The Next Generation Fornax Survey (NGFS). II. The Central Dwarf Galaxy Population

To detect LSB dwarf galaxy candidates, we first constructed RGB images from the observed u'g'i' frames to take advantage of the total flux captured in each passband while preserving color information. We then visually inspected these frames, looking explicitly for diffuse LSB galaxies. The RGB images allow us to easily identify dwarf galaxy candidates by considering their colors, sizes, and overall morphologies (e.g., comparatively flat surface brightness profile and nucleation). We also included LSB galaxies having SF knots or blue colors, not specifically selecting against these sources. While automated algorithms can prove very effective in detecting faint galaxies (NGVS paper, Ferrarese et al. 2016), for the purpose of this work, we present a by-eye classification done independently by several people.  The advantage of this method over automated algorithms like SE is obvious. For example, SE is only able to analyze one frame–passband combination at a time and often fails to detect extended LSB sources due to contamination by foreground stars, while visual inspection allows for the identification of galaxy candidates based on all aforementioned criteria simultaneously. We find that galaxy color is particularly effective in this regard since the colors of cluster dwarfs are expected to follow a cluster red sequence as seen in many galaxy aggregates (Gladders & Yee 2005; Roediger et al. 2017), with likely origins in the galaxy mass–metallicity relation. Combining this criterion with the diffuse morphologies arising from shallow dwarf surface-brightness profiles results in a straightforward detection strategy for dwarf galaxy candidates. Despite these advantages, the disadvantage of visual inspection is that it precludes us from quantifying a selection function to verify sample completeness and that it has the potential to introduce human bias. Hence, to avoid any personal detection biases, we (P.E., T.H.P., Y.O., M.A.T., K.A.M., K.X.R.) individually investigated the RGB images independently, yielding up to six separate dwarf galaxy candidate catalogs for each tile. Tile 1 has five independent candidate catalogs.

To estimate the reliability of our detections, we match the catalogs using TOPCAT (Taylor 2005) to quantify in how many catalogs a given source was found. We then assign quality flags to each dwarf galaxy candidate such that one found in all five catalogs is assigned a flag ${ \mathcal A }$, in four catalogs a flag ${ \mathcal B }$, and so on. The matching is done systematically so that we first match all flag ${ \mathcal A }$ objects and remove them from the corresponding catalogs. We continue by searching for flag ${ \mathcal B }$ sources, and we continue until all remaining sources are flag ${ \mathcal E }$, that is, untrustworthy candidates only identified by a single team member. In order to find all matches for a given flag k, all possible $\left(\genfrac{}{}{0em}{}{5}{k}\right)$ catalog combinations have to be matched, leading to lists of 145 flag ${ \mathcal A }$, 59 flag ${ \mathcal B }$, 54 flag ${ \mathcal C }$, 29 flag ${ \mathcal D }$, and 136 flag ${ \mathcal E }$ sources.

Figure 3 shows the distribution of quality flags, which illustrates the potential human detection bias given the large number of accumulated flag ${ \mathcal E }$ sources present in the merged candidate catalog. Conversely, those sources with multiple independent identifications, flags ${ \mathcal A }{ \mathcal B }{ \mathcal C }{ \mathcal D }$, show a strong trend toward unanimous detections. Flag ${ \mathcal E }$ illustrates the average number of sources uniquely identified by one person (solid line) as well as all accumulated sources (dashed line).

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The lower panel in Figure 3 shows the correlation between detection flags and median values of galaxy apparent g'-band magnitude, effective radius (r_e), and surface brightness (μ_g') for each flag. As expected, apparent magnitude and r_e show clear trends toward brighter and larger galaxies having flags ${ \mathcal A }/{ \mathcal B }$, while flags ${ \mathcal D }/{ \mathcal E }$ correspond to fainter and smaller sources. No obvious correlation is seen with μ_g'. We note that these correlations should be taken with caution, since we only measure structural parameters for a small subsample of ${ \mathcal D }{ \mathcal E }$ flags. Moving forward, we consider only galaxies with detection flags ${ \mathcal A }{ \mathcal B }{ \mathcal C }$, that is, with at least three independent identifications, to be dwarf galaxy candidates, yielding a final sample of 258 sources. Of these candidates, 75 (∼29%) show evidence of nucleation based on visual inspection of the u'-, g'-, and i'-band images, while 183 galaxies (∼71%) show no nucleus.

We compare our sample with galaxies flagged as likely members in the FCC (Ferguson 1989). Out of 340 FCC galaxies, 112 fall in our observed DECam footprint. We note that we could not reidentify FCC 162, which is reported to be located within the halo of the bright elliptical NGC 1379 (FCC 161), leaving 111 recovered FCC galaxies. Of these, 90 are fainter than M_B = −16 mag and, hence, can be considered as dwarf galaxies (Ferguson & Binggeli 1994; Tammann 1994). In addition, two galaxies with M_B ≲ −16 (FCC 136 and FCC 202) have explicitly been classified as dwarfs in the FCC catalog, resulting in a total number of 92 FCC dwarfs in our observed footprint. We also recover 45 galaxies from the Mieske et al. (2007) catalog that have not been classified as FCC galaxies. Finally, we checked for Mieske et al. (2007) dwarfs that are not in our sample and conclude that, based on their morphologies and colors, all are likely to be background galaxies. Summarizing, we find a sample of 258 – 92 – 45 = 121 previously uncataloged dwarf candidates. We note that this number is smaller than in our recent publication (see Muñoz et al. 2015), since in the present work we only consider galaxies with quality flags ${ \mathcal A }{ \mathcal B }{ \mathcal C }$ as dwarf identifications.

Figure 2 shows a schematic representation of the spatial distribution of the detected dwarf galaxy candidates and known bright galaxies in the central DECam tile of the NGFS footprint analyzed in this work (tile 1 in Figure 1). The symbol shape, alignment, size, and opacity of each galaxy marked in Figure 2 are scaled by the corresponding , PA, r_e, and M_g, respectively, as obtained from our galfit models. We point out that since precise 3D spatial information is not known, M_g may vary by up to ∼0.16 mag due to the unknown depth of the cluster.¹⁹

We determine the structural parameters for the 258 dwarf candidates in u', g', and i' filters utilizing the software package galfit (v3.0.5; Peng et al. 2010). galfit is an effective tool for extracting structural information from dwarf galaxies, allowing the user to model the two-dimensional distribution of the diffuse starlight in galaxies with numerous parametric functions. Utilizing the full 2D information for a given galaxy enables us to obtain reliable fits to the surface brightness distribution constrained by each nonmasked image pixel. Surface brightness profiles of dwarf galaxies are commonly well fit by a single-component Sérsic (1968) model:

$\begin{eqnarray}&&I(r)={I}_{e}\exp \{-{b}_{n}[{(r/{r}_{e})}^{1/n}-1]\},\end{eqnarray} \tag{ 1 }$

which is parameterized by the effective radius r_e, the intensity I_e at r_e, and the shape index n (also referred to as the Sérsic index) that defines the curvature of the model. The parameter b_n is linked to n such that half of the total light from the model is enclosed within r_e (Caon et al. 1993). We choose this single-component, ellipsoidal model to measure the global morphology of our dwarf galaxy candidates.

Our iterative fitting procedure is split into several steps. First we create postage stamp images for each dwarf candidate in the u'-, g'-, and i'-band frames and construct corresponding segmentation maps using SE. The segmentation maps are used to create bad-pixel masks for each dwarf, masking any nondwarf sources above a 2σ threshold. This initial step results in dwarf-only images that are used for subsequent model fits.

3.4.1. Automatic and Refined Fitting

In a first iteration, we fit galaxies assuming four different initial guesses for the Sérsic model parameters. By comparing between the four resulting model fits for each galaxy, we obtain a qualitative estimate of the robustness of a fit. In the best scenario, all initial guesses converge to the same solution, but in most cases two or three initial guesses converge to a single model, leaving one or two outliers. In the worst cases, all initial guesses yield different results. To properly assess the reliability of the fits, we compare the galaxy, model, and residual images for each dwarf in detail. In most cases where multiple initial guesses converge to the same result, visual inspection shows the fits to be reliable.

In the second iteration, we consider galaxies for which the automatic fitting procedure did not converge to a common solution, due to their diffuse natures or small extents. For these galaxies—the majority of our sample—the models display a severe mismatch with respect to the surface brightness distributions of the galaxies, or the residual images show signs of oversubtraction. We refine the fitting procedure for these galaxies as follows.

First, we estimate the total galaxy luminosity by running SE on the galaxy postage stamp images and use the resulting MAG_AUTO values from the corresponding segmentation as initial guesses for the galfit Sérsic models. Keeping these values fixed reduces the number of free parameters available for the next galaxy model, stabilizing the fit and resulting in more robust estimates of the remaining model parameters. We then use the new parameters and fix them and allow galfit to recompute the galaxy luminosity freely. In the final step, the newly determined galaxy magnitude was again fixed, and we recompute the other parameters, resulting in model parameters that are all consistently derived by galfit. In this way, all nonnucleated dwarfs are fit successfully, leaving little to no sign of the galaxies' light in the residual images (see Figure 4).

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3.4.2. Fitting Nucleated Dwarfs

We modify the above strategy for dwarf candidates that show evidence of nucleation in order to account for the excess light at their centers. While in principle a two-component model consisting of a King (1962) profile for the nucleus and a Sérsic profile for the spheroid would be preferred, the pixel-scale sizes of the nuclei preclude this approach. Very few stable solutions are found for the nuclei, and the addition of model parameters increases the likelihood of degenerate solutions, making this approach futile.

As a solution to this problem, for a given nucleated candidate, we instead mask the nucleus and fit a single Sérsic model to the diffuse spheroid iteratively. We first manually create a preliminary mask for the nucleus in the segmentation maps and use it to fit the galaxy light without the nuclear component. From the resultant residual images (including the nucleus), we generate an improved mask for the nucleus and any other sources contaminating the diffuse components of the dwarfs. We then repeat the fit using the improved mask and iteratively improve the mask and residual image. If the nucleus is not masked correctly, the Sérsic model will attempt to fit it partially, thus predicting a too-high n and producing symmetric regions of over- and undersubtraction in the residuals. Following this procedure, we find that three to four iterations result in clear nucleus–spheroid separation free of symmetric residuals in the circumnuclear regions, and give stable solutions for the spheroid components of all nucleated dwarf candidates confirmed by visual inspection.

Figure 4 shows models for eight (four nonnucleated and four nucleated) representative dwarf galaxies with successively decreasing average surface brightness in the range 24.0 ≲ μ_i'/mag ≲ 26.5. A comparison of the galaxies (top row), models (middle row), and residuals (bottom row) clearly illustrates the robustness of our modeling approach. In total, we derive structural properties for 246/258 (95%) of the detected dwarf candidates in the i' and g' bands, dropping to 144 (56%) in the u' band. While the lower fraction of modeled galaxies in the u' band is likely due to the lower sensitivity and comparatively low flux of galaxies in this particular passband, the 12 missing galaxies in the i' and g' bands are either too faint or too strongly contaminated by a bright nearby star. We list our photometric results in Table 1, including galaxy coordinates, all available total galaxy magnitudes derived from galfit, integrated galaxy colors, absolute g'-band magnitudes (M_g'), and estimated total stellar masses (${{ \mathcal M }}_{\star }$; see also Section 4.3). We also list the cross-identifications from the FCC and the Mieske et al. (2007) catalogs. Likewise, we list in Table 2 all available structural parameters derived by galfit in this work, also indicating for each galaxy whether or not a nucleus is present.

Table 1.  Photometric Properties and Stellar Masses of the Dwarf Galaxy Sample

ID	Referencea	α	δ	i'	g'	u'	(g' − i')0	(u' − g')0	(u' − i')0	Mgb	$\mathrm{log}{{ \mathcal M }}_{\star }$
		(J2000)	(J2000)	(mag)	(mag)	(mag)	(mag)	(mag)	(mag)	(mag)	(M⊙)
NGFS033309-352349	FCC114	03h33m0863	−35°23'4901	18.67	19.57	20.28	0.90	0.72	1.62	−11.94	7.11
NGFS033311-353956	...	03h33m1093	−35°39'5616	20.05	21.62	...	1.57	...	...	−9.89	7.05
NGFS033348-355010	FCC125	03h33m4842	−35°50'0966	17.64	18.50	19.64	0.86	1.15	2.01	−13.01	7.62
NGFS033350-355706	...	03h33m4987	−35°57'0617	20.91	21.57	...	0.66	...	...	−9.94	6.24
NGFS033400-354533	...	03h33m5975	−35°45'3326	18.30	19.52	20.05	1.22	0.54	1.76	−11.99	7.27
NGFS033406-351638	FCC127	03h34m0597	−35°16'3825	18.61	19.39	20.30	0.78	0.92	1.70	−12.12	7.17
NGFS033407-352838	...	03h34m0697	−35°28'3799	20.63	22.47	...	1.84	...	...	−9.04	6.96
NGFS033409-353100	FCC130	03h34m0918	−35°30'5950	17.38	18.10	...	0.72	...	...	−13.41	7.68
NGFS033412-351343	FCC131	03h34m1213	−35°13'4328	19.15	19.92	20.50	0.77	0.59	1.36	−11.59	6.88
NGFS033414-354910	...	03h34m1429	−35°49'1005	19.79	20.47	...	0.68	...	...	−11.04	6.70
NGFS033423-355042	...	03h34m2334	−35°50'4189	19.18	20.51	...	1.33	...	...	−11.00	7.28
NGFS033427-350621	...	03h34m2718	−35°06'2076	20.55	21.55	...	1.00	...	...	−9.96	6.56
NGFS033433-350236	...	03h34m3255	−35°02'3550	20.38	20.62	...	0.24	...	...	−10.89	6.23
NGFS033436-360315	...	03h34m3638	−36°03'1527	20.56	21.61	...	1.05	...	...	−9.90	6.58
NGFS033443-353115	...	03h34m4339	−35°31'1507	20.45	21.04	...	0.59	...	...	−10.47	6.39
NGFS033446-345334	...	03h34m4606	−34°53'3356	20.52	21.29	...	0.77	...	...	−10.22	6.45
NGFS033456-351127	FCC140	03h34m5641	−35°11'2742	17.61	18.25	19.37	0.64	1.12	1.76	−13.26	7.59
NGFS033458-351324	WFLSB6-2	03h34m5756	−35°13'2442	18.72	19.72	20.45	1.00	0.74	1.74	−11.79	7.11
NGFS033458-350235	FCC142	03h34m5819	−35°02'3480	17.34	18.37	19.45	1.03	1.08	2.11	−13.14	7.74
NGFS033500-351920	FCC144	03h35m0020	−35°19'2026	18.24	19.11	19.83	0.87	0.73	1.60	−12.40	7.28

Notes.

^aReference to galaxies listed in the FCC catalog (Ferguson 1989) and in Mieske et al. (2007). ^bAssuming a distance modulus of (m − M)₀ = 31.51 mag (Blakeslee et al. 2009).

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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Table 2.  Structural Properties of the Dwarf Sample

ID	Reference	Typea	i'				g'				u'
			reb	nc	d	PAe	reb	nc	d	PAe	reb	nc	d	PAe
NGFS033309-352349	FCC114	○	0.699	0.81	0.43	98	0.642	0.72	0.47	97	0.584	0.64	0.46	99
NGFS033311-353956	...	○	0.883	0.63	0.24	125	0.757	0.23	0.50	106	...	...	...	...
NGFS033348-355010	FCC125	○	0.896	0.71	0.15	141	0.866	0.65	0.14	139	0.766	0.50	0.13	150
NGFS033350-355706	...	○	0.435	0.45	0.39	114	0.503	0.50	0.43	136	...	...	...	...
NGFS033400-354533	...	○	0.563	0.87	0.24	21	0.421	0.63	0.17	30	0.622	1.13	0.30	29
NGFS033406-351638	FCC127	○	0.619	0.82	0.23	72	0.602	0.82	0.22	74	0.526	0.76	0.24	73
NGFS033407-352838	...	○	0.623	0.82	0.13	173	0.359	0.30	0.16	118	...	...	...	...
NGFS033409-353100	FCC130	○	1.819	0.80	0.17	135	2.008	0.91	0.18	130	...	...	...	...
NGFS033412-351343	FCC131	⊙	0.526	0.75	0.44	127	0.521	0.91	0.47	128	0.475	0.72	0.34	109
NGFS033414-354910	...	○	0.634	0.39	0.17	2	0.715	0.57	0.25	179	...	...	...	...
NGFS033423-355042	...	○	0.848	0.73	0.21	98	0.673	0.41	0.15	69	...	...	...	...
NGFS033427-350621	...	○	0.466	0.95	0.42	26	0.356	0.68	0.32	33	...	...	...	...
NGFS033433-350236	...	○	0.499	0.78	0.36	100	0.657	0.69	0.39	99	...	...	...	...
NGFS033436-360315	...	○	0.573	0.62	0.51	168	0.467	0.50	0.36	179	...	...	...	...
NGFS033443-353115	...	○	0.377	0.74	0.09	99	0.400	0.73	0.11	89	...	...	...	...
NGFS033446-345334	...	⊙	0.440	0.65	0.29	140	0.410	0.67	0.22	98	...	...	...	...
NGFS033456-351127	FCC140	⊙	0.898	0.81	0.46	95	0.968	0.89	0.47	94	0.795	0.63	0.47	94
NGFS033458-351324	WFLSB6-2	○	0.559	1.00	0.29	41	0.508	0.80	0.31	50	0.486	0.65	0.30	54
NGFS033458-350235	FCC142	⊙	1.011	1.34	0.06	134	0.847	1.02	0.06	149	0.708	0.92	0.11	16
NGFS033500-351920	FCC144	○	0.597	0.81	0.23	56	0.592	0.77	0.25	56	0.523	0.82	0.23	55

Notes.

^aMorphological galaxy type classification: ⊙ = nucleated, ○ = nonnucleated dwarf galaxy. ^bEffective radii given in kpc. ^cSérsic index (Sérsic 1968; Caon et al. 1993). ^dEllipticity  = 1 − b/a. ^ePosition angle in ° from north toward east.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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We show in Figure 5 the distribution functions of the structural parameters derived by galfit for the entire dwarf galaxy sample in the u', g', and i' filters. The upper panels show the distributions of effective radius (r_e), Sérsic profile shape parameter (n), ellipticity (), and position angle (PA), split by filter with u' in the top row followed by g' and i' below. The histogram bin widths were chosen based on Knuth's rule (Knuth 2006). Alternative visualizations of the distributions are shown by the solid relations, which are nonparametric Epanechnikov kernel probability density estimates (KDEs) for each parameter–filter combination. The lower panels show consistency plots for each structural parameter, as derived from the u', g', and i' filters.

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While r_e and n show well-defined peaks in their distributions, the and PA values are more broadly distributed. We find a characteristic effective radius consistent between the passbands in the range $0.1\leqslant {r}_{e}/\mathrm{kpc}\leqslant 2.0$ with a similar mean size of $\langle {r}_{e}{\rangle }_{g^{\prime} }=0.68\pm 0.02\,\mathrm{kpc}$, $\langle {r}_{e}{\rangle }_{i^{\prime} }=0.71\pm 0.03\,\mathrm{kpc}$, and $\langle {r}_{e}{\rangle }_{u^{\prime} }=0.69\pm 0.03\,\mathrm{kpc}$, which is at first impression indicative of a lack of significant stellar population gradients in the spheroid components.  We find in all filters similar minimum drop-offs in r_e and similar r_{e, max} ≈ 2 kpc. However, the r_e consistency plots in the bottom panels show that the u'-band half-light radii are systematically smaller than in the redder bands. This may be due to the lower surface brightness depth of our u'-band data or to stellar population gradients pointing toward bluer cores of dwarf galaxy spheroids. Quantitatively evaluating the detailed causes of this intriguing result goes beyond the scope of this paper. We will, however, return to this aspect in a future paper on the stellar population content of the NGFS dwarf galaxies. The distributions of Sérsic indices n closely follow Gaussian profiles in all passbands with similar mean values of $\langle n{\rangle }_{u^{\prime} }=0.83\pm 0.03$, $\langle n{\rangle }_{g^{\prime} }=0.78\,\pm 0.02$, and $\langle n{\rangle }_{i^{\prime} }=0.83\pm 0.02$. However, we note that there may be an observational bias giving rise to the narrow distributions in n, likely due to selection effects since we explicitly looked for diffuse galaxies in our search for dwarf galaxy candidates.

We find generally more platykurtic distributions in and PA than in r_e and n. Our measurement values are in the range 0.0 ≲  ≲ 0.7, with indications that may be bimodally distributed. Despite the visual impression, detailed Gaussian mixture modeling does not conclusively quantify whether a single-mode or a bimodal distribution is preferred. We find a marginal tendency of increasing average ellipticity toward bluer passbands.

Interestingly, we do not find any highly elongated dwarfs, with 97% of the NGFS dwarfs exhibiting ellipticities  < 0.55. This is in very good agreement with the result from Sánchez-Janssen et al. (2016) for dwarfs in the core of the Virgo cluster, and with the fast rotators in the atlas3d sample (Cappellari 2016). Finally, we see that position angles do not show any preferred alignment and populate the whole parameter range 0° ≲ PA ≲ 180° with very good consistency between the u', g', and i' filters.

The lower panels in Figure 5 compare the derived structural parameters in all three passbands. Assuming the galaxies are homologous in all passbands, that is, the same r_e, n, , and PA, one would expect all galaxies to follow unity, with the observed scatter arising from the statistical uncertainties of the measurements. However, this would also imply that the dwarf candidates do not exhibit color gradients, which is not necessarily true, as pointed out above. Hence, while the statistical measurement errors likely contribute to the observed scatter, intrinsic differences between galaxy models—such as color gradients—may also play a role. In general, the i'- versus u'-band comparison shows a systematically larger scatter than that of the i' versus g' bands, in part likely due to the shallower u'-band observations. Detailed consideration of the derived R² values reveals that r_e and PA show the tightest correlations, implying that these structural parameters constrain the galaxy models most efficiently in either of the filters. Meanwhile, the n distribution shows a much larger deviation from unity, indicating that it is more difficult for galfit to find one unique solution for the Sérsic index in all passbands. In any case, we note that the range in n is relatively small: 83% of the measured galaxies have shape parameters in the range 0.5 ≲ n ≲ 1.5, and variations on the order of ${\rm{\Delta }}n\simeq 0.1$ are expected.

We also highlight the nucleated dwarfs in the parameter distributions of the upper panels of Figure 5, which clearly show that the average spheroid of a nucleated dwarf has a larger half-light radius and more spherical light distribution, with a hint of a slightly more exponential-type Sérsic profile (i.e., n closer to 1) than their average nonnucleated counterpart. There is mild indication that the spheroid components of nucleated dwarf galaxies are more spheroidal, that is, show lower ellipticity, than their nonnucleated counterparts.  Except for effective radii, the nucleated dwarf samples show tighter correlations than the overall samples in the filter correlation plots. This is primarily because the nucleated dwarfs are on average brighter than nonnucleated dwarfs. We find that the nucleation fraction (${{ \mathcal F }}_{\mathrm{nuc}}$) is a strong function of galaxy luminosity, and ${{ \mathcal F }}_{\mathrm{nuc}}$ shows a strong tendency toward higher fractions in bins containing the brightest galaxies and declines to ∼0% when only the faintest galaxies are considered. Likewise, the cumulative ${{ \mathcal F }}_{\mathrm{nuc}}$ shows a similar trend, in that ${{ \mathcal F }}_{\mathrm{nuc}}=100 \%$ for exclusively bright galaxies and falls to the final value of ∼29% for the overall dwarf galaxy sample. The same trend of higher nucleation fractions in brighter dEs was found in the Virgo cluster by Grant et al. (2005) and Lisker et al. (2007), indicating a possibly generally valid trend. We furthermore note that, given the present seeing, low-luminosity nuclei that have low contrast with the host galaxy could remain unidentified and affect the derived nucleation fraction.

Color–magnitude diagrams (CMDs) of galaxies have long been used to infer the mass assembly and star formation histories of galaxies in large-area, deep surveys with ground and space-based telescopes (e.g., Baldry et al. 2004; Bell et al. 2004, 2012; Faber et al. 2007; Trayford et al. 2016; Roediger et al. 2017). Multipassband CMDs are powerful tools to obtain constraints of luminosity-weighted average stellar population ages and metallicities, as well as stellar masses of large samples of galaxies (e.g., Chilingarian & Zolotukhin 2012).

In the left panels of Figure 6 we show the (g' − i')₀, (u' − g')₀, and (u' − i')₀ versus g' CMDs for NGFS dwarf galaxies and compare them with other galaxy samples and theoretical predictions of color–magnitude relations. We account for foreground extinction toward Fornax by utilizing average extinction coefficients (A_u', A_g', and A_i') derived from several bright Fornax galaxies based on the recalibrated extinction maps of Schlafly & Finkbeiner (2011), noting that the extinction variance across the observed field is ${\sigma }_{{A}_{u^{\prime} }}\simeq 0.008$, ${\sigma }_{{A}_{g^{\prime} }}\simeq 0.006$, and ${\sigma }_{{A}_{i^{\prime} }}\,\simeq 0.003$ mag. Dashed lines show the iso-${{ \mathcal M }}_{\star }$ relations based on the Bell et al. (2003) color–${ \mathcal M }/L$ conversions (see also Section 4.3). Given the photometric limits of the combined data set, the sample reaches down to stellar masses of ∼10⁶ M_⊙, while the optical g'- and i'-band photometry reaches even lower values. All three panels clearly illustrate the expected red sequence for early-type cluster galaxies, where brighter systems exhibit redder colors than fainter ones. This color–magnitude relation of galaxies is commonly interpreted as a mass–metallicity relation since the deeper potential wells of more massive galaxies more easily retain metals produced throughout their star formation history (e.g., Kodama & Arimoto 1997; Poggianti et al. 2001; Tremonti et al. 2004; Savaglio et al. 2005; Baldry et al. 2008; Maiolino et al. 2008; Møller et al. 2013; Segers et al. 2016; Ma et al. 2016).

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We fit linear relations to the CMDs of NGFS dwarfs and derive shallow color gradients in the sense of ${\rm{\Delta }}{(g^{\prime} -i^{\prime} )}_{0}/{\rm{\Delta }}g^{\prime} ={{\rm{\nabla }}}_{{(g^{\prime} -i^{\prime} )}_{0}}=-0.01$, ${\rm{\Delta }}{(u^{\prime} -g^{\prime} )}_{0}/{\rm{\Delta }}g^{\prime} ={{\rm{\nabla }}}_{{(u^{\prime} -g^{\prime} )}_{0}}=-0.09$, and ${\rm{\Delta }}{(u^{\prime} -i^{\prime} )}_{0}/{\rm{\Delta }}g^{\prime} ={{\rm{\nabla }}}_{{(u^{\prime} -i^{\prime} )}_{0}}=-0.13$.

We note that the scatter present around the red sequence likely arises from effects intrinsic to the constituent stellar populations (e.g., spreads in ages or metallicities) or from photometric uncertainties. To quantify the scatter in the observed CMDs, we computed the variance of the measured values with respect to the linear fits, obtaining ${\sigma }_{{(g^{\prime} -i^{\prime} )}_{0}}=0.25$, ${\sigma }_{{(u^{\prime} -g^{\prime} )}_{0}}=0.24$, and ${\sigma }_{{(u^{\prime} -i^{\prime} )}_{0}}=0.27\,\mathrm{mag}$. We discuss in Section 4.2.3 the implications of these color variances in terms of stellar population properties.

4.2.1. Comparison with Other Environments

4.2.2. Comparison with Numerical Model Predictions

4.2.3. Stellar Population Properties

In order to study the physical scaling relations of the dwarf galaxy sample in relation with other stellar systems, we compute the stellar masses of our NGFS dwarf candidates using the prescriptions from Bell et al. (2003), which are good matches for the expected star formation histories of our NGFS spheroidal dwarf galaxies (Zhang et al. 2017). We parameterize the stellar mass-to-light ratios (${{ \mathcal M }}_{\star }/{L}_{\odot }$) by galaxy colors using the relation

$\begin{eqnarray}&&\mathrm{log}{({{ \mathcal M }}_{\star }/L)}_{\odot }={a}_{\lambda }+{b}_{\lambda }\times \mathrm{color},\end{eqnarray} \tag{ 2 }$

where the coefficients a_λ and b_λ define the transformation for different filter combinations, that is, colors (see Bell et al. 2003, their Table 7). We compute the g'- and i'-band ${{ \mathcal M }}_{\star }/{L}_{\odot }$ from our measured and dereddened (g' − i')₀, (u' − g')₀, and (u' − i')₀ galaxy colors, yielding up to six ${{ \mathcal M }}_{\star }$ estimates for a given galaxy. To compute ${{ \mathcal M }}_{\star }$, we derive galaxy luminosities in g' and i' considering absolute solar magnitudes measured by C. Willmer.²²  Finally, we average the individual ${{ \mathcal M }}_{\star }$ estimates and adopt error bars as the standard deviation of the sample of individual measurements. We obtain stellar masses in the range $5.5\lesssim \mathrm{log}{{ \mathcal M }}_{\star }/{M}_{\odot }\lesssim 9.4$. Figure 7 shows the comparison of the derived stellar masses with the apparent and absolute g'-band magnitudes. The corresponding ${{ \mathcal M }}_{\star }$ values, in the following always given in units of M_⊙, are summarized in Table 1.

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Elliptical galaxies are known to fall on a so-called fundamental plane (FP), a tight correlation between effective radius, central velocity dispersion, and the average effective surface brightness within the effective radius (e.g., Faber & Jackson 1976; Djorgovski & Davis 1987; Dressler et al. 1987; Faber et al. 1987; Bender et al. 1992; Burstein et al. 1997; Gallazzi et al. 2006). A similar relation was found by Tollerud et al. (2011), showing that dispersion-supported galaxies form a one-dimensional fundamental curve in the mass–radius–luminosity space from ultrafaint dwarf spheroidals to giant cluster spheroids. Since the FP shows very little residual scatter, it implies very similar mass-to-light ratios and suggests a uniform formation process for bright elliptical galaxies. Projecting the FP onto the luminosity versus surface-brightness plane, Kormendy (1985) had noted that there seems to be a dichotomy between the scaling relations of bright elliptical galaxies and dwarf galaxies. This dichotomy can be interpreted as the result of different formation mechanisms for giant ellipticals and dwarf spheroids, but it is still hotly debated in the literature (e.g., Binggeli 1994; Graham & Guzmán 2003; Ferrarese et al. 2006; Kormendy et al. 2009; Kormendy & Bender 2012). In order to investigate these possible differences in the formation process of dwarf galaxies in comparison to bright elliptical and spiral galaxies, we plot in Figure 8 the effective radius (r_eff, in units of parsec) as a function of stellar mass ${{ \mathcal M }}_{\star }/{M}_{\odot }$ and in Figure 9 the effective mass surface density (${{\rm{\Sigma }}}_{\mathrm{eff},{{ \mathcal M }}_{\star }}={{ \mathcal M }}_{\star }/2\pi {r}_{\mathrm{eff}}^{2}$, in units of M_⊙ pc⁻²) as a function of stellar mass ${{ \mathcal M }}_{\star }/{M}_{\odot }$ for our NGFS galaxy sample. We put the measurements in the larger context of several other families of stellar systems, covering a wide range in galaxy morphology and stellar mass from low-mass LG dSph galaxies with $\mathrm{log}{{ \mathcal M }}_{\star }\approx 3$ to giant elliptical galaxies at $\mathrm{log}{{ \mathcal M }}_{\star }\approx 12$.

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For the subsequent discussion, we divide the r_eff–${{ \mathcal M }}_{\star }$ and ${{\rm{\Sigma }}}_{\mathrm{eff},{{ \mathcal M }}_{\star }}$–${{ \mathcal M }}_{\star }$ diagrams in two hemispheres with (1) extended stellar systems ($\mathrm{log}{r}_{\mathrm{eff}}[\mathrm{pc}]\gtrsim 2.0$), such as dwarf spheroidal galaxies, dE, and giant elliptical (gE) galaxies, and (2) compact stellar systems ($\mathrm{log}{r}_{\mathrm{eff}}[\mathrm{pc}]\lesssim 2.0$) with two subsets, one of which represents globular clusters with two-body relaxation times shorter than a Hubble time (i.e., objects below the curve t_relax = Hubble time) and the other subset comprising nonrelaxed compact stellar systems, such as nuclear star clusters (NSCs) and ultracompact dwarfs (UCDs). For a description of this part of the parameter space, we refer the reader to Misgeld & Hilker (2011). We will not discuss the compact stellar systems further in this work, noting only that numerous recent studies have described the formation scenario of UCDs via tidal stripping of galaxies with NSCs on relatively short timescales (e.g., Bekki et al. 2003; Goerdt et al. 2008; Thomas et al. 2008; Pfeffer & Baumgardt 2013; Pfeffer et al. 2014, 2016; Liu et al. 2015; Zhang et al. 2015). Instead, we focus in the following on the extended stellar systems and the larger galaxy evolution context of our NGFS galaxy sample.

The NGFS sample dwarfs cover stellar masses in the range $\mathrm{log}{{ \mathcal M }}_{\star }\approx 5.5\mbox{--}9.5$ (see also Figure 7). The bulk of the NGFS dwarfs show ${{\rm{\Sigma }}}_{\mathrm{eff},{{ \mathcal M }}_{\star }}$ values in the range ∼1–10 M_⊙ pc⁻², with the most massive dwarfs reaching ∼100 M_⊙ pc⁻² (see Figures 8 and 9). Dwarf galaxies with relatively low stellar masses ($\mathrm{log}{{ \mathcal M }}_{\star }\simeq 5.5\mbox{--}8.0$) follow a scaling relation with r_eff that is positively inclined with respect to the lines of equal effective surface mass density, or iso-${{\rm{\Sigma }}}_{\mathrm{eff},{{ \mathcal M }}_{\star }}$ lines (see diagonal lines in Figure 8). Meanwhile, recent studies have revealed an expansive population of low-mass dwarfs in the Local Group, including dSphs and UFDs that extend toward even fainter magnitudes (Zucker et al. 2004, 2006a, 2006b; Willman et al. 2005; Belokurov et al. 2006, 2007, 2010, 2014; McConnachie et al. 2009; McConnachie 2012; Bechtol et al. 2015; Drlica-Wagner et al. 2015; Koposov et al. 2015; Laevens et al. 2015; Homma et al. 2016). Their size–mass–surface density scaling relations appear to line up seamlessly with our NGFS dwarf sample toward lower stellar masses and lower surface mass densities.

We approximate the scaling relations of our NGFS dwarfs with a locally weighted scatterplot smoothing (LOWESS) fit (e.g., Cleveland 1981), which is illustrated as a thick curve in Figures 8 and 9. To connect the LOWESS fit of the NGFS dwarf sample with more massive galaxies, we construct two samples that span the full stellar mass range $\mathrm{log}{{ \mathcal M }}_{\star }\approx 5.5\mbox{--}12.0$: (A) NGFS dwarfs + Virgo ETGs (Ferrarese et al. 2006) + Carnegie-Irvine E galaxies (Ho et al. 2011) shown as a brown curve; and (B) NGFS dwarfs + spiral galaxies from the ATLAS3D survey²³ (Cappellari et al. 2011) illustrated as a blue curve. While sample A assumes that dwarf galaxies are evolutionarily connected to more massive early-type galaxies through their morphology, sample B joins, somewhat ad hoc, the dwarf galaxy regime with more massive spirals under the premise that they form a dynamical family in which the angular momentum increases with stellar mass (for a discussion, see Cappellari 2016).

We disregard the class of UDGs for the rest of this work (but see Amorisco & Loeb 2016; Rong et al. 2017, for a theoretical discussion of this galaxy type), but note that the scaling relations in Figures 8 and 9 show a few NGFS objects consistent with massive dwarf galaxy candidates ($7.5\lesssim \mathrm{log}{{ \mathcal M }}_{\star }/{M}_{\odot }\lesssim 8.5$) beginning to encroach upon the parameter space occupied by UDGs, the existence of which has been recently reported in massive galaxy groups and clusters (e.g., Koda et al. 2015; Mihos et al. 2015; Muñoz et al. 2015; van Dokkum et al. 2015a; Martínez-Delgado et al. 2016; Merritt et al. 2016; Bennet et al. 2017; Janssens et al. 2017; Román & Trujillo 2017b; Shi et al. 2017; Trujillo et al. 2017; van der Burg et al. 2017; Venhola et al. 2017). UDGs show physical sizes reminiscent of giant galaxies, but ${{ \mathcal M }}_{\star }$ values that put them in the dwarf galaxy mass regime. The result is a systematically lower ${{\rm{\Sigma }}}_{\mathrm{eff},{{ \mathcal M }}_{\star }}$ that detaches UDGs from the scaling relations shown by the other dwarfs and intermediate stellar mass galaxies. Given their existence and characteristics, one might speculate that these galaxies are dominated by dark matter, shielding the baryons from the cluster environment (e.g., Mihos et al. 2015; Mowla et al. 2017).

For sample A, we find a galaxy size–mass scaling relation of the form ${r}_{\mathrm{eff}}\propto {{ \mathcal M }}_{\star }^{0.3\pm 0.1}$ in the stellar mass range $5.5\,\lesssim \mathrm{log}{{ \mathcal M }}_{\star }\lesssim 7.8$, the gradient of which decreases abruptly to zero at $\mathrm{log}{{ \mathcal M }}_{\star }\approx 8.0$ (i.e., ${{\rm{\nabla }}}_{\mathrm{LOWESS}}={\rm{\Delta }}\mathrm{log}{r}_{\mathrm{eff}}/{\rm{\Delta }}\mathrm{log}{{ \mathcal M }}_{\star }\approx 0$; see inset plot in Figure 8). The effective radius remains virtually independent of stellar mass for more massive galaxies and remains roughly constant at ∼1 kpc (albeit with a substantial scatter) up to about $\mathrm{log}{{ \mathcal M }}_{\star }\approx 9.5$, where it begins to gently increase again until it jumps abruptly at $\mathrm{log}{{ \mathcal M }}_{\star }\approx 10.5$ to values that are steeper than the iso-${{\rm{\Sigma }}}_{\mathrm{eff},{{ \mathcal M }}_{\star }}$ lines. The gradient at high stellar masses ($\mathrm{log}{{ \mathcal M }}_{\star }\gtrsim 10.8$) reaches ${r}_{\mathrm{eff}}\propto {{ \mathcal M }}_{\star }^{0.75\pm 0.05}$. For sample B, the gradient of the size–mass relation is relatively constant over the entire mass range ($\mathrm{log}{{ \mathcal M }}_{\star }\approx 5.5\mbox{--}12$) around ${r}_{\mathrm{eff}}\propto {{ \mathcal M }}_{\star }^{0.25\pm 0.1}$. Although we are dealing with incomplete and partly nonoverlapping parameter ranges for the individual data sets depicted in Figures 8 and 9, we observe a smooth transition between the low-mass dwarf regime over the range of intermediate stellar mass systems to the massive galaxies for our self-consistently observed and analyzed sample of NGFS galaxies. Here, the scaling relations become particularly diagnostic in the intermediate-mass regime ($8.5\lesssim \mathrm{log}{{ \mathcal M }}_{\star }\,\lesssim 10.0$), where the association of at least some of the NGFS galaxies with the sample B dynamical family cannot be excluded. Testing the internal dynamics of such galaxies is, therefore, of utmost interest.  The literature samples are augmenting the information content of the scaling relations for our NGFS data by extending its parameter space coverage, which leads us to the following discussion and interpretation of our measurements.

Dwarf galaxies in cluster environments are believed to have been and some are presently being affected by their environment, which is one of the mechanisms for the creation of the morphology–density or morphology–distance relation for dwarfs. Environmental effects include tidal stripping, ram pressure stripping, and harassment. Moreover, internal effects may play a role. For instance, winds have been invoked as one of the factors affecting their chemical enrichment, and feedback, in general, may have led to mass loss. How the size–stellar mass (i.e., r_eff–${{ \mathcal M }}_{\star }$) scaling relation for extended stellar systems can be interpreted in the context of the hierarchical galaxy formation picture has been extensively discussed in the recent literature (for a recent review, see Cappellari 2016, and references therein).

Based on the present NGFS data and the comparison with other stellar systems from the literature, the following discussion aims to highlight the implications of our findings for galaxy mass assembly over a stellar mass range of $5\lesssim \mathrm{log}{{ \mathcal M }}_{\star }\lesssim 12$. We want to emphasize that this discussion does not necessarily imply an evolutionary sequence in the sense that more massive stellar systems arise from less massive ones observed today. It is merely an empirical observation based on the derived gradients from Section 5.2 on how mass assembly occurs in these galaxies at various stellar masses.

First, we note that mass assembly along the iso-${{\rm{\Sigma }}}_{\mathrm{eff},{{ \mathcal M }}_{\star }}$ lines implies virtually density-invariant growth, indicating that to first order, mass assembly occurs homologously along these lines; as galaxies grow in size and stellar mass, they retain their surface brightness distribution and, hence, the effective stellar mass surface density.

From Figure 8 we find that as early-type systems (sample A) grow in stellar mass, the assembly of baryonic mass must occur in various phases and under the influence of different mechanisms, which depend on the total stellar mass of the system, for the observed relations to emerge. For dwarf galaxies, this mass assembly process occurs biased to regions inside the half-light/mass radius since the systems grow disproportionately more dense within r_eff as stellar mass increases; that is, their r_eff–${{ \mathcal M }}_{\star }$ relation is flatter with respect to the iso-${{\rm{\Sigma }}}_{\mathrm{eff},{{ \mathcal M }}_{\star }}$ lines. This trend prevails until ${{ \mathcal M }}_{\star }$ approaches $\mathrm{log}{{ \mathcal M }}_{\star }\approx 8.0$, where the r_eff–${{ \mathcal M }}_{\star }$ relation becomes flat with significant scatter. The constancy of r_eff in this respective mass range had already been pointed out by Smith Castelli et al. (2008) and Misgeld et al. (2008) and implies that stellar mass is being added both inside and outside the galaxy half-light/stellar-mass radii so that galaxy stellar mass growth occurs without experiencing changes in galaxy sizes, that is, is isometric. Consequently, this mode of stellar-mass growth is accompanied by packing increasingly more stellar mass within the same galaxy dimensions. This process may be triggered by ram pressure in dense galaxy cluster environments, which may temporarily induce enhanced star formation efficiency (e.g., Geha et al. 2012; Wetzel et al. 2013). The isometric stellar mass growth stops when the galaxies reach an apparent maximum stellar mass density of ${{\rm{\Sigma }}}_{\mathrm{eff},{{ \mathcal M }}_{\star }}\approx {10}^{4}\,{M}_{\odot }\,{\mathrm{pc}}^{-2}$ at around $\mathrm{log}{{ \mathcal M }}_{\star }\approx 10.5$. Beyond this point toward higher ${{ \mathcal M }}_{\star }$ values, galaxy stellar mass accumulation happens predominantly outside their half-light/mass radii, which is consistent with their r_eff–${{ \mathcal M }}_{\star }$ relations being steeper than the iso-${{\rm{\Sigma }}}_{\mathrm{eff},{{ \mathcal M }}_{\star }}$ lines. Similar findings have been put forward by studies of the redshift evolution of the r_eff–${{ \mathcal M }}_{\star }$ relation of massive galaxies (e.g., Huertas-Company et al. 2013; van Dokkum et al. 2015b).

This observed transition from centrally dominated to halo-dominated stellar mass accumulation goes hand in hand with the transition from cusp to core-dominated central surface brightness profiles of galaxies more massive than $\mathrm{log}{{ \mathcal M }}_{\star }\,\approx 9.0$ revealed by HST-based studies (see, e.g., Ferrarese et al. 2006; Côté et al. 2007). The homogeneous morphological analysis of our NGFS galaxy data set, with a much broader stellar mass coverage down to $\mathrm{log}{{ \mathcal M }}_{\star }\approx 5.5$, shows the consistency of this central morphological transition with global Sérsic model parameters. While single-component Sérsic fits represent the majority of our NGFS dwarfs very well (see Figure 4), the surface brightness profile fits of the most massive NGFS galaxies ($\mathrm{log}{{ \mathcal M }}_{\star }\gtrsim 9.0$) always show residuals, indicative of substructure in single-component fits, requiring up to two additional significant Sérsic components for the brightest systems. This corroborates the idea that the mass-assembly process of dSph and gE galaxies sees the predominance of different mechanisms in action, with the former being mainly assembled through dissipative processes such as wet mergers and gas infall that build the central stellar mass and lead to surface brightness profiles well represented by single-component Sérsic models (Ferrarese et al. 2006). The gE galaxies, on the other hand, form predominantly via nondissipative stellar mass accumulation (i.e., dry galaxy mergers) that preserves the phase-space configuration of the infalling material, which results in more complex surface brightness profiles that are indicative of halo mass accumulation. This bimodal galaxy growth is partly driven by the increasing importance of nuclear feedback processes with increasing total galaxy mass and has been extensively discussed in the recent literature (e.g., Croton et al. 2006; Dekel & Birnboim 2006; Fabian 2012; Kormendy & Ho 2013). Our study delivers a large dwarf galaxy sample, which can be used to constrain the details of quenching mechanisms in today's high-resolution numerical simulations (e.g., Bahé et al. 2017; Genel et al. 2018).

Future analyses using the NGFS galaxy sample from the entire survey footprint with an augmented SED filter coverage will allow us to conduct more extended and in-depth studies as a function of the cluster-centric radius and search for local anomalies that correlate with particular families of galaxies in the size–mass–surface density parameter space.