COSMIC WEB AND STAR FORMATION ACTIVITY IN GALAXIES AT z ∼ 1

This consists of a complete sample of Hα emitting star-forming galaxies at z = 0.845, selected through narrow-band near-infrared (J filter) observations, performed as a part of the High-z Emission Line Survey (HiZELS; Geach et al. 2008; Sobral et al. 2009, 2012, 2013), covering an area of ∼0.8 deg² in the COSMOS field (Scoville et al. 2007). The sample includes a total of 425 galaxies with K < 23 and log(M/$\mathrel {M_{\odot }})\ge$ 9, located in a narrow redshift slice of Δz = 0.03 centered at z = 0.845 (0.83 ⩽ z ⩽ 0.86). This sample is flux limited (∼8 × 10⁻¹⁷ erg s⁻¹ cm⁻² which is equivalent to the SFR limit of ∼1.5 $\mathrel {M_{\odot }\ \rm yr^{-1}}$ at z ∼ 0.84) and is selected homogeneously down to the rest-frame Hα + [N ii] equivalent width limit of ∼25 Å. For more properties of this sample, see, e.g., Sobral et al. (2011, 2014).

The control sample is based on the COSMOS UltraVISTA Ks-band selected photometric redshift catalog (Ilbert et al. 2013; McCracken et al. 2012). The Ks-band selected catalog consists of ground- and space-based imaging data in 30 bands. Due to the large number of filters covering a broad wavelength range, the photometric redshifts are very secure. It has been shown that at z < .5, the photo-z accuracy is better than 1% with less than 1% of catastrophic failure (Ilbert et al. 2013). At the redshift of this study, the median redshift uncertainty is Δz ∼ 0.01. Galaxies in the control sample have the same magnitude, mass, and areal coverage as the Hα sample and have more than 10% probability of belonging (P_limit = 0.1) to the redshift slice of Hα emitters (0.83 ⩽ z ⩽ 0.86). This probability weight is calculated by measuring what percentage of the photo-z probability distribution function (PDF) for each galaxy lies within the redshift slice defined by the narrow-band Hα sample. This results in a Ks-band selected sample containing 3920 galaxies. Increasing the P_limit results in a control sample less contaminated by foreground and background sources. However, this also has an increasing risk of losing sources; i.e., a less complete sample at z ∼ 0.84 (see Section 2.4). Here, we use a 10% cut as a trade-off between contamination and completeness. Nevertheless, we scrutinized a variety of probability limits (0.05, 0.2, 0.3, 0.4, and 0.5) and were able to retrieve the same results.

The underlying galaxies were later divided into quiescent and star-forming systems based on their rest-frame two-color NUV − r⁺ versus r⁺ − J plot. Previous studies show that the rest-frame NUV − r⁺ color is a better indicator of the recent star formation activity (Martin et al. 2007) and has a wider dynamical range compared to the rest-frame U − V color (Ilbert et al. 2013). Here, galaxies with rest-frame color NUV − r⁺ > 3.1 and NUV − r⁺ > 3(r⁺ − J) + 1 are selected as quiescent systems. Figure 1 shows the rest-frame NUV − r⁺ versus r⁺ − J distribution of galaxies in the control sample and the color cuts used to separate quiescent and star-forming systems. We clearly see two populations of galaxies. We stress that adding dust to the star-forming galaxies causes them to move diagonally from the bottom left to the top right of Figure 1, making them separable from the quiescent systems (Ilbert et al. 2013). The star-forming galaxies in the control sample will later be used, along with the Hα sample, to study the effects of different SFR estimators on the results.

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2.3.1. Mass and SFR for the Star-forming Sample

2.3.2. Mass and SFR for the Control Sample

In order to estimate the completeness and contamination in both the Hα and the underlying control samples, we use the VLT-VIMOS zCOSMOS spectroscopic survey (Lilly et al. 2007) selected as I < 22.5. Here, only the highly reliable spectroscopic redshifts are considered (Classes 3 & 4 with spectroscopic reliability >99.5%). Using the spectroscopic data, we estimate the completeness as the ratio of the number of underlying galaxies in the control sample that have spectroscopic redshifts within the Hα redshift slice (0.83 ⩽ z ⩽ 0.86) to the total number of galaxies with spectroscopic redshifts in the same slice. Contamination is computed as the fraction of galaxies in the underlying control sample with spectroscopic redshifts located outside the Hα redshift slice. Previous studies show the Hα sample to be <4% contaminated and >96% complete (see Sobral et al. 2010, 2013). For the control sample, we estimate the contamination and completeness to be 64% and 74%, respectively (Figure 2). As explained in Section 2.3.2, a probability limit of 10% (P_limit = 0.1) was used to select galaxies in the control sample; i.e., galaxies have a likelihood of >10% belonging to the redshift slice 0.83 ⩽ z ⩽ 0.86 set by the Hα sample. A higher probability limit results in a more reliable and less contaminated control sample. However, this also leads to a less complete and statistically smaller sample. Figure 2 shows completeness and contamination fractions in the control sample as a function of the probability limit (P_limit) used to define it. Completeness declines with increasing probability limit faster than contamination decreases.

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In estimating the contamination and completeness for the control sample, we assume that they are independent of the apparent magnitude and we can extrapolate the results from bright (I < 22.5) to faint galaxies. This is a valid assumption given that (1) at I < 24, a comparison between the photometric and spectroscopic data shows that the photo-z accuracy is ∼0.01 (Ilbert et al. 2009), smaller than the redshift slice defined by the Hα sample (∼0.03) and (2) the majority of galaxies in the control sample (∼93%) are brighter than I < 24.

We also stress that since massive red galaxies, which dominate denser environments, will have sharply peaked photo-z PDFs compared to less massive blue systems, they will be more complete and less contaminated. As a result, the completeness/contamination might be a function of the environment. We investigate the environmental dependence of completeness/contamination and find that although the completeness and contamination functions vary with the environment (highest completeness/lowest contamination in clusters), the correction factor (used in Sections 3.1 and 4.1) is almost independent of the environment (the higher completeness is accompanied by a lower contamination which leaves the correction factor almost intact) and this will not affect our results.

In order to identify and extract the LSS (filaments and clusters) in the underlying galaxy distribution, first we need to estimate the surface density field within the redshift slice defined by our narrow-band Hα survey (0.83 ⩽ z ⩽ 0.86). The surface density field is evaluated using the weighted adaptive kernel density estimator described in detail in B. Darvish et al. 2014 (in preparation). In this method, we first associate a weight to each galaxy, i, in the control sample (consisting of both quiescent and star-forming galaxies) using its photo-z PDF. The weight for each individual galaxy, w_i, is defined as the fraction of its photo-z PDF which lies within the boundaries of the redshift slice. This gives the probability of the galaxy belonging to the redshift slice associated with the Hα selected sample. The initial estimate of the surface density associated with the ith galaxy, $\hat{\Sigma }_i$, is found by summing over all the weighted fixed kernels placed on the positions of galaxies, j, where i ≠ j:

$$\begin{equation} \hat{\Sigma }_i= \frac{1}{\sum _{\!\!\!\begin{array}{l}\scriptstyle j=1\\ \scriptstyle j\ne i\end{array}}^{N} w_j}\sum _{{{ {\begin{array}{c}\scriptstyle j=1\\ \scriptstyle j\ne i\end{array}}}}}^{N} w_j K({\bf r_i, r_j,}{\rm h}), \end{equation} \tag{ 1 }$$

where N is the number of galaxies in the control sample, K(r_i, r_j,h) is the fixed kernel, $\bf r_i$ is the position of the galaxy for which the initial estimate of surface density is measured and $\bf r_j$ is the position of the rest of the galaxies. The width of the kernel is expressed by the parameter, h, which is a proxy for the degree of smoothing. For the first estimate of the density, this is taken to be fixed. For the kernel smoothing function, we use a 2D symmetric Gaussian defined as:

$$\begin{equation} K({\bf r_i, r_j,}{\rm h})=\frac{1}{2\pi {\rm h}^2}e^{-\frac{|\bf r_i-\bf r_j|^2}{2{\rm h}^2}} \end{equation} \tag{ 2 }$$

A large kernel width (h) results in over-smoothing of the density field which tends to wash out real features while a small value tends to break up regions into smaller uncorrelated substructures. Here, we use a fixed physical length of h = 0.5 Mpc which corresponds to the typical value of R₂₀₀ for X-ray clusters and groups in the COSMOS field (Finoguenov et al. 2007; George et al. 2011). However, a constant value of h for the whole field has the problem that it underestimates the surface density in crowded regions while it overestimates it in sparsely populated areas. To overcome this problem, we introduce the adaptive smoothing width, h_i, which is a measure of the local surface density associated with each galaxy, $\hat{\Sigma }_i$. This is defined as h_i = h × λ_i, where λ_i is a parameter that is inversely proportional to the square root of the surface density associated with the ith galaxy at the position of that galaxy (Silverman 1986):

$$\begin{equation} \lambda _i\propto \hat{\Sigma }({\bf r_i})^{-0.5} \end{equation} \tag{ 3 }$$

Having the adaptive kernel, we now calculate the surface density field, Σ(r), on each location on a fine 2D grid, r = (x, y) as:

$$\begin{equation} \Sigma ({\bf r})= \frac{1}{\sum _{\rm i=1}^{\rm N} {\rm w_i}}\sum _{\rm i=1}^{\rm N} {\rm w_i K}({\bf r, r_i,}{\rm h_i}) \end{equation} \tag{ 4 }$$

The surface density field is evaluated on a 300 × 240 grid with a grid size (resolution) of 0.005 deg (corresponding to ∼0.125 Mpc physical size at z ∼ 0.85). The estimated surface density field needs to be corrected for incompleteness and contamination in the control sample since the incompleteness tends to underestimate the density values whereas the contamination has a tendency to overestimate them. Thus, we introduce a correction factor, η, simply defined as:

$$\begin{equation} \eta =\frac{(1-{\rm contamination})}{{\rm completeness}}. \end{equation} \tag{ 5 }$$

The surface density field corrected for completeness and contamination, $\Sigma _c(\bf r)$, becomes:

$$\begin{equation} \Sigma _c({\bf r})=\eta \Sigma ({\bf r}). \end{equation} \tag{ 6 }$$

The density field corresponding to the underlying galaxies near the edge of the field covering Hα emitters is biased toward the smaller values, affecting the surface densities near the edge of the field. To minimize this edge effect, we make use of a larger underlying galaxy sample distributed well beyond the Hα coverage to estimate densities. Later, we limit our analysis to the area of Hα emitters.

We stress that since we use galaxy weights, w_is, to estimate the surface density field (Equations (1) and (4)), our method is immune to spurious structures due to possible random clustering of foreground and background galaxies. These contaminating galaxies would have smaller weights (because only the tail of their photo-z PDF would overlap the redshift slice associated with the Hα sample) and therefore, they contribute only marginally to the estimated density field.

We confirm the robustness of the estimated density field in this section by comparing it with the X-ray clusters/groups (Finoguenov et al. 2007; George et al. 2011) and Voronoi tessellation-based density field of Scoville et al. (2013). This is presented in Figure 3 where we find a very good agreement between our weighted adaptive kernel estimator and the independent estimation based on Voronoi tessellation (Scoville et al. 2013). There is also a good consistency between the overdense regions and the position of X-ray clusters/groups.

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To identify and extract spatial structures such as filaments and clusters in the underlying galaxy distribution, we utilize the 2D version of the MMF algorithm developed by Aragón-Calvo et al. (2007). This algorithm is able to assign a filament and a cluster signal to each point in the surface density field based on the local geometry of the point in question. If the local geometry of a point in the density field has a greater resemblance to a thread-like structure (filament) than a circular-like feature (cluster), its filamentary signal surpasses its cluster signal. The local geometry of each point is calculated based on the signs and ratio of eigenvalues of the Hessian matrix $H(\bf r)$ which is the second-order derivative of the surface density field:

$$\begin{equation} H(\bf r)= {\left[\!\!\begin{array}{cc}\nabla _{xx}\Sigma _c(\bf r)& \nabla _{xy}\Sigma _c(\bf r)\\ \nabla _{yx}\Sigma _c(\bf r)& \nabla _{yy}\Sigma _c(\bf r) \end{array}\!\!\right]}, \end{equation} \tag{ 7 }$$

where ∇_ijs denote the second derivatives in the i and j directions. Since structures have a variety of physical sizes, this algorithm builds a scale-independent structure map by smoothing the surface density field over a range of physical scales and eventually selecting the greatest cluster and filament signal among all the various signal values at different physical scales. Here, we use a circularly symmetric Gaussian smoothing function with various physical scales in the range ∼0.125–1.5 Mpc. Ultimately, each point in the density field has an associated filament-like value between 0 and 1 (filament signal, S_f) as well as a cluster-like value between 0 and 1 (cluster signal, S_c) that are interpolated into the positions of galaxies. S_f and S_c indicate the degree of resemblance of the local environment of any given point to a filament or cluster, respectively (Figure 4).

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Using the techniques developed in Sections 3.1 and 3.2, three environments are defined: clusters as regions with a cluster signal greater than 0.5 and also greater than or equal to that of a filament (S_c > 0.5 and S_c ⩾ S_f), filaments as regions with filament signals greater than 0.5 and greater than that of a cluster (S_f > 0.5 and S_f > S_c) and the remaining regions with both cluster and filament signals less than or equal to 0.5 (S_c ⩽ 0.5 and S_f ⩽ 0.5) as part of the general field. The structures identified over the area covered by the Hα narrow-band survey are shown in Figure 4. We demonstrate the filament signal values as a heat map whereas the cluster signal values are shown as contours. We have confirmed the resulting structures in Figure 4 by comparing them with the structures depicted from X-ray observations. The X-ray groups & clusters in the redshift range 0.82 ⩽ z ⩽ 0.87 (Finoguenov et al. 2007; George et al. 2011) are overlaid on our predicted structures in Figure 4 and show close agreement.

Using the defined environments, we estimate the average number density of Hα emitters to be δ_Hα = 1.53 ± 0.29, 0.45 ± 0.09, and 0.13 ± 0.01 arcmin⁻² in clusters, filaments, and the field, respectively. The errors are estimated assuming Poisson statistics. δ_Hα values clearly show that dense, intermediate, and sparse environments are respectively occupied by clusters, filaments, and the field. A better representation of the density in different classes of environment is seen in Figure 5. A normalized distribution of overdensity values of the surface density field (estimated in Section 3.1) within regions defined as clusters, filaments, and the field is shown in Figure 5. Although they inhabit relatively distinct values of overdensity, there is a substantial degree of overlap which means that a pure density-based definition of environment is not fully adequate to identify different structures. Intermediate densities do correspond mostly to filaments (even though only our analysis actually disentangles them from clusters and the field). Throughout this work, we use the environment defined based on the MMF algorithm as a robust indicator of the cosmic web.

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We also note that ideally, one wishes to select clusters and filaments with the highest signal value but practically, this leads to a statistically smaller sample size (especially for Hα emitters). The selection cut here (0.5) is due to a trade-off between the sample size and the reality (significance) of clusters and filaments. Nevertheless, we fine-tuned around the selection cut and examined some other values (0.3, 0.4, and 0.6) and found no significant change in the results.

Using the structures identified in Section 3.3, we now study the fraction of star-forming Hα emitters (the ratio of the number of Hα emitters to the total number of underlying galaxies in the control sample) in filaments, clusters, and the field. This fraction is corrected for contamination and incompleteness. In order to examine the effect of photometric selection on our result, we perform this on both our original Ks-band and I-band selected control samples in the COSMOS (the I-band selected catalog is from Capak et al. 2007). The correction factor, η, is 0.49 and 0.47 for the Ks- and I-band samples, respectively. An increase in the fraction of Hα emitters is seen in the filaments relative to both the cluster and the field environments (Figure 6). This trend is not influenced by the photometric selection wavelength (I-band versus Ks-band) in the underlying galaxy population. The error bars in Figure 6 are evaluated assuming Poisson statistics. As noted by Ilbert et al. (2013), the longer wavelength selection (Ks-band here) can more reliably detect galaxies at intermediate to high redshifts and we mention that the results based on the Ks band are likely more robust.

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The enhancement in the fraction of Hα emitters in filaments (i.e., intermediate densities) is consistent with previous studies, depicting the importance of intermediate environments, i.e., galaxy groups and the outskirts of galaxy clusters and filaments, in the evolution of galaxies. These results hold at low-z (z ≲ 0.5, Fadda et al. 2008; Tran et al. 2009; Biviano et al. 2011; Geach et al. 2011; Koyama et al. 2011; Mahajan et al. 2012), intermediate-z (z ∼ 1, Koyama et al. 2008, 2010; Sobral et al. 2011; Pintos-Castro et al. 2013), and high-z (z ≳ 1.5, Koyama et al. 2014; Santos et al. 2014).

At z ∼ 1, the closest work to our study in terms of sample selection is that of Sobral et al. (2011) who showed that at z ∼ 0.85, the fraction of Hα emitters from both COSMOS- and UDS-HiZELS surveys, when compared to the underlying population of galaxies at the same redshift, peaks at intermediate environments, in agreement with our result. Pintos-Castro et al. (2013) performed a thorough IR study of a super-structure at z ∼ 0.85 and showed that although the average star formation does not show any clear environmental dependence (see Section 4.2), the fraction of star-forming galaxies indicates that intermediate densities are preferred. They showed that the enhancement in the fraction of star-forming far-IR emitters in medium densities is seen for both optically red and blue far-IR emitters and also in different mass-binned samples. This is also consistent with our results here regarding the enhancement in the fraction of Hα emitters in filaments, although they used far-IR emitters as indicators of star-forming galaxies and number density of galaxies as a measure of environment. A combined narrow-band Hα and AKARI mid-IR imaging survey of a z = 0.81 super-structure by Koyama et al. (2010) revealed that the red Hα emitters and mid-IR galaxies are more commonly found in medium density environments such as cluster outskirts, groups, and filaments. This reinforced the results of a similar study of the same structure by Koyama et al. (2008), which showed that the fraction of both red and blue 15 μm selected galaxies is highest in medium density environments. Both of these studies by Koyama et al. (2008, 2010) at z ∼ 0.8 agree with our results in this section but we note that we are explicitly identifying filamentary structures as the drivers of such enhancement.

At lower redshift (z ≲ 0.5), there are several studies consistent with our results. For example, Geach et al. (2011) analyzed a super-structure at z = 0.55, comprising several dense regions connected by a filamentary structure, using GALEX NUV and Spitzer MIPS 24 μm data and showed that although on average, there is no significant difference between the SFRs of star-forming galaxies in the super-structure and the randomly selected field (compare Section 4.2), there are intermediate-scale regions within the super-structure where the probability of a galaxy undergoing star formation is enhanced. This increased probability is analogous to our results here regarding the elevation in the fraction of star-forming galaxies in filaments. At z ∼ 0.2, Fadda et al. (2008) discovered two galaxy filaments associated with a cluster (Abell (1763)) and found that starburst galaxies preferentially inhabit the two filaments compared to the cluster core and the outer regions excluding filaments. A more recent study of the same supercluster by Biviano et al. (2011) confirmed the previous results, showing that the filament contains the highest fraction of IR-emitting galaxies. These agree with our results although they used a different prescription to identify filaments and a redshift different from our sample. Studies on galaxy group scales at z ∼ 0.4 by Tran et al. (2009) & Koyama et al. (2011) also show an overall good agreement with our results in filaments. Recently, Stroe et al. (2014) found that the LF of Hα galaxies around the shock-induced radio relics of a cluster at z ∼ 0.2 is significantly boosted compared to the field. We argue that such enhancement could be driven by collapsing filamentary structures when two very massive clusters merge.

The enhancement in the fraction of star-forming galaxies at intermediate environments is also seen at higher redshifts. For example, Koyama et al. (2014) showed that for a rich cluster at z ∼ 1.5, Hα-emitting galaxies are preferentially located in the cluster outskirts and Santos et al. (2014) found a huge excess of the star-forming fraction relative to the corresponding passive fraction in a 1–3 Mpc distance from the center of a massive cluster compared to the cluster core and the field. Smail et al. (2014) also found no significant variation in mean SFR with environment for a structure at z ∼ 1.6—consistent with our results in Section 4.2—and that the highest density regions of this structure are devoid of the most actively star-forming galaxies (far-IR, submillimeter, MIPS, and radio sources), which instead are preferentially found in intermediate density environments.

In our study, we used a robust quantitative technique to identify structures with a special emphasis on filaments as locations with intermediate environments. Although the techniques used to identify the structures are different, our results are in close qualitative agreement with previous studies at different redshifts that were discussed above. We conclude that star-forming galaxies are more commonly found in intermediate density regimes at least out to z ∼ 1.5, regardless of how they are selected (Hα, IR, etc.) or how their environments are defined. For this study, it seems that filaments are likely responsible for this enhancement.

The boost in the star formation activity at intermediate environments is not confined to only an elevation in the star-forming fraction. For example, some studies have shown that the rise in the star formation activity at medium environments is a result of an increase in the mean SFR of galaxies (e.g., Coppin et al. 2012; Porter & Raychaudhury 2007; Porter et al. 2008) or due to an enhancement in both the SFR of galaxies and their fraction at intermediate density regimes (e.g., Fadda et al. 2008; Sobral et al. 2011). Here, we showed that filaments lead to an observed enhancement in the star formation fraction. In the following section, we will investigate whether this enhancement is a consequence of an increase in the SFR of many galaxies in filaments or merely due to some galaxies having their star formation switched on by filaments.

We now investigate the observed distribution of SFR, stellar mass, and specific star formation rate (sSFR) in different environments. For the star-forming galaxies in the Hα sample, the median SFR, stellar mass, and sSFR are independent of the environment (Table 1). The same is true for the underlying star-forming galaxies in the control sample (Table 2). The uncertainties in the median values are estimated from 10,000 bootstrap trials.

Table 1. Median SFR (Based on Hα Line), Stellar Mass, and sSFR in the Cosmic Web at z ∼ 0.8–0.9 for the Hα Sample

Cosmic Structure	SFR	Stellar Mass	sSFR
	($\mathrel {M_{\odot }\ \rm yr^{-1}}$)	log($\mathrel {M_{\odot }}$)	log(yr−1)
Cluster	4.47 ± 1.15	10.20 ± 0.24	−9.45 ± 0.22
Filament	4.50 ± 0.73	9.85 ± 0.10	−9.32 ± 0.13
Field	3.58 ± 0.14	10.01 ± 0.06	−9.43 ± 0.04

Note. The errors are estimated by bootstrap resampling from 10,000 trials.

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Table 2. Median SFR (form UV Flux), Stellar Mass, and sSFR in the Cosmic Web at z ∼ 0.8–0.9 for the Star-forming Control Sample

Cosmic Structure	SFR	Stellar Mass	sSFR
	($\mathrel {M_{\odot }\ \rm yr^{-1}}$)	log($\mathrel {M_{\odot }}$)	log(yr−1)
Cluster	9.57 ± 1.41	9.76 ± 0.04	−8.81 ± 0.05
Filament	11.13 ± 1.62	9.79 ± 0.06	−8.64 ± 0.05
Field	8.97 ± 0.30	9.68 ± 0.01	−8.67 ± 0.02

Note. The errors are estimated by bootstrap resampling from 10,000 trials.

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A comparison between the observed distribution of Hα-based SFRs in different environments reveals similarities (Figure 7), showing that the environment does not significantly affect the SFR of selected star-forming galaxies. The observed distribution of the stellar mass and the sSFR is also found to be independent of the environment for the Hα sample (Figure 7). These results also hold true for the selected star-forming galaxies in the control sample (Figure 8).

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We perform K-S tests to compare distribution of SFRs, stellar Masses, and sSFRs in different environments and the results are tabulated in Tables 3 and 4 for both the Hα emitters and the star-forming galaxies in the control sample. Here, the p-value is the probability that the two considered distributions are drawn from the same underlying parent population. It is unlikely that the observed distributions of SFRs, stellar masses, and sSFRs in different environments are extracted from different parent populations, with an evaluated p-value >0.01 in all cases.

The results in this section are consistent with other independent studies at different redshifts (Peng et al. 2010; Geach et al. 2011; Wijesinghe et al. 2012; Koyama et al. 2010, 2013a, 2013b, 2014; Feruglio et al. 2010; Ideue et al. 2012; Muzzin et al. 2012; Pintos-Castro et al. 2013; Bouché & Lowenthal 2005; Grützbauch et al. 2011; Brodwin et al. 2013; Hayashi et al. 2014; Santos et al. 2014; Smail et al. 2014). Here, we found no significant evidence that the cosmic web affects the stellar mass, SFR, and sSFR of the observed star-forming galaxies at z ∼ 1; a result that might be partially explained by selection biases.

To further investigate this, we study the environmental (filament, cluster, and field) dependence of the SFR–mass relation—often known as the "main sequence" of star-forming galaxies—for the Hα emitting galaxies and the star-forming galaxies in the control sample. The mean SFR–mass relation for the Hα sample appears to be independent of the environment (Figure 9). Using the nonlinear least-squares Marquardt–Levenberg algorithm, we perform a linear fit (log(SFR) = alog(Mass) + b) to the log(SFR)–log(Mass) relation for Hα emitters in filaments, clusters, and the field, separately. For clusters and filaments, the slope of the linear fit is fixed to the slope of the best-fitting line for the field Hα sample. The slope of the best-fitting line is a = 0.27 ± 0.02 with the intercept being b = −1.99 ± 0.04, −2.04 ± 0.05 and −2.13 ± 0.17 for cluster, filament, and the field Hα emitters, respectively. The intercepts are consistent within the uncertainties. We also evaluate the observed scatter around the mean SFR–mass relation in different environments. The observed scatter for the Hα sample is found to be ≲0.2 dex, independent of the environment. It is worth mentioning that the typical observational uncertainty in the Hα SFR (Section 2.3.1) is greater than the observed scatter around the mean SFR–mass relation. It is noteworthy that a slight increase in the median Hα SFR is seen in clusters compared to the field. However, this enhancement is not significant and is within uncertainties.

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In another attempt to quantify the environmental dependence of the SFR–mass relation, we use the generalized two-dimensional K-S test (Fasano & Franceschini 1987) to determine the probability that the populations of cluster, filament, and field Hα emitters on the log(SFR)–log(Mass) plane are drawn from the same parent distribution. The derived p-value is 0.09 (cluster versus filament), 0.06 (cluster versus field) and 0.12 (filament versus field), implying that they are unlikely to be drawn from different parent populations on the log SFR–log Mass plane (The p-value is >0.01 in all cases).

The environmental independence of the median SFR and the mean SFR–Mass relation for the Hα star-forming galaxies might be effected by the selection biases in the data. In other words, the median SFR of star-forming galaxies might be intrinsically different in different environments but due to selection effects, this difference does not mirror itself into the observed median SFR and/or the mean SFR–Mass relation.

Since the Hα selected sample is flux limited (i.e., SFR limited), the SFR–mass relation could be entirely driven by the fixed Hα SFR limit, the shape of the Hα luminosity function and the mass-dependent dust correction we use in this work. Due to the shape of the luminosity function and the SFR limit of the Hα sample (∼1.5 $\mathrel {M_{\odot }\ \rm yr^{-1}}$), the majority of galaxies tend to crowd near the selection limit which defines a relatively narrow horizontal strip in the SFR–mass plane. A mass-dependent dust correction to the Hα sample then introduces a slope in the relation. Since these selection biases apply equally to all environments, this leads all environments to give the same results.

In order to check this, we perform a simulation. We select a mock sample of galaxies with the stellar mass randomly drawn from 9 < log(M/$\mathrel {M_{\odot }}$) < 11 and the SFR randomly drawn from the Hα luminosity function based on the HiZELS survey (L* = 42.25 erg s⁻¹, α = −1.56). We emphasize that in randomly selecting these galaxies, no assumption about an intrinsic correlation between SFR and stellar mass is made. We dust-redden the sample using the mass-dependent dust correction equation used in this work (Section 2.3) and apply the HiZELS Hα SFR limit (1.5 $\mathrel {M_{\odot }\ \rm yr^{-1}}$) to mimic the observational selection of the HiZELS survey. We later undo the dust extinction on the galaxies that passed the SFR selection limit. Figure 10 (blue symbols) shows the SFR–mass relation for these simulated galaxies considering the selection effects. This resembles what we observe in Figure 9, despite the fact that we initially introduced no intrinsic relation between SFR and stellar mass a priori. The slope of the SFR–mass relation for these simulated galaxies is a = 0.22 ± 0.02, similar to that of Figure 9, within errors.

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To further investigate the selection effects on the results, we double the intrinsic SFR of every galaxy and assume that they happen to be located in filaments. This means that more galaxies will pass the Hα selection limit due to the shape of the luminosity function. The fraction of galaxies that now pass the selection limit is increased by a factor of ∼2.2 (see Figure 6). However, the median SFR and the mean SFR–mass relation do not change significantly. Figure 10 (red symbols) shows the SFR–mass relation for the new simulated galaxies (in filaments) with twice the intrinsic SFR. This SFR–mass relation looks similar to that of the blue symbols although the intrinsic SFR of each individual galaxy is doubled. The median SFR for detected galaxies is only slightly increased from 5.30 ± 0.22 to 5.91 ± 0.19. The slope and intercept values are now a = 0.22 ± 0.02 and b = −1.38 ± 0.17, respectively, and remain almost the same within uncertainties (these values are a = 0.22 ± 0.02 and b = −1.36 ± 0.20 for blue symbols).

We conclude that the environmental invariance of the median SFR and the mean SFR–mass relation for the Hα star-forming galaxies is partly due to selection biases. In other words, the intrinsic SFR of star-forming galaxies might be a function of the environment but is not completely seen in the observed SFR–mass relation or the median SFR due to selection effects. The intrinsic enhancement of SFR of Hα emitters in filaments, together with the selection biases, has the same effect of elevating the observed fraction of Hα star-forming galaxies in filaments (results in Section 4.1), while leaving the observed median SFR and the mean SFR–Mass relation almost intact. Therefore, from the Hα sample alone, the selection biases are sufficiently strong that we cannot conclude whether it is the average SFR of all galaxies that increases in filaments or whether some galaxies have their star formation switched on by filaments that lead to an enhancement in the star-forming fraction.

We find similar results for the SFR–mass relation based on the rest-frame NUV − r⁺ versus r⁺ − J selected star-forming galaxies in the control sample (Figure 11); i.e., the mean SFR–mass relation for selected star-forming galaxies in the control sample is found to be independent of the environment. As explained in Section 2.3.2, the SFR of the control sample is based on the UV continuum and IR flux (where available). A linear fit to the logSFR–LogMass data results in a slope of a = 0.46 ± 0.02 and intercepts b = −3.52 ± 0.04, −3.45 ± 0.04 and −3.50 ± 0.18 for cluster, filament, and field star-forming galaxies in the control sample, respectively (the slope is fixed to that for the field sample). We evaluate the intrinsic scatter around the mean SFR–mass relation in different environments after subtracting in quadrature the typical observational uncertainty in SFR (Section 2.3.2) from the observed scatter. The intrinsic scatter for the star-forming galaxies in the control sample is ∼0.4 dex, regardless of the environment. Also, similar to the results from the Hα sample, the 2D K-S test exhibits that the environmental discrepancies are insignificant, with p = 0.43, 0.05, and 0.11 for cluster and filament, cluster and field, and filament and field, respectively.

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We stress that the estimated SFRs for the Hα emitters and the underlying star-forming galaxies have different origins, calculated based on different recipes and are based on different diagnostics. We apply the K-S test to the distribution of log(Hα SFR/UV SFR) for the Hα emitters with available UV SFR in three different environments. The K-S test p-value is p = 0.59, 0.12, and 0.53 for cluster and filament, cluster and field, and filament and field, respectively, indicating that the result is insensitive to the SFR estimators used in this analysis. We emphasize that our main purpose here was to investigate whether the environment affects the SF activity in star-forming galaxies and not to compare different SFR diagnostics.

Similar to the Hα selected sample, the results based on the star-forming galaxies in the control sample are not completely free from selection biases. It is more difficult to model the effect of the selection bias for the star-forming galaxies in the control sample. However, they might be affected by similar potential biases. The selection of these star-forming galaxies is based on some color–color cuts and if their SFRs were to increase, then some galaxies that did not initially pass the color selection criteria would now do so, probably leading to the same bias.

The environmental independence of the SFR–Mass relation for the Hα sample, as well as the star-forming galaxies in the control sample, is in agreement with previous studies at low-z (z ≲ 0.5, Peng et al. 2010; Biviano et al. 2011; Wijesinghe et al. 2012; Koyama et al. 2013b; Lin et al. 2014), intermediate-z (z ∼ 1, Koyama et al. 2010; Peng et al. 2010; Ideue et al. 2012; Muzzin et al. 2012; Koyama et al. 2013b; Lin et al. 2014), and high-z (z ≳ 1.5, Hayashi et al. 2011; Grützbauch et al. 2011; Koyama et al. 2013b, 2014).

These studies cover a wide redshift range (0.05 ≲ z ≲ 3) with their galaxy samples selected differently from a variety of surveys (SDSS, COSMOS, zCOSMOS, GAMA, GCLASS, Pan-STARRS1, GOODS-NICMOS and some specifically targeted structures). They have used different proxies for the definition of environment (the majority of them are based on the local number density of galaxies) and the SFR was estimated with different indicators. This includes dust-corrected Hα-based SFR (Peng et al. 2010; Koyama et al. 2010, 2013b, 2014), [O ii] λ3727 (Hayashi et al. 2011; Ideue et al. 2012; Muzzin et al. 2012), total IR luminosity (Biviano et al. 2011), extinction-corrected Hα EW (Wijesinghe et al. 2012), SED template-fitting (Peng et al. 2010), rest-frame UV flux (Grützbauch et al. 2011) and rest-frame U and B magnitudes (Lin et al. 2014). They all have shown that for star-forming galaxies, the SFR–mass or sSFR–mass relation is almost independent of the environment, consistent with our results.

We found that the SFR–mass relation for star-forming galaxies does not depend on the environment, regardless of the methods used to define environment or to estimate SFR. However, it is important to note that the environmental independence of the SFR–mass relation, as seen in this work and some similar studies, might be partially due to selection effects.