Galaxy And Mass Assembly (GAMA): The Merging Potential of Brightest Group Galaxies

The GAMA Galaxy Group Catalogue (G³C) is the catalog of all of the galaxy groups defined in the GAMA survey (Robotham et al. 2011). We use version 10 of the catalog here and briefly describe the key measurements.

The G³C uses a friends-of-friends (FoF) algorithm to identify groups. The halo mass is estimated using the measured values of the halo velocity dispersion (σ) and the group radius (R). The halo velocity dispersion is calculated using the gapper estimator introduced by Beers et al. (1990), which is developed to be robust to outliers in smaller number samples. The group radius used is that which contains 50% of galaxies in the group (Rad₅₀). This is chosen such that the group radius is robust against potential interloping galaxies (Robotham et al. 2011). For a stable system, the halo mass equates to M_halo = A σ² R. In GAMA, the constant A is calculated by comparison between the group-finder outputs from observations and mock observations of simulations (Robotham et al. 2011), and the total halo mass of a group is estimated as M = 10.0σ² R. We also estimated the impact of determining halo masses of our groups using the weak-lensing-calibrated halo mass scaling relations in Viola et al. (2015) and find that these do not qualitatively change our conclusions.

Three approaches were considered to determine the central galaxy of GAMA groups in Robotham et al. (2011). The first approach determined the center of the cluster to be the center of light, which is a good proxy for center of mass. The second approach was an iterative process where the center of light was derived at each step from the r_AB -band luminosity of all the galaxies identified within the group. The most distant galaxy from the center of light was rejected. This process was repeated until two galaxies remained, of which the brighter r_AB -band galaxy was used as the group center. The third approach simply defined the group center by the brightest member of the group, i.e., the BGG. Robotham et al. (2011) found that the iterative method produced the most robust estimate of the central galaxy of the group, and we therefore use that here.

The stellar masses of galaxies in the GAMA survey are estimated by Taylor et al. (2011) by fitting model spectral energy distributions to Sloan Digital Sky Survey (SDSS; York et al. 2000) ugriz imaging reprocessed by the GAMA team (Hill et al. 2011). When observing galaxies at varying distances with an aperture of a fixed size, different fractions of a galaxy's luminosity will be observed. The flux of each galaxy is measured within a flexible circular aperture, where the size of the aperture is determined by the observed radial surface brightness profile of the galaxy. Since only a fraction of each galaxy's luminosity is considered for the stellar mass estimate, a linear scale factor, fluxscale, is calculated to account for the unobserved luminosity of each galaxy from the ratio between the aperture r-band flux and the total r-band flux inferred from fitting a single Sérsic profile truncated at 10 R_e (Kelvin et al. 2012). We apply this scale factor in this work.

The GAMA survey is apparent magnitude limited; we therefore select a volume-limited sample to ensure a robust analysis.

The distribution of BGG stellar mass with redshift is shown in the top panel of Figure 1. The density of BGGs with z ∼ 0.25 is lower compared to the rest of the sample, due to the 5577 Å sky line passing through key spectral features. We therefore limit our sample to groups with redshifts z < 0.2. We also impose a lower limit on the redshift, z ≥ 0.07, due to the low volume sampled below this.

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We define a minimum BGG stellar mass limit across our sample such that this minimum stellar mass is observed for galaxies of all colors across our redshift range. At z = 0.2, this minimum complete BGG stellar mass is 10^11.0 M_⊙, which we apply to our sample. We also apply an upper limit, 10^11.6 M_⊙, on the stellar mass of BGGs to remove unrealistically massive BGGs that likely occur as a result of image contamination. This volume limit yields a sample of 640 groups. The distribution of halo mass is also affected by GAMA's apparent magnitude selection limit. We apply a volume limit to this too, limiting the halo mass of groups to a lower limit of M_h = 10^12.8 M_⊙ and an upper limit of 10^14.2 M_⊙. This selection results in a volume-limited sample of 550 groups and is illustrated in Figure 1 with BGG stellar mass in the top panel and group halo mass in the bottom panel.

Our sample of 550 groups contains 4207 noncentral member galaxies that have the potential to merge with their BGG (illustrated by the gray points in Figure 2). The distribution of these galaxies in redshift is similarly affected by GAMA's apparent magnitude selection limit. We place a conservative initial volume limit of M^* = 10^10.2 M_⊙ allowing for the range of galaxy colors at GAMA's m_r = 19.8 mag limit at our z ∼ 0.2 limit. This yields a maximum possible BGG-to-companion stellar mass ratio M_BGG/M_CC ∼ 6 when compared to the least massive BGGs in our sample (i.e., ∼ 10^11.0 M_⊙).

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Within the literature (e.g., De Lucia & Blaizot 2007; McIntosh et al. 2008; Liu et al. 2009; Robotham et al. 2014; Groenewald et al. 2017), a close-companion galaxy with a BGG-to-companion stellar mass ratio M_BGG/M_CC ≤ 4 is considered a major merger, whereas those with stellar mass ratios > 4 are considered minor mergers. The lower stellar mass limit imposed on our sample of potential close-companion galaxies does not produce a robust sample of minor merger candidates. Henceforth, we focus only on major mergers with stellar mass ratios M_BGG/M_CC ≤ 4.

A galaxy may be considered a close companion to a BGG if it has a small projected separation (r_p ) and relative velocity (Δv) to the BGG. Taking into account both of these parameters ensures an unbiased sample with less of the line-of-sight contamination that may be present in purely photometric samples (Kitzbichler & White 2008).

A recent analysis of the Illustris-1 simulation (Vogelsberger et al. 2014; Ventou et al. 2019) suggests that major close-companion galaxies at low redshift (z < 0.5) with a projected distance r_p ≤ 25 kpc and a velocity of Δv ≤ 150 km s⁻¹ relative to the BGG with stellar mass > 10^9.5 M_⊙ have a 75% chance of merging by z = 0. Ventou et al. (2019) suggest the following selection criteria for selecting spectroscopic close-companion galaxies that are likely to merge: r_p ≤ 50 kpc and Δv ≤ 300 km s⁻¹. However, numerous observational studies (e.g., McIntosh et al. 2008; Liu et al. 2009; Robotham et al. 2014; Groenewald et al. 2017) apply a more conservative projected separation of r_p ≤ 30 kpc.

To construct a robust sample of close-companion galaxies, we follow the recommendations of Ventou et al. (2019) and identify close-companion galaxies as galaxies with Δv ≤ 300 km s⁻¹ and use the conservative projected separation limit r_p ≤ 30 kpc. This selection criteria results in 17 close-companion galaxies. We note here that when we expand the sample to r_p ≤ 50 kpc, the sample increases to 31 close-companion galaxies. To be consistent with the literature, we only consider those within r_p ≤ 30 kpc for the remainder of our analysis. These close-companion galaxies are represented by the red points in Figure 2.

Figure 3 illustrates the distribution of companion stellar mass with respect to BGG stellar mass and demonstrates equivalent BGG-to-CC stellar mass ratios. Each black line represents stellar mass ratios with the thickest line representing M_BGG/M_CC = 1 and the weakest line equivalent to 4. This illustrates that the companions within our sample are distributed uniformly between stellar mass ratios 1 ≤ M_BGG/M_CC < 4.

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We investigate the fraction of close-companion galaxies within our sample. This is also known as the pair fraction and is defined as:

$$\begin{eqnarray}&&{f}_{\mathrm{pair}}=\displaystyle \frac{{N}_{\mathrm{CCs}}}{{N}_{\mathrm{BGGs}}},\end{eqnarray} \tag{ 1 }$$

where N_BGGs is the total number of BGGs in the sample and N_CCs is the total number of identified close-companion galaxies. The 1σ uncertainties used throughout are calculated using the binomial confidence interval described in Cameron (2011), because it is robust to the small sample sizes present in our analysis.

Given that we have a sample of 550 BGGs and identified 17 close-companion galaxies within our sample of noncentral galaxies, this yields a pair fraction of f_pair = 0.03 ± 0.01. However, as mentioned in Section 3.2, simulations show that close-companion galaxies with r_p ≤ 25 kpc and Δv ≤ 150 km s^-1 have a 75% chance of merging by z = 0 so the pair fraction calculated here is an upper limit. The pair fraction is henceforth used to calculate the maximum potential stellar mass growth of the BGGs in our sample.

We also investigate the influence of halo mass on the BGG pair fraction and illustrate this in Figure 4. While there is no statistically significant dependence in this halo mass range (i.e., 10^12.8 M_⊙ ≤ M_halo ≤ 10^14.2 M_⊙), we do note a systematic decrease of the BGG pair fraction with increasing halo mass. We also investigated this relationship with the less conservative limit of r_p ≤ 50 kpc and found a similar result.

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The next step in determining the potential stellar mass growth of BGGs is to calculate their merger rate, which requires knowledge of the time it takes for a close-companion galaxy to merge with the BGG, i.e., the merging timescale. A commonly used merging timescale in galaxy merging literature is that derived by Kitzbichler & White (2008) using the Millenium Simulation (Springel et al. 2005).

Kitzbichler & White (2008) find that at redshifts z ≪ 1, the average merging timescale derived for a close-companion galaxy with stellar mass > 5 × 10⁹ h⁻¹ M_⊙, within Δv ≤ 300 km s⁻¹ and a projected radius r_p ≤ 50 kpc, is given by:

$$\begin{eqnarray}&&\langle {T}_{\mathrm{merge}}\rangle ={T}_{0}\displaystyle \frac{{r}_{p}}{{r}_{0}}{\left(\displaystyle \frac{{M}_{* }}{{M}_{0}}\right)}^{-0.3}\left(1+\displaystyle \frac{z}{8}\right),\end{eqnarray} \tag{ 2 }$$

where T₀ = 2.2 Gyr, r₀ = 50h⁻¹ kpc, M₀ = 4 × 10¹⁰ h⁻¹ M_⊙, and z is the median redshift of the cluster. Using this method, the close-companion galaxies identified in this work are predicted to merge with their respective BGGs in 0.53 ± 0.19 Gyr on average.

Other recent investigations into the average merger rate of galaxies use an observability timescale (e.g., Lotz et al. 2008, 2011; Mundy et al. 2017; Duncan et al. 2019). This observability timescale is the average timescale during which merging galaxies can be observed depending on the method used to identify the merger (e.g., close galaxy pair selection utilized in this work). Lotz et al. (2011) derive this quantity for a number of merger selections. They suggest that the timescale for major close-companion galaxies identified through pair selection is ∼0.33 Gyr for 5h⁻¹ < r_p < 20h⁻¹ kpc, and ∼0.63 Gyr for 10h⁻¹ < r_p < 30h⁻¹ kpc, which is consistent with the merging timescale calculated for our close-companion galaxies using Equation (2). In order to provide a robust comparison to previous analyses (e.g., McIntosh et al. 2008; Liu et al. 2009; Groenewald et al. 2017) of the stellar mass growth of BGGs we use the timescales predicted by Kitzbichler & White (2008), which are also utilized in these previous studies.

The average merger rate of a sample of BGGs, i.e., the number of mergers per BGG per gigayear is then calculated as follows:

$$\begin{eqnarray}&&\langle {R}_{\mathrm{merge}}\rangle =\displaystyle \frac{{f}_{\mathrm{pair}}}{\langle {T}_{\mathrm{merge}}\rangle }.\end{eqnarray} \tag{ 3 }$$

The uncertainty on 〈R_merge〉 is calculated using the standard propagation of uncertainties.

The close-companion galaxies in our sample of groups merge with their respective BGGs in 0.53 ± 0.19 Gyr on average. Therefore, the BGGs in our sample experience on average 0.06 ± 0.03 mergers per gigayear.

The potential stellar mass growth rate of BGGs, ΔM_* (M_⊙ Gyr⁻¹) is calculated using a modified version of Equation (7) from Groenewald et al. (2017). Their equation determines the overall growth of BGGs evolved from a particular redshift to z = 0. In this study we are interested in the potential average mass growth of BGGs at low redshifts, so we modify their equation such that the result is the average stellar mass growth per gigayear. Our modified equation is as follows:

$$\begin{eqnarray}&&{\rm{\Delta }}{M}_{* }=\langle {R}_{\mathrm{merge}}\rangle \times \langle {M}_{* }{\rangle }_{\mathrm{CC}},\end{eqnarray} \tag{ 4 }$$

where 〈M_*〉_CC is the average stellar mass of the close-companion galaxies in our sample in M_⊙.

The close-companion galaxies in our sample have an average stellar mass of 〈M_*〉_CC = 8.18 ± 3.34 × 10¹⁰ M_⊙, which contribute a total stellar mass of ΔM_* = 0.47 ± 0.30 × 10¹⁰ M_⊙ per gigayear.

We calculate the fractional contribution of mergers toward the stellar mass growth of BGGs per gigayear. We modify Equation (8) from Groenewald et al. (2017) to calculate the fractional contribution made by merging close-companion galaxies in our sample but not incorporating their growth to z = 0. This is defined per gigayear, by:

$$\begin{eqnarray}&&F=\displaystyle \frac{{\rm{\Delta }}{M}_{* }}{\langle {M}_{* }{\rangle }_{\mathrm{BGG}}(t=0)+{\rm{\Delta }}{M}_{* }},\end{eqnarray} \tag{ 5 }$$

where 〈M_*〉_BGG(t = 0) is the average stellar mass of BGGs in the sample at the present day. While BGGs do grow in stellar mass from the formation of stars, it is rare to find star-forming BGGs at z ≤ 0.5 (< 1%; e.g., Liu et al. 2012; Fraser-McKelvie et al. 2014; Webb et al. 2015; Groenewald et al. 2017; Cerulo et al. 2019). Those BGGs that are forming stars grow by ∼1%–3% in stellar mass from star formation (e.g., Liu et al. 2012). Furthermore, it is estimated that the contribution of stellar mass to BGGs via minor mergers is just as significant as that through major mergers (e.g., Edwards & Patton 2012); however, we cannot robustly measure the stellar mass growth of BGGs due to minor mergers and so we focus here on their growth only via major mergers.

We find that BGGs in our sample spanning the redshift range 0.07 ≤ z ≤ 0.20 grow in stellar mass due to major mergers by 2.19% ± 1.52% Gyr⁻¹, assuming that all of the stellar mass of a merging close-companion galaxy is accreted onto the BGG. This is similar to the predicted stellar mass growth from star formation of star-forming BGG (∼1%–3% e.g., Liu et al. 2012)

In Figure 5 we compare our pair fraction to earlier studies. Both McIntosh et al. (2008) and Liu et al. (2009) have studied the BGG pair fraction at z ≤ 0.12. McIntosh et al. (2008) investigated the incidence of major mergers with mass ratios ≤4 in the Sloan Digital Sky Survey (SDSS). They used a volume-limited sample of 845 groups with halo masses > 2.5 × 10¹³ M_⊙ and refined their search for merger candidates within 30 kpc by visually inspecting their sample of 221 galaxy pairs for the presence of morphological features associated with merging events. This was done in lieu of setting a limit on the relative velocities of the close-companion galaxies due to the purely photometric sample used in their analyses. From this they found a pair fraction of f_pair = 0.045 ± 0.007. This is represented by the red point in Figure 5.

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Liu et al. (2009) similarly searched for ongoing major mergers (≤4) in a sample of BGGs from the SDSS C4 cluster catalog (Miller et al. 2005) with redshifts 0.03 ≤ z ≤ 0.12. They also searched for close-companion galaxies within 30 kpc that showed significant signs of interaction in the form of significant asymmetry in residual images. They concluded that 18 of their 515 BGGs were involved in major mergers, i.e., f_pair = 0.035 ± 0.008 indicated in Figure 5 by the magenta point.

The blue points in Figure 5 represent the pair fraction calculated in Groenewald et al. (2017). They studied more massive groups (M_h > 2.2 × 10¹⁵ M_⊙) constructed from the redMaPPer catalog (Rykoff et al. 2014). They split their sample into four redshift ranges, the first two of which overlap with the redshift covered by our sample. These two low redshift ranges result in a pair fraction f_pair ∼ 0.05.

We calculate a major merger pair fraction of f_pair = 0.03 ± 0.01 over similar redshifts to those in McIntosh et al. (2008), Liu et al. (2009) and Groenewald et al. (2017). This is in agreement with these earlier studies.

Casteels et al. (2014) also investigated the major merger pair fraction in the GAMA survey at redshifts 0.001 < z < 0.2. They examined the mass-dependent major merger rate of GAMA galaxies with stellar masses 10^8.0 < M_* < 10^11.5 M_⊙ and found the major merger pair fraction to be consistent at ∼ 0.013–0.02 between 10^9.5 < M_* < 10^11.5 M_⊙ an major merger pair fraction is approximately half the major merger pair fraction calculated in this work (i.e., 0.03 ± 0.01); however, we note that their sample is not limited to central galaxies, and so we do not directly compare it to our result in Figure 5.

We also investigate the role the BGG's environment plays on the pair fraction (see Figure 4). Liu et al. (2009) also examined the relation between the fraction of BGGs involved in major mergers and the richness of the cluster, defined as the number of cluster members within a 1h⁻¹ Mpc radius centered on the BGG. The pair fraction of BGGs in Liu et al. (2009) appeared to increase with increasing cluster richness with a BGG pair fraction of ∼0.01 at a richness of ∼15 up to ∼0.055 at a richness of ∼45. While our total pair fractions across halo mass are in agreement with those in Liu et al. (2009), Figure 4 shows that we find that the major merger pair fraction tends to decrease with halo mass, however, we note that relationship is not statistically significant.

The BGG pair fraction and the mean merging timescale of close-companion galaxies are key ingredients in the calculation of the BGG merger rate. We have estimated the merging timescale of close-companion galaxies in our sample using the merging timescale derived in Kitzbichler & White (2008). The merging timescale is largely influenced by the stellar mass of the infalling close-companion galaxies and their projected separation from the BGG. Our sample of close-companion galaxies range in stellar mass between $10.5\lt \mathrm{log}[{M}_{* }/{{M}}_{\odot }]\lt 11.2$ and have projected separations within 30 kpc. The mean merging timescale for all of the close-companion galaxies in our sample is 0.53 ± 0.19 Gyr.

A pair fraction of 0.03 ± 0.01 and a mean merging timescale of 0.53 ± 0.19 Gyr yields an average merger rate of 0.06 ± 0.03 Gyr⁻¹. This implies that the BGGs in our sample experience on average one major merger every 16 Gyr since z = 0.2, significantly longer than the age of the universe. This is consistent with simulations (e.g., Hopkins et al. 2010) and observations at similar redshifts (e.g., McIntosh et al. 2008; Edwards & Patton 2012; Liu et al. 2012).

Figure 6 shows the comparison of our measured merger rates with the previous studies introduced in Section 5.1. While some of these samples have higher stellar mass companions than our sample, we find them all to have consistent merger rates.

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The average merger rate and the mean stellar mass of close-companion galaxies are used to estimate the potential stellar mass growth rate of BGGs in our sample. The average stellar mass of the close-companion galaxies in our sample is 8.18 ± 3.34 × 10¹⁰ M_⊙. The BGGs in our sample therefore increase their stellar mass by 0.47 ± 0.30 × 10¹⁰ M_⊙ Gyr⁻¹ due to major mergers, which is equivalent to a fractional mass increase of 2.19 ± 1.52% Gyr⁻¹.

5.3.1. Observational Studies of Close-companion Galaxies

We compare the values calculated in McIntosh et al. (2008); Liu et al. (2009, 2015); Groenewald et al. (2017) with the stellar mass growth we have estimated in Figure 7. It is important to note that only McIntosh et al. (2008) have calculated the stellar mass growth of BGGs per gigayear. All other studies mentioned in this comparison estimate the stellar mass growth over a redshift range. In order to obtain a comparison to these results, we convert them to a stellar mass growth per gigayear by dividing the stellar mass growth by the lookback time that corresponds to the redshift range using the same cosmology.

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Numerical simulations that investigate the buildup of the intracluster light (ICL; e.g., Conroy et al. 2007; Murante et al. 2007; Puchwein et al. 2010; Laporte et al. 2013; Contini et al. 2014) due to galaxy mergers predict that 30%–80% of a merging close-companion galaxy's stellar mass contributes to the mass of the ICL rather than the BGG. Many observational studies that investigate the stellar mass buildup of BGGs take this into account and assume a conservative fraction, f = 0.5 (e.g., Liu et al. 2009, 2015; Groenewald et al. 2017). This study investigates the potential for stellar mass buildup of BGGs, hence we do not assume this mass fraction. Henceforth, we divide out the fractions used in these studies to present a consistent comparison to our result.

McIntosh et al. (2008) estimate the rate of stellar mass accretion by major mergers via,

$$\begin{eqnarray}&&{\dot{M}}_{\mathrm{BGG}}=\displaystyle \frac{{\rm{\Sigma }}{M}_{* ,i}f}{{N}_{\mathrm{BGG}}}\times \displaystyle \frac{1}{{t}_{\mathrm{merge}}},\end{eqnarray} \tag{ 6 }$$

where N_BGG is the total number of BGGs in the sample; M_*,i is the stellar mass of the ith close-companion galaxy; and f is the fraction of stellar mass of the companion galaxy that is accreted onto the BGG. They find that BGGs in large groups with redshifts z ≤ 0.12 gain up to ${2.4}_{-0.6}^{+1.1}\times {10}^{10}$ M_⊙ Gyr⁻¹ assuming that all of the companion's stellar mass is accreted onto the BGG. The stellar mass growth calculated by McIntosh et al. (2008) is equivalent to an average stellar mass growth of 1%–5% Gyr⁻¹. This is represented in Figure 7 by the red point.

Liu et al. (2009) found that major mergers contribute 5.0% ± 1.7% Gyr⁻¹ when all of the major companion's stellar mass is accreted onto the BGG. This is represented by the magenta point in Figure 7. In a later study, Liu et al. (2015) found that major mergers contribute 70% ± 15% to the stellar mass of present day BGGs since z = 0.6. This corresponds to an average stellar mass growth of 12.2% ± 2.6% Gyr⁻¹ from z = 0.6 (green point in Figure 7), which is substantially larger than their earlier estimate of the potential stellar mass growth rate as well as what we calculate here. We will return to this discrepancy later in this section.

Edwards & Patton (2012) also identify close-companion galaxies of BGGs in order to quantify the rate at which these galaxies grow via mergers. They used deep images from the Canada–France–Hawaii Telescope Legacy Survey and analyzed close-companion galaxies within 50 kpc (using photometric redshifts) of their BGGs with luminosity ratios up to L_BGG/L_CC = 20. The luminosity in major companions is 1.14 ± 0.28 × 10¹⁰ L_⊙, whereas it is almost double when including minor companions, i.e., 2.14 ± 0.31 × 10¹⁰ L_⊙. They find that these close-companion galaxies could increase the stellar mass of a 5 × 10¹¹ M_⊙ BGG by up to ∼ 10% over the redshift range 0.15 ≤ z ≤ 0.39. This potential stellar mass growth is attributed to both major and minor close-companion galaxies; therefore, we do not directly compare it to our result in Figure 7.

The stellar mass growth of galaxies from an earlier release of the GAMA Galaxy Group catalog was also investigated by Robotham et al. (2014). They investigated major mergers of galaxies with stellar masses 10⁸ − 10¹² M_⊙ and found that the fraction of mass being added by merging is approximately 2.0%–5.6%. This is represented in Figure 7 by the dark red point.

Groenewald et al. (2017) investigated the stellar mass buildup of BGGs between 0.08 ≤ z ≤ 0.50. They found major mergers contribute on average 48% ± 17% toward the stellar mass of present day BGGs since z = 0.32. This corresponds to a stellar mass growth rate of ∼ 17% Gyr⁻¹. These results are plotted as blue points in Figure 7. They find significantly higher stellar mass growth from major mergers than we do here.

Overall, we find that our results are in good agreement with the stellar mass growth calculated by McIntosh et al. (2008); Liu et al. (2009) and Robotham et al. (2014). However, the growth predicted by Liu et al. (2015) and Groenewald et al. (2017) is significantly larger. This is not unexpected due to the different methods employed by these studies. These growth rates were calculated with either purely photometric galaxy surveys (e.g., McIntosh et al. 2008; Liu et al. 2009; Edwards & Patton 2012; Liu et al. 2015) or incomplete spectroscopic surveys (e.g., Groenewald et al. 2017). McIntosh et al. (2008) and Liu et al. (2009) refined their search for close-companion galaxies by visually inspecting their sample of BGGs for signs of merging. This ensures that the galaxies selected are true close-companion galaxies such that their growth rates are consistent with our robust measurements from a highly complete spectroscopic survey. The stellar mass growth rates estimated by Edwards & Patton (2012), Liu et al. (2015) and Groenewald et al. (2017) are larger suggesting that the corrections applied for close-companion galaxies are not conservative enough.

5.3.2. Observational Studies of Change in Stellar Mass

5.3.3. Stellar Mass Growth in Models