THE WiggleZ DARK ENERGY SURVEY: GALAXY EVOLUTION AT 0.25 ⩽ z ⩽ 0.75 USING THE SECOND RED-SEQUENCE CLUSTER SURVEY

The WiggleZ Dark Energy Survey is a spectroscopic survey of 240,000 UV-selected emission-line galaxies, designed to map a cosmic volume of ∼1 Gpc³. Its primary goal is to precisely measure the scale of baryon acoustic oscillation imprinted on the spatial distribution of these galaxies at 0.2 ⩽ z ⩽ 1 (e.g., Blake et al. 2011). The details of the survey are presented in Drinkwater et al. (2010); here, we present a brief summary.

The survey selects targets from areas totaling ∼1000 deg² from seven equatorial regions. Target galaxies are selected using the far-UV (FUV) and near-UV (NUV) data from the Galaxy Evolution Explorer (GALEX) Medium Imaging Survey (Martin et al. 2005) using the criteria of FUV − NUV ⩾ 1 or no FUV detection. The targets must also satisfy NUV ⩽ 22.8 and the NUV signal-to-noise ratio (S/N) ⩾ 3. Further selection criteria based on optical photometry are also applied to attempt to maximize the probability that the targets are blue star-forming galaxies at z ⩾ 0.5, the primary sample for the WiggleZ project science. The optical data are obtained from SDSS DR4 (Adelman-McCarthy et al. 2006) and RCS2 (see Section 2.2). In order to select blue star-forming galaxies and exclude spurious matches between GALEX and optical data, all WiggleZ targets must also have −0.5 ⩽ NUV − r' ⩽ 2. To avoid low-z galaxies, a 20 ⩽ r' ⩽ 22.5 criterion together with two different sets of optical color–color selections is applied. All these selection criteria give a target density of ∼350 galaxies deg⁻², or ∼2.6% ± 0.2% of optically detected galaxies. There is no further morphology selection to remove any "stellar" objects, since galactic stars ought to fail the survey selection criteria.

The SDSS data have a depth of [22.0, 22.2, 22.2, 21.3, 20.5] in the u'g'r'i'z' passbands, while the RCS2 data have a much deeper depth, with average 5σ point source limits of [24.4, 24.3, 22.8] in the g'r'z' passbands. Since we want to study the galaxy population properties and their evolution to as high a redshift as possible, in this paper we use only the RCS2 regions of the WiggleZ survey.

The WiggleZ observations were conducted using the AAOmega spectrograph (the former 2dF upgraded; Sharp 2006) on the 3.9 m Anglo-Australian Telescope (AAT) from 2006 August to 2011 January. AAOmega is a fiber spectrograph containing 400 fibers including 8 guide fibers. Each fiber has a diameter of 2''. The field of view is 2° in diameter. The typical exposure time is 60 minutes per AAOmega configuration. This exposure time is too short to allow a significant detection of galaxy continuum for the fainter galaxies, but sufficient to detect emission lines for redshift measurement. Using the 580V and 385R gratings for the blue and red arms with the 670 nm dichroic, the spectra have a wavelength range from 4700 Å to 9500 Å, with a dispersion of ∼1.1 Å pixel⁻¹ in the blue arm and ∼1.6 Å pixel⁻¹ in the red arm, providing spectral resolutions of ∼3.5 Å and ∼5.3 Å, respectively. The observing conditions varied significantly, with the seeing typically ranging from 1'' to 25.

Detailed descriptions of the data reduction technique and reliability are given in Drinkwater et al. (2010) and summarized here. The data were reduced during each observing run using the automated 2dFdr software developed at the Australian Astronomical Observatory, including bias subtraction, flat field, and wavelength calibration. The redshift of each spectrum was measured using an evolved version of runz, which was the software used for 2dFGRS (Colless et al. 2001) and 2SLAQ (Cannon et al. 2006). The software has been modified to optimize the use of emission lines to derive redshifts. The commonly detected emission lines in WiggleZ spectra are [O ii] λ3727, H_β, [O iii] λ4959/5007, H_α, and [N ii] λ6583. Even though runz automatically generates an integer quality flag (Q_zspec) in the range of 1–5 based on how well the template fits a given spectrum, all WiggleZ spectra were extensively checked visually, and each spectrum was manually assigned a new quality flag. The redshift confidence increases with larger Q_zspec. The redshift reliability has been cross-checked internally using repeated galaxies. A subset of redshifts was also compared to DEEP2 galaxies. While there may be some debates on distinguishing Q_zspec = 4 and Q_zspec = 5 objects, as they are close to being 100% reliable, the critical separation occurs between Q_zspec = 2 and Q_zspec = 3. For objects with Q_zspec = 3, the redshift reliability is ∼79%.

As of 2009 October, the survey yielded ∼260,000 spectra in total from all seven equatorial regions, and ∼160,000 of them are useful with Q_zspec = 3, 4, 5. Part of the WiggleZ spectral database has been released to the public at http://wigglez.swin.edu.au/ds. More details about the project and data can be found in Drinkwater et al. (2010).

Observationally speaking, galaxies appear to be primarily divided into two classes. One is red passive galaxies and the other is blue star-forming galaxies. These two classes of galaxies form the so-called "red sequence" and "blue cloud" in a color–magnitude space. In fact, red galaxies may be a mix of truly old passive galaxies and dusty star-forming galaxies, and they cannot be distinguished well using a single optical color. However, Wolf et al. (2005) showed that dusty star-forming galaxies can be well separated from old passive ones in a color–color space, as long as one color brackets the 4000 Å break and the other is at a longer wavelength. They found that dusty red galaxies actually form a continuous tail extending from the blue cloud, while old red galaxies form a separate structure of their own (the red sequence). This makes the color–color diagram a powerful diagnostic tool.

Figure 6 presents the observed color–color diagrams for neighbors in five redshift bins, where the colors of the three models from Figure 2 are overlaid as crosses for reference. For a better visual presentation, the pixels (Δ(g' − r') × Δ(r' − z')) in the color–color intensity plot are subdivided by a factor of four into smaller pixels in units of 0.0125 mag, and then smoothed by a kernel of 10 × 10 pixels. The intensity scale is in units of counts per small pixels after normalizing the net counts to 1 × 10⁴ in each redshift bin. We also overplot the WiggleZ galaxies as the non-filled contours with a Δ(r' − z') = 1 offset for clarity. We observe that, for all redshift bins, both the WiggleZ galaxies and most of their neighbors populate a similar color–color plot, with the exception that the WiggleZ galaxies do not show a clump of red-passive galaxies. They both exhibit a continuous sequence in all redshift divisions. The sequence runs from the blue star-forming regions toward the red passive area, marked by the model colors; but no WiggleZ markers have colors as red as the red passive galaxies, indicating that they contain little dust. We note that this is likely a reflection of the survey design, as the WiggleZ galaxies are selected primarily by UV fluxes.

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Although most of the neighbor galaxies reside in the star-forming sequence, some neighbors populate the region of passive red galaxies. These red neighbors are red-sequence galaxies, and we will discuss their properties later in the paper. Some neighbors in the lower redshift bins, however, exhibit redder (z' − r') colors than that expected from passive red galaxies at their fixed redshift, and form roughly a continuous sequence from the blue star-forming galaxies. These neighbors are possible dusty galaxies. We note that such estimation is approximate, since the regions in the color–color diagram for dusty reddened star-forming galaxies may change at different redshifts due to the shifting of the 4000 Å break in the observed frame. At z ∼ 0.6 and beyond, the use of the current color–color diagram to distinguish between dusty star-forming and red passive galaxies is not optimal, because the 4000 Å break is shifted beyond the center of the r' passband, and having only one passband (z') at longer wavelengths is not sufficient to distinguish between passive and dusty spectral energy distributions (SEDs). Using a rough color cutoff to define dusty galaxies as (r' − z') − C_E > 0.3 and g' − r' ⩾ ΔC where C_E is the color of the red elliptical model in Figure 2 and ΔC is the color halfway between the red and green models in the same figure, we estimate about 5.2% ± 1.0%, 2.4% ± 0.8%, and 0.2% ± 0.5% of the galaxies in the three lower redshift bins in increasing redshift order may be dusty star-forming galaxies. From these fractions, we conclude that dust-reddened star-forming galaxies are not likely a significant component in the WiggleZ neighbors, at least for z ≲ 0.6. Note that the decrease in the dusty galaxy fraction is likely due to the shifting of the r' toward the 4000 Å break and possibly the different luminosity depths in the redshift bins, and does not necessarily reflect a real change.

Since the star formation properties of the WiggleZ galaxies themselves are not uniform across redshift due to the complex selection criteria, we want to examine whether the properties of the neighbors vary with the star formation activity of the WiggleZ markers. We use the [O ii] λ3727 emission line equivalent width (EW) of the WiggleZ markers as the proxy for the specific star formation rate of the markers and probe where neighbors around markers with different EW([O ii] λ3727) populate the observed color–color diagrams.

First, we measure the [O ii] λ3727 EW of the markers. The observed spectra have weak continuum due to the short exposure time (∼1 hr); hence the measured EW is noisy for the fainter galaxies. To measure the EW([O ii] λ3727), we define a window of 10 Å centered at 3727.8 Å as the region for the [O ii] λ3727 line. The continuum level is determined using a window of 30 Å on each side of the [O ii] line (on the rest frame), starting at 3677.8 Å and 3757.8 Å. Either a linear or a second-order polynomial function, whichever returns the smallest χ², is chosen to describe the fitted continuum within the windows. The spectrum is then subtracted by this fitted continuum. A bi-Gaussian function is then applied based on the data points within all three windows. The flux of the [O ii] λ3727 line is accordingly the total net flux under this fitted bi-Gaussian curve. We divide the WiggleZ galaxies into three bins based on the 33.3% percentiles of the EW([O ii] λ3727) at each redshift bin. Galaxies without any [O ii] λ3727 detection are excluded. The median and the 1σ uncertainty of the computed EW([O ii] λ3727) are about 112.5 ± 32.6 Å and 17.7 ± 8.0 Å for the highest and lowest EW([O ii] λ3727) bins at z = 0.25–0.35, respectively.

We re-stack the observed CCM cubes of the neighbors by dividing the sample into bins of EW([O ii] λ3727) within each redshift bin and present them in Figure 7, where the WiggleZ markers themselves are again offset by Δ(r' − z') = 1 for clarity. From Figure 7, it is clear that the color–color distributions for neighbors of WiggleZ galaxies of different EW([O ii]) are very similar within the same redshift bin. Kolmogorov–Smirnov tests of pairs of both g' − r' and r' − z' distributions find no significant difference between the different EW([O ii] λ3727) bins within the same redshift bin. The smallest significant level in all the pair-wise comparisons is 0.22. This implies that the properties of the neighbors do not strongly depend on the properties of the WiggleZ galaxies. Furthermore, we find that the N_net distributions of the neighbors within 0.25 Mpc, although not shown here, are identical among all WiggleZ galaxies with different EW([O ii] λ3727) at a fixed redshift bin. This adds to the growing evidence that the environment has little influence on the properties of star-forming galaxies (e.g., Balogh et al. 2004, 2009; Yee et al. 2005; Carter et al. 2001; Rines et al. 2005; Cassata et al. 2007). Therefore, we conclude that the insignificant dependence between the properties of the neighbors and the markers allows us to explore galaxy evolution using the neighbors, even though the WiggleZ galaxies may cover different ranges of properties at different redshifts due to the survey selection criteria; for example, the r' = 20–22.5 criterion naturally selects more massive galaxies at higher redshifts.

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Since one of the primary WiggleZ target selection criteria is based on UV flux, we also check whether the NUV luminosity of the markers affects the color properties of the neighbors. This is essentially testing whether the total star formation rate of the markers affects the color–color distributions of the neighboring galaxies. To do so, we divide the markers into three groups in each redshift bin based on their rest-frame NUV luminosity. Because the sample of the markers is not complete to the same rest-frame NUV depth, direct comparisons between different redshift bins cannot be made. However, within the same redshift bin, we can compare the color–color distributions of the markers and their neighbors over its range of rest-frame NUV luminosity. The result is presented in Figure 8. As in the case of EW([O ii] λ3727), we observe, and confirm with Kolmogorov–Smirnov tests, that within a fixed redshift bin the color distributions of the neighbors around markers with different NUV luminosities are statistically identical. This supports our conclusion of Figure 7 that the properties of the neighbors are not significantly affected by, or strongly correlated with, the characteristics of the markers. We also find that the optical color distributions of the markers themselves do not strongly depend on the absolute NUV luminosity.

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Since active galactic nucleus (AGN) activities in galaxies are sometimes responsible for emission lines, we are also interested in whether the neighbors of the AGN hosts have similar properties as those of normal star-forming galaxies, i.e., the rest of the WiggleZ galaxies. The most common way to distinguish AGNs and star-forming galaxies is based on the ratios of [O iii]/H_β and [N ii]/H_α emission lines, the so-called BPT plot (Baldwin et al. 1981). This method works only at z < 0.48 for the WiggleZ survey where all these emission lines can be detected within the spectral wavelength coverage. Recently Bongiorno et al. (2010) have used a method similar to the BPT plot to separate AGNs and star-forming galaxies at 0.50 ⩽ z ⩽ 0.92, i.e., [O iii] λ5007 /H_β versus [O ii]/H_β, in the zCOSMOS survey. The separation in this diagnostic diagram was derived empirically using the observed data by studying the positions in the diagram of AGN and star-forming galaxies which were classified based on the BPT plot (e.g., Rola et al. 1997; Lamareille et al. 2004). We present the [O ii]/H_β versus [O iii]/H_β plot for all our WiggleZ galaxies at 0.25 ⩽ z ⩽ 0.75 in Figure 9, where we overplot the analytical expression of Equation (3) of Bongiorno et al. (2010) for the demarcation curves between star-forming galaxies and AGNs. We divide the WiggleZ markers into three groups based on their locations on the [O ii]/H_β plot. Group A is those located below the analytical expression in the star-forming region. Group B contains a mix of star-forming and AGN galaxies, located in a narrow strip region centered at the analytical expression. Group C is the AGN candidates lying above the analytical expression. These groups contribute about 67%, 20%, and 13% of the galaxies, respectively.

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We find that the neighbors of each group have similar N_net distribution (Figure 10), and occupy essentially identical regions on the color–color diagram. The N_net here is computed using a limit of $M_{r^{\prime }}^*+1$, with $M_{r^{\prime }}^*$ derived in Section 4.5. This echoes our conclusion that the properties of the neighbors are not strongly affected by the properties of the markers themselves. Our results suggest that WiggleZ galaxies hosting an AGN are in environments similar to other WiggleZ galaxies. This conclusion is consistent with other more detailed studies of Seyfert galaxies that the average environment of their hosts is not significantly different from other galaxies of similar properties (e.g., De Robertis et al. 1998; Schmitt 2001).

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The GLF of the neighbors is constructed by projecting the CCM cube along the z-axis (i.e., the r' magnitude) to produce counts as a function of the r' magnitude. We have conducted and cross-checked the analyses using both the observed and rest-frame CCM cubes. Here, we present only the results using the rest-frame CCM cubes, for which g', r', and z' have been k-corrected to z = 0.50. We note that the observed r' band at z = 0.5 is approximately equivalent to the rest B band.

We also separate the neighbors into red and blue populations. The division between the red and blue populations is chosen to be the g' − r' color halfway between the non-evolving early-type and the star-forming τ model of Figure 2 at each redshift, equivalent to 0.27 mag bluer than the red-sequence color. To adjust for minor systematic effects in the photometry, the g' − r' color (at rest z = 0.5) of the red sequence in each redshift bin in Figure 11 is determined empirically as the reference. This is done by examining the g' − r' color distribution of galaxies in each redshift bin which are brighter than $^{0.5}M_{r^{\prime }}^*+1$ and have colors redder than (g' − r')_rs − 0.27, where (g' − r')_rs is the non-evolving rest-frame model early-type galaxy color of Figure 2. The distribution is fitted with a Gaussian, and the peak is used as the red-sequence color. The red-sequence colors and the boundaries between the red and blue populations are indicated in Figure 11 by the dotted and solid horizontal lines, respectively. We note that the computed g' − r' red-sequence colors are essentially identical to those of the models, with the exception of the z = 0.3 bin, where the g' − r' separation for red and blue galaxies appears to be ∼0.06 bluer than the computed color of (g' − r')_rs − 0.27.

The GLF results are presented in Figure 12. We denote the three subsamples of galaxies and their GLF as "All," "Blue," and "Red." The errors in the y-axis in each r' bin are computed using Poisson statistics. We also compute the GLF using the same method for the RCS-WSF sample for comparison with the WiggleZ neighbor galaxies at the two lower redshift bins, allowing us to examine the effects of environment on galaxy evolution. The CMD and the resultant GLFs for the cluster sample are plotted in Figure 13.

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We fit the GLF discussed above using the Schechter function. We determine the completeness limit in $^{0.5}M_{r^{\prime }}$ for each redshift bin by examining the total net counts in 0.1 mag bins as a function of $^{0.5}M_{r^{\prime }}$, smoothed by a three-bin kernel. We use the bin 0.1 mag brighter than the peak as the limit for fitting the Schechter function, giving ^0.5M_lim = [−17.9, −18.6, −19.0, −19.8, −20.3] for the five redshift bins. These limits are marked as vertical purple (dashed) lines in Figure 12.

To investigate the shape of the GLF, we first allow α to vary in fitting the Schechter function. The results of the Schechter function fits are tabulated in Table 3. As evident from the CMD (Figure 11), the GLFs in Figure 12 of the WiggleZ neighbor galaxy populations are dominated by blue galaxies. It is not surprising that the GLFs of the "All" and the "Blue" subsamples are similar, because ∼80% of the neighbors are blue galaxies.

Table 3. Parameters for Luminosity Functions of the WiggleZ Neighbors

All Neighbors
Redshift	$^{0.5}M_{r^{\prime }}^*$	α
Fitting α
0.25–0.35	−21.46 ± 0.18	−1.42 ± 0.05
0.35–0.45	−21.33 ± 0.21	−1.35 ± 0.08
0.45–0.55	−20.89 ± 0.14	−0.89 ± 0.10
0.55–0.65	−21.23 ± 0.15	−0.97 ± 0.12
0.65–0.75	−21.10 ± 0.16	−0.76 ± 0.18
Redshift	$^{0.5}M_{r^{\prime }}^*$	$^{0.5}M_{r^{\prime }}^*$	$^{0.5}M_{r^{\prime }}^*$
	α = −1.50	α = −1.30	α = −1.00
0.25–0.35	−21.68 ± 0.11	−21.16 ± 0.08	−20.60 ± 0.06
0.35–0.45	−21.70 ± 0.12	−21.22 ± 0.09	−20.69 ± 0.06
0.45–0.55	−21.92 ± 0.10	−21.51 ± 0.08	−21.02 ± 0.05
0.55–0.65	−21.98 ± 0.09	−21.65 ± 0.07	−21.26 ± 0.05
0.65–0.75	−21.89 ± 0.08	−21.63 ± 0.06	−21.30 ± 0.05
Q	−0.64 ± 0.32	−1.31 ± 0.24	−1.95 ± 0.19
$^{0.5}M_{r^{\prime }}^*(z=0.5)$	−21.84 ± 0.05	−21.44 ± 0.04	−20.98 ± 0.03
Blue Neighbors
Redshift	$^{0.5}M_{r^{\prime }}^*$	α
Fitting α
0.25–0.35	−21.41 ± 0.25	−1.56 ± 0.06
0.35–0.45	−21.34 ± 0.29	−1.49 ± 0.10
0.45–0.55	−20.90 ± 0.17	−1.02 ± 0.11
0.55–0.65	−21.19 ± 0.19	−1.05 ± 0.15
0.65–0.75	−21.02 ± 0.18	−0.74 ± 0.21
Redshift	$^{0.5}M_{r^{\prime }}^*$	$^{0.5}M_{r^{\prime }}^*$	$^{0.5}M_{r^{\prime }}^*$
	α = −1.50	α = −1.30	α = −1.00
0.25–0.35	−21.23 ± 0.11	−20.76 ± 0.08	−20.23 ± 0.06
0.35–0.45	−21.34 ± 0.13	−20.90 ± 0.10	−20.40 ± 0.07
0.45–0.55	−21.72 ± 0.11	−21.32 ± 0.09	−20.87 ± 0.06
0.55–0.65	−21.80 ± 0.10	−21.49 ± 0.08	−21.13 ± 0.06
0.65–0.75	−21.79 ± 0.09	−21.55 ± 0.07	−21.24 ± 0.06
Q	−1.49 ± 0.34	−2.10 ± 0.26	−2.71 ± 0.20
$^{0.5}M_{r^{\prime }}^*(z=0.5)$	−21.58 ± 0.05	−21.21 ± 0.04	−20.78 ± 0.03
Red Neighbors
Redshift	$^{0.5}M_{r^{\prime }}^*$	α
Fitting α
0.25–0.35	−20.23 ± 0.20	0.099 ± 0.27
0.35–0.45	−20.74 ± 0.22	−0.50 ± 0.19
0.45–0.55	−20.60 ± 0.20	−0.26 ± 0.21
0.55–0.65	−21.21 ± 0.24	−0.64 ± 0.22
0.65–0.75	−21.33 ± 0.38	−0.77 ± 0.37
Redshift	$^{0.5}M_{r^{\prime }}^*$
	α = −0.70	α = −0.40
0.25–0.35	−20.51 ± 0.12	−20.40 ± 0.09
0.35–0.45	−20.96 ± 0.10	−20.63 ± 0.09
0.45–0.55	−20.99 ± 0.09	−20.73 ± 0.08
0.55–0.65	−21.28 ± 0.09	−20.98 ± 0.07
0.65–0.75	−21.26 ± 0.11	−21.01 ± 0.09
Q	−1.79 ± 0.37	−1.59 ± 0.30
$^{0.5}M_{r^{\prime }}^*(z=0.5)$	−21.02 ± 0.05	−20.76 ± 0.04

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For the "Blue" and "All" samples, we find that the fitted α appears to become less steep at higher redshift. However, this could in part be the result of the different sampling magnitudes in the subsamples; the shallower absolute magnitude limits in the higher redshift bins make α less well determined. This is especially true at the highest redshift bin, where the completeness limit is only about 1–1.5 mag past M*. Discarding the z = 0.7 bin, the derived α for the "All" and "Blue" subsamples ranges between ∼ − 1.0 and ∼ − 1.5, comparable to values in the literature for star-forming or late-type galaxies (e.g., Wolf et al. 2003; Christlein et al. 2009; Liu et al. 2008). The possibility that the apparent changes in α at different redshifts are due to the change in the sampling limit can be demonstrated by fitting the three low-redshift bins for the "Blue" subsample to a common limit of $^{0.5}M_{r^{\prime }}= -19.0$, which is complete for the three bins. We obtain the results: α = [−1.15 ± 0.17, −1.38 ± 0.16, −1.03 ± 0.12] for z = [0.3, 0.4, 0.5], which are consistent with being identical at ∼1.75σ.

We overplot the Schechter LF in Figure 12 with fixed α = [−1.50, −1.30, −1.00] fitted for the "Blue" subsamples to show the ability of the data to distinguish between the faint-end slopes within this range. By combining the three lower redshift bins (0.25 < z < 0.55) where the data are of sufficient depth to obtain a robust measurement of α, we find for the "Blue" galaxies a best-fit α of −1.18 ± 0.08. For consistency of comparison of $^{0.5}M_{r^{\prime }}$ among redshift bins, we adopt an α of −1.3 for all redshift bins, and tabulate the fitted $^{0.5}M_{r^{\prime }}^*$ in Table 3.

The best fitting results for $^{0.5}M_{r^{\prime }}^*$ and α for the WiggleZ "Red" neighbor galaxy samples at different redshift bins are also presented in Table 3. For the lower redshift bins, where the data are of sufficient depth, the GLF is considerably less steep at the faint end compared to that of the "Blue" subsample. At higher redshifts, the red GLFs can be described by a steeper α, but this is again likely because the faint end of the GLF is not observable at these redshifts. We use the three lower redshift bins to establish a more robust estimate of the faint-end slope of the red galaxy GLF. We obtain α = −0.45 ± 0.13 by summing the data (to $^{0.5}M_{r^{\prime }}=-19.0$) in these bins.

For the purpose of comparison, we perform the same analysis for the RCS-WSF sample of markers in RCS2 clusters. Here, the CMD shows a very strong red sequence and the total GLF is dominated by red galaxies, as shown in Figure 13. The faint ends of the "Blue" galaxy GLF in the two redshift bins have a similar α as those for the corresponding subsamples of the WiggleZ neighbors. For the purpose of comparing M*, we also fit the RCS-WSF "Blue" samples using α = [−1.50, −1.30, −1.00] with the results listed in Table 4.

Table 4. Parameters for Luminosity Functions of the RCS-WSF Sample

All Neighbors
Redshift	$^{0.5}M_{r^{\prime }}^*$	α
Fitting α
0.25–0.35	−21.04 ± 0.08	−1.10 ± 0.03
0.35–0.45	−21.05 ± 0.10	−0.94 ± 0.06
Redshift	$^{0.5}M_{r^{\prime }}^*$	$^{0.5}M_{r^{\prime }}^*$	$^{0.5}M_{r^{\prime }}^*$
	α = −1.50	α = −1.30	α = −1.00
0.25–0.35	−22.14 ± 0.07	−21.53 ± 0.05	−20.81 ± 0.03
0.35–0.45	−22.14 ± 0.09	−21.67 ± 0.06	−21.13 ± 0.05
Blue Neighbors
Redshift	$^{0.5}M_{r^{\prime }}^*$	α
Fitting α
0.25–0.35	−20.94 ± 0.41	−1.52 ± 0.03
0.35–0.45	−21.59 ± 0.73	−1.55 ± 0.06
Redshift	$^{0.5}M_{r^{\prime }}^*$	$^{0.5}M_{r^{\prime }}^*$	$^{0.5}M_{r^{\prime }}^*$
	α = −1.50	α = −1.30	α = −1.00
0.25–0.35	−20.87 ± 0.18	−20.30 ± 0.13	−20.00 ± −0.0
0.35–0.45	−21.39 ± 0.29	−20.82 ± 0.21	−20.20 ± 0.15
Red Neighbors
Redshift	$^{0.5}M_{r^{\prime }}^*$	α
Fitting α
0.25–0.35	−20.52 ± 0.09	−0.64 ± 0.06
0.35–0.45	−20.81 ± 0.09	−0.66 ± 0.06
Redshift	$^{0.5}M_{r^{\prime }}^*$
	α = −0.70	α = −0.40
0.25–0.35	−20.62 ± 0.04	−20.14 ± 0.04
0.35–0.45	−20.86 ± 0.04	−20.45 ± 0.03

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Opposite to the WiggleZ neighbor samples, the GLF of the RCS-WSF sample of cluster galaxy targets is dominated by the "Red" galaxy sample. The faint-end slope for these red galaxies appears to be significantly steeper than that of the WiggleZ counterpart, with α being steeper than −0.65. The combined "Red" GLF for the two redshift bins of the RCS-WSF data produces a best fitting α = −0.74  ±  0.06. A similar combination for the WiggleZ neighbor sample produces α = −0.18  ±  0.17. In order to provide a consistent comparison for the $^{0.5}M_{r^{\prime }}^*$ values for the "Red" WiggleZ neighbor sample and the "Red" RCS2 cluster neighbor sample, we also refit all the red galaxy subsamples using α = −0.4 and −0.7, and the results are tabulated in Table 3.

We examine the evolution of the $M^*_{r^{\prime }}$ parameter of the Schechter LF by assuming a simple linear dependence between $M^*_{r^{\prime }}$ and redshift, as used by Lin et al. (1999) and others. We can write $^{0.5}M_{r^{\prime }}^*(z)$ = $m_{r^{\prime }}^*\,{-}\,{\rm DM}\,{-}\,(k\,{-}\,k_{z\,{=}\,0.50})\,{+}\,Q(z\,{-}\,0.5)$, where DM is the distance modulus and k is the k-correction. The evolution term Q is derived from a linear fit to $^{0.5}M_{r^{\prime }}^*$ as a function of redshift in the form of $^{0.5}M_{r^{\prime }}^*(z)$ = $^{0.5}M_{r^{\prime }}^*(z=0.5) + Q(z-0.5)$. The derived Q depends on the value of α; a steeper α results in a smaller Q. Because the fitted α and $M_{r^{\prime }}^*$ correlate with each other and α are marginally different in our redshift divisions, we use $M_{r^{\prime }}^*$ derived with α = −1.30 for the "All" and "Blue" subsamples and α = −0.40 for the "Red" neighbors, obtaining Q = [−1.31 ± 0.24,−2.10 ± 0.26,−1.59 ± 0.30] for the "All," "Blue," and "Red" subsamples, respectively. The results are shown in Figure 14 and tabulated in Table 3. We also derive Q using α = −1.0 and −1.5 for the "All" and "Blue" neighbors, and α = −0.7 and −0.4 for the "Red" subsample. These fits are shown in Figure 14 as a dotted line for each redshift bin.

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We adopt the parameterization of $^{0.5}M_{r^{\prime }}^*(z) = -21.44 - 1.31(z-0.5)$ from the "All" sample in the derivation of the red-galaxy fraction in the following subsection.

Our WiggleZ galaxy neighbor sample represents a complete census of galaxies in the neighborhood of star-forming galaxies over the redshift range of 0.25–0.75. On the color–magnitude plane, we separate the galaxy sample into red and blue galaxy subsamples. The GLFs for both the "Blue" and "Red" galaxy samples can be fitted very well with single Schechter functions. Based on the low-redshift bins, where there is sufficient depth to measure the faint-end slope unambiguously, they have different shapes such that the red galaxies have a dipping faint end (best fitted with α ≳ −0.6), whereas the blue galaxies have a steep rising faint end which is best fitted with α ∼ −1.3. This is similar in general to what is seen in clusters, where red-sequence galaxies typically have a turnover in the GLF, while the blue galaxies increase in number steeply at the faint end (e.g., Barkhouse et al. 2007; Wolf et al. 2009).

We can make a direct comparison between the WiggleZ neighbor sample, representing galaxies associated with star-forming galaxies, and the neighbors of the RCS-WSF sample, representing galaxies in dense cluster environments, by combining the z ∼ 0.3 and 0.4 subsamples. We find the "Blue" galaxy samples to have essentially identical GLF parameters: α = −1.42 ± 0.08 and −1.57 ± 0.13, and ^0.5M*_r = −21.15 ± 0.19 and −21.37 ± 0.47. The red galaxy GLFs for the two samples appear to have different faint-end slopes at the 4.3σ level, with α = −0.18 ± 0.17, and −0.74 ± 0.06 for the WiggleZ neighbors and the RCS-WSF neighbors. The RCS-WSF red galaxy neighbors also have a marginally brighter ^0.5M*_r of −20.78 ± 0.09, compared to −20.42 ± 0.15 for the WiggleZ neighbor sample, at the 2σ level. However, this difference is most likely a reflection of the different α used in the best fits; fitting both "Red" GLFs using a common α = −0.5 for z = 0.25 to 0.45, we obtained $^{0.5}M_{r^{\prime }}^*$ = −20.42 ± 0.09 and −20.53 ± 0.07 for the RCS-WSF and the WiggleZ neighbor sample, respectively. We will further discuss the difference in the GLF shape in Section 5.4.

We use the parameter Q (see Section 4.5) to measure the evolution of M*, with the assumption of α being constant with redshift for the faint end of the GLF. The results for different samples and α are shown in Figure 14. There is a general brightening of M* with larger redshift. An interesting trend is that red-sequence galaxies may have a lower Q value than that of blue-cloud galaxies, ∼ − 1.6 versus ∼ − 2.1, but only at 1.3σ.

Using a sample drawn from the DEEP2 and COMBO-17 data and with SDSS data as the local universe epoch, Faber et al. (2007) studied the evolution of the GLF in the redshift range of 0.1 ⩽ z < 1 in the M_B band, which is similar in rest wavelength to our $^{0.5}M_{r^{\prime }}$ band. They obtained Q values of −1.23 ± 0.36, −1.34 ± 0.22, −1.20 ± 0.21, over the range of z ∼ 0 to 1, for their "All," "Blue," and "Red" samples. These values appear to be lower from those derived in our samples (see Table 3) at moderately significant levels, especially for the "Blue" sample. However, the comparison is much more similar if we limit their data to the same redshift range as ours. In Figure 14, we plot their M*_B data points. For a more direct comparison, we also convert their B band to our $^{0.5}M_{r^{\prime }}$ by applying color corrections based on B − r' colors from GISSEL (Bruzual & Charlot 2003) to convert M_B to $M_{r^{\prime }}$ at zero redshift, and then k-correct $M_{r^{\prime }}$ to $^{0.5}M_{r^{\prime }}$. These data are also plotted in Figure 14.

We refit the Q factor from Faber et al. (2007) using their data within the redshift range covered by our WiggleZ neighbor sample. We find Q = [−1.45 ± 0.25, −2.02 ± 0.32, −0.67 ± 0.38] (in their B band) for their "All," "Blue," and "Red" samples, respectively, compared to our values of −1.31 ± 0.24, −2.10 ± 0.26 (α = −1.3), and −1.59 ± 0.30 (α = −0.4) in Table 3. Thus, the derived Q values from the two studies over the same redshift range are similar, especially for the "All" and "Blue" samples. For the "Red" samples, the WiggleZ neighbors have a steeper evolution, at the ∼2σ level. We note that over this redshift range the Faber et al. results also produce a relatively significant lower Q value for their "Red" sample compared to that for their "Blue" sample, at the 2.7σ level, reinforcing a possible similar trend in the WiggleZ samples. The marginally steeper evolution of the "Red" samples in the two data sets could be a reflection of the difference in the selection for the red galaxy samples. This possible discrepancy could be an indication that there is a difference in the evolution of early-type galaxies based on the environment. The red galaxies in the WiggleZ neighbor sample are primarily in low-density regions, conducive to star formation; while those in the Faber et al. sample include red galaxies in all environments, with an expected bias toward high-density regions. Thus, it is perhaps not surprising that the two samples have different Q values, with the red GLF in low-density regions evolving more rapidly. However, we note that the differences discussed in this subsection are at the ∼2σ levels. Considerably more detailed studies are needed to firmly establish the differences in the evolution of the GLF of different galaxy populations in different environments.

We observe that f_red is remarkably similar at 0.25 ⩽ z < 0.65, with a value of ∼0.28. A linear fit to the four points gives a slope of −0.070 ± 0.098. The f_red drops to about 0.20 for the z = 0.7 bin. This drop, between the z = 0.6 and 0.7 bins, is statistically significant at the ∼3.5σ level. If we assume the best linear fit for f_red from the four data points with z < 0.65, the f_red at z = 0.7 is 4.8σ below the extrapolation from the fit. An alternative simpler description of the trend is a linear decrease; however, this linear fit, to all five points, has a reduced χ² of 3.1, indicating that it is not a good description of the data.

To investigate whether there is a change in the dependence of f_red on z at z ∼ 0.7, we extend the measurement of f_red to z ∼ 0.8. The WiggleZ sample has a large number of galaxies at 0.75 < z < 0.85, which we have not included in our analysis because the RCS2 photometry is only complete to a relatively shallow absolute magnitude limit of −20.6. Nevertheless, this bin is complete to $^{0.5}M_{r^{\prime }}$ + 1.2, and hence, we perform the same analysis using the 5819 WiggleZ galaxies in this redshift bin as markers. The f_red computed using this sample is plotted in Figure 15. It shows a continuous drop from the z = 0.7 data point. A linear fit applied to all six data points from z = 0.3 to z = 0.8 with a limiting magnitude of M* + 1.2 produces a reduced χ² of 6.3, indicating a poor fit. Thus, the addition of the higher redshift data adds confidence to the conclusion that there is an onset of a significant drop in the red-galaxy fraction at z > 0.65.

We compare our results to Iovino et al. (2010), who derived the blue galaxy fraction F_blue for galaxy samples in different environments from the zCOSMOS survey. Of particular interest is their "All" and "Isolated" subsamples of Sample III, with a depth of M = M* + 1.5, covering the redshift range of ∼0.2–0.6. Iovino et al. (2010) parameterize the evolution of F_blue by a power law of the form equivalent to f_red(z) = 1 − F_blue(0)(1  +  z)^β, with F_blue(0) = 0.58 ± 0.10 and β = 0.69  ±  0.44 for the Isolated sample, using three data points. We plot their F_blue(z) as f_red in Figure 15 using their parameterization. Our f_red has values more similar to their Isolated sample, and well below their "All" sample. This is consistent with our expectation that the WiggleZ neighborhoods have by-and-large a low galaxy density environment, dominated by star-forming galaxies.

For a more direct comparison, we fit our f_red with the power law over a longer redshift range (z = 0.20–0.70) than Iovino et al. (2010), and obtain (for M* + 1.4) F_blue(0) = 0.59 ± 0.04, and β = 0.52 ± 0.13 with a reduced χ² ∼ 3.1. Thus, our data show a similar rate of decrease of f_red with increasing redshift as that found by Iovino et al. (2010). However, we note that both of the fitting models to our data—the linear fit and the power-law fit—have reduced χ² considerably larger than 1: ∼3–4 for both using data up to z = 0.7 and z = 0.8. This indicates that a simple continuous decrease of f_red with redshift is likely not a good description of its evolution.

Thus, an interesting result is that our data, covering a longer redshift baseline than the Iovino et al. (2010) study, show a more or less constant f_red up to z ∼ 0.6 before seeing a drop. Such a description of the change in f_red for galaxies in poor environments with redshift is in fact also consistent with the data of the "Isolated" sample of Iovino et al. (2010), with their three F_blue data points covering the redshift between 0.2 and 0.6 being consistent with having similar values within their uncertainties. We note that the more or less constant f_red ∼0.3 for z ≲ 0.6 for the WiggleZ neighbor samples is similar to that obtained for galaxies in low-density regions at the local universe at z ∼ 0; e.g., Balogh et al. (2004) derived f_red ∼ 0.35 from the SDSS sample for their low local-galaxy density samples of galaxies of M_V ≲ −20. The f_red for the WiggleZ galaxy neighbors extrapolates to ∼0.32 at z = 0. Thus, there appears to be a relatively small amount of evolution in f_red in low galaxy density regions from z ∼ 0.6 all the way to z ∼ 0.

Because the WiggleZ sample is selected in part by observed UV and optical fluxes of the objects, this abrupt increase in the change in f_red between the 0.6 and 0.7 redshift bins could conceivably be contributed by some unknown correlation or thresholding effect between the star formation rate or luminosity of the markers and the properties of their neighbors. To test the effect of the UV flux selection criterion, we select two subsamples of markers within an identical UV absolute luminosity range which is complete in the both z ∼ 0.6 and z ∼ 0.7 bins (M_NUV ⩽ −20.7), and compute their f_red. We obtain f_red = 0.293 ± 0.022, and 0.207 ± 0.017 for the neighbors in the two redshift bins, indicating a similar and significant (at ∼3σ) drop to that when the whole sample without control on M_NUV is used. Similarly, we compare the f_red of neighbors of subsamples of markers with the same r' absolute magnitude ($^{0.5}M_{r^{\prime }}$ between −21.5 and −22.5) in the last two redshift bins, and obtain f_red = 0.255 ± 0.045 and 0.176 ± 0.033; again, showing a drop similar to that obtained using the whole redshift bins. Thus, we can conclude that the drop in f_red between z ∼ 0.6 and 0.7 is likely not a result of the different star formation properties of the central markers.

Our data allow us to look at the redshift evolution of the red-galaxy fraction f_red up to z ∼ 0.7 using samples complete to an absolute luminosity about 1.5 mag beyond M*. Under the simplest assumption of a sample of galaxies in a closed volume, f_red allows us to follow the end result of the process of galaxies having their star formation quenched and eventually turning red, becoming a member of the red sequence (e.g., Kodama & Bower 2001). However, the use of a luminosity limit produces ambiguities in how to interpret the average change in the galaxy population between the different epochs, since galaxies of a given mass may enter and leave the sample depending on their star formation state. To assist in the interpretation of the observed change in f_red with redshift, we illustrate in Figure 16 the possible flows of galaxies into and out of luminosity-limited blue and red galaxy samples.

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In a simple picture, the number of galaxies in the blue cloud can be augmented by new star formation in galaxies fainter than the luminosity limit, boosting them into the sample, adding to the blue galaxy counts. This replenishment is represented by the white arrows (A) in Figure 16. In a field situation, where infall in general is not a major process, one can consider this replenishment generally being controlled by the canonical down-sizing scenario of star formation—lower mass galaxies may start forming stars, and in some instances, boosting the luminosity of the galaxy into the blue cloud sample.

On the other hand, one would expect a continuous flow of galaxies from the blue cloud into the red sequence as galaxies evolve. This would primarily be created by the quenching of star formation in galaxies in the blue cloud by various processes. There are several paths that this transformation into the red sequence may take and are illustrated by the three black arrows (B1, B2, and B3) schematically. The luminosity of a galaxy will generally fade as its star formation is quenched and turns red (B1 and B2), and some of them will become fainter than the sample magnitude limit and leave the sample. There is also a possibility that the galaxy becomes brighter if the cessation of star formation follows a major merger (arrow B3). However, in poor environments, it is unlikely that this is a dominant event; e.g., Hsieh et al. (2008) found that approximately 6% of galaxies may have undergone a major merger since z ∼ 0.8.

In the WiggleZ sample of neighbors of strong star-forming galaxies we find that f_red is essentially flat from z ∼ 0.6 to the present, with evidence of a decrease at z ≳ 0.6. In the simplest picture, the change in f_red over redshift can be interpreted as a change in the relative flow rates of galaxies into the red sequence and into the blue cloud. Thus, at z ≲ 0.6 we can effectively conclude that the rate of transformation of blue galaxies into red galaxies, which builds up the red sequence, is approximately equal to the replenishment rate of blue galaxies brighter than the sampling limit; while at z ≳ 0.6 the rate of transformation of blue galaxies into red galaxies is lower than the replenishment rate of blue galaxies, so that there is a net decrease of red galaxies relative to the blue galaxies.

However, the change in f_red with redshift does not give us unambiguous information on the actual changes in these rates. If we assume that the rate of the buildup of the red sequence is constant over the redshift range of ∼0.8–0.2, we would then conclude that the rate of replenishment of blue galaxies (into the luminosity-limited sample) is decreasing from z ∼ 0.8 to 0.6, and then becomes stable, or decreasing at a much lower rate, at z ≲ 0.6. Alternatively, if we assume that the replenishment of blue galaxies is constant, then the rate of transformation of blue cloud galaxies into the red sequence is increasing from z ∼ 0.8 to 0.6 and becomes stable at z ≲ 0.6. The detailed picture is certain to be more complex. In a more general picture, the environment will be a major factor that affects these rates of flows. An important effect to consider is the infall of galaxies into a high-density region such as the parent halo of a galaxy cluster or group. We will discuss this effect in Section 5.4, in conjunction with the evolution of f_red in clusters.

We have also derived f_red for the RCS-WSF cluster neighborhood sample for the z ∼ 0.3 and z ∼ 0.4 bins, which are plotted as open circles in Figure 15. They show a clear difference due to the environments of the galaxies; the cluster neighborhood samples have f_red of ∼0.8, indicative of high galaxy density regions. While we do not have the redshift range to examine the evolution of f_red in clusters, studies using similar techniques of large samples of clusters show a continuous decrease of f_red with redshift, i.e., the Butcher–Oemler effect (Butcher & Oemler 1984). For instances, Loh et al. (2008), using a sample of approximately 1000 clusters from RCS1 at 0.4 ⩽ z ⩽ 0.9, show a steady decrease in f_red of about 0.4; while the spectroscopic sample of Ellingson et al. (2001) indicates a steady drop of f_red from 0.9 to 0.7 at z = 0.2–0.5.

Comparing these results with the WiggleZ neighbor sample, there appears to be a rather different behavior in the change in f_red as a function of redshift for galaxies in regions around star-forming galaxies from those in high galaxy density regions around massive halos. Instead of a steady decline in f_red with increasing redshift, the f_red for the WiggleZ neighbors have a basically flat dependence on z, and show a significant drop only at z ≳ 0.65. Similarly, Iovino et al. (2010) show that galaxies classified as being in a group environment have a much steeper dependence of their blue-galaxy fraction on redshift than those considered to be in isolated environments. This difference in the evolution of f_red can be considered as a clear demonstration of the effect of environment on the evolution timescale of galaxy populations.