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Appendix A: Photometric and spectroscopic SED fitting

For the initial SED fitting used to generate photometric redshifts for spectroscopically untargeted objects, only ground-based optical and NIR photometry (i.e., CFHTLS/WIRDS) were used because the SERVS data had not been incorporated into the full photometric redshift catalog at the time of publication. This lack of observed-frame coverage redward of λ_obs ≳ 2 μm is, however, of limited consequence, since this fitting is used here only for photometric redshifts. Redshifts derived in this manner are known, even up to the highest redshifts of our sample, to be relatively invariant under the inclusion of Spitzer imaging (see, e.g., Bradač et al. 2014; Ryan et al. 2014) for datasets with broadband filters that probe both the Lyman-limit/Lyα break and the Balmer/4000 Å break. Regardless, we tested this assumption on our own data for the subset of galaxies with secure spectroscopic redshifts at z> 2, the redshift range of interest for this study. No statistically significant difference in the normalized absolute median deviation, σ_{Δz/ (1 + zs)}, (NMAD; Hoaglin et al. 1983), or the catastrophic outlier rate (i.e., | z_p − z_s | /(1 + z_s) > 0.15, see Ilbert et al. 2013) was found between photometric redshifts determined with and without SERVS data included. A comparison of the photometric redshifts derived from the CFHTLS/WIRDS photometry and spectroscopic redshifts of all objects targeted in the CFHTLS-D1 field that have a secure spectroscopic redshift yielded a catastrophic outlier rate of 9.7%, a rate considerably higher than the VVDS data alone (see Lemaux et al. 2013). However, once catastrophic outliers were rejected, the NMAD was σ_{Δz/ (1 + zs)} = 0.030, essentially identical to VVDS.

For those objects that had been targeted with spectroscopy, the SED fitting process was performed separately on objects with and without secure spectroscopic redshifts. For the former, spectroscopic redshifts were used as a prior to fix the redshift of the source prior to the SED-fitting, and for the latter, the redshift, as with untargeted objects, was left unconstrained. The models used and the range of parameters were identical to those of the previous fitting and are described in Lemaux et al. (2013) and references therein. The SERVS data, previously unused, was incorporated for this instance of the SED fitting as the physical parameters derived from the SED fitting are heavily used in this study and are known to be sensitive to the inclusion of IRAC data (see discussion in Bradač et al. 2014). Two other changes relative to the version of the fitting presented in Lemaux et al. (2013) were made at this point. The first was to use best-fit model, i.e., the combination of template and physical parameters that minimized the χ² with respect to photometric data, rather than the median of the probability distribution function (PDF). This choice was made because roughly 15% of our spectroscopic sample were significantly detected in an insufficient number of photometric bands to satisfactorily calculate a PDF. For the 85% of the sample for which a comparison could be made, no systematic offset was observed between the best-fit and median stellar masses, luminosity-weighted stellar ages, and SFRs, with a negligibly small scatter between the two estimators of 0.04 dex for all three parameters. The second change made in this version of the SED fitting was the use of MAG_AUTO measurements instead of the scaled aperture magnitude measurements used in the Lemaux et al. (2013). Though the former are known to be more susceptible to blending, we preferred these measurements as they showed greater consistency with the aperture-corrected SERVS magnitudes.

Because it has been suggested that high-redshift galaxies have star formation histories (SFHs), which deviate considerably from the simple exponentially decaying tau model (e.g., Maraston et al. 2010; Reddy et al. 2012; Schaerer et al 2013; Buat et al. 2014; though see also, e.g., Ryan et al. 2014; Sklias et al. 2014), the effect of changing the SFH was tested by rerunning SED fitting using Bruzual & Charlot (2003; hereafter BC03) delayed tau models with an identical initial mass function (Chabrier 2003) and an identical range of extinctions, taus, and metallicities. For the two physical parameters that are of paramount interest for this study, stellar mass and SFR, only a small systematic offset of 0.05 dex between the best-fit parameters of the two different SFHs was observed, with the delayed tau model yielding slightly higher SFRs and slightly lower stellar masses. The rms scatter between the two sets of parameters measured with the two different SFHs was also small: 0.04 dex for both parameters. Because all of the comparisons that are made in this paper are internal, it would have no effect on our results if the SFHs of galaxies in our sample were globally mischaracterized to the same level. However, since we made comparisons between galaxies in different environments, it is possible that the SFHs of galaxies depends on environment (e.g., Kauffmann et al. 2004), which would lead to a differential bias in the physical parameters. It is therefore comforting that, at least for these two SFHs, the differences between the physical parameters derived for the two sets of models is negligibly small. Because of its consistency with the previous SED fitting and to ease comparisons with the vast majority of other studies, we decided to adopt those parameters derived from the exponentially decaying tau model. With these sets of models, the typical (random) uncertainty in the stellar mass and SFRs of galaxies in the range of interest for this study (i.e., 9 < log (ℳ_s) < 12, 2.9 <z_spec< 3.7) coming from the SED fitting process were 0.16 and 0.10 dex, respectively.

Spectra were fit using the GOSSIP software, a package created to to fit the spectro-photometric emission of a galaxy with a set of synthetic models with a library builder that allows for the construction of various resolution BC03 and Maraston (2005, 2011) models. For this study, we fit only exponentially decaying BC03 models with the same assumptions and those spanning the same parameter space as those adopted for the photometric SED fitting described above. Among the many improvements that have been recently implemented on GOSSIP, one of the most important targets for the redshift range of VUDS is related to the treatment of the intergalactic medium (IGM) extinction. While a typical assumption is to employ the IGM model of Madau (1995), which produces, for a given redshift, a single IGM extinction curve, GOSSIP is able to choose up to five different IGM curves along various sight lines, which provides a more realistic determination of the resultant physical parameters. Both GOSSIP and the improvements that have been made to it for general use with the VUDS survey will be explained in an upcoming paper (Thomas et al., in prep.).

Appendix B: Details of the halo mass estimates of Cl J0227-0421

The initial methodology used to determine an estimate on the halo mass of Cl J0227-0421 utilized the information provided by the dynamics of the member galaxies. The implicit assumption in this method is that the protocluster is in a virialized state, an assumption that almost certainly does not hold at this redshift given the limited time member galaxies have had to interact with the potential. The high degree of skewness observed in the differential velocity distribution of the spectral members quoted in Sect. 3.1 attests to the failure of this assumption. In the case of a structure in the initial stages of its collapse, the measured velocity dispersion will potentially decrease relative to the virial value owing to galaxies appearing compressed along the redshift dimension (e.g., Steidel et al. 1998). At later stages, however, the measured velocity dispersion will be an overestimate of the virial value as galaxies that have fallen from long distances begin to make their first passes through the protocluster core. Given the young age of the universe at z ~ 3.3, the former is the stronger of the two possibilities. However, with no knowledge of the true evolutionary stage of the dynamics of the spectral members of Cl J0227-0421, we remained doubtful about this point, and simply calculated the dynamical mass with the knowledge that this quantity can be a lower or an upper limit. The virial dynamical mass was calculated via (B.1)where G is Newton’s gravitational constant and H(z) is the value of the Hubble parameter at the redshift of interest. This formula is used directly to calculate the dynamical mass at the virial radius reported in Table 2.

The calculation relating the stellar mass of members of the protocluster to the total mass was done in the following manner. Loosely following the methodology of Strazzullo et al. (2013), we adopt the relationship between halo mass and the stellar mass of members within r₂₀₀, the radius at which the mean density is 200 times that of the critical density, calibrated using data from the Sloan Digital Sky Survey (SDSS) by Andreon (2012). To determine the amount of stellar content in Cl J0227-0421, we summed the stellar masses of all spectral members with stellar masses in excess of 10⁹M_⊙, chosen as it is roughly the turnover in number counts of all VUDS galaxies with secure spectroscopic redshifts from 2.9 <z< 3.7, the redshift bounds used to define our field sample in Sect. 4.1. The large projected radius over which we sum the stellar mass of spectral members (i.e., R_proj< 3) was motivated by the high likelihood of such galaxies becoming as virialized members by z ~ 0 (Chiang et al. 2013; Zemp 2013), the redshift at which the Andreon (2012) relation was calibrated. Since the virial radius is typically defined to be smaller than r₂₀₀ (Biviano et al. 2006; Poggianti et al. 2009), such galaxies should be accounted for in this relation.

A large number of the objects within the protocluster bounds are, however, not sampled spectroscopically or do not have a secure spectroscopic redshift. To account for this lack of sampling, we calculated the probability of being a true member by comparing the spectroscopic and photometric redshifts of those objects with secure spectroscopic redshifts. Two probabilities were calculated, one for objects with photometric redshifts consistent with the redshift of the protocluster and those that were not. The correction to the composite stellar mass is then (B.2)

where N_{p, mem} is the number of photometric redshift members that went untargeted or that have questionable spectroscopic redshifts within the bounds of the protocluster, and N_{p, nm} is the equivalent quantity for photometric redshift non-members.

The two probabilities, defined as the likelihood of being a spectral member in the event that an object is a photometric redshift member or non-member, were determined to be 31.0%¹⁸ and 0.4%, resulting in a correction factor of 5.5. In this calculation the assumption is made that the untargeted members have an identical stellar mass distribution to the spectral members, which is reasonable given that the VUDS sample should be representative of galaxy populations at these redshifts bounded by this stellar mass limit. The quantity in Eq. (B.2) was further corrected for galaxies between 10⁸< ℳ_s< 10⁹M_⊙ by integrating the stellar mass functions (multiplied by ℳ_s) derived by Ilbert et al. (2013) for galaxies at 3 <z< 4. The lower limit of this correction is set by the rough stellar mass completeness limit of SDSS at the redshift of those clusters used for calibration (Panter et al. 2007). The resultant total corrected stellar mass is 3.22M_⊙, where the errors were determined from the SED fitting process. It is interesting to note that this corrected total stellar mass rivals the total stellar mass contained in red-sequence galaxies in massive, z ~ 1 clusters (e.g., Overzier et al. 2009; Rettura et al. 2010; Lemaux et al. 2012). Under the assumption that the correction made here is appropriate, and under the additional assumption that ~4 Gyr of evolution within a (pro to) cluster environment is enough to, by and large, quench member galaxies, it appears that a large amount of the requisite stellar mass needed to populate the red sequence of lower redshift clusters is already in place in Cl J0227-0421. Using the relationship of Andreon (2012), the halo mass within r₅₀₀ corresponding to the composite corrected stellar mass calculated from the members of Cl J0227-0421 is M_{Σℳs, 500} = 1.35 ± 0.53 × 10¹⁴M_⊙ at z ~ 3.3. However, to compare this value fairly to the previous estimate it is necessary to correct the halo mass to that at the virial radius. This correction was done by modeling the halo mass profile as an NFW profile with a concentration at the virial radius of c_vir = 2.5 (Duffy et al. 2008). A correction factor of c_NFW = 1.39 ± 0.48 was determined by the ratio of the total mass contained within r_vir to that contained within r₅₀₀ as determined by the velocity dispersion. This correction factor was used to derive the final z = 3.3 halo mass estimate coming from this method which is given in Table 2.

The halo mass limit placed on Cl J0227-0421 from the X-ray imaging data was performed as follows. To measure the X-ray flux limit at the position of Cl J0227-0421, all bright X-ray sources in the vicinity of the protocluster were optimally masked using the methodology presented in Clerc et al. (2012). A bright source, identified as a local galaxy (z = 0.053), lies within close proximity (1′) of the protocluster center, further compounding the difficulty of the measurement because the shot noise from this source is the overwhelming source of background noise in some parts of the adopted apertures. After masking, we integrated the count rate in concentric annuli and subsequently corrected for vignetting with the uncertainties derived through Poisson statistics. The measurement yields the total (summing three EPIC detectors: MOS1, MOS2, PN) count rate into the [0.5−2] keV band within physical aperture corresponding to 0.5 Mpc at z ~ 3.3 and centered on the protocluster optical (i.e., number-weighted) position. These corrected count rates were then converted into a flux limit in the [0.5−2] keV band using a constant conversion factor of 9 × 10^-13 ergs cm^-2 counts^-1 (Adami et al. 2011), resulting in the limit quoted in Sect. 3.1.1. All random errors quoted for this method are Poissonian. This flux limit was converted into a rest-frame luminosity using the method described in Sect. 3.1.1, which resulted in a luminosity limit of L_{X, [0.1 − 2.4 keV] ,rest}< 3.98 ± 0.96 × 10⁴⁵ ergs s^-1. The relationship between the X-ray luminosity in the rest-frame [0.1−2.4] keV, as measured at r₅₀₀¹⁹ and the hydrostatic equilibrium mass is given as (Arnaud et al. 2010; Piffaretti et al. 2011) (B.3)where h(z) = H(z) /H₀, log (c) = 0.274 ± 0.037, and α = 1.64 ± 0.12. Just as the member dynamics are unlikely to be governed by the virial theorem, the protocluster ICM, if it exists, is almost certainly not going to be in hydrostatic equilibrium, and thus this method only serves to crudely place limits on the halo mass. Using the above formula and correcting to the virial radius with an NFW as with the previous method results in the hydrostatic halo mass limit given in Table 2.

The galaxy overdensity, δ_gal, calculated in Sect. 3.1.1 within the “effective” radius of Cl J0227-0421 was transformed into the matter overdensity, δ_m, via (Steidel et al. 1998): (B.4)and (B.5)where C is defined as factor to correct the observed volume for redshift space distortions such that C = V_apparent/V_true, where V_apparent is the measured volume and V_true is the volume after correction. This factor, discussed extensively in Steidel et al. (1998), has a complicated dependence on both the magnitude and the directionality of the velocities of the member galaxies. As in Cucciati et al. (2014), we made the assumption here that the structure is under collapse, such that C< 1 (i.e., the galaxies are compressed in redshift space) and that the velocities are

isotropic. Under these assumptions, f in Eq. (B.5) can be approximated as , the matter density relative to critical of the universe at redshift z (for further details see Lahav et al. 1991; Padmanabhan 1993; Steidel et al. 1998). Solving the above system of equations results in a correction factor of and a matter overdensity of . The latter value can be translated into a z = 0 halo mass via (Chiang et al. 2013) (B.6)where V_e is the effective volume, i.e., (2R_e)³, where R_e is measured in comoving Mpc, and C_e is an additional correction factor to account for mass outside of the effective radius. In Chiang et al. (2013), C_e was found to be 2.5; i.e., 40% of the mass was contained within a box defined by R_e, and that is the value we adopt here. In principle, under the assumptions made here it is necessary to decrease the observed R_e along the line-of-sight dimension (i.e., a smaller redshift window) by a factor C to match the simulated volume that is absent of distortions due to peculiar velocities. However, the value of δ_gal for Cl J0227-0421 is essentially invariant with respect to the redshift window chosen (for Δz_spec< 0.08) and, given the large uncertainty in the value of C, both in the formal error and the number of assumptions, we make no attempt to correct our observed redshift window for this effect. An additional uncertainty in this calculation relates to the scatter of δ_m and ℳ_{δm, tot,z = 0} of simulated clusters. Because of the relatively small number of z = 0 clusters in the analysis of Chiang et al. (2013) at or exceeding the total mass of the predicted descendant of Cl J0227-0421, this scatter is highly uncertain. Because of this uncertainty, and because the inclusion of this scatter in the formal error on the total mass calculated from this method does not change the interpretation of our results, we chose to ignore it. The total halo mass derived in Eq. (B.6) is then converted to a halo mass at the virial radius using the method defined in the previous mass calculations, resulting in the value given in Table 2.

© ESO, 2014