The VIMOS Public Extragalactic Redshift Survey (VIPERS):Thanks: 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-Hawaii Telescope (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 Scientifique (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://www.vipers.inaf.it/.

The optical photometric catalogue is based on $u^{*}g^{\prime}r^{\prime}i^{\prime}z^{\prime}$ data from the T0005 release of the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS)²² 2 CFHTLS web site: http://www.cfht.hawaii.edu/Science/CFHTLS/. The data were collected with the 3.6m CFH optical/infrared telescope on the Mauna Kea summit. The four independent contiguous Wide (CFHTLS-W) patches cover between 25 to 72 deg² resulting in a total area of $\sim$155 deg², of which VIPERS targets two CFHTLS-W fields, W1 and W4. The final CFHTLS-W photometric catalog reaches in the optical filter bands 80% completeness limit in AB for point sources of $u^{*}$$=$$25.2$, $g^{\prime}$$=$$25.5$, $r^{\prime}$$=$$25.0$, $i^{\prime}$$=$$24.8$, $z^{\prime}$$=$$23.9$ (Mellier et al., 2008; Goranova et al., 2009). For all bands, total apparent magnitudes were measured in Sextractor using mag_auto in Kron-like (Kron, 1980) elliptical apertures as measured from the $i^{\prime}$-band image with a minimum Kron radius of 1.2 arcsec (equal in all other bands). Apparent magnitudes were corrected for Galactic extinction using the COBE dust maps by (Schlegel et al., 1998), with a median extinction of $E(B-V)$$\sim$0.025 mag in W1 and $\sim$0.05 mag in W4. For VIPERS objects with $i^{\prime}_{AB}$$<$$22.5$ at $0$$<$$z$$<$$1.0$, the CFHTLS T0005 photometric redshifts have a 1-$\sigma$ uncertainty of $\sigma_{z}/(1+z)=0.045$, whereas in the redshift range $1.0$$<$$z$$<$$1.5$ the uncertainty is $\sigma_{z}/(1+z)\sim 0.090$ (Coupon et al., 2009; Scodeggio et al., 2011). For galaxies at $0.4$$<$$z$$<$$1.3$, typical errors in the observed $u^{*}g^{\prime}r^{\prime}i^{\prime}z^{\prime}$ CFHTLS photometry that include all measurement uncertainties (e.g., zero-point and absolute photometric calibration, tile-to-tile offset, etc) are of the order $\langle\sigma_{u^{*}g^{\prime}r^{\prime}i^{\prime}z^{\prime}}\rangle=0.038\pm 0.029$. There is a multitude of ancillary data available for the two VIPERS fields which will be explored in a series of future papers. In the following, we limit the discussion to the relevant photometric data used for the present analysis. Both W1 and W4 are covered at NIR wavelengths by various photometric surveys. A dedicated WIRcam $K_{s}$ follow-up survey of the VIPERS fields (Arnouts et al. 2014, in preparation) was conducted for $\sim$80% of the area in W1 and $\sim$96% in W4 with a 5$\sigma$ completeness level for point sources of $K_{s}$$\sim$$22.0$ mag (AB). In W1 and W4 23,759 and 27,371 VIPERS objects have a $K_{s}$ counterpart, respectively. Further, 4,591 objects ($\sim$15%) in W4 that have no WIRCAM $K_{s}$-band photometry are covered by UKIDSS-DR9 or, when available, UKIDSS-UDS-DR8 $YJHK$ data. For 1004 and 1500 spectroscopic sources in W1 and W4, respectively no $K$-band data is available. However, only 801 out of these 2504 VIPERS galaxies without $K$-band photometry and $2\leq z_{\rm flg}\leq 9.5$ are located at $0.5$$<$$z$$<$$1.2$. Based on consistency tests with respect to uncertainties originating from the photometric calibration (e.g., zero-point variations or sky-subtraction errors), we conclude that the $K_{\rm WIRCAM}$ photometry is more reliable than the $K_{\rm UKIDSS}$ data (e.g., Davidzon et al., 2013, hereafter D13). Thus, when both $K$-band data are available, we decided to keep the former and neglect the latter.

Through a collaborative effort, we have supplemented our multi-wavelength photometry with deep GALEX observations in the FUV (1350-1750Å) and NUV (1750-2800Å) (Arnouts et al. 2014, in preparation). A total of $T_{\rm exp}>30$ ksec/field yields a 90 % completeness level of extended sources at $24.50$ mag (AB) in both FUV and NUV bands. Overall, 18,838 sources ($\sim$63%) in W1 and 3,688 ($\sim$13%) objects in W4 have a NUV counterpart. In W1 and W4 there are 4,528 galaxies ($\sim$15%) and 1,552 objects ($\sim$5%) with an associated FUV flux, respectively.

The VIMOS Public Extragalactic Redshift Survey (VIPERS)³³ 3 VIPERS web site: http://www.vipers.inaf.it, is an ongoing ESO Large Programme designed to measure in detail the spatial distribution, clustering, and other statistical properties of the large-scale distribution of $\sim$$10^{5}$ galaxies across all galaxy types down to $i^{\prime}_{AB}$$<$$22.5$. In addition, this survey also measures the physical parameters of galaxies, like stellar mass or star formation activity, over an unprecedented volume of $5\times 10^{7}$ h^-3 Mpc³ at $0.5$$<$$z$$<$$1.2$ (Guzzo et al., 2013a; Guzzo et al., 2013b). The VIPERS sample selection is based on accurate optical 5-band CFHTLS photometry, combined with a simple and robust pre-selection in the $(g^{\prime}-r^{\prime})$ vs $(r^{\prime}-i^{\prime})$ colour-colour plane to efficiently remove galaxies with $z$$<$$0.5$ (Guzzo et al., 2013a). Spectroscopic observations have been collected with the VIsible MultiObject Spectrograph (VIMOS; (Le Fèvre et al., 2000; Le Fèvre et al., 2002) at the ESO Very-Large-Telescope (VLT) in multi-object-spectroscopy (MOS) mode using the low-resolution red (LR-Red) grism ($\lambda_{\rm blaze}=5810\penalty\ \AA$) at moderate resolution ($R=210$, 1^′′ slit). This gives a wavelength coverage of $5500$$<$$\lambda_{\rm eff}$$<$$9500$ Å with internal dispersion of 7.15 $\rm{\AA}$ pix^-1 (Scodeggio et al., 2005). The combination of our target selection with an efficient, and aggressive observing strategy using shorter slits (Scodeggio et al., 2009), that doubles the multiplexing of VIMOS MOS mode while at the same time keeping the problematic effects of fringing patterns ($\lambda_{{\rm obs}}$$\ga$$8100$ Å) under control, allows us to double the galaxy sampling rate in the redshift range of interest ($\sim$40%) when compared to the sampling of a purely magnitude-limited sample.

The data set used in the present study is based on the VIPERS PDR-1, which was made public in Fall 2013 (Garilli et al., 2013). The survey description, together with its motivation, the sample selection and the spectroscopic observations are presented in Guzzo et al. (2013a). The VIPERS data reduction pipeline (Easylife), the survey database system and its tools are described in (Garilli et al., 2012). There are several complementary scientific investigations using the VIPERS PDR-1 (Bel et al., 2013; de la Torre et al., 2013; Malek et al., 2013; Marulli et al., 2013, D13,). Previous works include a CFHTLS power spectrum analysis (Granett et al., 2012) and a principal component analysis of VIPERS spectra (Marchetti et al., 2013).

The VIPERS PDR-1 contains all spectroscopic observations in the VIPERS database until the end of the 2011/2012 observing campaign and covers an effective area of $\sim$10.32 deg² which is 61.3% of the planned total area ($\sim$24 deg²). For 55,358 objects (93.8% of total, excluding non-extracted spectra), the automatic redshift measurement software tool EZ (Garilli et al., 2010) was able to derive an estimate of the spectroscopic redshift. All automatic measurements were validated (or corrected, if necessary) via visual inspection by two VIPERS Team members independently, who also assigned a quality flag $z_{\rm flg}$ (i.e., a confidence level) to the final redshift measurement. In total, 53,608 galaxy redshifts have been measured. Finally, a comparison between the spectroscopic and the photometric redshift measurements was carried out, storing the result in the quality flag decimal value. The spectroscopic redshift measurement accuracy, reliability and flag classification system have been extensively tested and verified through repeated observations of 1215 galaxies (Scodeggio et al., 2011; Garilli et al., 2010; Guzzo et al., 2013a).

All spectrophotometric rest-frame properties of the VIPERS galaxies were derived using the SED fitting program Hyperzmass, an updated version of the photometric redshift code Hyperz (Bolzonella et al., 2000; Bolzonella et al., 2010). For the spectroscopic PDR-1 catalogue, the dust content of the galaxies was modelled with both the Prevot-Bouchet extinction law, that is based on the Small Magellanic Cloud dust properties (Prevot et al., 1984; Bouchet et al., 1985), and an extinction relation calibrated using starburst galaxies (Calzetti et al., 2000). The choice between the two extinction relations was performed on the basis of the smallest derived $\chi^{2}$ value. The final extinction magnitudes range between $A_{V}=0$ (no dust attenuation) to $A_{V}=3$ (strong dust attenuation).

Absolute luminosities were derived using the apparent magnitude that most closely resembles the observed photometric passband, shifted to the redshift of the galaxy under consideration. Thanks to our extensive multi-wavelength photometry (from $FUV$ to MIR wavelengths), the $k$-correction factor was as small as possible and much less sensitive to the adopted SED template type than using a global filter transformation that is confined to a single specific filter passband (Ilbert et al., 2005, see appendix A of). The following analysis is restricted to rest-frame Johnson $U$, $B$, and $V$ bands as they are covered across the whole optical to NIR observed filters over the redshift range of our main interest. Typical uncertainties in the SED fitting process that include measurement uncertainties in the zero-point, SED extrapolation, and adopted template libraries, range, for example, in the $B$-band from $\sigma_{B}=0.04$ ($0.4$$<$$z$$<$$0.7$) to $\sigma_{B}=0.05$ ($0.7$$<$$z$$<$$0.9$) and $\sigma_{B}=0.07$ ($0.9$$<$$z$$<$$1.1$) to $\sigma_{B}=0.14$ ($1.1$$<$$z$$<$$1.3$). These uncertainties are included in the final error budget and are used in the derivation of the intrinsic scatter of the CMR (see Section 5.3). In this work, we focus on exploring the differences between the two main populations of passive and star forming galaxies using the rest-frame $(U-V)$ colours. For the $U$-band we adopt the original $U_{J}$-Johnson filter (Johnson & Morgan, 1953); hereafter $U$-band), which is particularly sensitive at blue wavelengths and allows a precise distinction between red and blue galaxies. One advantage is that the $U$-band filter response traces the 4000 Å break and therefore the $U$-band is a good proxy for the stellar population age of galaxies (Bruzual, 1983; Kauffmann et al., 2003). In Appendix A we discuss our filter choice and provide a comparison to other $U$-band filters used in the literature.

Spectrophotometric galaxy types were derived by fitting the magnitudes with a small set of spectral templates as described in (Ilbert et al., 2006). In particular, the six reference templates consist of four locally observed spectral-energy-distributions (hereafter SEDs) (Coleman et al., 1980) and two starburst SEDs from Kinney et al. (1996). All templates were first individually extrapolated to UV and MIR wavelengths, then pairs of templates were interpolated to create a final set of 62 synthetic SEDs, and finally those were optimized with Le Phare (Arnouts et al., 1999; Ilbert et al., 2006). As our templates are constructed from real observed galaxies rather than synthetically generated templates, they already contain the typical amount of dust present for that given spectral galaxy class. The whole spectroscopic sample is then classified into four galaxy types, corresponding to early-type spheroids and spiral bulge-dominated galaxies (elliptical, lenticular and S0/Sa, hereafter E/S0), early-type spiral galaxies (hereafter Sa/Sb), late-type spiral galaxies (hereafter Sc/Sd), and starburst and irregular galaxies (hereafter SB/Irr).

Figure 1 shows the luminosity-redshift relation of VIPERS. Galaxies are divided into their respective SED type classes. Because the flux intensity decreases with the square of the luminosity distance ($S=L/4\pi\,D_{\rm L}^{2}$), with increasing redshift any galaxy sample will be incomplete at faint luminosities. The solid line denotes the selection boundaries for a sample completeness of 90%, which was derived as in Marulli et al. (2013).

In our subsequent analysis, the SED type classification serves as primary reference against which the completeness and contamination levels of each independent selection criteria of early-type galaxies are compared to. The pros are that for the SED type assessment the complete optical to NIR multi-wavelength information can be applied. The broader wavelength coverage reduces the number of possible contaminations from special objects for any given galaxy type. Our concept of using the SED type classification as a reference for selecting early-type galaxies gets independent support from a recent zCOSMOS study (Moresco et al., 2013).

The sample used for the present work is composed of 44,982 galaxies ($N_{\rm W1}=23,210$ and $N_{\rm W4}=21,772$) with $2\leq z_{\rm flg}\leq 9.5$ (corresponding to a confidence level $>$95% in the redshift measurement) covering the redshift range between $0.40<z<1.3$ and look-back times of $\sim$4.2–8.7 Gyr. An additional 763 objects with $z<0.4$ and 244 galaxies with $z>1.3$ exist with the same quality flags, but have been excluded due to sample incompleteness. The redshift distribution of these data is presented in Figure 2. The mean redshift is $\overline{z}=0.715$ (indicated with a dashed line), and the median is $\langle z\rangle=0.694$. Figure 2 also shows the redshift distribution of the different galaxy SED types. Using repeated observations of 1215 galaxies with $z_{\rm flg}\in{2,3,4}$ (excluding stars and AGNs), the typical (root-mean-square) uncertainty in the spectroscopic redshift measurements is $\delta_{z}/(1+z)=0.00047$, which corresponds to a radial velocity accuracy (1-$\sigma$ scatter) for individual VIPERS measurements of $\delta_{v}=141(1+z)$ km sec^-1.

In order to draw robust conclusions from the observed distribution of physical parameters in the VIPERS galaxy sample, we have to consider the influence of possible systematic effects which might enter our spectroscopic sample. In particular, a potential bias may arise if galaxies with extreme (e.g., colour) properties are under- or over-represented in the final spectroscopic sample. Such systematics could be either due to incompleteness in colours of the parent photometric sample, or a variable redshift measurement success rate.

One popular approach to distinguish the red and blue galaxy population is to use a fixed cut in galaxy colours, not-evolving with redshift (Bell et al., 2004b; Franzetti et al., 2007, e.g.,). When using this method, many works adopted the slope in the CMR as defined by elliptical galaxies in the Coma cluster, which is well-known and where selection effects are under control. There are two main motivations for using this criterion: (i) straightforward comparison to previous works in the literature, (ii) limiting possible uncertainties due to zero-point variations in the photometry that arise from the transformation of observed magnitudes to the rest-frame at different redshifts.

Here we follow the prescription outlined by Bell et al. (2004b), which we refer to as the “classical approach”. Galaxies that have rest-frame colours $(U-V)>1$, regardless of their morphological or SED type, are considered as part of the RS. The evolution of the RS is derived by fitting a linear relation between colour and absolute magnitude, keeping the slope of the relation fixed to the Coma cluster value at all redshifts. As redshift progresses the assumption of a non-evolving selection cut with redshift becomes problematic as the number density of early-type galaxies with intermediate mass ($10.8<\log(M_{\star}/M_{\odot})<11.1$) decreases by a factor of $\sim 2.5$ and that of high mass galaxies ($\log(M_{\star}/M_{\odot})\geq 11.4$) by 45% from $z=0.6$ to $z=1.2$ (D13). Therefore, the classical approach will select only the reddest and most luminous (hence also most massive) early-type galaxies, which are not representative of the whole early-type galaxy population. These massive early-type galaxies have formed the bulk of their stars at high redshift ($z>2$) and will therefore comprise quiescent evolved stellar populations. However, any selection method using optical colours only, will contain a non-negligible contribution of dusty red galaxies (Strateva et al., 2001; Cimatti et al., 2002; Gavazzi et al., 2003; Bell et al., 2004a; Weiner et al., 2005). To disentangle the contamination of the early-type galaxy samples due to such effects, we will later on use a combination of GALEX $NUV$ and NIR colours (Section 4.3).

The most evident aspect of the distribution of galaxy colours is of course the colour bimodality. In the VIPERS data, as in local surveys, this is a very general feature that is evidenced when using different rest-frame $UBVRI$ colour combinations, spectral diagnostics such as the 4000 Å break (Garilli et al., 2013) or morphological quantities (Krywult et al. 2014, in preparation). In this work we use the $(U-V)$ colour, as it is highly sensitive to the slope of the blue/ultraviolet continuum, representing a natural tracer for SF galaxies (see Appendix A). In particular, our $U$-band filter represents a good measure of the overall SF activity in our galaxies. However, similar to the classical method the colour bimodality does not take into account the contamination by AGNs or dust-obscured red galaxies (see Section 4.3).

Red galaxy samples selected on the basis of optical colours contain a substantial contamination of $\sim$30-40% by Seyfert 2 AGNs and/or dust obscured SF galaxies (Strateva et al., 2001; Cimatti et al., 2002; Gavazzi et al., 2003; Bell et al., 2004a; Giallongo et al., 2005; Weiner et al., 2005; Franzetti et al., 2007; Haines et al., 2008; Gallazzi et al., 2009). Dust obscuration is less significant at low redshift, where $\sim$75% of red galaxies contain little amount of dust (Gavazzi et al., 2003; Bell et al., 2004a; Wolf et al., 2005) and for the remaining objects current space-based facilities permit a visual detection of the dust features up to $z$$\sim$$1$ (McIntosh et al., 2005b; Fritz et al., 2009a; Fritz et al., 2009b; Tasca et al., 2009, e.g.,).

However, at high redshift ($z>1$) the presence of dust becomes a major complication, with red galaxy samples getting significantly contaminated by dusty SF galaxies. This affects both the colour measurements and the assessment of intrinsic colour variations in the galaxies. Several alternative methods have been proposed to identify systems with colours dominated by internal dust absorption, such as mid-IR photometry (Papovich et al., 2005), an optical-NIR rest-frame colour combination, e.g., $UVJ$ selection (Williams et al., 2009), or visual dust extinction constraints from SED modelling (Brammer et al., 2009; Brammer et al., 2011) or a using a $UV$-optical-NIR colour combination (Salim et al., 2005; Arnouts et al., 2007, e.g.,).

To explore the effects of possible dust obscuration within our early-type sample, we introduce a combination of GALEX $UV$, optical and $NIR$ fluxes. In Figure 7 we illustrate our selection of passive red galaxies in the rest-frame $(NUV-r^{\prime})\,vs\,(r^{\prime}-K)$ plane (Arnouts et al., 2013). A similar classification into quiescent and SF galaxies with different star formation activity level can be obtained using $(NUV-r^{\prime})\,vs\,(r^{\prime}-J)$ colours (Ilbert et al., 2010), although our addition of the $K$-band permits a much sharper separation between quiescent and galaxies with low SF activity, particularly for dust-obscured red objects at $z>0.8$ with $(r^{\prime}-J)>0.8$ (AB). Further, $NUV-r^{\prime}$ colours represent an excellent indicator for the current-to-past star formation ratio. This ratio decreases with mass for star forming galaxies (Salim et al., 2005; Arnouts et al., 2007). While the $NUV$ passband traces stellar populations with a mean light-weighted age $\langle t\rangle\sim 10^{8}$ yr, the $r^{\prime}$ band is sensitive to $\langle t\rangle\geq 10^{8}$ yr (Martin et al., 2005) and the current to the past averaged SF rates correlates with the birth parameter $b$ as $b=\mathrm{SFR}(t<10^{8})/\langle\mathrm{SFR}\rangle$. Passive galaxies with de Vaucouleurs light profiles can be associated with $NUV-r^{\prime}\geq 1.70$ (Vega) and $b\leq 0.1$ (Salim et al., 2005). We then define early-type galaxies (hereafter $NUVr^{\prime}$ selection) as all the galaxies which are redder than

which is indicated as the solid line in Figure 7.

This cut is approximately equivalent to a cut at a constant star formation rate in the total galaxy sample (Williams et al., 2009, see e.g.,) the black $<\mathrm{sSFR}>$ arrow in the figure denotes the direction of increasing sSFR), and it is therefore quite effective at selecting galaxies with early-type SEDs. This method represents an alternative approach to the one suggested by Arnouts et al. (2007) and is a similarly powerful tool to identify dusty galaxies among the early-type galaxy population.

In the following analysis, we adopt the SED type classification as our reference selection method (see Section 2.4). For each of the other selection criteria we derive their completeness in early-type galaxies (i.e., the fraction of the SED early-type galaxies which are classified as early-type galaxies with that particular selection criterion) and the contamination due to late-type galaxies (i.e., the fraction of galaxies classified as early-type with that particular selection criterion which are instead classified as late-type galaxies on the basis of the SED type classification). Figure 8 illustrates the early-type completeness and late-type contamination as a function of redshift for each selection criterion. Different lines give the completeness of red galaxies and contamination of non-red galaxies for the various selection methods, classical approach (dotted line and filled circles), colour-bimodality (solid line and blue triangles), $NUVr^{\prime}$ selection (dashed line and open circles).

Our colour-bimodality selection of early-types proves to be highly efficient ($\sim$85%), even up to the highest redshifts. Moreover, the contamination by late-types is $<$10% up to $z=0.8$ and reaches $\sim$30% in the highest redshift bins. The classical approach produces a smaller contamination ($\sim$5-20%), however at the costly price of a much smaller completeness ($<$80% at $z>0.7$). In the highest redshift bin ($z>1$) its completeness is only $\sim$45%. In terms of completeness in early-types at high redshift, the $NUV-r^{\prime}$ selection is better than the classical approach, whereas at the same time keeping the contamination from late-type galaxies at a low level ($\leq$20% up to $z=1.1$). For the highest redshift bin, the contamination is larger and similar to that of the colour bimodality approach. Across all redshifts, the fraction of early-types in the $NUV-r^{\prime}$ method remains quite stable at $\sim$80-85%, even up to $z=1.3$. The colour bimodality criterion has an almost constant completeness in early-type galaxies of $\sim$90% up to $z=1$, but it contains a slightly higher late-type contamination of $\sim$5-10% than the $NUV-r^{\prime}$ sample.

For galaxies undergoing a pure passive evolution of their stellar populations it is quite simple to predict their photometric evolution in terms of luminosity and rest-frame colours. By comparing these predictions with the observed evolution of galaxies on the RS, it is therefore possible to place some constraints on the evolutionary path of the RS objects. One method often adopted to quantify the evolution in the observed properties of these galaxies is to consider the change in the best fitting linear relation between luminosity and rest-frame colour, i.e. the evolution of the average colour of the RS objects at a fixed absolute magnitude (Bell et al., 2004b; Weiner et al., 2005; Franzetti et al., 2007, e.g.,). The apparent simplicity of this analysis is however hiding important sources of uncertainty in the interpretation of the observed evolution. The most important one is of course the operational definition of the RS galaxies, as discussed in the previous sections, which in turn results into an uncertainty on the contaminating fraction of star-forming galaxies. We also need to consider differences in the magnitudes used to derive the observed and the rest-frame colours (aperture magnitudes versus pseudo-total ones), and also the priors used to constrain the fit. Finally, many data sets at high redshift suffer from low sample statistics that do not allow for a reliable determination of the slope of the RS relation, and therefore the fit is carried out using a fixed slope at all redshifts.

This approach was adopted in the case of the COMBO-17 photometric galaxy survey by Bell et al. (2004b), who established the following evolution of the RS relation:

where $h=0.7$, assuming a fixed slope of $d(U_{J}-V_{J})_{\rm RS}/d(M_{V})=-0.08$, as derived for elliptical galaxies in the local Coma cluster (BLE92). Another variation of this definition is a fixed (non-evolving) parallel cut on the blue part of the CMR that globally separates passive red (non-SF) galaxies from blue SF galaxies (Wolf et al., 2009; Ruhland et al., 2009; Brammer et al., 2009; Whitaker et al., 2010, e.g.,).

Local E+S0 galaxies in field and group environments display both a similar slope ($d(U_{J}-V_{J})_{\rm RS}/d(M_{V})=-0.05$) and scatter ($\delta(U_{J}-V_{J})=0.06$ mag (Schweizer & Seitzer, 1992) across the CMR as their counterparts in clusters. However, it is still unclear if the assumption of a fixed slope holds also for field galaxies at higher redshift.

If we adopt the same methodology to fit the RS sample selected using the classical approach described in section 4.1, we obtain a fit to the RS which is illustrated by the dotted red lines shown in the panels of Figure 4. It is evident that this best-fitting relation with a fixed Coma cluster slope is somewhat too steep for the VIPERS data. We should consider that our colours are based on the CFHTLS mag_auto magnitudes that were measured in Kron-like elliptical apertures (see Section 2.1), and which are an approximation for total magnitudes⁴⁴ 4 Bertin & Arnouts (1996) suggest that Kron-like aperture measurements miss a somewhat uniform $\sim$6% of the total flux for galaxies., while those used by BLE92 were based on fixed-aperture photometry. A difference in slope is therefore somewhat to be expected, as demonstrated by Scodeggio (2001): a CMR constructed using colour measurements within fixed apertures is steeper than a CMR based on colours established with apertures covering the effective radius of the galaxy (or pseudo-total magnitudes, for that matter).

Since the combination of large size and accurate photometry of VIPERS allows us to derive with high precision the slope and scatter of the RS as a function of redshift, we decided to explore the different results one would obtain with and without the fixed-slope constraint on the fitting of the RS. Figure 9 illustrates the CMR for VIPERS for two redshift slices at $0.5<z\leq 0.7$ and $0.7<z\leq 0.9$. When we define RS galaxies using the bimodality in colour distribution, as described in Section 4.2.1 (the partitioning colour is identified in Figure 9 by the dotted line), we obtain the following RS best-fitting relations at redshift $\langle z\rangle=0.55$:

and at redshift $\langle z\rangle=0.80$:

For consistency with the classical method, we fitted a free variable slope to the whole redshift interval at $0.4<z\leq 1.3$ probed by VIPERS, giving similar results within the uncertainties as shown for the two redshift slices in Figure 9. We therefore conclude that there is no evidence of an evolving slope from $z=1$ to $z=0.4$.

The slope we obtain is significantly flatter than the one obtained for the Coma cluster by BLE92, but entirely compatible with the flatter slope obtained by Scodeggio (2001) using variable apertures to cover a fixed fraction of the galaxy total light. However, the effect that the different slope might have on the observed evolution of the properties of the RS turns out to be almost negligible. The mean RS colour that is deduced from the best-fitting linear relation where the bulk of the RS galaxies are located (absolute magnitude range between $-22$ and $-20$), changes by less than 0.05 magnitudes, which is significantly less than the redshift evolution discussed in the following section.

Figure 10 displays the evolution of the RS for the VIPERS sample (filled circles) as a function of redshift. To allow a fair comparison of our results with previous works, the evolution of the RS has been computed following the classical RS approach (see Section 4.1 and 5.1). The literature data comprise various surveys, using either spectroscopic ($z_{\rm sp}$) or photometric redshifts ($z_{\rm ph}$): the COMBO-17 sample (Bell et al., 2004b), $z_{\rm ph}$, open circles), a study in the Extended Chandra Deep Field South (E-CDFS, (Ruhland et al., 2009), $z_{\rm sp}$, crosses), an SDSS and DEEP2 analysis (Blanton, 2006), $z_{\rm sp}$, inverted triangles), the multi-wavelength medium NIR-band photometric study of NEWFIRM Medium-Band-Survey (NMBS, (Whitaker et al., 2010), $z_{\rm ph}$, open squares), and the results of the VVDS (Franzetti et al., 2007), $z_{\rm sp}$, triangles). The solid line is a fit to the VIPERS data but also including the SDSS measurement (Bell et al., 2004b), filled black square) as a local reference point at $z=0$. Note that Blanton (2006) derived a slightly different measurement for SDSS (inverted triangle) which is consistent with the SDSS scatter. The measurement uncertainties on the RS intercepts which arise from Poissonian statistics were derived using bisector fits with the errors on the bisectors being evaluated through a bootstrap resampling of the data (Fritz et al., 2005). The total observed measurement errors including systematic uncertainties due to filter transformations and zero-point variations in the photometry are shown with the blue error corridor. For comparison purposes, the observed measurement error bars of the COMBO-17 data (Bell et al., 2004b) are shown as a grey shaded area.

The average evolution of the VIPERS RS for the classical selection criterion can be expressed as

Table 2 lists the $(U-V)$ colour intercept evolution at $M_{V}-5\ {\rm log}\ h=-20$ as a function of redshift for a fixed slope of $d(U-V)/d(M_{V})=-0.08$. If the VIPERS sample is split into sub-samples for the W1 and W4 fields, a similar evolution of the RS with similar uncertainties is found. Uncertainties due to cosmic variance have only a weak influence on the derived evolution.

Overall, the VIPERS results themselves show a similar evolution with redshift compared to various surveys in the literature which adopted the classical approach but with a significantly higher precision and statistics. Galaxies located on the RS display a moderate evolution of the intercept of $\Delta(U-V)=0.44\pm 0.12$ since $z\sim 1.3$ up to the present-day. Across the redshift interval $0.4<z<1.3$ the average RS intercept of VIPERS evolves as $\Delta(U-V)=0.28\pm 0.14$. This result alone is inconsistent with stellar population synthesis predictions of $\Delta(U-V)=0.09\pm 0.02$ that assume a high formation redshift for the bulk of the stars at $z_{\rm form}=4$ and a subsequent passive evolution of their stellar populations across the redshift range $0.4<z<1.3$ (see Section 7.1). However, there could be a small systematic difference in the adopted photometric zero-point (most likely due to the different $U$-band filters) which partially contributes to the intercept evolution at $z\gtrsim 0.8$. The most significant difference visible in Figure 10 is at redshift $z\sim 1.1$ between the VIPERS and VVDS point, but differences in sample selection and area coverage (the VVDS being a purely magnitude limited survey to $i^{\prime}_{\rm AB}<24.0$ over $\sim$0.7 deg²), can totally explain this difference. At lower redshift the VIPERS data are entirely consistent with previous measurements.

We have tested the impact of various systematic effects on our data. In general, possible systematic differences in the evolution of the intercept among the different surveys are most likely either due to sample statistics, differences in the filter systems or the impact of cosmic variance. In Appendices B and C we discuss the completeness of the VIPERS sample at high redshift and the systematic uncertainties introduced due to cosmic variance. VIPERS comprises the largest number of galaxies between $0.5<z<1.2$ and at the same time covers the widest sky area in comparison to previous galaxy surveys. Therefore, both restrictions due to low number statistics or cosmic variance can be largely ruled out. Nevertheless, we have estimated the systematic effect of cosmic variance using the prescription by (Moster et al., 2011, see Appendix C for details). For RS galaxies between $0.4<z<1.3$, the uncertainties arising from cosmic variance vary in the range $0.04<\log(M_{\star}/M_{\odot})<0.07$, with a median of $\langle\log(M_{\star}/M_{\odot})\rangle=0.05$. We have also tested the impact on our findings of practical choice, e.g., using different redshift bin sizes, but our choice does not affect the results within the measured uncertainties. A quantitative comparison with previous works is complicated by the fact that many surveys do not provide the exact prescription of their used filter transmission curves. This introduces uncertainties in the adopted filter passband transformations and conversion to rest-frame magnitudes when comparing different surveys, which depend on their used spectral templates (see also Appendix A). At the left bottom of Figure 10 the typical average uncertainty in filter transformations is indicated with an error bar. This uncertainty combines contributions from using different $U$ and $V$-band filter passbands and uncertainties introduced from the conversion to absolute rest-frame colours.

In Figure 11 we compare the measured evolution of the RS with redshift for different selection criteria, but keeping a fixed, non-evolving intercept as for the classical method. The RS evolution is shown for the colour-bimodality criterion (blue filled triangles), SED type classification (green open squares), the $NUVr^{\prime}$ selection (red open circles), and the classical method (black filled circles). In comparison to the classical approach, all other methods show a steeper evolution. It is somewhat expected that the classical approach displays a weaker evolution as this method is biased towards the few most brightest and reddest galaxies, whereas the other criteria consider the overall early-type galaxy population including also early-type galaxies with bluer colours. It is interesting to note that among the alternative selection criteria of early-type galaxies there are not large variations. The method based on the SED types produces results very similar to those obtained by the colour-bimodality and the $NUVr^{\prime}$ selection. The good agreement among these different selection methods suggests that our early-type galaxy sample contains little amount of dust and that the effects of dust obscuration become more dominant at higher redshifts ($z>1.3$).

Apart from different selection criteria, internal colour variations in the galaxies might impact the derived results. For bright, low-redshift galaxies ($z\lesssim 0.45$), the adopted aperture in the photometry might restrict our colour measurements to the central (redder) parts of the galaxies. Internal colour gradients could change the evolution of the RS intercept at the 10% level, resulting in bluer average colours for low redshift galaxies (Peletier et al., 1990, e.g.,). As throughout our analysis the same aperture size is adopted in all photometric bands, possible internal colour gradients are neglected, which might give slightly steeper colour relations for brighter galaxies. In particular, the effect of internal colour gradients might cause our lowest redshift bin to display a slightly redder evolution of the RS intercept compared to the redshift evolution found for the higher redshift data.

Over the past years observations have found evidence for a rapid increase of the total stellar mass of passive red-sequence galaxies since $z\sim 1$ (Bell et al., 2004b; Brown et al., 2007; Bundy et al., 2005; Faber et al., 2007; Scarlata et al., 2007, e.g.,). This evolutionary process reveals itself in terms of an increase in the number density of quiescent sub-$L^{*}$ galaxies (Borch et al., 2006; Faber et al., 2007, e.g.,). One possible scenario is that the red-sequence population is continuously supplied with a population of massive blue galaxies that have their star-formation activity truncated or quenched over a short time scale (Bell et al., 2004b; Bell et al., 2007; Faber et al., 2007). Such processes would manifest themselves primarily in a larger scatter in the CMR because the continuous agglomeration of blue galaxies onto the RS will cause a broadening of the RS.

Figure 12 illustrates the evolution of the scatter of the RS galaxies as a function of redshift. We compute the intrinsic scatter (filled symbols) by subtracting the scatter due to measurement uncertainties from the observed scatter (open symbols) in quadrature. The results are shown for the classical approach (blue circles) and the SED type selection (green squares). Several interesting trends can be seen. The scatter derived from the classical method is constant up to $z=1$, whereas the scatter measured on the basis of the SED type classification is increasing with redshift. Our highest-redshift measurement at $z=1.07$ is partly affected by incompleteness effects and the real scatter is most likely larger by $\Delta(U-V)=0.05$ mag. The VIPERS sample is in good agreement with previous field galaxy surveys in the E-CDFS (Ruhland et al., 2009) and the NMBS (Whitaker et al., 2010) that use a similar computation for the scatter of the RS, whereas field galaxies from the PISCES project (Tanaka et al., 2005) display somewhat a larger scatter. Interestingly, all field galaxy surveys predict a larger scatter of the RS than the one obtained for cluster galaxies, both in the local galaxy cluster represented by the Coma cluster (open triangle, BLE92) and at higher redshift for several high-redshift galaxy clusters (star symbols). The cluster measurements comprise data for 13 clusters in the literature over the redshift range $0.18<z\lesssim 1.46$ (Ellis et al., 1997; Blakeslee et al., 2003; Blanton, 2006; Mei et al., 2006a; Mei et al., 2006b; van Dokkum et al., 2008; Hilton et al., 2009). Despite possible differences in the colour measurements between cluster and field studies (the former usually adopt fixed apertures and restrict the RS to a few of the most luminous cluster members), the scatter in the rest-frame $(U-V)$ colour for quiescent galaxies in the field increases with redshift and is a factor of more than two larger than in clusters at the same redshift. This points towards a dependence of the scatter and its evolution on the environment. A possibility is that field galaxies consist of younger stellar populations compared to their cluster counterparts (Bernardi et al., 1998; Fritz et al., 2009a). Alternatively, the larger scatter in the field environment could be the result of a mixed population of old and young quiescent galaxies, whereas in clusters the RS is only populated by older red galaxies that formed their bulk of stars at higher redshift.

Figure 14 shows the $B$-band LF of the total VIPERS sample (left panel) and the LF of red galaxies (right panel) compared to LF estimates from the literature. For display purposes, only the red galaxy sample selected on the basis of the colour-bimodality is shown. The literature data include the LF of VVDS (Ilbert et al., 2005, blue squares), DEEP2+COMBO-17 data (Faber et al., 2007, orange dashed line), and the LFs of early-type galaxies in the VVDS (Zucca et al., 2006, blue squares), red galaxies in the NDWFS (Brown et al., 2007, green long-dashed line), and the LF of galaxies in AGES (Cool et al., 2012, brown dot-dashed line). As the different LFs were not constructed in exactly identical redshift intervals, the numbers in the brackets denote the redshift range of the respective LF. Overall, we find a good agreement between the different LFs across the redshift range $0.5<z<1.3$, with possibly some differences for bright galaxies. The unique large volume probed by VIPERS at high redshift leads to a higher completeness for rare, very luminous galaxies ($M_{V}-5\ {\rm log}\ h<-23$) at high redshift ($z=0.8-1.3$), extending by more than one magnitude the effective sampling of the bright-end of the LF. As demonstrated in Section 3, these very luminous objects are also massive systems up to masses of $\log(M_{\star}/M_{\odot})\leq 11.7$ at $z\sim 1$.

To assess the evolution of the RS as a function of redshift we confront our measurements of the CMR intercept with the predictions of stellar population synthesis modelling.

In the context of single burst models, the evolution of the CMR intercept follows the global trends of the expected passive reddening and fading of stellar populations formed at high redshift (van Dokkum & Franx, 2001; Franzetti et al., 2007). Variations of the CMR intercept as a function of redshift are mainly driven by the a priori assumed star formation history. The intercept itself depends instead primarily on variations of the metallicity content of the stellar populations with minor contributions due to variations in the stellar population ages.

We have constructed stellar population (SP) models using the PEGASE2 library (Fioc & Rocca-Volmerange, 1997). The SP models are parameterised by a short-burst of SF starting at an initial formation redshift in the range $1.5<z_{\rm f}<5.0$ and with a duration $\tau$ in the range $0.1-3.0$ Gyr. The metallicity content in the models is not held fixed but varies as the stellar population evolves with redshift.

Figure 15 shows the comparison of the predicted rest-frame colour evolution for different stellar population models with our observational VIPERS results. For display purposes, only a limited range of models, those that best reproduce the observations, are shown. The dotted lines are for a formation redshift of 2.5, while the dashed ones are for a formation redshift of 3. The VIPERS data rule out several model predictions with relatively high confidence. Models where the most-recent star formation burst in galaxies was established at $z_{\rm f}\leq 1.5$ predict too much evolution in the RS, and do not match our data. Conversely, models with a formation redshift of $z_{\rm f}\geq 4$ result in a much smaller evolution of the $(U-V)$ colour across the redshift range covered by our data, giving colours at $z=1$ that are already too red and allowing only for a very modest colour evolution of $\Delta(U-V)\sim 0.2$ mag to the present day. Furthermore, the observations rule out SFHs with either a very extended burst ($\tau>0.8$), mainly because of the fact that the RS is already in place at $z\sim 0.9$, or with an extremely short one ($\tau<0.3$), mainly because in that case all the stars would have low metallicity and the resulting RS would be bluer than observed at $z<0.6$. Our data favour SFHs with $0.5\leq\tau\leq 0.8$, although models with $0.1\leq\tau\leq 0.3$ and $z_{\rm f}=2.5$ cannot be completely ruled out. These latter predictions also nicely describe the data at lower redshift down to the present-day values indicated by local SDSS reference value (black filled square). In particular, the model prescriptions with $0.7\leq\tau\leq 0.8$ precisely end up in the SDSS measurement at $z=0$. From this comparison, we conclude that assuming a starting point at $z=1.3$, the build-up of the RS happened rapidly within a very short time span of only $\sim$1.5 Gyr. In such a scenario, early-type galaxies at high redshift ($0.9\lesssim z\lesssim 1.1$) that have not yet moved to the RS should still show signs of recent SF activity.

The evolution of the LF parameters provides important information on the evolution of the galaxy population and the different transformation processes the galaxies experience. Changes in the characteristic Schechter magnitude $M^{*}$ reflect the aging of the stellar populations in galaxies, while changes in $\phi^{*}$ give information on the galaxy number density, allowing us to estimate the fraction of objects that undergo merging or fading processes.

Figure 16 shows the evolution of the Schechter function parameters $M_{B}^{*}$ and $\phi^{*}$ with redshift for the total VIPERS sample (left panels) and for red galaxies only (right panels). In the top panels, the dashed lines indicate the evolution in $M_{B}^{*}$ as predicted by the PEGASE models with formation redshift $z_{\rm f}=2$ and various burst duration $\tau$ (see Section 7.1), which were calibrated to match the local SDSS measurements. For comparison, we also show literature data including the COMBO-17 (Bell et al., 2004b), FDF (Gabasch et al., 2004), field early-type galaxies in GOODS (Ferreras et al., 2005), VVDS (Ilbert et al., 2005), early-type galaxies from the VVDS (Zucca et al., 2006), and DEEP2 and COMBO-17 data sets (Faber et al., 2007), red galaxies in the NDWFS (Brown et al., 2007), and galaxies in AGES (Cool et al., 2012). Magnitudes of the different surveys were transformed to the concordance cosmology and converted to Johnson-Cousins $B$-band magnitudes in the Vega system using $M_{J}=M_{AB}+0.084$ mag. For the total VIPERS galaxy population $M_{B}^{*}$ brightens by $\sim$$1.04\pm 0.06$ mag over the redshift range $z=0.5$ to $z=1.3$ (see upper left panel), while RS galaxies show a brightening of $M_{B}^{*}$ of $1.09\pm 0.10$ mag. There are slight differences in the $M_{B}^{*}$ evolution between red galaxies classified with the bimodality and the SED type classification. The SED type classification is in better agreement with the PEGASE models as in this selection criterion galaxies with somewhat younger ages are also considered. Overall, the number density $\phi^{*}$ for red galaxies rises over the past 9 Gyr, with a stronger increase from $z=1.3$ to $z\sim 0.7$, followed by a weaker rise from $z<0.7$ to the present-day. This result confirms our findings on the evolution of the RS and indicates first a rise in the build-up of massive galaxies at $0.7\lesssim z\lesssim 1.3$ over a relatively short time period of $\sim$1.5 Gyr, followed by a continuous slower assembly over cosmic time.

To probe in more detail the mass assembly of the RS, we compare in Figure 16 the number density evolution of red, quiescent galaxies to predictions from stellar population synthesis models that involve a shut down of star formation, such as a sharp truncation or a quenching process. Sharp truncation models, resulting in a purely passive evolution of the stellar population, can reproduce quite well the evolution of $M^{*}$, but they fail to explain the build-up of the number density. An example of such a model prediction, constructed with a simple stellar population with a single metallicity formed at $z=3$ is shown by the dotted line in the bottom panels of the figure. In contrast, quenching models predict a gradual increase in the RS galaxies number density with time. Here we have taken the quenching models from Harker et al. (2006), which consist of a 1 Gyr long burst of star formation at $z=5$, which consumes 80%-99% of the gas reservoir, followed by progressive quenching of the star forming galaxies starting at $z_{\rm quench}=1.5$ or $z_{\rm quench}=2$. We notice that the resulting star formation history for these models is actually quite similar to the one we used to derive the models used in the previous section to describe the evolution of the RS colour. The $\phi^{*}$ of the quenched models was normalised to the observed $\phi^{*}$ of red galaxies at $z=0.5$. Note that despite the simple assumptions in the models, they describe the observed trends reasonably well.

The lower right panel of Figure 16 shows that the evolution of the red galaxy populations in VIPERS follows quite closely the tracks for quenching models with quenching onset at $z_{\rm quench}=1.5$ (dot-dashed line), with possibly an indication that an even later onset of the quenching could better represent the highest redshift bin data. A similar picture can be drawn from other surveys (Ferreras et al., 2005; Zucca et al., 2006; Faber et al., 2007), although these data show a larger scatter because of higher measurement uncertainties. For the VIPERS colour bimodality sample the $\phi^{*}$ of the RS galaxies rises by a factor of $4.4\pm 0.9$ from $z=1$ to the present-day, whereas for the SED-sample the $\phi^{*}$ of RS galaxies increases by a factor of $5.8\pm 0.9$ over the same time interval. The $\phi^{*}$ of the quenching model rises by a factor of 3.8 for $z_{\rm quench}=2.0$ and by a factor of 5.1 for $z_{\rm quench}=1.5$. Both model values are within the observed ranges, although the VIPERS data at high redshift ($z>0.9$) prefer the predictions with $z_{\rm quench}=1.5$. We find therefore another indirect indication towards early-type galaxies at high redshift ($0.9\lesssim z\lesssim 1.1$) still showing signs of recent SF activity.

To verify the indirect evidence for a recent star formation activity among redshift $z\sim 1$ RS galaxies, discussed in the previous sections, we analyse directly the properties of these galaxies by stacking their spectra. Figure 17 illustrates examples of (rest frame) stacked early-type galaxy spectra at low-redshift ($0.5<z<0.6$, black) and at high-redshift ($0.9<z<1.0$, red) selected on the basis of the SED type classification. Spectra of RS galaxies selected using the colour-bimodality method or the $NUVr^{\prime}$ criteria are virtually indistinguishable from the ones shown. For the stacking process early-type galaxies within an absolute magnitude range of $-22.5\geq M_{V}\geq-23.0$ were selected. The stacked spectra comprise a similar number of individual spectra ($N_{\rm spec}\sim 100$ at $0.5<z<0.6$, $N_{\rm spec}\sim 180$ at $0.9<z<1.0$) and represent the typical averaged spectra of early-type galaxies at the respective redshift range. At low-redshift the stacked spectrum is that of a purely passive, red and quiescent galaxy. However, the high-redshift counterpart displays clear signs of ongoing SF as indicated by the detection of a weak [O II] 3727 emission line.

To quantify and constrain the recent star formation in the stacked spectra of early-type galaxies at high-redshift, the main questions of interest are the SFR, the mass fraction involved in the star formation and the duration of the star formation episode. As the individual spectra used in the stacking have been re-normalized to reproduce the total flux observed photometrically for each galaxy, we assume the measured [O II] 3727 equivalent width to be representative for the global value of the average VIPERS galaxy. Transforming the observed [O II] 3727 equivalent widths to rest-frame and assuming the relationship by Kennicutt (1992) with a global extinction correction of E(H$\alpha$)=1 mag, we derive for the whole sample of early-type galaxies a median SFR of $1.8$ $M_{\odot}\,{\rm yr}^{-1}$. The different stacked spectra result in similar SFRs estimates: $NUVr^{\prime}$: median $\langle\mathrm{SFR}\rangle=1.9$ $M_{\odot}\,{\rm yr}^{-1}$, colour-bimodality: $\langle\mathrm{SFR}\rangle=2.2$ $M_{\odot}\,{\rm yr}^{-1}$, SED types: $\langle\mathrm{SFR}\rangle=1.3$ $M_{\odot}\,{\rm yr}^{-1}$. This suggests that a fraction between 1 and 3% of the stellar mass of each galaxy is on average involved in the star formation burst which will exhaust the gas within $\sim$0.10-0.14 Gyr, adopting a burst duration time scale of $t_{\rm d}\propto M_{*}/\mathrm{SFR}$ (Noeske et al., 2007).

In the nearby universe a non negligible fraction of passive galaxies on the red sequence shows signs of emission lines with characteristic line ratios of low ionisation nuclear emission-line regions (Yan et al., 2006; Schawinski et al., 2007, LINERs,). Red galaxies with strong LINER features exhibit on average younger ages than their passive counterparts without emission, suggesting a connection between the local galaxy activity and internal processes [e.g., shock ionization by starburst winds, photoionization by (post-AGB) stars or AGNs] or external mechanisms that could be responsible for the emission enhancement [e.g., cooling flows, photoionization by low-luminosity-AGNs (LLAGNs), shock ionization due to gas accretion, galaxy interactions and merger activity]. Because of the spectral coverage, VIPERS galaxy spectra at high redshift are restricted to the [O II] 3727 emission line as a star formation proxy. To quantify a possible contribution of LLAGNs in our red galaxy sample, we have analysed the morphologies of massive galaxies with $M_{\odot}>11.2$. The majority of these objects appear to be indeed isolated and massive systems. There is only a small fraction ($<20$%) of galaxies which shows some signs of disturbed morphologies or possible galaxy interaction with a close neighbour. This suggests that external mechanisms play only a minor rule in triggering star formation activity. It is outside the scope of the current work to speculate about possible physical triggering mechnanisms for the quenching of star formation. In the future, we will explore in more detail which processes are responsible and contribute to the star formation/AGN activity detected in our galaxies.

Our findings support the scenario for the build-up of the RS described in Section 7.1, where massive early-type galaxies show evidence for ongoing SF activity at $z\sim 1$ and subsequently experience an efficient shut-down mechanism of their SF over a short time scale of $\sim$1.5 Gyr with a rapid exhaustion of their gas reservoirs.