values of ΔBev ranging from –1.5 to 1.0 in increments of 0.5 mag. Contour lines rep-resent thegalaxy surface density of the whole VIPERSgalaxy sample studied in this paper, in steps of0.2 dex. The coloured regions highlight the redshift and luminosity limits presented in Figs.1 and7. The blue and red arrows indicate the change of values of UBV and Sérsic index log(n)as a function of redshift and luminosity. In Sect. 3.1 we show that the UBV rest-frame colour is well correlated with the sSFR. The approximate relation of UBV colour versus sSFR is presented on the right-hand sideof Fig. 8. J. Krywult et al.: VIPERS: evolution of shape and colour bimodalities The UBV rest-frame colour versus log(n)diagram allows us to make a division, at the intermediate redshift z ≈ 0.7, between the late-type galaxies (presumably, disk-like, blue and mostly star-forming) with UBV < 1.2andn < 1.5and early-typegalaxies (presumably,spheroidal, red and mostly quiescent) for which UBV > 1.2 and n > 1.5. The UBV versus n plot also oﬀers a possibility to separate twogalaxy populations usinga line per-pendicular to the connection between the maxima and passing through the minimum along the same line.Asimilar method has been proposedby Kelvinetal.(2012). Figure8visually connects fourgalaxy parameters and allows ustopresentthecoevolutionofthe propertiesofgalaxiesbelonging to the early-and late-type classes. Infact, from this fgure, it is already clear that the evolution of the relation between UBV and n is markedly diﬀerent for early-and late-typegalaxies, similar to the fndings of other studies (e.g. Blanton et al. 2003).We also fnd that the Sérsic index n of both main mor-phologicalgalaxy types (disk-likeand spheroidal) increases with both their luminosity and cosmic time. This result is consis-tent with observations and numerical simulations (e.g. Conselice 2003;Conselice et al. 2005;Treu et al. 2005;Bundy et al. 2005; Brook et al. 2006;Aceves et al. 2006;Hopkins et al. 2007). 7.1. Early-type galaxies The results presented in the previous sections allow us to give a general overview of the colours and structural properties of early-type galaxies (ETGs). Figure 8 shows explicitly the ef-fect of evolution and luminosity on the colours and structural properties of ETGs. Firstly, it confrms that ETGs si-multaneously become redder and more concentrated with both cosmic time and increasing luminosity (presumably correlated with stellar mass)(Trujilloetal. 2001b; Graham&Guzmán 2003; Tamm&Tenjes 2006; van Dokkum et al. 2010, 2013; Patel et al. 2013;Buitrago et al. 2013). However, the eﬀects of Fig.
8.
UBV rest-frame colour versus Sérsic indexlog(n)relation of late-type (lower left corner) and early-type (upper right corner)galaxies. Dots indicate redshift from z = 0.5 to1.0 in increments of0.1. Black solid lines connect the values of ΔBev from −1.5to1in0.5magnitude increments. The arrows show the direction ofthe redshiftand luminositygalaxyevolution. The right plot presents the UBV colour versus sSFR relation. The0.2dexbackground con-tour lines show the bivariate number density of all studied VIPERSgalaxies in our sample (0.5 < z < 0.95). The yellow coloured regions mark the analysed redshift and luminosity lim-its, as presentedin Figs. 1and7. increasing luminosity and cosmic time on early-type galaxies act in diﬀerent directions. This means that we cannot take a low-luminosity, early-type galaxy at z = 1.0 and simply wait a few Gyr for it to become as red and as concentrated as its high-luminosity counterpart was at z = 1.0. At z = 1.0, we see thatalow-luminosity(ΔBev =+1.0)redgalaxyis0.10mag bluer in UBV and 0.6 times less concentrated than its 10 times more luminous(ΔBev = −1.5) red counterpart. Followingagalaxyevolutionary track, we see that whilea galaxy can rapidly redden to match its high-luminosity counter-part by z = 0.63, over the same time-scale it only marginally increasesits concentrationbyafactorequalto1.17,thatis,only a quarter of the amount needed to match that of high-luminosity ETGs at z = 1.0. Indeed, even at z = 0(assuming an extrapolation of the linear trends) its Sérsic index will not have increased suﬃciently. Low-luminosity early-types are known to have later forma-tionepochsandmoreextendedburstsofstar formationthantheir high-luminosity counterparts and have delayed star formation histories (e.g. Thomas et al. 2005). The delayed star formation can also be seen tentatively from the plot in Fig. 8, where low luminositygalaxies seemtohave,onaverage,largervaluesof sSFR than brighter ones at a fxed redshift. The results presented here confrm that while it is possi-ble to account for this delay by matching low-luminosity ETGs observed at lower redshifts to higher-mass ETGs seen at earlier epochs, and to frst order to have stellar populations of equivalent ages (although the metallicities will diﬀer), the lowerluminosity ETGs will still have quite diﬀerent structural properties, being much less concentrated at fxed stellar age. This fundamental diﬀerence likely refects the less active merger history of lower-luminosity (mass) ETGs (e.g. Rodriguez-Gomez et al. 2016; Lacey&Cole 1993; Aceves et al. 2006; De Lucia et al. 2006), meaning they cannotbuildup the moreextended stellar halos of high-mass ETGs. A120, page 13 of 21 If we assume that the increase in n is due to major mergers (e.g. Aceves et al. 2006)and the continual accretion of material onto the outskirts of the galaxy, the trends of Fig. 8 suggest that low-luminosity ETGs do not undergo suﬃcient minor mergers at late epochs to “catch up” the much more active merger history of high-mass ETGs at z > 1. 7.2. Late-type galaxies At frst sight, Fig. 8suggests that late-typegalaxies(LTGs) show very similar trends to early-type, becoming simultaneously red-der and more concentrated, both with cosmic time (decreasing z) and increasing luminosity. Moreover, the evolution from z = 1 to z = 0.5in theUBV vs. log(n)plane is similar in magnitude and direction to that of the early-type population, leaving the separation between the two populations virtually unchanged, as is presented in Fig. 7. Hence, the bimodality appears to neither strengthen nor weaken with time, at least for the redshift range studied here. Interestingly however, the relative impacts of time and lu-minosity on UBV colour and log(n)appear to have fipped in comparison to those seen among the ETGs. The concentration ofLTGs is most dependent on cosmic time, while UBV colour increases mostly with luminosity. At z = 1.0, a low-luminosity LTG(ΔBev =+1.0) is 0.375 mag bluer and 1.6 times less con-centrated than its 10 times more luminous counterpart(ΔBev = −1.5). By following its evolutionary track, it is able to change its structure suﬃciently rapidly to match the Sérsic index of its high-luminosity counterpartby z = 0.41,butover this same time perioditisonlyexpectedto become0.18mag redder,halfofthat required to match the UBV colour of the high-luminosityLTG at z = 1. Given the well known systematic decline in specifc-SFRs among LTGs over 0 < z < 1, in which both high-and low-luminosity (stellar mass) spirals see their star formation drop exponentially and in step (e.g. Noeske et al. 2007;Zheng et al. 2007), it is interesting to note that their structural parameters are changing more rapidly than their colours, while UBV colour is more dependent on luminosity. It should infact be easier to makea spiralgalaxy redderby reducing star formation, than an early-typegalaxy,asthe responsetoareductioninstar formation is greatest when thegalaxy is initially blue (see e.g. Fig. 2and the right-handplotofFig. 8).Oneexplanation couldbe thatthe large change in UBV colour with luminosity amongLTGs more greatly refects the increased reddening due to dust in massive spirals rather than a decrease in specifc-SFR. Theoretically,itisexpected that thebulge fractionof merger remnants increases with the decreasinggas fraction of the pro-genitors (e.g. Robertson et al. 2006; Hopkins et al. 2009). The higher luminosity (mass) disk-likegalaxieshavea higherbulge fraction due to major-and intermediate-mass ratio mergers. The dense luminous part ofgalaxies is undisturbed during this pro-cess and luminous material dominates the central regions of mergers’ remnants(Barnes&Hernquist 1992), and their Sérsic index value increases, as shown in this study. 8. Summary Inthispaperwepresentthecoevolutionofgalaxy morphological properties and colours over the redshift range from z = 0.5to 1, combining high-quality imaging data from the CFHT Legacy Survey with the large number of redshift and extended photometry from the VIPERS survey. We used this new dataset to investigate the coevolution ofgalaxy Sérsic index and UBV rest-frame colour. Thegalaxy structural parameters were mea-suredbyGALFIT fttingthe Sérsic profletothe i-band CFHTLS T0006 images.Todo this,thePSFofthe imageswas precisely estimated and approximatedover the wholeof each1◦× 1◦ tile. The resultant parameters were carefully tested using a set of different methods, which confrms the good quality of the fts and reliability of their ftted values. Our results can be summarised as follows: – We fnd a clear bimodality of the UBV rest-frame colour and Sérsic index distribution, very well approximated by a sum of two Gaussians over the explored redshift and luminosity ranges.We parametrisedthe positionofthetwo maxima in UBV and n distributions as a function of luminosity and redshift. This parametrisation allow us to analyse the colours and structural parameters of the red and blue, or the spheroidal and disk-likegalaxies based on their location in the luminosity-redshift space. – The 1D and 2D methods show the evident bimodality both of the UBV rest-frame colour and Sérsic index distribution up to redshift z = 1. – The combination of the UBV rest-frame colour and Sérsic index n, as a function of redshift and luminosity, leads to a precise statistical descriptionof the structureofgalaxies and theirevolution.Our methodof analysis connects fourgalaxy parameters, that is, UBV colour,Sérsic index, luminosity and redshift, and allows us to present the coevolution of the propertiesofgalaxies belongingtotheearly-and late-type classes together with their evolution. – We fnd that both early-and late-type galaxies simultaneously become redder and more concentrated with both cosmic time and increasing luminosity. Early type galaxies, however, display only a slow change in their concentrations between z = 1andz = 0.5. Their high concentrations were already established at z ∼ 1and depend much more strongly on their luminosity than redshift.In contrast, late-typegalaxies clearly become more concentrated with cosmic time from z ∼ 1, with only minor evolution in colour, which remains mainly dependent on their luminosity. This fipped luminosity (mass) and redshift dependence likely refects diﬀerent evolutionary tracks of early-and late-type galaxies before and after z ∼ 1. We demonstrated that the method presented in this paper is an improvedway for separating early-and late-typegalaxies, and to study how their colour and morphology depend on luminosity and redshift. This can be used in further investigation ofgalaxy evolution. Acknowledgements. The authors thank the referee for very helpful critique and for useful and constructive comments. We acknowledge the crucial contribution of the ESO staﬀ for the management of service observations. In particu-lar, we are deeply grateful to M. Hilker for his constant help and support of this program. Italian participationto VIPERShasbeen fundedbyINAF through PRIN 2008, 2010 and 2014 programs. L.G. and B.R.G. acknowledge support of the European Research Council through the Darklight ERC Advanced Research Grant (# 291521). OLF acknowledges support of the European Research Council through the EARLYERC Advanced Research Grant (# 268107). A.P., K.M., and J.K. have been supported by the National Science Centre (grants UMO2012/07/B/ST9/04425 and UMO-2013/09/D/ST9/04030), R.T. acknowledge f-nancial support from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement No. 202686. E.B., F.M. and L.M. acknowledge the support from grants ASI-INAFI/023/12/0and PRIN MIUR 2010-2011. L.M. also acknowledges f-nancial support from PRIN INAF 2012. Research conducted within the scope of the HECOLS International Associated Laboratory, supported in part by the Polish NCN grant Dec-2013/08/M/ST9/00664. A120, page 14 of 21 J. Krywult et al.: VIPERS: evolution of shape and colour bimodalities References Abraham,R.G.,Tanvir,N.R., Santiago,B.X.,etal.1996, MNRAS,279,L47 Abraham,R.G.,vandenBergh,S.,&Nair,P. 2003, ApJ,588,218 Aceves, H.,Velázquez, H.,&Cruz,F. 2006, MNRAS, 373, 632 Arnouts,S.,Walcher,C.J.,Le Fèvre,O.,etal.2007, A&A,476,137 Arnouts, S., Le Floc’h, E., Chevallard, J., et al. 2013, A&A, 558, A67 Baldry, I. K., Glazebrook, K., Brinkmann, J., et al. 2004, ApJ, 600, 681 Ball,N.M.,Loveday,J.,&Brunner,R.J.2008, MNRAS,383,907 Barden, M., Rix, H.-W., Somerville, R. S., et al. 2005, ApJ, 635, 959 Barnes,J.E.,&Hernquist,L.1992, ARA&A,30,705 Bassett,R.,Papovich,C., Lotz,J.M.,etal. 2013, ApJ,770,58 Bell,E.F.,Wolf,C., Meisenheimer,K.,etal.2004, ApJ,608,752 Bertin,E.,&Arnouts,S.1996, A&AS,117,393 Blanton,M.R.,&Berlind,A.A.2007, ApJ,664,791 Blanton,M.R.,Hogg,D.W., Bahcall,N.A.,etal.2003, ApJ,594,186 Bolzonella, M.,Kova ˇ c, K., Pozzetti, L., et al. 2010, A&A, 524, A76 Boulade, O., Charlot, X., Abbon, P., et al. 2000, in Optical and IR Telescope Instrumentation and Detectors, eds. M. Iye,&A.F. Moorwood, Proc. SPIE, 4008, 657 Brammer,G.B., Whitaker,K.E.,van Dokkum,P.G.,etal.2009, ApJ,706,L173 Brook,C.B.,Kawata,D., Martel,H., Gibson,B.K.,&Bailin,J.2006, ApJ,639, 126 Buitrago,F.,Trujillo,I., Conselice,C.J.,& Häußler,B. 2013, MNRAS, 428, 1460 Bundy,K.,Ellis,R.S.,&Conselice,C.J.2005, ApJ,625,621 Bundy, K., Ellis, R. S., Conselice, C. J., et al. 2006, ApJ, 651, 120 Cappellari, M., Emsellem, E., Krajnovi ´ c, D., et al. 2011, MNRAS, 416, 1680 Cassata,P.,Giavalisco,M.,Guo,Y.,etal. 2011, ApJ,743,96 Cheung, E., Athanassoula, E., Masters, K. L., et al. 2014, in Structure and Dynamics of Disk Galaxies, eds. M. S. Seigar,&P.Treuthardt, ASP Conf. Ser., 480, 165 Cimatti,A.,Daddi,E.,&Renzini,A.2006, A&A,453,L29 Ciotti,L.,&Bertin,G.1999, A&A,352,447 Conselice,C.J. 2003, ApJS, 147,1 Conselice,C.J., Bershady,M.A.,&Jangren,A.2000, ApJ,529,886 Conselice, C. J., Bundy, K., Ellis, R. S., et al. 2005, ApJ, 628, 160 Coppa, G., Mignoli, M., Zamorani, G., et al. 2011, A&A, 535, A10 Cross, N. J. G., Bouwens, R. J., Benítez, N., et al. 2004, AJ, 128, 1990 Cuillandre, J.-C., Mellier,Y., Dupin, J.-P., et al. 1996, PASP, 108, 1120 Dahlquist, G., & Bjorck, A. 1974, Numerical methods (Englewood Cliﬀs: Prentice-Hall) Davari,R.,Ho,L.C.,Peng,C.Y.,&Huang,S. 2014, ApJ,787,69 Davidzon, I., Cucciati, O., Bolzonella, M., et al. 2016, A&A, 586, A23 De Lucia,G., Springel,V., White,S.D.M., Croton,D.,&Kauﬀmann, G. 2006, MNRAS, 366, 499 deSouza,R.E., Gadotti,D.A.,&dosAnjos,S.2004, ApJS,153,411 deVaucouleurs,G.1948, Annales d’Astrophysique,11,247 deVaucouleurs,G. 1961, ApJS,5, 233 D’Onofrio, M. 2001, MNRAS, 326, 1517 Driver,S.P.,Allen,P.D., Graham,A.W.,etal.2006, MNRAS,368,414 Driver,S.P.,Hill,D.T.,Kelvin,L.S.,etal.2011, MNRAS,413,971 Eales, S., Fullard, A., Allen, M., et al. 2015, MNRAS, 452, 3489 Faber,S.M.,Willmer,C.N.A.,Wolf,C.,etal. 2007,ApJ,665,265 Ferrarese, L., Cé,P., Jordán, A., et al. 2006, ApJS, 164, 334 Frei,Z., Guhathakurta,P.,Gunn,J.E.,&Tyson,J.A.1996, AJ,111,174 Fritz,A.,&Ziegler,B.L.2009, Astron.Nachr.,330,1010 Fritz,A.,Bm,A.,&Ziegler,B.L.2009, MNRAS,393,1467 Fritz, A., Scodeggio, M., Ilbert, O., et al. 2014, A&A, 563, A92 Galloway,M.A.,Willett,K.W.,Fortson,L.F.,etal.2015, MNRAS,448,3442 Garilli, B., Guzzo, L., Scodeggio, M., et al. 2014, A&A, 562, A23 González,J.E., Lacey,C.G., Baugh,C.M., Frenk,C.S.,&Benson,A.J. 2009, MNRAS, 397, 1254 Goodman,J.W. 1985, J.Opt. Soc.Am.A,2, 1448 Goranova,Y., Hudelot,P., Magnard,F.,etal.2009,The CFHTLST0006 Release, Tech. rep., Terapix/Institut d’Astrophysique de Paris, http://terapix.
iap.fr/cplt/T0006-doc.pdf
Graham,A.W.,&Driver,S.P. 2005, PASA,22,118 Graham,A.W.,&Guzmán,R.2003, AJ,125,2936 Griﬃth,R.L., Cooper,M.C.,Newman,J.A.,etal.2012, ApJS,200,9 Guo,Y., McIntosh,D.H.,Mo,H.J.,etal.2009, MNRAS,398,1129 Guzzo,L.,&TheVipersTeam.2013, The Messenger,151,41 Guzzo, L., Scodeggio, M., Garilli, B., et al. 2014, A&A, 566, A108 Häussler, B., McIntosh, D. H., Barden, M., et al. 2007, ApJS, 172, 615 Häußler, B., Barden, M., Bamford, S. P., & Rojas, A. 2011, in Astronomical Data Analysis Software and Systems XX, eds. I. N. Evans, A. Accomazzi, D.J. Mink,&A.H. Rots, ASP Conf. Ser., 442, 155 Haynes,M.P.,&Giovanelli,R. 1984, AJ,89,758 Hogg,D.W.,&Lang,D. 2013, PASP, 125, 719 Holhjem,K., Schirmer,M.,&Dahle,H.2009, A&A,504,1 Hopkins,P.F.,Bundy,K., Hernquist,L.,&Ellis,R.S.2007, ApJ,659,976 Hopkins,P.F.,Cox,T.J.,Younger,J.D.,&Hernquist,L.2009, ApJ,691,1168 Hubble,E.P. 1926, ApJ,64,321 Huertas-Company, M., Pérez-González, P. G., Mei, S., et al. 2015, ApJ, 809, 95 Kartaltepe,J.S., Mozena,M.,Kocevski,D.,etal.2015, ApJS,221,11 Kelvin,L.S.,Driver,S.P., Robotham,A.S.G.,etal.2012,MNRAS,421,1007 Kennicutt, Jr., R. C. 1998,ARA&A, 36, 189 Kolmogorov, A. 1961, inTurbulence, ClassicPapers on Statistical Theory, eds. S.K. Friedlander,&L.Topper(New-York: Interscience Publishers Inc.), 151 Kovaˇ c, K., Lilly, S. J., Knobel, C., et al. 2010, ApJ, 718, 86 Lacey,C.,&Cole,S.1993, MNRAS,262,627 Lackner,C.N.,&Gunn,J.E.2012, MNRAS,421,2277 Le Fèvre, O., Saisse, M., Mancini, D., et al. 2003, in Instrument Design and Performance for Optical/Infrared Ground-basedTelescopes, eds. M. Iye,& A.F.M. Moorwood, Proc. SPIE, 4841, 1670 Le Fèvre, O., Cassata,P., Cucciati, O., et al. 2013, A&A, 559, A14 Lilly, S. J., Le Fèvre, O., Renzini, A., et al. 2007, ApJS, 172, 70 Lintott, C. J., Schawinski, K., Slosar, A., et al. 2008, MNRAS, 389, 1179 Loh,Y.-S.,Rich,R.M., Heinis,S.,etal.2010, MNRAS,407,55 Longhetti,M., Saracco,P.,Severgnini,P.,etal.2007, MNRAS,374,614 Lotz,J.M., Primack,J.,&Madau,P.2004, AJ,128,163 Lotz,J.M.,Davis,M.,Faber,S.M.,etal. 2008, ApJ,672,177 Mellier, Y., Bertin, E., Hudelot, P., et al. 2008, The CFHTLS T0005 Release Tech. rep., Terapix/Institut d’Astrophysique de Paris, http://terapix.
iap.fr/cplt/oldSite/Descart/CFHTLS-T0005-Release.pdf
Melvin,T., Masters, K., Lintott, C., et al. 2014, MNRAS, 438, 2882 Mendez, A. J., Coil, A. L., Lotz, J., et al. 2011, ApJ, 736, 110 Moﬀat,A.F.J. 1969, A&A,3, 455 Moresco, M., Pozzetti, L., Cimatti, A., et al. 2010, A&A, 524, A67 Morishita,T., Ichikawa,T.,&Kajisawa,M.2014, ApJ,785,18 Mosleh,M.,Williams,R.J.,&Franx,M.2013, ApJ,777,117 Moutard,T., Arnouts, S., Ilbert, O., et al. 2016, A&A, 590, A103 Nandra,K., Georgakakis,A.,Willmer,C.N.A.,etal. 2007, ApJ,660,L11 Noeske,K.G.,Faber,S.M.,Weiner,B.J.,etal. 2007, ApJ,660,L47 Noordermeer,E.,vander Hulst,J.M., Sancisi,R.,Swaters,R.A.,&van Albada, T. S. 2005,A&A, 442, 137 Padmanabhan, N., Seljak, U., Strauss, M. A., et al. 2004,New Ast., 9, 329 Pannella, M., Gabasch, A., Goranova,Y., et al. 2009,ApJ, 701, 787 Patel,S.G.,van Dokkum,P.G.,Franx,M.,etal.2013,ApJ,766,15 Peng,C.Y.,Ho,L.C.,Impey,C.D.,&Rix, H.-W. 2002, AJ,124,266 Peng,Y.-J., Lilly,S.J.,Kovaˇ c, K., et al. 2010, ApJ, 721, 193 Peng,Y.-J.,Lilly,S.J., Renzini,A.,&Carollo,M.2012, ApJ,757,4 Pignatelli, E.,Fasano, G.,&Cassata,P. 2006, A&A, 446, 373 Pozzetti, L., Bolzonella, M., Zucca, E., et al. 2010, A&A, 523, A13 Ravindranath, S., Ferguson, H. C., Conselice, C., et al. 2004, ApJ, 604, L9 Roberts,M.S.,&Haynes,M.P.1994, ARA&A,32,115 Robertson,B., Bullock,J.S.,Cox,T.J.,etal.2006, ApJ,645,986 Rodriguez-Gomez,V., Pillepich,A.,Sales,L.V.,etal.2016, MNRAS,458,2371 Sandage, A. 1961, The Hubble atlas of galaxies (Washington: Carnegie Institution) Schawinski, K.,Virani, S., Simmons, B., et al. 2009, ApJ, 692, L19 Schechter,P. 1976, ApJ, 203, 297 Schechter,P.L., Mateo,M.,&Saha,A.1993, PASP,105,1342 Scodeggio, M., Franzetti,P., Garilli, B., Le Fèvre, O.,& Guzzo, L. 2009, The Messenger, 135, 13 Sérsic, J. L. 1963, Boletin de la Asociacion Argentina de Astronomia, 6, 41 Simard,L.,Willmer,C.N.A.,Vogt,N.P.,etal. 2002, ApJS,142,1 Simmons,B.D.,Melvin,T., Lintott,C.,etal.2014, MNRAS,445,3466 Strateva, I.,Ivezi ´ c, Ž., Knapp, G. R., et al. 2001, AJ, 122, 1861 Tamm,A.,&Tenjes,P. 2006,A&A,449,67 Tasca, L. A. M., Kneib, J.-P., Iovino, A., et al. 2009,A&A, 503, 379 Tewes, M., Cantale, N., Courbin,F., Kitching,T.,& Meylan, G. 2012, A&A, 544, A8 Treu,T.,Ellis,R.S.,Liao,T.X.,&van Dokkum,P.G.2005,ApJ,622,L5 Trujillo,I., Aguerri,J.A.L., Gutiérrez,C.M.,&Cepa,J. 2001a,AJ,122,38 Trujillo,I., Graham,A.W.,&Caon,N.2001b,MNRAS,326,869 vanderWel,A., Holden,B.P.,Franx,M.,etal.2007, ApJ,670,206 van Dokkum,P.G., Whitaker,K.E., Brammer,G.,etal.2010, ApJ,709,1018 van Dokkum,P.G.,Leja,J., Nelson,E.J.,etal.2013, ApJ,771,L35 VanWaerbeke,L., Mellier,Y.,Erben,T.,etal.2000,A&A,358,30 Vikram,V.,Wadadekar,Y.,Kembhavi, A. K.,&Vijayagovindan, G.V. 2010, MNRAS, 409, 1379 Vulcani,B., Bamford,S.P., Häußler,B.,etal.2014,MNRAS,441,1340 Wetzel,A.R.,Tinker,J.L., Conroy,C.,&vanden Bosch,F.C.2014, MNRAS, 439, 2687 A120, page 15 of 21 Willmer,C.N.A.,Faber,S.M.,Koo,D.C.,etal. 2006,ApJ,647,853 Wyder,T.K., Martin,D.C., Schiminovich,D.,etal.2007,ApJS,173,293 Yan,H.,Yan,L., Zamojski,M.A.,etal.2011,ApJ,728,L22 Young,C.K.,&Currie,M.J.1994,MNRAS,268,L11 Zheng,X.Z., Bell,E.F.,Papovich,C.,etal. 2007, ApJ,661,L41 Zucca, E., Ilbert, O., Bardelli, S., et al. 2006, A&A, 455, 879 1 InstituteofPhysics,JanKochanowskiUniversity,ul. Swietokrzyska 15, 25-406 Kielce, Poland e-mail: krywult@ujk.edu.pl 2 Aix Marseille Université, CNRS, LAM (Laboratoire d’Astrophysique de Marseille) UMR 7326, 13388 Marseille, France 3 Astronomical Observatory of the Jagiellonian University, Orla 171, 30-001 Cracow, Poland 4 National Centre for Nuclear Research, ul. Hoza 69, 00-681 Warszawa, Poland 5 INAF–Istitutodi Astrofsica SpazialeeFisica Cosmica Bologna,via Gobetti 101, 40129 Bologna, Italy 6 INAF–Osservatorio Astronomico di Bologna, via Ranzani 1, 40127 Bologna, Italy 7 INAF–Osservatorio Astronomico di Brera, via E. Bianchi 46, 23807 Merate, Italy 8 INAF–Istituto di Astrofsica Spaziale e Fisica Cosmica Milano, via Bassini 15, 20133 Milano, Italy 9 Dipartimento di Fisica, Università di Milano-Bicocca, P.zza della Scienza 3, 20126 Milano, Italy 10 INAF–Osservatorio Astrofsico di Torino, 10025 Pino Torinese, Italy 11 Aix-Marseille Université, CNRS, CPT (Centre de Physique Théorique) UMR 7332, 13288 Marseille, France 12 Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre,via dellaVascaNavale84, 00146Roma,Italy 13 INFN, Sezione di Roma Tre, via della Vasca Navale 84, 00146 Roma, Italy 14 INAF–Osservatorio Astronomico di Roma, via Frascati 33, 00040 Monte Porzio Catone (RM), Italy 15 INAF–Osservatorio Astronomico diTrieste, via G. B.Tiepolo 11, 34143Trieste, Italy 16 National Centre for Nuclear Research, ul. Hoza 69, 00-681, Warszawa, Poland 17 Dipartimento di Fisica e Astronomia – Università di Bologna, viale Berti Pichat6/2, 40127 Bologna, Italy 18 INFN, Sezione di Bologna, viale Berti Pichat6/2, 40127 Bologna, Italy 19 Institute d’Astrophysique de Paris, UMR7095 CNRS, Université Pierreet Marie Curie,98bis Boulevard Arago, 75014Paris, France 20 Division ofParticle and Astrophysical Science, Nagoya University, Furo-cho, Chikusa-ku, 464-8602 Nagoya, Japan 21 Institute of Cosmology and Gravitation, Dennis Sciama Building, University of Portsmouth, Burnaby Road, Portsmouth, PO1 3FX, UK 22 INAF–Istituto di Radioastronomia, via Gobetti 101, 40129 Bologna, Italy 23 IRAP,9 av.du colonel Roche,BP 44346, 31028Toulouse Cedex4, France 24 Astronomical Observatory of the University of Geneva, ch. d`Ecogia 16, 1290Versoix, Switzerland A120, page 16 of 21 J. Krywult et al.: VIPERS: evolution of shape and colour bimodalities Fig.
A.1.
Comparison between Sérsic parameters of approximately 4000 simulatedgalaxies and their recoveredvalues. Bottom plots show the fractional deviation of the parameters as a function of the half-light radius re in pixels, minor to major axis ratio b/a, and apparent magnitude m and Sérsic index n. The red line shows the median, whereas the blue line denotes the1σ scatter around the median, defned to enclose 68%ofthe pointsatagiveninputvalue. Appendix A: Tests of the GALFIT results To assess the robustness of the presented galaxy profle ft-ting procedure we performed simulations similar to those presented in the literature (Häussler et al. 2007; Longhetti et al. 2007;Guo et al. 2009;Pannella et al. 2009;Mosleh et al. 2013). To estimate the accuracyof the results obtained from GALFIT, we appliedexactly the same ftting procedure as that used for the real objects to a set of approximately 4000 (i.e. ∼10% of a real sample) artifcialgalaxies. Simulated objects were generated using the Sérsic parameters from the GALFIT output of the randomly selected VIPERS galaxies, with reduced χDoF2 value smaller than 1.2. This way gives more realistic parameter distributions of thegalaxy pop-ulation than randomly generated parameters and allows us to compare both results for each single object. GALFIT was used to create the artifcialgalaxies. Each simulated profle was added to a diﬀerent background image.To construct the background we applieda method similarto that proposedby Longhettietal. (2007).The background image has been obtained by mosaicing diﬀerent portions of the object-free regions of the CFHTLS tile into one large image. Then, the generated profle of each galaxy was superimposed on the randomly selected region of the background. The advantage of this method is that the background retains the same noise Table A.1. Median fractional deviation of the half-light radius re, Sér-sic index n, apparent magnitude m axis ratio b/a with the ±34% uncertainties about the median and in three magnitude bins from 19.5 to 22.5 mag. Parameter Magnitude bin [mag] 19.5–21.8 21.8–22.2 22.2–22.5 −0.02+0.01 −0.02+0.02 −0.01+0.06 Δre/re −0.03 −0.02 −0.06 Δn/n −0.01+0.03 −0.01+0.06 −0.02+0.08 −0.03 −0.06 −0.09 Δmag 0.01+0.01 0.01+0.01 +0.01+0.01 −0.01 −0.01 −0.01 Δ(b/a) 0.00+0.01 −0.01+0.02 −0.02+0.03 (b/a) −0.01 −0.02 −0.03 Notes. Thegalaxy numberineachbinisequalto781. characteristic as the real CCD image. Finally thegalaxy profle was convolved with the PSF of the i-band image generated at the galaxy position. Simulated imagesofgalaxies preparedin thisway were analysed by SExtractor and GALFIT using the same procedure as that used for the real objects. The results of our tests are presented in Fig. A.1. The top plot of each panel shows the relation
ship between the input and output parametervalues, whereas the bottom one presents the estimated uncertainty of the Sérsic profle parameters, that is, the half-light radius re in pixels, Sérsic index n, axis ratio b/a and apparent magnitude m. The red lines in the bottom fgures show the median and the blue lines indicate the1σ scatter around the median, defned as that which encloses 68% of the points. The results of the tests presented in Fig. A.1 andTable A.1 demonstrate that the Sérsic function parameters are well re-covered: the fractional derivative scatter around the median of galaxy apparent magnitude m is very small and only slightly increases for the less luminous galaxies. Similar results from GIM2D and GALFIT were obtainedby Pannellaetal. (2009). Simulations show that the error of the recovered value of the half-light radius reis larger for smallergalaxies.However,even in this case, the diﬀerence between input and output parameters presented in Fig. A.1 is less than 10%. The small systematic diﬀerences between thosevalueswas also reportedin other studies(Häussler et al. 2007;Longhetti et al. 2007;Guo et al. 2009). Moreover, we found that the axis ratio b/a of thegalaxy light A120, page 17 of 21 profle is robust. The uncertainty of this parameter is in the order of a few percent. The analysis shows that the Sérsic index n is also well re-covered. However, in this case we observe a larger fractional de-viation scatter around the median than for the two previously mentioned parameters. Figure A.1 shows that the fractional de-viation of the Sérsic index n is almost uniformly distributedover the n. Similar scatter of the reconstructed parameters is also reported in other studies(Häussler et al. 2007; Longhetti et al. 2007;Guo et al. 2009). The test shows that the error of the half-light radius re is larger for smallergalaxies and decreases with the object’s size. This eﬀect is strongly correlated with the FWHM size of the PSF: for small re values, comparable with the FWHM, the image deconvolution becomes less accurate (e.g. Trujillo et al. 2001a). The carried out simulations show good agreement between the input and output Sérsic function parameters. The1σ deviationofvalues(i.e. containing68%ofpoints)aboutthe parameter median is narrow, and, for the majority of the tested objects, the error of recovered parameters is less than 10%. In the study of the distant galaxies, the typical size of a galaxy registered on the CCD images is small and can infuence their estimated light profle parameters.We alsoverifed the ac-curacyof the Sérsic index n and half-light radius re asa function of the apparent magnitude. The results are shown in Fig. A.2. Asexpected, this fgure shows thatfaintgalaxiesexhibit larger random uncertainties in their Sérsic index Δn/ninp and half-light radius Δre/re,inp. Figure A.2 shows that, in both cases, the error of recovered parametersis smallerforthe brightergalaxiesand,asexpected, systematically increases forfaint objects.Forfaintgalaxies, the external partof the objects canfall under theskysurface brightness and this eﬀect can lead to increases in the value of Sérsic index n. The test shows no systematic bias. The distribution of errors in the whole analysed luminosity range is symmetric. The last test we present shows the fractional diﬀerence of the Sérsic index asa functionof redshift and luminosity.Todo thiswe appliedthe same binningaswas usedin our analysisand presented in Figs. 3,5 and7, to estimate the reliability of our study. The simulated, approximately 4000 objects were generated using the Sérsic parameters from the GALFIT output as de-scribed in the frst test. Galaxies were then divided into redshiftluminosity samples to compute the mean and standard deviation of the distributions of the fractional diﬀerence Δn/ninp. Figure A.3 presents the results and shows histograms and medianvalue with the ±34% scatter around the median. The his-tograms show that the accuracyof the Sérsic index n estimation decreases with redshiftbut increases with luminosity. The most accurate value of n we get is for the nearby and most luminous galaxies.Asexpected,faintgalaxiesexhibit larger random uncertainties in their Sérsic index n parameter, consistent with the A120, page 18 of 21 J. Krywult et al.: VIPERS: evolution of shape and colour bimodalities previous test. The histograms and numerical values presented in Fig. A.3 show no systematic deviation of the Sérsic index ftted to thegalaxy images. The tests presented here show that Sérsic function parameters computedby GALFIT from CFHTLS CCD imagesof the VIPERSgalaxies are robust. Appendix B: Modelling of the PSF The CFHTLS images were obtained with MegaCam at the prime-focus with wide-feld corrector (Boulade et al. 2000). However, while the corrector is optimised to produce a uniformly high-quality image over the whole feld of view, it also introduces large-scale non-linear geometrical distortions(Cuillandreetal. 1996). Thiseﬀect, together with the seeing, signifcantly disturbs the isotropyof the PSF and has to be corrected before any further measurements are done from the images. There are many methods of PSF construction. The atmospheric turbulent structureis well characterisedbyKolmogorov statistics(Kolmogorov 1961;Goodman 1985).To reproduce the observed PSF, an additional distortion coming from the telescope optics needs to be modeled, by the sum of Gaussians or Gaussian-like functions, forexample (e.g. Schechter et al. 1993; Hogg&Lang 2013), the Moﬀat(1969)function, their combi-nation or the Gauss-Laguerre function as applied by Bertin in PSFEx from astromatic package2. It is expected that the high image resolution(FWHM < 0.100)of space telescopes, free from the atmosphere infuence, should allow for better modelling of the optics aberrations than ground-based ones. In this case the more precise PSF estimation, given by PSFEx, for example, is needed. In this study we used the Moﬀat function(Moﬀat 1969). It allows us to precisely reconstruct the anisotropyof the CFHT feld of view as shown in the tests presented at the end of this section. The elliptical PSF for the CFHTLS images has been ap-proximated by the Moﬀat(1969)function 2!−β r I(r)= I01+ , (B.1) α where I0 is the central luminosity, β is the profle shape parame-ter and α is the half-light radius of the profle. To construct a proper PSF for the VIPERSgalaxies across the whole 1◦× 1◦ CCD feld we carefully selected stars from each CFHTLS tile. The stars were taken from the stellar branch of the SExtractor(Bertin&Arnouts 1996)MAG_AUTOversus FWHM_IMAGE diagram within the apparent magnitude range from 18 to 22 mag. Figure B.1 presents two examples of this diagram computed from images with good and bad quality. In the frst plot, the vertical region dominated by the point-like ob-jects is sharp, whereas in the second one it is signifcantly wider. To remove small and distorted stars, the objects with SExtractor ISOAREA_IMAGE ≤ 10 pixels and ELLIPTICITY > 0.2 were rejected from the analysis.Visual inspectionof the CCD images confrmed that these criteria very accurately select isolated and non-distorted point-like objects. The average number of stars used for the approximation of the Moﬀat parameters, and uniformly distributed in each 1◦× 1◦ CFHTLS tile, is approximately 2000 and varies from feld to feld (between ∼1000 and ∼3500). However, the applied method might be somewhat restrictive. Because of the image distortion presented in some CFHTLS tiles, there are regions where no PSF stars were selected by this http://www.astromatic.net/software/psfex
algorithm, as shown in the top-left plot in Fig. B.2. This occurs mainly in the regions close to the tile border, covering approximately 2% of the total VIPERS area. Since the quality of the PSF plays such an important role in the GALFIT image deconvolution, weexcludedgalaxies from these regions from the presented analysis. From the theoretical point of view,the shape of the PSF plays an important role in the inverse problem of image reconstruction, that is, estimation of the Sérsic function parameters (e.g. Trujillo et al. 2001a). At frst, the FWHM of the modeled PSF should correctly refect the light distribution in point-like ob-jects. Due to optics aberrations, obstruction and mechanical problems the real PSF has wings which also need to be correctly modelled. However, when the PSF is regular, it has small wings and the FWHM of the PSF is correctly estimated, the requirement of the high quality PSF model is not crucial to obtain reasonably recovered galaxy structural parameters (e.g. Davari et al. 2014;Trujillo et al. 2001a). In the following step, the Moﬀat function was ftted to the images of stars extracted from the CFHTLS tiles in the form of the postage stamps of size 35×35 pixels each, which is more than ten times larger than the FWHM. Then, for each CFHTLS tile of size of1◦× 1◦, the ftted parameters of the Moﬀat function were approximated by the two-dimensional Chebyshev polynomial. The Chebyshev approximation was used due to its numerical stability and the smallest maximum deviation from the approximated function(Dahlquist&Bjorck 1974).We have checked polynomialsofdegreesfrom5to11andfoundthata polynominaldegreeof7best approximatestheMoﬀat function parameters across the CFHTLS tile. In this way, we obtained an analytical form of howeach of the Moﬀat function parametersvaries across the whole feld, which allowed us to compute the PSF at the po-sitionofeverygalaxyin the tile. In the following two steps we verify the computed PSF ap-proximation. We exclude stellar-like sources which show too much diﬀerence between the data and the model, and repeat the Moﬀat function ftting to the remaining stars, as shown above. Finally,we getthe best description of the Moﬀat function in each CFHTLS tile point. The frst verifcation of our PSF modelling was performed using the whisker plot(VanWaerbekeetal. 2000;Tewesetal. 2012). This diagram demonstrates how the ellipticity e and the orientation θ of PSF stars vary across the feld. Each selected star is represented by a line whose length represents the star el-lipticity e, and is orientated to match the position angle of the star’s major axis. The colour of each line represents the i-band A120, page 19 of 21 A120, page 20 of 21 J. Krywult et al.: VIPERS: evolution of shape and colour bimodalities magnitude of the star. The frst plot in the top row of Fig. B.2 shows a strong anisotropy of observed stars which should be corrected for. To do this, we applied the complex ellipticities (Tewes et al. 2012)defned by − 1 e = exp(i2θ)= |e| (cos(2θ)+ i sin(2θ))= e1 + i · e2, (B.2) + 1 where the elongation is defned as = b/a. This representation is commonly used in anisotropy determination in gravitational lensing analysis(Holhjem et al. 2009;VanWaerbeke et al. 2000). We performeda3σ clipping procedure on the corrected stel-lar complex ellipticities e1 and e2(Tewes et al. 2012), which re-moved most of the stars whose shape was deformed. After this procedure, for each tile, the parameters of the Moﬀat function were approximated again by the two-dimensional Chebyshev polynomial degree of 7. This iteration leads us to the fnal ana-lytical approximation of the PSF coeﬃcients used to reconstruct thePSFatthe positionofeach VIPERSgalaxy. As an example of the method described above, Fig. B.2 presents the selected plots obtained from the fnal Moﬀat function parameters for the lower quality CFHTLS_022539-041200 tile in i-band. The diagrams in the second row of the fgure were obtained from our global PSF approximation. The plots presented in the frst and second rows show very good correlations between the observed and approximated results. The last row in Fig. B.2 shows the PSFs of stars after the correction for anisotropy. One can observe that the feld corrected for telescope anisotropyis almost uniform, which confrms the high quality of our PSF approximation. Even for a tile with an image distortion as high as the one presented in this example, our method accurately maps the variation of the PSF across the whole feld of view. The tests presented above demonstrate that the anisotropyof images produced by wide-feld cameras on modern telescopes can be large. Strong distortions introduced by the optics significantly change the ellipticity and orientation of the PSF. In the example presented in Fig. B.2 the PSF ellipticity varies from a value near 0 up to e ≈ 0.3 and there is a large range of PSF positional angle. When the FWHM size of the PSF is significantly smaller than the galaxy size, we can obtain accurately recoveredgalaxy morphological parameters (e.g. Davari et al. 2014;Trujillo et al. 2001a). However, if the FWHM andgalaxy are comparable in size, the recovered parameters are biased due to the wrong PSF shape. Thus precise PSF modelling plays a vital role in the successful galaxy image decomposition by GALFIT. A120, page 21 of 21