2.1. SGP region

Our focal investigation is centred on the Southern Galactic Pole (SGP), covering an area of 384 square degrees within the celestial coordinates ranging from 340° to 26° in Right Ascension and $-35.3^{\circ}$ to $-25.8^{\circ}$ in Declination. The primary source of spectroscopic redshift measurements in our dataset is derived from the 2-degree Field Galaxy Redshift Survey (2dFGRS) and the Galaxy and Mass Assembly Survey (GAMA; Colless et al. Reference Colless2001; Driver et al. Reference Driver2009). Within our dataset, 2dFGRS stands as the primary spectroscopic survey in our sample, having a magnitude limit of $b_{J} = 19.45$ . However, in the G23 field (339.0 $\leq$ RA $\leq$ 351.0, −35 $\leq$ Dec $\leq$ −30), the GAMA G23 survey surpasses the completeness of 2dFGRS by approximately 2.3 times, attributed to its fainter magnitude threshold of $i = 19.2$ . Additionally, our dataset incorporates spectroscopic redshifts from the 2-degree Field Lensing Survey (2dFLenS), the 6-degree Field Galaxy Redshift Survey (6dFGRS), the 2MASS Redshift Survey (2MRS), and the Million Quasars catalogue (MILLIQUAS; Blake et al. Reference Blake2016; Jones et al. Reference Jones2004; Macri et al. Reference Macri2019; Flesch Reference Flesch2021). However, these supplementary measurements constitute a minor portion of our study and represent only a small fraction of galaxies in their respective regions. This culminated effort results in a contiguous celestial coverage up to a redshift of 0.1, incorporating 24 656 spectroscopic sources. Further details regarding the survey origins for these sources are outlined in Table 1. The 441 sources that are not accounted for in Table 1 originate from the WISE Extended Source Catalogue (WXSC; Jarrett et al. Reference Jarrett2013; Jarrett et al. Reference Jarrett2019) and not any single spectroscopic survey.Footnote ^a

Table 1. Sources of redshift measurements for the sample. ‘Detected’ indicates whether a given spectroscopic survey detected a source. It’s worth noting that multiple surveys may detect the same source. The ‘Used’ column indicates the number of detected sources that served as the primary spectroscopic measurements in our sample.

Ensuring a comprehensive understanding of the implications of combining these surveys into a contiguous region is crucial, as the resulting dataset exhibits inherent inhomogeneity attributable to the differing completeness levels of the individual surveys. This disparity necessitates a meticulous understanding and control of the dataset’s inhomogeneity to ensure the reliability of subsequent analyses. Further details on the steps taken to address and mitigate this inhomogeneity are expanded upon in Section 2.4.

2.2. WISE photometry and derived quantities

2.2.2. WISE stellar masses

An important aspect of studying galaxy evolution is the reliance on accurate estimations of the fundamental physical properties of galaxies. All stellar mass ( $M_{\star}$ ) measurements are derived as outlined in Jarrett et al. (Reference Jarrett2023), which improves upon the previously established $M_{\star}$ -MIR relation in Cluver et al. (Reference Cluver2014). The new stellar mass relations are formulated through the use of three weighted mass-to-light (M/L, $\Upsilon_{\star}$ ) scaling relations. Through the combined use of these relations, a galaxy’s stellar mass can be derived within 0.10–0.12 dex accuracy for galaxies with W1 luminosity $\gt 10^{9}$ L $_{\odot}$ and 0.15–0.25 dex accuracy for galaxies with $ \lt +10^{9}$ L $_{\odot}$ .

The first of these relations incorporates the WISE W1 band 3.4 $\mu$ m flux to produce a third-order cubic polynomial M/L relation ( $\Upsilon_{\star}^{3.4\,\mu \mathrm{m}}$ ):

(1) \begin{align} \log M_{\star} = & \, A_{0} + A_{1} \cdot \log L_{W1} + A_{2} \cdot (\log L_{W1})^2 \nonumber \\& \qquad\qquad + A_{3} \cdot (\log L_{W1})^3,\end{align}

where the A coefficients are $-12.62$ , 5.0, $-0.44$ , and 0.016, respectively, and $L_{W1}$ is the W1 band rest-frame luminosity in units of L $_{\odot}$ .

The W1 M/L is a good initial measurement of a galaxy’s stellar mass but does not handle some of the varying physical properties of galaxies. In particular, late-type galaxies have young stellar populations with large variances in morphology types. The W1 M/L relation is a good approximation when dealing with early-type galaxies with old stellar populations. To enhance the W1 M/L relation and account for such variations within galaxies, photometric colours can be incorporated to better indicate the dynamical features of a galaxy. Thus, when WISE colour information is available, the W1 M/L scaling relation is downgraded by a factor of 5 in the weighted stellar mass calculation. The WISE colours adopted by Jarrett et al. (Reference Jarrett2023) are the W1-W2 and the W1-W3 colours with their respective equations:

(2) \begin{align} \log \Upsilon_{\star}^{3.4\,\mu \mathrm{m}} = A_{0} + A_{1} \cdot (C12),\end{align}

where the A coefficients are $-0.38$ and $-1.05$ , respectively, and C12 is the WISE W1-W2 colour in Vega magnitudes.

(3) \begin{align}\log \Upsilon_{\star}^{3.4\,\mu \mathrm{m}} = A_{0} \cdot \exp(-10^{0.4(C13-A_{1})}),\end{align}

where the A coefficients are 0.45 and 4.69, respectively, and C13 is the WISE W1-W3 colour in Vega magnitudes.

Figure 1. WISE derived stellar masses as a function of redshift. The red dashed line indicates our redshift-dependent stellar mass completeness cut for our sample.

The combined weighted mean of the calculated stellar mass from the three M/L relations of Equations (1), (2), and (3) have relatively low scatter. Due to the availability of well-derived WISE measurements in the SGP region, 98% (22 559) of our WISE sources have reliable W1-W2 colours and 65% (14 884) have reliable W1-W3 colours. We therefore expect high-quality derived stellar mass measurements from the M/L relation from Jarrett et al. (Reference Jarrett2023).

2.2.3. WISE mass complete sample

In our primary analysis, which focuses on stellar mass relationships, it is essential to use a mass-complete sample to ensure robust and unbiased results. To achieve this, we define our mass completeness over the redshift range of interest ( $z \lt 0.1$ ), implementing a carefully redshift-dependent calibrated stellar mass cut that follows the GAMA mass completeness methodology from Taylor et al. (Reference Taylor2015). This selection enhances the statistical power of our analysis, particularly by increasing the number of low-mass galaxies, a key area of interest. Additionally, given the minimal evolutionary changes within this redshift range, this cut ensures that our sample remains representative whilst minimising potential biases. Fig. 1 visually demonstrates the redshift-dependent mass completeness applied in our analysis. Thus, over our redshift range, our stellar mass completeness is in the form:

(4) \begin{align} \log M_{\star} \: (M_{\odot}) = A_0 \cdot \frac{\ln(A_1 \cdot z +A_2)}{\ln A_3} + A_4,\end{align}

where the A coefficients are 0.45, 26.5, 1, 1.5, and 8, respectively. This redshift dependent stellar mass cut is applied throughout the entire analysis unless, explicitly stated otherwise (Section 3.5).

2.2.4. WISE star formation rates

Building on the work of Cluver et al. (Reference Cluver2020) we measure star formation rates (SFR) using only WISE which provides a consistent set of measurements across a wide area and is well matched in sensitivity for star-forming galaxies to $z \lt 0.1$ . This is additionally an opportunity to test the performance of these SFRs across different environment regimes. SFRs are derived using the relations in Cluver et al. (under review) which updates the calibration of Cluver et al. (Reference Cluver2017) based on the relationship between WISE W3 and W4 to total infrared luminosity (LTIR). We include the SFR $_{W3}$ and SFR $_{W4}$ equations here for convenience:

(5) \begin{align} \log SFR_{W3} \: (\mathrm{M}_{\odot} \: \mathrm{yr}^{-1}) = & \,0.89 (\pm0.02) \log L_{W3} (L_{\odot}) \nonumber \\& - 7.93 (\pm 0.20), \end{align}

(6) \begin{align} \log SFR_{W4} \: (\mathrm{M}_{\odot} \: \mathrm{yr}^{-1}) = & \,0.91 (\pm0.03) \log L_{W4} (L_{\odot}) \nonumber \\&- 8.02 (\pm 0.23), \end{align}

(7) \begin{align} \log SFR_{W4} \: (\mathrm{M}_{\odot} \: \mathrm{yr}^{-1}) =& \,0.89 (\pm0.02) \log L_{W4} (L_{\odot}) \nonumber \\&- 8.18 (\pm 0.19), \end{align}

where for sources with $\log (L_{W3}/L_{W4}) \geq -0.1$ , Equation (6) is used to calculate the SFR $_{W4}$ and for sources with $\log (L_{W3}/L_{W4}) \lt -0.1$ , Equation (7) is used.

SFRs are determined using an invariance-weighting of SFR $_{W3}$ and SFR $_{W4}$ and include a correction to account for star formation in low-mass galaxies with relatively low dust content, as determined in the nearby universe using the relationship between global dust density and UV-to-IR emission.

2.2.5. WISE colour-colour relation

We produce the WISE colour-colour relations of WISE W1-W2 versus W1-W3 for the mass-complete sample to help refine our star-forming main sequence (SFMS) relation in Section 2.2.6. In Fig. 2, we present the mid-IR colour-colour (W1-W2 and W1-W3) relation for galaxies with reliable measurements as indicated by the signal-to-noise (S/N; S/N $ \gt $ 7 and $ \gt $ 3, respectively), excluding colour-colour upper limits (UL). The galaxies are colour-coded based on their corrected Mid-Infrared (MIR $_{cor}$ ) Star Formation Rate (Cluver et al. under review). We incorporate the designated regions outlined by Jarrett et al. (Reference Jarrett2019), along with the colour-colour sequence fit from Jarrett et al. (Reference Jarrett2023).

Figure 2. WISE mid-infrared colour-colour (W1-W2 vs. W1-W3) distribution of the sample. The points are colour-coded by SFR, where the black points represent SFR UL. The black dashed line delineates stellar-dominated, quenched galaxies (W1-W3 $ \lt $ 2) and dusty star-forming galaxies (W1-W3 $ \gt $ 2). The red dotted line indicates the AGN threshold from Stern et al. (Reference Stern2012) and the red dashed lines designate the QSO/AGN region from Jarrett et al. (Reference Jarrett2011). The cyan fit indicates the colour-colour sequence from Jarrett et al. (Reference Jarrett2023). The magenta and dashed magenta lines are fit to the distribution of points and the upper 2 $\sigma$ offset, which indicates mid-infrared ‘warm’ galaxies.

Fig. 2 serves as a valuable diagnostic tool for discerning distinct galaxy populations, specifically, those dominated by stellar processes (quenched), engaged in dusty SF, and hosting AGN systems (Yao et al. Reference Yao2020). As anticipated from the colour-colour relation, a clear trend emerges, with SF generally being lowest at small W1-W3 colour values and increasing towards the right. Conversely, the disjunction in W1-W2 colour between the primary galaxy population and those at larger or redder W1-W2 values effectively segregates the main galaxy population from extreme cases and AGN. This demarcation is particularly advantageous, considering that sources falling into these categories are prone to yielding unreliable MIR-derived stellar masses and SFRs due to potential contamination from AGN hot-dust accretion (see Jarrett et al. Reference Jarrett2011; Stern et al. Reference Stern2012).

In addressing these challenges, we follow the works of Yao et al. (Reference Yao2022) and establish a conservative warm/AGN delineation by employing the best fit and augmenting the W1-W2 offset by 2 $\sigma$ of W1-W2. This delineation effectively segregates extreme cases and AGN from the primary galaxy population, which will be utilised to help constrain the star-forming main sequence in Section 2.2.6. The WISE colour-colour best fit and offset are expressed by the following equation:

(8) \begin{align}W1-W2 = A_0 \cdot \exp\left(\frac{W1-W3}{A_1}\right) + A_2 + 2\sigma.\end{align}

Here, the best-fit coefficients A are determined to be 0.004, 1.01, and $-0.029$ , respectively, with a standard deviation of 0.26. The fit to the WISE colour-colour relation exhibits high precision and closely aligns with the fit reported by Jarrett et al. (Reference Jarrett2023), where a substantially higher S/N was employed in establishing the relation.

2.2.6. WISE star-forming main sequence

To investigate the environmental impact on a galaxy’s star formation rate, it is crucial to understand the baseline relationship between star formation and stellar mass (the star formation history of the galaxy) (e.g. Vulcani et al. Reference Vulcani2015; Trussler et al. Reference Trussler2020; Finn et al. Reference Finn2023; Lopes, Ribeiro, & Brambila Reference Lopes, Ribeiro and Brambila2023). The SFR-stellar mass relation serves as a potent intrinsic tool, facilitating the classification of galaxies into either efficiently or inefficiently star-forming (Peng et al. Reference Peng2010; Vulcani et al. Reference Vulcani2015; Calvi et al. Reference Calvi2018; Bluck et al. Reference Bluck2020; Epinat et al. Reference Epinat2023; Goubert et al. Reference Goubert, Bluck, Piotrowska and Maiolino2024). By scrutinising this relationship across diverse local environments, such as galaxy pairs or groups, we can discern how environmental factors shape the SF properties of galaxies.

Central to examining this relationship is the concept of the SFMS, which refers to the region where efficient star-forming galaxies reside. This relationship can be differentiated through the SFR or specific star formation rate (sSFR; $SFR/M_{\star}$ ) – stellar mass relation. It provides us with the means to extract the typical rate at which galaxies of varying masses convert gas into stars, providing a benchmark for the typical SF behaviour.

Figure 3. The figure illustrates the star-forming main sequence (SFMS) illustrated with the sSFR vs. stellar mass relation. Grey points denote SFMS galaxies, whilst the black contours display the density of their distributions. The magenta solid line represents the 2nd-order polynomial fit for the SFMS. The grey dashed line indicates the $\log sSFR = -11.0$ threshold for segregating star-forming and quenched galaxies and the light grey solid lines denote lines of constant star formation.

To fit the SFMS, we utilised our redshift-dependent mass complete sample (see Section 2.2.3) and removed quiescent galaxies by applying a $\log sSFR \geq -11.0$ threshold, a commonly used SF quenching separator (e.g. Houston, Croton, & Sinha Reference Houston, Croton and Sinha2023; Oxland et al. Reference Oxland, Parker, de Carvalho and Sampaio2024) and a W1-W3 $\geq 2$ colour cut (Jarrett et al. Reference Jarrett2023) to remove stellar dominated galaxies and keep only dusty, star-forming galaxies. Additionally, to ensure the accuracy and reliability of our SFMS relation, we implement several quality criteria: the first involves removing SFR UL and low SFR S/N ratios (S/N $ \lt $ 2), while the second entails excluding galaxies with a W1-W2 colour exceeding the warm line defined by Equation (8), as illustrated in Fig. 2. These quality checks safeguard the SFMS against contamination from infrared-warm galaxies (e.g. AGNs) and low-quality measurements. The galaxies removed by the SFMS selection cuts can be viewed in Fig. C1 in Appendix C. By employing these methodologies, we establish a robust SFMS, depicted in Fig. 3, with a best-fit relation expressed by the equation:

(9) \begin{align} \log SFR \: (\mathrm{M}_{\odot} \: \mathrm{yr}^{-1}) = & \, A_0 \log M_{\star}^{2} \: (M_{\odot}) \nonumber \\ & + A_1 \log M_{\star} \: (M_{\odot}) + A_2, \end{align}

the coefficients $A_0$ , $A_1$ , and $A_2$ are determined to be $-0.15$ , 3.65, and $-21.22$ , respectively. In the next sections, we make use of our derived quantities to explore the properties and behaviours of the galaxies in our data set as a function of environment.

2.3. Group finding

To identify and establish galaxy groups, we have adopted a friends-of-friends (FoF) approach using the FoFpy,Footnote ^b Python package from Lambert et al. (Reference Lambert, Kraan-Korteweg, Jarrett and Macri2020). Based on graph theory principles, the friends-of-friends algorithm aims to establish associations between galaxies, determining whether they are gravitationally linked based on their proximity in both projected and radial velocity space. The algorithm treats galaxies as nodes in a graph and utilises links to establish connections between these nodes.

The FoFpy software package provides a range of inputs. The first pair of inputs are $D_\mathrm{initial}$ and $D_\mathrm{final}$ . These represent the scaling factors used by the algorithm to determine the angular separation limits (see $D_{0}$ in Eq. 1 in Lambert et al. (Reference Lambert, Kraan-Korteweg, Jarrett and Macri2020) for an explicit formalism). The projected angular separation of two galaxies is calculated as:

(10) \begin{align}D = \sin \left(\frac{\theta_{ij}}{2} \right) \cdot \frac{v_{\text{avg}}}{H_{0}},\end{align}

where $\theta_{ij}$ is the angular separation of two galaxies and $v_{avg}$ is the average line-of-sight velocity of two galaxies, where the line-of-sight velocity is cz. The non-relativistic velocity formula is adopted as we are constrained to the nearby universe.

Additionally, the input parameters $v_\mathrm{initial}$ and $v_\mathrm{final}$ signify the minimum and maximum disparities in line-of-sight velocities between the galaxies, calculated as:

(11) \begin{align}v = |v_{i} - v_{j}|.\end{align}

Moreover, the algorithm integrates rigid constraint parameters, denoted as $D_\mathrm{max}$ and $v_\mathrm{max}$ , specifying the maximum allowable angular and line-of-sight velocity separations for the entire group. The number of trials ( $n_\mathrm{trials}$ ) specifies the number of times the algorithm will run. During each trial, the algorithm integrates between various steps of the initial and final parameters, considering different starting points depending on the number of trials specified. Lastly, the Cutoff parameter determines the probability threshold at which the algorithm stops considering two nodes as linked. When two nodes are associated through a link, the algorithm assigns a probability value between 0 and 1 to express the likelihood of this linkage, and the cut-off parameter sets the threshold below which the association is disregarded.

To enhance the output of the FoF algorithm, we incorporated simulations conducted through TAO, utilising the Millennium dark matter simulation (Springel et al. Reference Springel2005) and the Semi-Analytic Galaxy Evolution model (SAGE; Croton et al. Reference Croton2006), and optimised the inputs for the FoF finder. We began by applying a mass cut of $M_{\star} \gt 10^{8} \mathrm{M}_{\odot}$ , followed by testing the FoF finder on this sample by separately applying the 2dFGRS ( $b_{J} = 19.45$ ) and GAMA G23 ( $i = 19.2$ ) magnitude limits. The simulations provided galaxy groups, which were then used as a baseline for calibrating the FoFpy algorithm, improving its performance. This process enabled us to evaluate the algorithm’s ability to reproduce galaxy groups within the two survey fields, and through these trials, we determined the optimal parameters so that both fields could be used in tandem with a single set of parameters.

By iterating this process numerous times, we discovered that the most effective way to implement the FoFpy package was to conduct two separate runs. The initial run designated the ‘1 ${\mathrm{st}}$ Pass’, would run on the entire dataset using less constrained limits to extract larger gravitationally bound groups as they could extend further in their dynamical ranges. Using the outputs of the 1 ${\mathrm{st}}$ Pass mode, we filtered out galaxies belonging to groups that contained 10 or more galaxies. The FoFpy package would then be re-run on the remaining galaxies, this was designated the ‘2 ${\mathrm{nd}}$ Pass’. The 2 ${\mathrm{nd}}$ Pass mode employed stricter constraints to more accurately identify galaxy groups with lower memberships, as this placed better constraints on these less dynamically ranged groups.

The input parameters for both the 1 ${\mathrm{st}}$ and 2 ${\mathrm{nd}}$ passes can be found in Table 2. We then applied the FoF finder to the entire sample, producing a more comprehensive view of the local universe and identifying more accurate galaxy groups compared to using a mass or magnitude-limited sample, which can introduce errors such as the fragmentation of groups. This approach was significantly supported by the 3D visualisation tool Partiview (Levy Reference Levy2010), allowing us to visually inspect the groups for quality control and parameter validation by reviewing the links between group members. This analysis also enabled direct comparison with mock datasets, ensuring our linking lengths matched those in the simulated groups.

Table 2. Input parameters of FoFpy Python package for the 1st & 2nd Pass.

Figure 4. 2D cone representation of the distribution of galaxy groups within the sample. Panel (a) illustrates galaxy groups binned by the number of members associated with each group by the FoF finder. Panel (b) depicts the $\alpha$ correction applied to each galaxy group, adjusting the total members within each group. Finally, panel (c) presents the distribution of galaxy groups binned by their corrected number of members after applying the $\alpha$ correction. The grey region indicates the GAMA G23 area within its right ascension limits.

2.4. Group completeness

The spatial distribution within the designated research area exhibits inhomogeneity arising from variations in survey completeness. Within the 2dFGRS volume chosen for this study, the high completeness of the GAMA G23 volume introduces this inhomogeneity. The GAMA G23 region ( $338.1 \lt $ RA $ \lt 351.9$ and $-35.0 \lt $ Dec $\lt -30.0$ ) demonstrates notably higher completeness out to $z=0.1$ . This volume encompasses a total of 5 844 galaxies, however, upon excluding those exclusively detected by GAMA, the remaining sample contains 2 515 galaxies. Consequently, within the G23 volume of our sample, the completeness, augmented by GAMA, is approximately 2.3 times higher than the remainder of the SGP volume. This discrepancy is particularly pronounced closer to our redshift limit of 0.1, but increasing becomes a noteworthy effect beyond $z \gt 0.06$ .

As the spectroscopic surveys utilised are magnitude-limited, some galaxies inherently exist beyond these magnitude limits and are not accounted for in these surveys. To address this issue, we again utilise Millenium simulations running SAGE to categorise the completeness of our groups across the redshift range. By having the initial simulation with a stellar mass cut of $M_{\star} \gt 10^{8} \mathrm{M}_{\odot}$ , ensuring that all galaxies can be adequately resolved from the surrounding dark matter in the SAGE simulation and that the galaxies would make significant physical contributions to the ‘local environment’. We then impose a 2dFGRS magnitude limit of $b_{J} = 19.45$ (the main magnitude limit for the SGP region) and contrast it to the GAMA G23 magnitude limit of $i = 19.2$ . By comparing group memberships from simulations before and after applying magnitude limits across 25 simulated light cones, we established scaling relationships that increase the number of galaxies within a group as a function of redshift and the observed group membership, providing a more accurate quantification of environment and the underlying dark matter halo occupation. The scaling parameter ( $\alpha$ ) is simply a coefficient to multiply the group membership total to obtain a corrected membership total. For example, if a galaxy group was observed to have 8 members and $\alpha$ was 1.5 due to its redshift position, the ‘corrected number of members’ (Nm $_\mathrm{cor}$ ) would be 12. Fig. 4 shows the relation between $\alpha$ and redshift for different group memberships for each 2dFGRS and GAMA G23. This informs about the expected number of galaxies missing from each group and their relative uncertainties. The equations for the scaling parameters established in Fig. 5 can be found in Appendix A in Table A1.

Figure 5. Comparison of the multiplicity correction factor ( $\alpha$ ) for group membership (as defined in Section 2.4) versus redshift for different galaxy group membership bins. Panel (a) illustrates this relation for the 2dFGRS field, where the correction factors are notably larger, particularly at redshifts near our limit. This dataset also exhibits significantly more variability, as evidenced by the shaded 1 $\sigma$ regions. In contrast, panel (b) displays the corresponding data for the GAMA G23 field.

Insights gleaned from the simulations reveal that low membership groups (3–5 members, 6–9 members, and 10–19 members) necessitate smaller correction factors, albeit with significantly larger uncertainties, particularly at higher redshifts. Conversely, larger membership groups (20–39 members and 40+ members) require more substantial correction factors but exhibit smaller uncertainties, thus affording greater precision in corrections up to higher redshifts. These tendencies are notably accentuated within the 2dFGRS field when compared to the GAMA field. This distinction arises due to the superior completeness of the GAMA survey, which results in comparatively well-constrained correction factors for the ‘smaller’ membership groups.

It is evident that as we extend our analysis to larger redshifts, the uncertainties associated with smaller group memberships within the 2dFGRS field become pronounced. For instance, at $z\sim 0.06$ , the uncertainties for 3–5 member groups in the 2dFGRS field match those of the GAMA field at $z=0.1$ . Similarly, at $z\sim 0.07$ , the uncertainties for 6–9 member groups in the 2dFGRS field converge with those of the GAMA field at $z=0.1$ , and at $z\sim 0.08$ , the uncertainties for 10–19 member groups in the 2dFGRS field align with those of the GAMA field at $z=0.1$ . This underscores the importance of survey completeness on the reliability and precision of correction factors, especially for smaller group memberships at larger redshifts.

This analysis enables us to make more accurate assessments and interpretations of the galaxy population within the SGP region and make a statistically more accurate quantification of environment, compensating for the potential incompleteness arising from survey magnitude limits. This, in turn, allows us to scale our galaxy groups to these relations in the various fields, and the effects can be seen in Fig. 4. This is a useful exercise in preparation for more comprehensive spectroscopic surveys such as the upcoming 4-metre Multi-Object Spectrograph Telescope Hemisphere Survey (4HS; Taylor et al. Reference Taylor2023b ), which will survey the whole southern sky in the local ( $z \lt 0.1$ ) universe, but with varying completeness in some areas. By understanding how to control and handle varying survey completeness we will be able to maximise the science that can be produced with the spectroscopic information and minimise the error.

The sample is systematically partitioned to categorise galaxies based on their respective small-scale environment. The decision to separate the group sample into five halo occupation distributions (HOD) was made to ensure a relatively even distribution of numbers across the bins whilst representing progressively larger structures. We have explored the utilisation of alternate HOD bins, this did not affect the overall results. Thus our choice of bins balanced the need of maintaining robust statistics, minimising errors while preserving the structural progression of small-scale environments. In Fig. 6, we demonstrate the HOD distribution as a function of redshift. Table 3 provides a breakdown of the total number of galaxies in each small-scale environment and specifies the count of galaxies that have been cross-matched with WISE.

Figure 6. Halo occupation distribution (HOD) bins plotted as a function of redshift for the galaxy group sample within the redshift range $z \lt 0.1$ . The HOD bins are separated into five ranges: 3–5, 6–9, 10–19, 20–39, and 40+ corrected members.

Table 3. Local environment sample numbers and cross-match statistics. The groups refer to the group membership after the group membership correction has been applied.

In the context of this analysis, the term ‘field’ is operationally defined to encompass galaxies that are not affiliated with either a group or close pair environment. These field galaxies serve as the control within the sample, as they lack association to any small-scale environment.

2.5. Group membership – halo mass relation

Throughout our analysis, we have adopted group membership as a surrogate for the scale of environmental for the galaxy groups. This choice stems from the considerable uncertainty surrounding halo mass estimations for low membership groups. Typically, observational methods rely on the virial theorem, which establishes a relationship between the group velocity dispersion and virial mass. However, for low membership galaxy groups, this relationship can exhibit significant variability, as further discussed in Appendix B. Our investigation into various observational techniques for determining halo mass has revealed deviations exceeding 2 dex for low membership groups when compared to our simulated data discussed in Sections 2.3 and 2.4. This discrepancy is also acknowledged by Hess & Wilcots (Reference Hess and Wilcots2013), who describe group membership as the HOD and propose that it offers a more stable alternative to halo mass estimation, particularly for low membership groups.

This bias in halo mass estimation can be attributed to the reliance of the virial theorem on gravitationally stable systems, a condition not always met by low membership groups. Additionally, the variance in peculiar velocities further complicates the derivation of a reliable halo mass estimate based solely on velocity dispersion. Given these inherent uncertainties, we have chosen group membership as a more robust and intuitive indicator of the galactic environment rather than relying directly on halo mass. This approach is particularly pertinent to our focus on low-mass groups.

It is worth noting that there exists a correlation between group membership and halo mass, as evidenced in Table 4, where we present the mean halo mass given by $M_{200}$ ( $M_{\odot}$ ) derived from the SAGE simulations for each galaxy group membership bin employed in our analysis. This table utilises all the light cones outlined in Section 2.4 and provides the mean values of halo mass for our chosen HODs. Additionally, we provide the $1 \sigma$ variance of these binned halo masses. The distribution of these halo masses can be found in Fig. B2. It is worth noting that the local group falls between the expected halo masses of the 3–5 and 6–9 member groups, but closer to the 3–5 groups with a halo mass of $\sim \log 12.5 \: (\mathrm{M}_{\odot})$ (Sawala, Teeriaho, & Johansson Reference Sawala, Teeriaho and Johansson2023).

Table 4. Relation between halo mass and group membership HOD. The halo masses are derived from the Millennium-SAGE simulations, with the mean and 1 $\sigma$ values obtained from the histogram distribution in Fig. B1.

2.6. Pair selection

In addition to galaxy groups, we specifically examine close galaxy pairs to investigate the behaviour of interacting galaxies. Close pairs were chosen as the best method to study closely interacting systems, acknowledging the inherent challenges such as projection effects, the inclusion of pairs within larger groups, and potential completeness issues near our redshift limit. We do not aim to define a state-of-the-art pair sample; rather, our goal is to gather a selection of closely interacting galaxies to explore how extreme interactions and probable future mergers influence star formation relative to galaxies in the field and within groups, and whether these potential pre-mergers exhibit enhanced environmental effects seen in group environments.

Close pairs were defined as galaxies with a projected spatial separation of $r_\mathrm{sep} \lt 50\,:\,\text{h}^{-1} \text{kpc}$ and a radial velocity difference of $v_\mathrm{sep} \lt 500\,:\,\text{km s}^{-1}$ , ensuring no additional galaxies met this criterion for each pair. This follows the works of Robotham et al. (Reference Robotham2014), Bok et al. (Reference Bok2020), and Contreras-Santos et al. (Reference Contreras-Santos2022), who identified it as an optimal pair selection method. Despite the separation criteria, the linking lengths for galaxy groups (see Section 2.3) can extend beyond these limits, resulting in some close pairs also being members of larger groups. Additionally, close pairs near the redshift limit may include neighbouring galaxies below the detection threshold, leading to potential misclassifications.

Identifying galaxy pairs presents challenges, particularly due to variations in peculiar velocities within group environments. According to Contreras-Santos et al. (Reference Contreras-Santos2022), our selection criteria accurately identify galaxy pairs in approximately 50–60% of cases across the angular separation range. Nonetheless, this method remains one of the most reliable for producing pair samples in large surveys. We do not exclude pairs near the redshift limit or those within groups, as our focus is on studying the effects of close interactions rather than ensuring a pure pair sample. This approach also enables a more direct comparison with previous studies that do not separate or exclude pairs within groups (e.g. Lambas et al. Reference Lambas, Tissera, Alonso and Coldwell2003; Ellison et al. Reference Ellison2010; Woods et al. Reference Woods2010; Scudder et al. Reference Scudder, Ellison, Torrey, Patton and Mendel2012; Hopkins et al. Reference Hopkins2013; Robotham et al. Reference Robotham2014; Davies et al. Reference Davies2015; Bok et al. Reference Bok2020; Sun et al. Reference Sun, Barger, Frinchaboy and Pan2020; Steffen et al. Reference Steffen2021; Shah et al. Reference Shah2022; Li, Ho, & Shangguan Reference Li, Ho and Shangguan2023), especially given the high uncertainty in correctly associating galaxy pairs. As shown in Table 3, we have 674 galaxies within close pairs and 673 have been cross-matched with WISE. Of the 673 cross-matched pairs, 449 pairs are in groups, and 224 are ‘isolated’ and not part of any group.

All candidate pairs underwent visual confirmation using WISE and DESI Legacy Imaging Surveys (Dey et al. Reference Dey2019), providing better constraints on our selection. However, WISE data posed limitations for pairs with angular separations smaller than 6", roughly the beam width of W1, making it difficult to resolve secondary galaxies. Such pairs were excluded from further analysis. For pairs with separations between 6" and 10", resolution depended on the relative sizes of the galaxies, while separations beyond 10" were consistently well-resolved in WISE. At $z = 0.05$ , a separation of 6" corresponds to $8.8 \: \text{h}^{-1}$ kpc, and 10" corresponds to $14.7 \: \text{h}^{-1}$ kpc.

3.1. Star formation quenching in local galaxy environments

In the subsequent analysis, we will employ the quenching line of $\log sSFR = -11.0$ , as defined in Section 2.2.6, to identify quenched galaxies and quantify this as a quenched fraction. The quenched fraction is calculated as the ratio of quenched galaxies to the total number of galaxies within a specified sample and stellar mass range. Through analysis across various stellar mass bins, we aim to investigate the environmental dependence of SF quenching through the evolving quenched fraction across different local environments.

Given the robustness of our constructed sSFR-SM relations, this section of the analysis will incorporate our mass-complete sample (see Section 2.2.3, including IR warm sources and low-S/N. SFR UL values, provided they adhere to the criteria outlined in Cluver et al. (Reference Cluver2020) are included here for completeness. SFR ULs typically arise from the W3 flux being below the detectable threshold. These sources are checked to see if the W3 flux (given the distance to the source) is above or below this threshold. UL values above this threshold are included within the analysis of the quenched fractions and correlate to a quiescent galaxy, those below the threshold are treated conservatively and are included as a star-forming galaxy within the binning, so as not to boost the quenched fraction artificially. For more details on how UL were treated in the analysis see Appendix D.

In Fig. 7, we scrutinise the quenched fraction across different local environments, encompassing ‘field’ galaxies, close pairs, and all galaxies within groups, thereby spanning a continuum of low-density to high-density small-scale environments. Fig. 7, along with subsequent figures in this analysis, have their associated uncertainties derived using bootstrap resampling. This method involves repeatedly sampling the data with replacement to estimate the variability and confidence intervals for the observed metrics.

Figure 7. The fraction of quenched galaxies per given stellar mass bin across various local galaxy environments. The quenched fraction represents the ratio of quenched galaxies to the total number of galaxies per mass bin. Each mass bin has a width of 0.3 dex, with errors calculated via bootstrap resampling within each bin. The total number of quenched galaxies and the total number of galaxies for each mass bin are provided below the distributions. The quenched fraction’s evolution is observed across different environments and stellar masses.

Our findings show a changing quenched fraction across various stellar mass bins. Specifically, the stellar mass bin $M_{\star} = 10^{9.75}\,\mathrm{M}_{\odot}$ exhibits the lowest quenched fraction for all local environments, indicative of the highest efficiency of SF within galaxies across all mass ranges. Conversely, for mass bins with $M_{\star} \lt 10^{9.75}\,\mathrm{M}_{\odot}$ , we observe a gradual increase in the quenched fraction as we descend to lower stellar masses. This trend suggests that SF in these low-massed galaxies is less efficient. This is particularly evident in smaller dwarf galaxies which exhibit lower efficiency in converting available gas into stars (Moster, Naab, & White Reference Moster, Naab and White2013; Hunt et al. Reference Hunt, Tortora, Ginolfi and Schneider2020).

In the larger stellar mass range ( $M_{\star} \gt 10^{9.75}\,\mathrm{M}_{\odot}$ ), we observe a consistent rise in the quenched fraction with increasing stellar mass. This observation is to be expected, as galaxies evolve through the combination of in-situ SF and merger processes, evolving into sizable, high-mass galaxies, which result in SF inefficiencies or global SF quenching due to mass-related quenching mechanisms (Gabor et al. Reference Gabor, Davé, Finlator and Oppenheimer2010; Peng et al. Reference Peng2010; Bluck et al. Reference Bluck2020; Taylor et al. Reference Taylor2023a ).

Contrasting the close pairs to the field population, at low stellar masses ( $M_{\star} \lt 10^{9.75}\,\mathrm{M}_{\odot}$ ), the close pairs demonstrate a lower quenched fraction to their field counterparts, which suggests that low-mass close pairs exhibit more efficient SF. This result has been observed in prior observational studies, such as those by Hopkins et al. (Reference Hopkins2013) and Sun et al. (Reference Sun, Barger, Frinchaboy and Pan2020), where gravitational and tidal interactions between paired galaxies facilitate the funnelling of gas into central regions, effectively constraining gas outflows, fostering conditions conducive to central SF. These effects in close pairs synthesise in an overall increase to the galaxy’s SFR (Ellison et al. Reference Ellison2010). However, our analysis encounters limitations in the lowest mass bin due to diminished statistical significance, underscoring the need for a larger sample size to probe this mass range’s aggregate behaviour effectively.

In contrast, at higher stellar masses ( $M_{\star} \gt 10^{9.75}\,\mathrm{M}_{\odot}$ ), close pairs exhibit a higher degree of suppression compared to their field counterparts, suggesting a potential relationship between the close pair environment and SF quenching in higher-mass galaxies. This will be examined more in-depth within Section 3.5. Additionally, Appendix E explores the differences between close pairs within and outside groups, where we observe variation between the two at $M_{\star} \gt 10^{10}\,\mathrm{M}_{\odot}$ . However, due to the limited sample size and uncertainty in pair classifications, these differences are not statistically significant. For this reason, we maintain a unified close pair sample in the main analysis to ensure consistency with prior research (e.g. Lambas et al. Reference Lambas, Tissera, Alonso and Coldwell2003; Ellison et al. Reference Ellison2010; Woods et al. Reference Woods2010; Scudder et al. Reference Scudder, Ellison, Torrey, Patton and Mendel2012; Hopkins et al. Reference Hopkins2013; Robotham et al. Reference Robotham2014; Davies et al. Reference Davies2015; Bok et al. Reference Bok2020; Sun et al. Reference Sun, Barger, Frinchaboy and Pan2020; Steffen et al. Reference Steffen2021; Shah et al. Reference Shah2022; Li et al. Reference Li, Ho and Shangguan2023). Future studies, with more complete data from upcoming surveys such as 4HS (Taylor et al. Reference Taylor2023b ), could further investigate the distinct behaviours of close pairs in and out of groups, offering a more controlled definition of close pairs.

The quenched fraction of the grouped galaxies in the low stellar mass range ( $M_{\star} \lt 10^{9.75}\,\mathrm{M}_{\odot}$ ) is more closely aligned with the field, albeit with a slight increase in the quenched fraction. These findings indicate that in the low-mass regime, group galaxies closely resemble their field counterparts, with a minor impact on their quenched fraction. This observed relation diverges at the higher mass end ( $M_{\star} \gt 10^{9.75}\,\mathrm{M}_{\odot}$ ), where a significant offset between the quenched fraction of the field and grouped galaxies exists. This observation is in agreement with previous works (e.g. Davies et al. Reference Davies2019; Cluver et al. Reference Cluver2020; Contini et al. Reference Contini2020; González Delgado et al. Reference González Delgado2022), which also show larger SF suppression in galaxy groups than in the field, which also is in agreement with the morphology density relation (e.g. Dressler et al. 1997; Capak et al. Reference Capak2007).

3.2. Star formation in local galaxy environments

We next explore changes within only the SF population of galaxies as a function of local environment. This is done in the form of $\Delta sSFR$ , the dex difference between the sSFR measurement and the sSFR from the SFMS polynomial fit of Equation (9) ( $\Delta sSFR = \log sSFR - \log sSFR_{fit}$ ). Thus a galaxy with $\Delta sSFR = 0$ lies directly on the SFMS fit, a galaxy with $\Delta sSFR \gt 0$ is more efficiently star-forming than the SFMS fit and $\Delta sSFR \lt 0$ is less efficiently star-forming. Hence, a change in $\Delta sSFR$ indicates an increase or decrease in SF efficiency within the star-forming population.

In Sections 3.2 and 3.4, the analysis of the $\Delta sSFR$ is primarily qualitative, serving to highlight any variations between different small-scale environments while controlling for stellar mass. This approach facilitates an initial exploration of environmental effects to SF. In Section 4.2, we further refine this analysis and discuss the impact of environment by introducing a new metric (environmental star formation deficiency) that quantifies the fractional excess of $\Delta sSFR$ across these small-scale environments, relative to the field, and subject it to a quantitative statistical evaluation.

Figure 8. The relationship between $\Delta sSFR$ and stellar mass across various local galaxy environments is depicted. Contours in each panel illustrate the distribution of all non-SFR UL and SFR S/N $ \gt $ 2 galaxies within the mass-complete sample, delineating the SF population. The median values of each distribution are depicted alongside the field galaxy median distribution in pink within each panel to highlight the relative environmental effects. A $\Delta sSFR \gt 0$ is more efficiently SF than the SFMS fit in Fig. 3 and $\Delta sSFR \lt 0$ is less efficiently SF. Median values are binned in stellar mass bins of 0.3 dex, with errors computed via bootstrap resampling within each bin. The total number of sources used in the median distributions, that is, non SFR-UL and SFR S/N $ \gt $ 2 sources, is indicated in the lower left with the same colouring as the median distribution. The close pair distribution shows an increase in SF activity at most masses, with a relative decrease at high masses. Group galaxies exhibit relative similarities to the field, except at low and high masses where they show similarities to close pairs.

To analyse only the SF population of galaxies, we do not include SFR ULs; as previously outlined in Section 3.1 and Appendix D these indicate a quiescent galaxy (given they are above the detectable W3 threshold). We do not include measurements with a SFR S/N $ \lt $ 2 within this analysis, as their position along the $\Delta sSFR$ plane is highly uncertain. This selection allows the inclusion of galaxies with $\log sSFR \lt -11.0$ , as this is quite a conservative quenching separator, especially for high-massed galaxies. Not all galaxies with $\log \text{sSFR} \lt -11.0$ at higher stellar masses are fully quiescent; rather, they are significantly less efficient compared to their lower-mass counterparts. The $\Delta sSFR$ of the SF populations for the different local galaxy environments are contoured in Fig. 8. In each panel of Fig. 8, the running median of the field $\Delta sSFR$ distribution is plotted by the pink distribution and contrasted with the close pairs in cyan in the middle panel, and groups in green on the right panel.

In contrasting the close galaxy pairs to the field distribution, the close pairs exhibit heightened SF efficiency in the star-forming population at lower stellar masses (seen by an increase in $\Delta sSFR$ ), suggesting enhanced interactions or gas accretion processes. As stellar mass increases within the close pairs, the SF efficiency observed at lower masses decreases relative to the field, becoming less efficient than the field population at $M_{\star} \sim 10^{10.4}\,\mathrm{M}_{\odot}$ . In the largest mass bin, the close pairs exhibit significantly larger SF inefficiencies compared to the field (seen by a relative decrease in $\Delta sSFR$ ). Among the close pair sample, we observe that low-mass galaxies exhibit few quenched members (Fig. 7), accompanied by an enhancement in $\Delta sSFR$ , suggesting an increase in star formation activity. Conversely, at higher stellar masses, we find both elevated quenched fractions (Fig. 7) and suppressed $\Delta sSFR$ , indicating these galaxies are undergoing quenching processes. This contrast suggests that while low-mass galaxies in pairs may experience star formation enhancement, higher-mass pairs are more likely progressing towards quenching.

The combined galaxy group distribution closely resembles the field environment, particularly throughout the low mass regime ( $M_{\star} \lt 10^{9.75}\,\mathrm{M}_{\odot}$ ), except for the lowest mass bin, where we see an increase in $\Delta sSFR$ compared to the field. The similarities between the field and galaxy group relations deviate at $M_{\star} \gt 10^{10.1}\,\mathrm{M}_{\odot}$ , marked by a gradual downturn in $\Delta sSFR$ for the groups. The offset in $\Delta sSFR$ between the two populations increases with increasing stellar mass. The offsets observed at stellar masses such as $M_{\star} \sim 10^{10.4}\,\mathrm{M}_{\odot}$ are unlikely to be attributable to secular processes at this mass range. Instead, they suggest the presence of environmental influences, potentially arising from mechanisms such as galaxy harassment, strangulation, tidal stripping, or ram pressure stripping (e.g. Moore et al. Reference Moore, Katz, Lake, Dressler and Oemler1996; Taranu et al. Reference Taranu2014; Bahé et al. Reference Bahé2019).

3.3. Star formation quenching in group environments

In the following analysis, we will employ the methodologies for the quenched fraction utilised in Section 3.1 applying this methodology to the group galaxies. We separate the group sample by placing galaxies into their discretised membership bins ranging from 3-5, 6-9, 10-19, 20-39, and 40+ corrected members as outlined in Section 2.4. Our objective is to investigate whether the increase in group membership/small-scale environment impacts SF processes within galaxies.

Fig. 9 presents the quenched fraction of the different membership groups as a function of stellar mass to assess the impact of group environments on SF quenching. To contextualise these results, they are juxtaposed with the distribution of the control field sample, represented by the black dot-dashed line initially depicted as the pink line in Fig. 7. This enables a relative assessment of the impact of growing small-scale group environment on SF quenching processes.

Figure 9. The fraction of quenched galaxies within galaxy groups per given stellar mass bin across varying levels of galaxy group membership. The quenched fraction represents the ratio of quenched galaxies to the total number of galaxies per mass bin. The field population quenched fraction is depicted with a dash-dot black line to highlight the relative effects of environment. Each mass bin has a width of 0.3 dex, with errors computed via bootstrap resampling within each bin. The total number of quenched galaxies and the total number of galaxies for each mass bin are provided below the distributions. A noticeable evolution of the quenched fraction is evident across different group environments and stellar masses.

In smaller-membership groups (3–5, 6–9, and 10–19 corrected members), we observe that in the low-mass range ( $M_{\star} \lt 10^{9.75}\,\mathrm{M}_{\odot}$ ), the group environment generally mirrors the trends observed in field galaxies. The 10–19 membership groups in this low mass range demonstrate a slight increase in the quenched fraction compared to the other ‘small groups’, but it does not significantly deviate from the field sample until the second lowest mass bin, where a significant increase is observed. Following the increase, it then drops below the field sample within the lowest massed bin. The number statistics for the two lowest and largest massed bins for the various galaxy group sizes in Fig. 9 is substantially less than the rest of the population, and thus the results should be interpreted cautiously due to their significantly lower statistical power, likely necessitating a larger dataset to discern the true underlying trends.

The observed results are consistent with earlier research conducted by Kauffmann et al. (Reference Kauffmann2004) and Peng et al. (Reference Peng2010), which revealed that low-mass galaxies inhabiting environments with low densities or smaller-sized groups tend to display SF levels akin to those of galaxies not associated to groups or residing in even less dense environments.

Conversely, we observe a notable deviation between the group environments and the field distribution when examining the low-mass ( $M_{\star} \leq 10^{9.75} \mathrm{M}_{\odot}$ ) range within larger groups (20–39 and 40+ corrected members). Here we see a rise in the quenched fraction, except for the lowest mass bin, where larger groups display a lower fraction compared to the field. As previously discussed, the lowest-massed bin is subject to relatively low statistical significance. However, this result necessitates further investigation to ascertain its significance. The heightened quenched fraction seen elsewhere within the low mass range is particularly evident in the 40+ corrected membership groups and suggests a potential influence of ram pressure stripping on low-mass galaxies as they encounter massive, hot dark matter halos. This mechanism has been previously documented in studies observationally and through simulations (e.g. Kapferer et al. Reference Kapferer, Kronberger, Ferrari, Riser and Schindler2008; Ebeling, Stephenson, & Edge Reference Ebeling, Stephenson and Edge2014; Taranu et al. Reference Taranu2014; Merluzzi et al. Reference Merluzzi2016), where interactions between galaxies and the ICM result in the removal of neutral gas from galaxies. Consequently, this rapid gas loss leads to inefficient SF or the quenching of SF, especially within the discs of these galaxies. However, if these galaxies are gas-rich, it can result in centralised regions of SF and a net increase in their overall SFR, which can potentially explain our findings in the lowest mass bins.

In the high mass range ( $M_{\star} \gt 10^{9.75}\,\mathrm{M}_{\odot}$ ), there is a noticeable deviation of the quenched fraction between the group environments and the field distribution across all group sizes. This offset becomes more pronounced as group size increases. Notably, as galaxy groups increase in their membership, larger quenched fractions are observed, indicating heightened effectiveness of environmental SF quenching. This result may be influenced by the varying stellar mass function across different galaxy group environments (Alpaslan et al. Reference Alpaslan2015; Etherington et al. Reference Etherington2017; Papovich et al. Reference Papovich2018), with larger groups more likely to host massive, ‘red and dead’ galaxies. However, this does not seem to drive the observed results. As noted by Calvi et al. (Reference Calvi, Poggianti, Vulcani and Fasano2013), the stellar mass function may not change significantly across field and group environments, which is supported by our finding that the relative number of galaxies in the highest stellar mass bins remains similar across different HODs. In this mass range, mass quenching effects dominate, as shown by the field sample, but are further amplified by environmental processes that become increasingly pronounced with larger group sizes. The impact of the group environments is consistent with previous studies such as Davies et al. (Reference Davies2019) and Cluver et al. (Reference Cluver2020), which found an increase in the passive fraction as a function of halo mass when controlling for stellar mass, mirroring our observations due to the relation between halo mass and group size discussed in Section 2.5. Additionally, our results align with those of González Delgado et al. (Reference González Delgado2022), demonstrating that while mass quenching effects dominate in the larger stellar mass range, environmental effects play a significant role in amplifying the suppression of SF.

3.4. Star formation in group environments

We apply the methodologies outlined in Section 3.2 to our galaxy group sample to investigate the environmental impact on the SF population of galaxies, using the relative variance in $\Delta sSFR$ as the probe. In Fig. 10, the running median distribution for each binned group is compared to the field’s median distribution, depicted by the pink line and originally established in Fig. 8. As described in Section 3.2, SFR ULs and SFR low S/N measurements are excluded from the contouring and running medians to represent the SF population accurately.

Figure 10. The relationship between $\Delta sSFR$ and stellar mass across various galaxy group environments is depicted. Contours in each panel illustrate the distribution of all non-SFR UL and SFR S/N $ \gt $ 2 galaxies within the mass-complete sample, delineating the SF population. Median values of each distribution are depicted alongside the field galaxy median distribution in pink within each panel to highlight the relative environmental effects. A $\Delta sSFR \gt 0$ is more efficiently SF than the SFMS fit in Fig. 3 and $\Delta sSFR \lt 0$ is less efficiently SF. Median values are binned in stellar mass bins of 0.3 dex, with errors computed via bootstrap resampling within each bin. The total number of sources used in the median distributions, that is, non SFR-UL and SFR S/N $ \gt $ 2 sources, is indicated in the lower left with the same colouring as the median distribution. The group galaxies show a decrease in their SF at large stellar masses compared to the field, which increases with group membership.

Our findings from Fig. 10 highlight a discernible evolutionary shift in SF efficiency as galaxy groups increase in size. We observe that the offset in $\Delta sSFR$ between the field and group samples grows with increasing group size, particularly at higher stellar masses.

In 3–5 and 6–9 membership groups, the median SF population typically mirrors the field distribution, except for a slight decrease in $\Delta sSFR$ beyond $10^{10.4}\,\mathrm{ M}_{\odot}$ . As we increase to 10–19 member groups and larger, there is an increasing offset between the galaxy groups distributions and that of the field. The relative decrease in $\Delta sSFR$ compared to the field in these galaxy groups becomes more pronounced in larger galaxy groups as their membership increases. The initial deviation between the field and the galaxy groups shifts to lower stellar masses as group membership increases. This initial offset begins at $10^{10.4}\,\mathrm{M}_{\odot}$ for 10–19 membership groups and evolves to $10^{9.8}\,\mathrm{M}_{\odot}$ for 40+ membership groups.

In low-membership groups, the star formation SF inefficiencies among higher-mass galaxies are primarily driven by secular processes. As we examine slightly larger groups, while secular quenching mechanisms continue to play a dominant role in suppressing SF, the environmental conditions within these groups further enhance the suppression of SF, leading to the pre-processing of SF within the groups. At the lowest stellar mass bin for all groups, we see an increase in $\Delta sSFR$ relative to the field. This trend may potentially indicate similar interactions experienced by the low-mass close pairs, as further analysed in Section 3.5.

In summary, our analysis reveals that as galaxy groups increase in membership/HOD, the deviation in SF efficiency from the field population becomes more pronounced, particularly at higher stellar masses, suggesting a complex interplay between stellar mass and environmental effects present in group environments on SF dynamics that we will further discussed in Section 4.

3.5. Star formation in close pairs

In this section of our analysis, we drop the use of the redshift-dependent mass complete cut to the sample. This extension is prompted by several considerations, with a key factor being the limitations posed by the low number statistics of our close pairs, which hinders an in-depth analysis while we control for stellar mass. By incorporating all close pairs, we augment our sample by an additional 20%. Another rationale for this stems from the treatment of our group samples, which involved applying completeness corrections. This step was omitted for the pairs due to the significant variability in results, especially near our redshift limit. The identified close pairs at higher redshifts likely correspond to small galaxy groups. Our aim is not to constrain a highly complete sample of close pairs but rather to investigate the diverse effects resulting from galaxy-galaxy interactions and potential pre-mergers.

Following previous works (e.g. Robotham et al. Reference Robotham2014; Davies et al. Reference Davies2015; Li et al. Reference Li, Ho and Shangguan2023), we classify our close pairs into minor pairs, which have a stellar mass ratio less than 1:4 ( $M_{sec}/M_{prim} \lt 0.25$ ), and major pairs, which have a stellar mass ratio greater than 1:4 ( $M_{sec}/M_{prim} \geq 0.25$ ). $M_{sec}$ refers to the secondary galaxy in the pair which is the less massive galaxy and $M_{prim}$ refers to the primary galaxy in the pair, the most massive. Minor pairs provide us insight as to the effects of what happens when a more massive galaxy interacts with a comparatively lower-massed galaxy, while major pairs offer insight into the effects of two relatively equally massed galaxies interacting with each other. The distribution of mass ratios among the close pairs is illustrated in Fig. 11, where a dashed line delineates the distinction between major and minor pairs. This results in the sample being comprised of 53% as minor pairs, while 47% are classified as major pairs.

Figure 11. Stellar mass ratio of the secondary and primary galaxy of the close pairs. The dashed black line separates those we associate as minor pairs (left of the dashed line) and that of major pairs (right of the dashed line).

Figure 12. The relationship between $\Delta sSFR$ and stellar mass across various close pair environments is depicted. Contours in each panel illustrate the distribution of all non-SFR UL and SFR S/N $ \gt $ 2 galaxies within the mass-complete sample, delineating the SF population. The median values of each distribution are depicted alongside the field galaxy median distribution in pink within each panel to highlight the relative environmental effects. A $\Delta sSFR \gt 0$ is more efficiently SF than the SFMS fit in Fig. 3 and $\Delta sSFR \lt 0$ is less efficiently SF. Median values are binned in stellar mass bins of 0.4 dex, with errors computed via bootstrap resampling within each bin. The total number of sources used in the median distributions, that is, non SFR-UL and SFR S/N $ \gt $ 2 sources, is indicated in the lower left with the same colouring as the median distribution. There is a significantly varying SF trend between the major/minor and primary/secondary pairs, ranging from SF enhancements to SF deficiencies across the stellar mass range.

By categorising our close pairs into major and minor pairs and identifying primary and secondary galaxies, we can analyse the median distribution of $\Delta sSFR$ while controlling for stellar mass across a range of interaction scales. As depicted in Fig. 12, in line with the analysis in Sections 3.2 and 3.4, we examine the variations within the SF population of these galaxies.

The median distributions of $\Delta sSFR$ for major primaries and major secondaries demonstrate notably similar behaviour, as expected. Given their comparable masses, it is anticipated that these two galaxy populations would behave similarly during their interactions. The SF population of major pairs exhibit enhancements in their SF efficiency compared to the field at stellar masses lower than $10^{10}\,\mathrm{M}_{\odot}$ , aligning with the findings of Woods et al. (Reference Woods2010), who observed a tendency for major pairs in SDSS to display heightened levels of SF compared to the field. However, at $M_{\star} \gt 10^{10}\,\mathrm{M}_{\odot}$ , the major pairs follow the SF distribution observed in the field.

Conversely, minor pairs exhibit a diverse range of star-forming behaviours. Minor primaries align with the field distribution until $M_{\star} \gt 10^{10.5}\,\mathrm{M}_{\odot}$ , where a decrease in SF efficiency relative to the field is observed. Notably, SF is detectable at larger stellar masses for minor primaries compared to the field in Fig. 8, extending our analysis close to a stellar mass of $10^{11.3}\,\mathrm{M}_{\odot}$ . This suggests that, although less efficient at these stellar masses, the star-forming population in minor primaries remains active rather than transitioning to a quenched state with no ongoing SF, as observed in the field, or already quenched galaxies undergo ‘re-animation’ and see a resurgence in their SF. If SF were quenched at these large stellar masses, it would manifest as a SFR UL value, which is notably lacking in the major primaries relative to the field. This discrepancy underscores the resilience of SF processes within minor primaries, possibly facilitated by mechanisms such as tidal stripping of gas from the less massive member, which may serve to fuel new SF processes (Mihos Reference Mihos, Mulchaey, Dressler and Oemler2004; Spilker et al. Reference Spilker2022), or more likely, tidal torques help compress the gas reservoirs, fuelling new SF, particularly in central regions (Mihos & Hernquist Reference Mihos and Hernquist1994; Moreno et al. Reference Moreno2021; Li et al. Reference Li, Ho and Shangguan2023).

Our expanded sample extends to lower stellar masses, where the median distribution demonstrates large SF efficiencies relative to the field. Conversely, at stellar masses greater than $10^{10}\,\mathrm{M}_{\odot}$ , minor secondaries exhibit a transition to a less efficient state of SF compared to the field. In contrast to Davies et al. (Reference Davies2015), who noted heightened levels of suppressed SF in minor secondaries when looking at a mass range between $10^{9.5}$ – $10^{11}\,\mathrm{M}_{\odot}$ , we only detect this at within our largest stellar mass bin. Davies et al. (Reference Davies2015) suggests that the SF suppression in minor secondaries occurs in very short ( $\lesssim+100$ Myr) and is not evident in long-duration SFR tracers such as the mid-IR, however, it’s worth noting that minor secondaries show a relative increase in the amount of UL values compared to other pair populations, suggestive of a diverse range of SF behaviours; encompassing both enhanced and highly inefficient SF processes.

To examine the correlation between proximity and induced SF, we analyse the relationship between the quenched fraction of close pairs and their projected separation ( $r_\mathrm{sep}$ ). Fig. 13 illustrates this by separating close pairs into major/minor and primary/secondary classifications, testing the effects of varying interaction scales. This approach is consistent with prior studies that investigate the impact of pair dynamics on SF (Lambas et al. Reference Lambas, Tissera, Alonso and Coldwell2003; Ellison et al. Reference Ellison, Patton, Simard and McConnachie2008; Li et al. Reference Li, Kauffmann, Heckman, Jing and White2008; Scudder et al. Reference Scudder, Ellison, Torrey, Patton and Mendel2012; Patton et al. Reference Patton, Torrey, Ellison, Mendel and Scudder2013; Bustamante et al. Reference Bustamante, Ellison, Patton and Sparre2020; Patton et al. Reference Patton2020; Steffen et al. Reference Steffen2021). While we acknowledge that stellar mass plays a critical role in quenching, as demonstrated earlier, the sample size was insufficient to separate the data into mass bins, as done by Davies et al. (Reference Davies2015). A larger dataset would enable a more detailed, mass-segregated analysis.

Figure 13. The quenched fraction vs. projected separation of close pairs. We separate the close pairs into major primaries (teal crosses), major secondaries (yellow crosses), minor primaries (purple dots) and minor secondaries (magenta dots). Each distribution has been segmented into projected separation bins with a width of 9 h-1 kpc. The number of suppressed and total number of galaxies in each bin are displayed in the lower region of the figure. Errors have been computed using bootstrap resampling within each bin. There is a general trend of decreasing suppressed fraction as the projected separation decreases amongst the galaxy pairs.

We observe a correlation between projected separation and the quenched fraction, where the quenched fraction of minor pairs decreases as the projected separation decreases. This effect is more pronounced for minor primaries than minor secondaries. Conversely, major pairs do not exhibit any clear trends over the range of projected separations chosen in this analysis. These findings for our minor pairs align with previous studies by Lambas et al. (Reference Lambas, Tissera, Alonso and Coldwell2003), Ellison et al. (Reference Ellison2010), Scudder et al. (Reference Scudder, Ellison, Torrey, Patton and Mendel2012), Davies et al. (Reference Davies2015), Steffen et al. (Reference Steffen2021), Shah et al. (Reference Shah2022), which demonstrated increased levels of star formation as a function of decreasing projected separation, particularly for pairs with separations of $r_\mathrm{sep} \lt 30 \: \text{h}^{-1} \text{kpc}$ .

We emphasise the analysis of close galaxy pairs is a difficult challenge, as there are numerous factors influencing their evolutionary trajectories, particularly across different stellar mass regimes. A more extensive dataset is necessary to unravel the underlying mechanisms driving these complexities. Moreover, more detailed observational studies on individual interacting close pairs such as detailed HI studies are essential to understanding the observed trends we find, particularly those observed to deviate from the ‘typical’ evolutionary pathways.