The Nature of Ultra-diffuse Galaxies in Distant Massive Galaxy Clusters: Abell 370 in the Hubble Frontier Fields

We obtained deep and high-resolution images of Abell 370 from the HFF archive (Lotz et al., 2017). We chose drizzled images of ACS/WFC $F606W(V)$, $F814W(I)$, WFC3/IR $F105W(Y)$, and $F160W(H)$ for our analysis. The HFF images we used cover two fields with different clustercentric distances ($r/r_{200}$): the central field ($r/r_{200}<0.2$) and the parallel field ($r/r_{200}\sim 0.6-0.8$) located at $6^{\prime}$ southeast of the central field. We used the areas that both ACS/WFC and WFC3/IR covered: $\sim$5.5 $\rm acrmin^{2}$ for the central field, and $\sim$5.0 $\rm arcmin^{2}$ for the parallel field. The pixel scale of all the drizzled images is $0\farcs 03$ per pixel, and the scale for the distance to Abell 370 is $4.984$ $\rm kpc$ $\rm arcsec^{-1}$.

Among the multi-wavelength bands of the HFF images, $F814W$ and $F105W$ images are the most useful for finding UDGs in Abell 370. This is because $F814W$ and $F105W$ have the longest exposure times among the available bands, and the spectral energy distributions (SEDs) of cluster galaxies are dominant at these wavelengths considering the cluster redshift ($z=0.375$). The exposure times for the images of the central field are $36.3$ hours ($F814W$) and $19.3$ hours ($F105W$), and those of the parallel field images are $29.3$ hours ($F814W$) and $20.3$ hours ($F105W$). The FWHMs of point spread functions (PSFs) are $0\farcs 09$ ($\sim$0.45 $\rm kpc$) in $F814W$ and $0\farcs 16$ ($\sim$0.80 $\rm kpc$) in $F105W$. We adopted the foreground extinction values of $A_{F814W}=0.049$ mag and $A_{F105W}=0.031$ mag given in the HFF-DeepSpace photometric catalogs (Shipley et al., 2018) for CMDs and CCDs.

To estimate background contributions, we used ACS/WFC $F814W$ and WFC3/IR $F105W$ images of the Hubble eXtreme Deep Field (XDF) (Illingworth et al., 2013). The total exposure times are $14.1$ hours in $F814W$ and $74.1$ hours in $F105W$. We chose only the deepest regions of the whole XDF, the HUDF09 and the HUDF12 programs, which cover $\sim 5.06$ $\rm arcmin^{2}$. Thus, the areas for the central field of Abell 370 ($\sim 5.50$ $\rm arcmin^{2}$), the parallel field ($\sim 5.00$ $\rm arcmin^{2}$), and the XDF ($\sim 5.06$ $\rm arcmin^{2}$) are similar. Galaxies in the XDF have a wide range of redshifts, but we assume all of them have the same redshift as Abell 370 ($z=0.375$) to estimate the background contamination in the sample of Abell 370.

Figure 1 shows the color composite images of the central field (left panel) and the parallel field (right panel) of Abell 370. In the left panel, the central field shows diverse types of galaxies: two brightest cluster galaxies (BCGs) dubbed “BCG-N” and “BCG-S”, a sequence of bright red ellipticals at the north, and a large number of gravitationally lensed galaxies. Among them, examples of LSB galaxies including UDGs and LSB dwarfs (LDws) (see the text in §2.2) are marked by magenta and yellow circles. ‘C’ and ‘P’ in the names of these LSB galaxies mean the central field and the parallel field of Abell 370. In the right panel, the parallel field seems to have a much lower number density of bright galaxies. This means that the parallel field has a fewer number of cluster member galaxies than the central field. We marked some examples of UDGs and LSB dwarfs in the parallel field with circles.

Figure 2 shows the zoom-in thumbnail images of the LSB galaxies marked in Figure 1. The first column is the color images, and the second is $F814W$ band images. We estimated the sizes and surface brightness of these galaxies using GALFIT version 3.0.5 (Peng et al., 2010) as described in §2.2. The third and fourth column show the results from GALFIT, which are galaxy model images and subtracted images, respectively. The subtracted images show little of original galaxy images, showing that GALFIT did a good job in galaxy modeling. Most of the LSB galaxies show red colors in their color composite images. However, one of them (UDG-C02) shows a much bluer color than the others. We discuss this with our CMDs and CCDs in §3.

We performed dual mode photometry using SExtractor (Bertin & Arnouts, 1996). We set $F814W$ images as detection images. Our configuration parameters for SExtractor photometry are summarized in Table 2. These parameters are very similar to those used in Lee et al. (2017), which are considered to be effective for detecting LSB galaxies. We used the magnitude zeropoints of the AB system for the standard calibration. In the initial output catalogs of SExtractor, 18,315 sources were extracted in the central field and 15,998 sources in the parallel field. Table 3 shows the numbers of sources in each step of the sample selection. Each sample selection step is described below.

First, we selected initial galaxy candidates using the basic parameter criteria: MAGERR_AUTO $<1.0$, FLAGS $<4$, CLASS_STAR $<0.4$, and $-0.5<F814W-F105W<1.0$. This left 3,748 objects in the central field, 2,789 objects in the parallel field, and 2,252 objects in the area of the XDF we used (the HUDF09 and the HUDF12). Next, we classified these objects into two types of galaxies, bright galaxies and LSB galaxies. We used the surface brightness and effective radii conditions: bright galaxies with MU_MAX($F814W$) $<22.5$ mag arcsec^-2 and FLUX_RADIUS $>1.0$ $\rm kpc$, and LSB galaxies with MU_MAX($F814W$) $>22.5$ mag arcsec^-2 , FLUX_RADIUS $>1.0$ $\rm kpc$, and B_IMAGE$/$A_IMAGE $>0.3$. We set the minimum effective radii (FLUX_RADIUS) to be $1.0$ $\rm kpc$, because we intended to select our galaxy samples with effective radii larger than $2\times\rm FWHM$ ($\sim 0.90$ $\rm kpc$). We also set the minimum value of the axis ratio (B_IMAGE$/$A_IMAGE) to be 0.3 in order to exclude gravitational lenses and elongated artifacts. As a result of all these processes, the numbers of selected bright galaxies are 334, 115, and 84 in the central field, the parallel field, and the XDF. The numbers of selected LSB galaxies are 714, 342, and 339 in each field.

Then, we utilized GALFIT to estimate the surface brightness and effective radii of the selected galaxies more precisely. We made input images of each galaxy trimmed with a size of $4\farcs 5\times 4\farcs 5$ in order to estimate background values locally. This could minimize the effect of diffuse light from bright galaxies in background estimation. The PSF convolution size is set to be about $5\farcs 4$, which is sufficient to give the PSF effect to the entire area of the input images. Other GALFIT configurations and masking methods are similar to those of Lee et al. (2017). Most galaxies were fitted by a single Sérsic law, and nucleated galaxies were fitted with their central nuclei masked.

We divided the sample of LSB galaxies into “UDGs” and “LSB dwarfs”. We used the selection criteria adopted in van der Burg et al. (2016) and Lee et al. (2017): $\langle\mu\rangle_{\rm e,abs}(r^{\prime})$ $>23.8$ mag arcsec^-2 and $R_{\rm eff,c}$ $>1.5$ $\rm kpc$ for UDGs, and $\langle\mu\rangle_{\rm e,abs}(r^{\prime})$ $>23.8$ mag arcsec^-2 and $R_{\rm eff,c}$ $=1.0-1.5$ $\rm kpc$  for LSB dwarfs. In this study, these criteria are used for comparison of the Abell 370 UDGs and the UDGs found in the local universe. In addition, we selected LSB dwarfs as smaller counterparts of UDGs. We checked whether UDGs and LSB dwarfs have consistent properties in the result section. $\langle\mu\rangle_{\rm e,abs}(r^{\prime})$ is the SDSS $r^{\prime}$-band absolute mean surface brightness at the effective radii, and $R_{\rm eff,c}$ is the circularized effective radii. We transformed the $F814W$ magnitudes to SDSS $r^{\prime}$ system using simple stellar population (SSP) models derived from GALAXEV (Bruzual & Charlot, 2003). We adopted an age of 12 Gyr, the Chabrier initial mass function (Chabrier, 2003), and $[Z/Z_{\odot}]=-0.7$ $(Z=0.004)$ for obtaining SSP models.

Finally, we performed visual inspection of all selected galaxies to get rid of artifacts, tidal structures, gravitational lenses, and blended sources. If some galaxies show unreasonable GALFIT results or residuals due to interfering light from neighboring galaxies or saturated stars, we redid manual masking and GALFIT configurations until we obtained reasonable solutions. The selected galaxies are represented in the selection diagram of the circularized effective radii vs. the SDSS $r^{\prime}$-band absolute mean surface brightness at the effective radii, as plotted in Figure 3, and their census is summarized in “Step 2” of Table 3. Examples of selected UDGs and LSB dwarfs are displayed in Figure 2. There are 315, 106, and 80 bright galaxies in the central field, the parallel field, and the XDF. For UDGs, there are 39, 16, and 1 UDGs in each field. For LSB dwarfs, there are 87, 35, and 18 sources in each field. These initial samples are used to select the final samples in §3.1.1.

We carried out artificial galaxy tests for the HFF $F814W$ images of the central field, the parallel field, and the XDF (the HUDF09 and the HUDF12) to compute the detection limits and the completeness as a function of clustercentric radius. Utilizing artdata/gallist task in IRAF, we generated a total of 120,000 mock galaxies with uniform distributions of $F814W$ magnitude, size, and spatial number density in each field. We set 800 bins of $F814W$ magnitude and effective radii: the magnitude bins are from 20 mag to 30 mag with an interval of 0.25 mag, and the effective radii bins are from 0.75 kpc to 8.22 kpc with a linear interval of 0.37 kpc. There are 150 mock galaxies in each magnitude-size bin. The axis ratios of mock galaxies are set to follow a Gaussian distribution with a mean value of $\langle b/a\rangle=0.75$, which is the mean value of the axis ratios of Coma LSB galaxies (Yagi et al., 2016).

Figure 4 shows the results of artificial galaxy tests. The 50% surface brightness limit, which is about 27 mag arcsec^-2 in the absolute SDSS $r^{\prime}$ magnitude, is similar in all the three fields. However, it appears that the central field of Abell 370 has slightly lower completeness values for detecting LSB galaxies than the parallel field and the XDF. Figure 5 displays the calculated radial completeness as a function of clustercentric distance. All the magnitude bins show lower completeness values at the Abell 370 central field than the parallel field. This is because of diffuse light and a high number density of bright galaxies in the cluster central field. These completeness values in each radial bin are applied to compute the RDPs of galaxies in §3.4.

In Figure 9, we display the de-reddened CCDs ($(F606W-F814W)_{0}$ vs. $(F814W-F160W)_{0}$) of the galaxies in Abell 370 as well as those in Abell S1063 and Abell 2744. We adopted the foreground extinctions of each filter as listed in Shipley et al. (2018). We plot the number density contours of the bright galaxies in the red sequence, the UDGs, and the LSB dwarfs in these CCDs. Then, we overlay the simple stellar population (SSP) models from GALAXEV. In order to construct the SSP models, we adopt the following options: spectral templates from Bruzual & Charlot (2003), instantaneous burst star formation history (SFH), no dust, and the Chabrier initial mass function (Chabrier, 2003). We set the range of ages of 0.1, 1, 3, and 9 Gyr at the redshifts of the three HFF clusters. We set the range of metallicities with $[Z/Z_{\odot}]=-1.7$, $-0.7$, $0.0$ (solar), and $+0.4$.

The upper panels of Figure 9 show the de-reddened CCDs of bright red sequence galaxies, UDGs, and LSB dwarfs in Abell 370. In this figure, the UDGs and the LSB dwarfs show a similar range of colors. For Abell 370, the peak values of the color distribution of the UDGs ($(F606W-F814W)_{0}=0.79$ and $(F814W-F160W)_{0}=0.39$) and the LSB dwarfs ($(F606W-F814W)_{0}=0.65$ and $(F814W-F160W)_{0}=0.32$) are bluer than those of the bright red sequence galaxies ($(F606W-F814W)_{0}=0.88$ and $(F814W-F160W)_{0}=0.59$), as listed in Table 6. These color ranges of the UDGs and the LSB dwarfs are consistent with the old-age SSP models for low metallicity ($[Z/Z_{\odot}]\lesssim-0.7$). On the other hand, the colors of bright red sequence galaxies are better matched with the SSP models with higher metallicity ($[Z/Z_{\odot}]\gtrsim 0.0$). These trends of Abell 370 are similarly seen in the other HFF clusters, Abell S1063 and Abell 2744.

In the upper left panel of this figure, we mark UDG-C02 (the bluest UDG) and UDG-C22 (the largest UDG) of Abell 370. UDG-C02 seems to have an age younger than the other UDGs by a few Gyr. This implies that UDG-C02 includes recently formed stars. In contrast, UDG-C22 shows red colors close to the mean values of the UDGs. This means that UDG-C22 is made of old stars, which is similar to most UDGs in Abell 370. These SSP models presume oversimplied SFHs and dust contents of galaxies, but they are still useful to compare the relative difference of ages and metallicities between bright galaxies and LSB galaxies.

We estimate the structural parameters of the galaxies in Abell 370 such as Sérsic indices ($n$), and axis ratios ($b/a$) using GALFIT. We compare these structural parameters of Abell 370 UDGs with those of the known UDGs in the Coma cluster. The Coma cluster is known to host a large number of LSB galaxies (Yagi et al., 2016), so that it serves as a very useful reference. We select 193 Coma UDGs out of the whole sample of Coma LSBs given by Yagi et al. (2016), using the same size criteria as used in this work ($R_{\rm eff,c}$ $>1.5$ kpc).

Figure 10 shows the comparison of the structural parameters of Abell 370 UDGs with Coma UDGs. The upper panels of Figure 10 compare the Sérsic indices $n$ of UDGs in the two clusters. Overall, the Sérsic indices of UDGs in the two clusters have similar distributions with $\langle n\rangle\lesssim 1$. These results are consistent with those of UDGs and dwarf galaxies in other clusters such as Fornax and Abell 168 ($\langle n\rangle\sim 0.7$) (Muñoz et al., 2015; Román & Trujillo, 2017a). In Lee et al. (2017), the mean values of the Sérsic indices of UDGs in Abell S1063 and Abell 2744 are also $\langle n\rangle\simeq 1.0$. UDGs with $n>2$ are rare in these galaxy clusters. This indicates that most cluster UDGs have exponential light profiles regardless of their host cluster.

The lower panels of Figure 10 describe the distribution of axis ratios $b/a$ of UDGs in the two clusters. In the Coma cluster, there are no UDGs with $b/a<0.3$, although Yagi et al. (2016) did not use any selection criterion of $b/a>0.3$. The axis ratios of UDGs in these two clusters also have consistent distributions with the mean values of $\langle b/a\rangle\sim 0.7$. These mean values are similar to those of UDGs in Abell S1063 ($\langle b/a\rangle=0.66$) and Abell 2744 ($\langle b/a\rangle=0.68$). This means the morphology of cluster UDGs is closer to round shapes rather than to elongated shapes.

In the left panel of Figure 11, we plot the spatial distributions of bright galaxies in the red sequence, UDGs, and LSB dwarfs in the central field of Abell 370. The center of the Abell 370 cluster is set to be at the middle point between BCG-N and BCG-S (R.A. (2000)$=2^{\rm h}39^{\rm m}52\fs 94$, Decl.(2000)$=-1^{\circ}34^{\prime}37\farcs 0$), as adopted by Lagattuta et al. (2017). We divide this field into two radial bins based on the clustercentric radius of $0\farcm 5~{}(\sim 150~{}\rm kpc)$ (the gray circle). Bright galaxies seem to be more centrally concentrated in the inner region ($r<0\farcm 5$) than LSB galaxies. It is noted that only one UDG is found in the inner region ($r<0\farcm 5$), while most UDGs are seen in the outer region ($r>0\farcm 5$).

We derive the RDPs of the bright red sequence galaxies, UDGs, and LSB dwarfs, using the data from the central field and the parallel field. We estimate their background number density using the data for the XDF, and subtract them from the results of Abell 370. We correct the resulting number density profiles using the completeness values derived from artificial galaxy tests (as described in §2.3 and Figure 5).

The right panel of Figure 11 shows the RDPs for Abell 370. The RDP of the bright red sequence galaxies shows a clear central concentration. In contrast, the central concentration of the UDGs and LSB dwarfs is much weaker than that of the bright red sequence galaxies. It is noted that the RDPs of the UDGs and LSB dwarfs show a drop or flattening in the innermost bin ($r<0\farcm 5$), while that of the bright red sequence galaxies keeps increasing as clustercentric distances decrease.

These features of RDPs for Abell 370 are similar to those of Abell S1063 and Abell 2744 (see Figure 7 in Lee et al. (2017)). However, the numbers of UDGs and LSB dwarfs in the inner region of each cluster are too small to obtain statistically meaningful conclusions. Therefore, we stack the RDPs of the three HFF clusters: Abell 370 (this work), Abell S1063, and Abell 2744. Before stacking we normalized the clustercentric distance with respect to the virial radius ($r_{200}$) of each cluster: $r_{200}=8\farcm 52$ for Abell 370, $8\farcm 64$ for Abell S1063, and $9\farcm 16$ for Abell 2744. In Figure 12 (left panel), we display the stacked RDPs of the bright red sequence galaxies, UDGs, and LSB dwarfs. Again, the stacked RDPs of the UDGs and LSB dwarfs show a flattening or drop in the inner region (log $r/r_{200}<-1.0$), in contrast to the RDP of the bright red sequence galaxies which rises as clustercentric distances decrease. Janssens et al. (2019) also found similar central depletion or flattening of the RDPs of UDGs in all the six HFF clusters.

In addition, we compare the RDPs of the HFF clusters with those of other clusters. The middle panel of Figure 12 shows the RDPs of the three galaxy populations in the Coma cluster. We select bright red sequence galaxies in the Coma cluster from SDSS DR14 (Abolfathi et al., 2018) by using the following criteria: magnitude ($r^{\prime}<18$ mag), color (($g^{\prime}-r^{\prime}$) color for the red sequence of the Coma cluster), clustercentric distance ($r_{\rm cl}<r_{200}=97\farcm 92$ (Kubo et al., 2007)), and radial velocity ($v_{r}({\rm Coma})-v_{r}(r_{\rm cl})<v_{r}<v_{r}({\rm Coma})+v_{r}(r_{\rm cl})$), where $v_{r}({\rm Coma})$ is the systematic velocity of the Coma cluster ($v_{r}({\rm Coma})=6925.0~{}{\rm km~{}s^{-1}}$ in Struble & Rood (1999)) and $v_{r}(r_{\rm cl})=(GM_{200}r_{\rm cl}^{-1})^{1/2}$. We divide Coma LSB galaxies in Yagi et al. (2016) into UDGs ($R_{\rm eff,c}>1.5$ $\rm kpc$) and LSB dwarfs ($R_{\rm eff,c}=1.0-1.5$ $\rm kpc$), applying the same criteria as in this study. The RDPs of the bright red sequence galaxies, UDGs, and LSBs in Coma show very similar trends to those of the three HFF clusters.

In the right panel, we display the RDPs of UDGs in nearby low-mass clusters in the literature: 8 MENeaCS clusters ($z=0.044-0.063$) with median virial mass of $M_{200}=5.55\times 10^{14}$ $M_{\odot}$ in van der Burg et al. (2016), and 8 KIWICS clusters ($z=0.02-0.03$) with median virial mass of $M_{200}=3.35\times 10^{13}~{}M_{\odot}$ in Mancera Piña et al. (2019). The RDPs of UDGs in these low-mass clusters show a trend consistent with those of the HFF clusters and the Coma cluster.

In the same figure, we overlay the RDP of the UDGs in simulated clusters given by Rong et al. (2017). These simulated clusters also have low masses of $M_{200}=10^{13}-10^{14}~{}M_{\odot}$. The RDP of the simulated UDGs similarly shows a flattening in the inner region. The flattening or dropping features of the RDPs of UDGs appear to be universal in galaxy clusters regardless of virial masses or redshifts of their host clusters. From the comparison of the RDPs of UDGs from low to high mass clusters and in simulated clusters, we conclude that the RDPs of UDGs (as well as LSB dwarfs) show a flattening in the inner region of the clusters. We discuss this aspect further in §4.1.

The abundance (total number) of galaxies inside the virial radii ($r_{200}$) of their host systems can help us understand the correlation between the number of galaxies and their environments. The abundance of galaxies UDGs ($N$(UDG)) is known to have a power-law relation with the virial masses ($M_{200}$) of their host systems: $N({\rm UDG})\propto M_{200}^{\alpha}$ (van der Burg et al., 2016; Lee et al., 2017; Román & Trujillo, 2017b; van der Burg et al., 2017; Mancera Piña et al., 2018). In this relation, the $\alpha$-value is a key parameter to determine how efficiently galaxies are formed and survive in their environments. If $\alpha<1$, galaxies in low density environments have relatively higher number densities per mass of their host systems. This implies that the galaxies are preferentially formed and survive in fields or galaxy groups rather than in massive galaxy clusters. In contrast, $\alpha>1$ means that galaxies are formed more efficiently or survive longer in high density environments. $\alpha=1$ means that the number of galaxies simply depends on the masses of their host systems. These galaxies do not strongly depend on environmental effects.

We estimate the abundance of UDGs ($N$(UDG)) within the virial radius of Abell 370, by integrating the RDPs from the inner region to the outskirts at its virial radius. We obtained a value of $N$(UDG)$=644\pm 104$. This value is consistent, within the error, with the value given by Janssens et al. (2019), $N$(UDG)$=711^{+213}_{-210}$ for Abell 370.

We counted UDGs in other host systems from previous studies, using the same criterion as used in this study. Table 7 provides a list of $N$(UDG) and $M_{200}$ of the host systems. In Figure 13, we show the relation between $N$(UDG) and $M_{200}$ of Abell 370, in comparison with those of UDGs in other host systems in the literature: massive galaxy clusters (Yagi et al., 2016; Lee et al., 2017), low-mass clusters (van der Burg et al., 2016; Román & Trujillo, 2017a; Venhola et al., 2017; Mancera Piña et al., 2019), galaxy groups (van der Burg et al., 2017), and compact galaxy groups (Román & Trujillo, 2017b; Shi et al., 2017).

In the figure, $N$(UDG) and $M_{200}$ show a tight correlation, but the scatter increases at low-mass host systems. This scatter is significantly large for the mass of $M_{200}<10^{13}$ $M_{\odot}$, because low-mass host systems have only a small number of UDG. Fitting the data for $M_{200}>10^{13}M_{\odot}$, we obtain ${\rm log}~{}N({\rm UDG})=(0.99\pm 0.05)\times{\rm log}~{}M_{200}+(-12.53\pm 0.67)$ with a root mean square (RMS) of 0.19 dex, where the value of $\alpha$ is basically one. Similarly, we derive $\alpha=0.97\pm 0.05$ for $M_{200}>10^{12}M_{\odot}$. If we use the entire range of the virial mass for fitting, we obtain $\alpha=0.92\pm 0.05$. Thus, the $\alpha$-value is close to one. This indicates that the efficiency of the formation or survival of UDGs is little dependent on their environments.

If we fit the virial mass in terms of UDG abundance for $M_{200}>10^{13}M_{\odot}$, we obtain ${\rm log}~{}M_{200}=(1.01\pm 0.05)\times{\rm log}~{}N({\rm UDG})+(12.61\pm 0.10)$ with an RMS value of $0.19$ dex. This relation can be used to estimate the virial masses of the host systems using the abundance of UDGs.

Dynamical mass of UDGs is a critical parameter to understand the nature of UDGs. Various methods have been applied to estimate dynamical masses of UDGs in the literature. First, direct measurements of velocity dispersions of UDGs with spectroscopy can be used to estimate their virial masses under the assumption that UDGs are pressure-supported systems. For example, Martín-Navarro et al. (2019) obtained $\sigma_{v}=56^{+10}_{-10}$ km s^-1, and $M_{200}\sim 5\times 10^{11}~{}M_{\odot}$ for DGSAT-I. Second, the total number of GCs is useful for mass estimation of their hosts. There are well-known relations between the number of GCs ($N_{\rm GC}$) and halo masses ($M_{\rm halo}$) (Harris et al. (2017) and references therein). Since this method is easier than spectroscopy, a number of studies applied this method to the sample of Coma UDGs including DF17 ($N_{\rm GC}=25\pm 11$ and $M_{\rm halo}\sim 9\times 10^{10}~{}M_{\odot}$), DF44 ($N_{\rm GC}=76\pm 18$ and $M_{\rm halo}\sim 8\times 10^{11}~{}M_{\odot}$), and DFX1 ($N_{\rm GC}=63\pm 17$ and $M_{\rm halo}\sim 5\times 10^{11}~{}M_{\odot}$) (Beasley & Trujillo, 2016; Peng & Lim, 2016; van Dokkum et al., 2016, 2017; Amorisco et al., 2018; Lim et al., 2018). Third, HI line widths can be used to estimate the dynamical mass of gas-rich UDGs. Trujillo et al. (2017) measured the HI line width of UGC 2162, a blue isolated gas-rich UDG, to be $W(\rm HI)=126$ km s^-1  and derived a virial mass of $M_{200}\sim 8\times 10^{10}$ $M_{\odot}$. Fourth, weak lensing analysis can be used to estimate virial mass of UDGs. Sifón et al. (2018) used this method and constrained the maximum virial mass range of UDGs in the MENeaCS clusters: $M_{200}<6.3\times 10^{11}~{}M_{\odot}$ with the 95% confidence level.

In the case of Abell 370 UDGs/LSB dwarfs, none of the above methods can be used. We estimate dynamical masses of UDGs/LSB dwarfs approximately, using the fundamental manifold method based on photometric parameters as suggested by Zaritsky (2017). Zaritsky et al. (2008) suggested a fundamental manifold of galaxies, with which we can derive kinematic terms from their sizes and surface brightness. The kinetic term is defined by $V=\sqrt{\sigma_{v}^{2}+v_{\rm rot}^{2}/2}$, where $\sigma_{v}$ is the velocity dispersion and $v_{\rm rot}$ is the rotation velocity. Zaritsky et al. (2008) used 1,925 galaxies from bright ellipticals ($-22.0<M_{r^{\prime}}<-18.5$) to low-mass disk galaxies ($-16.0<M_{r^{\prime}}<-13.5$) (Geha et al., 2006; Zaritsky et al., 2006a, b; Pizagno et al., 2007; Simon & Geha, 2007; Springob et al., 2007) in order to empirically calibrate the scaling relations. They suggested that the derived relations can be applied to any types of galaxies regardless of their morphology. Zaritsky (2017) applied this method to estimate the kinetic terms of LSB galaxies including UDGs after performing an observational correction (see the equations (1), (2) in Zaritsky (2017)). Then, they estimated the virial masses of the UDGs using these derived kinetic terms. Lee et al. (2017) and Chan et al. (2018) also used this method to estimate dynamical masses of UDGs in massive clusters and simulations. We estimate dynamical masses of UDGs and LSB galaxies in Abell 370, assuming that these galaxies are pressure-supported systems and their halo mass profiles follow the NFW profiles (see the equation (3) in Lee et al. (2017) and the related text).

However, Zaritsky (2017) used only two UDGs with spectroscopic measurements (DF44 and VCC 1287) to check the validity of applying the fundamental manifold method to UDGs. Here we check it again using an increased sample of 13 UDGs/LSB dwarfs which have velocity dispersion measurements: 9 Coma UDGs in Chilingarian et al. (2019), Coma DF44 (van Dokkum et al., 2019), Coma DFX1 (van Dokkum et al., 2017), DGSAT-1 (Martín-Navarro et al., 2019), and VCC 1287 (Beasley et al., 2016). 6 of the 9 Coma UDGs in Chilingarian et al. (2019) have effective radii smaller than 1.5 kpc, so they correspond to LSB dwarfs in this study.

In Figure 14, we plotted estimated kinetic terms ($V_{\rm est}$) versus observed kinetic terms ($V_{\rm obs}$) for these 13 UDGs/LSB dwarfs (it is an updated version of Fig. 1 in Zaritsky (2017)). For comparison, we plotted also the sample of GCs (McLaughlin & van der Marel, 2005), ultra-compact dwarfs (UCDs) (Mieske et al., 2008; Chilingarian et al., 2011; Seth et al., 2014; Ahn et al., 2017; Afanasiev et al., 2018; Ahn et al., 2018), satellite galaxies in the Local Group (McConnachie, 2012), and stellar clusters (Zaritsky et al., 2012, 2013, 2014). We assumed $v_{\rm rot}=0$ except for a few dwarf galaxies in the Local Group and UCDs. This figure shows that the 13 UDGs/LSB dwarfs follow very well the relation of other passive stellar systems. We fit the data for all stellar systems including UDGs/LSB dwarfs with a power law, obtaining ${\rm log}~{}V_{\rm est}=(0.90\pm 0.03)\times{\rm log}~{}V_{\rm obs}+(0.04\pm 0.03)$ with an RMS value of 0.16 dex.

This relation is very similar to the relation for the non-UDG sample given by Zaritsky (2017), ${\rm log}~{}V_{\rm est}=0.88\times{\rm log}~{}V_{\rm obs}+0.07$. This indicates that the fundamental manifold method can be applied to the UDG/LSB dwarf regime.

Figure 15 displays the dynamical mass distributions of UDGs and LSB dwarfs in Abell 370 derived from the fundamental manifold method in this study. We marked UDG-C22, the largest one, by a yellow star symbol. The x-axis is the 3D half-light radius ($R_{1/2}=4R_{\rm eff,c}/3$), and the y-axis is the enclosed dynamical mass within $R_{1/2}$. The curved solid lines denote the virial masses ($M_{200}$) of $10^{10}$, $10^{11}$, and $10^{12}~{}M_{\odot}$ derived from the NFW mass profiles. For comparison, we also plotted other known UDGs/LSB dwarfs with spectroscopic measurements in the literature (Beasley et al., 2016; van Dokkum et al., 2016, 2017; Chilingarian et al., 2019; Martín-Navarro et al., 2019) as in Figure 14.

Several features are noted in Figure 15. First, the locations of Abell 370 UDGs/LSB dwarfs are overlapped with those of other UDGs with spectroscopic measurements. This implies that the dynamical mass range of Abell 370 UDGs/LSB dwarfs is similar to that of the other UDGs/LSB dwarfs. Second, UDGs have relatively larger enclosed masses than LSB dwarfs. Thus, UDGs are larger and more massive than LSB dwarfs. Third, most UDGs and LSB dwarfs have virial masses with $M_{200}=10^{10}-10^{11}$ $M_{\odot}$. This implies that a majority of UDGs are dwarf-like galaxies. Fourth, a few UDGs in Abell 370 have larger virial masses, $10^{11}<M_{200}<10^{12}$ $M_{\odot}$. Among them, UDG-C22, the largest one in Abell 370, has the largest mass. Interestingly DGSAT-I, the largest in the other UDG sample, has a mass similar to that of UDG-C22.

We display the size-luminosity relation of UDGs and LSB dwarfs of Abell 370 in Figure 16. For comparison, we also plotted other passive stellar systems: giant ellipticals and bulges in spirals (Bender et al., 1993), Coma LSBs (Yagi et al., 2016), Fornax dwarfs (Muñoz et al., 2015; Ordenes-Briceño et al., 2018), UCDs (Pandya et al., 2016), dwarf galaxies in the Local Group (McConnachie, 2012), and GCs in the Milky Way (MW) and M31 (Harris, 2010; Peacock et al., 2010). Ultra-faint dwarfs (UFDs, $M_{V}>-7.7$ mag) in the Local Group are marked by thin diamonds. In the figure, we added the loci of surface brightness for $\langle\mu\rangle_{\rm e,abs}(V)=20-30~{}{\rm mag~{}arcsec^{-2}}$ with an interval of 2 magnitude.

Figure 16 shows following features. First, UDGs/LSB dwarfs in Abell 370 occupy the larger and brighter side of UDGs/LSB dwarfs in Coma, Fornax, and the Local Group. Second, UDGs in Abell 370 are just a larger and brighter version of LSB dwarfs, not showing any clear distinction between the two types. Third, UDGs/LSB dwarfs are obviously separated from the high surface bright objects such as giant ellitical galaxies and spiral bulges, UCDs, and globular clusters.

In §3.4, we find that the RDPs of UDGs show a flattening (or a slight drop) in the inner region of their host systems, while the RDPs of bright red sequence galaxies do not. This can be seen from low-mass clusters to high mass clusters. The RDPs of UDGs and LSB dwarfs in the three HFF clusters also show a similar trend.

Most previous studies interpreted that tidal disruptions of UDGs contributed to their low number densities in the central region. van der Burg et al. (2016) and Lee et al. (2017) suggested that some UDGs were disrupted by the strong gravitational potential near the center of clusters. They noted that most UDGs could be easily disrupted because of their low masses. In addition, Venhola et al. (2017) and Wittmann et al. (2017) also found that the number densities of UDGs in the central region of the Fornax cluster and the Perseus cluster are lower than in the outer region. These studies pointed out that it is difficult for UDGs to survive in the strong tidal interactions of the cluster central regions.

Observationally, tidally disrupted UDGs are frequently found from the local Universe to distant galaxy clusters. UDGs around massive galaxies such as And XIX (near M31) (Collins et al., 2013, 2019), CenA-MM-Dw3 (near NGC 5128) (Crnojević et al., 2016), and Scl-MM-Dw2 (near NGC 253) (Toloba et al., 2016) show tidal features toward their neighboring massive galaxies. In cluster environments, several UDGs in the Virgo cluster (Mihos et al., 2015; Toloba et al., 2018) and the HFF clusters (Lee et al., 2017) also have tidally disrupted features near bright galaxies in the clusters. Thus, our results support the tidal disruption scenario for low number densities of UDGs as well as LSB dwarfs in the central regions of their host systems.

In this study, we find that the relation between UDG abundance and the virial mass of their host systems is described well by a simple power-law relation with an index of $\alpha=0.99\pm 0.05$ for $M_{200}>10^{13}~{}M_{\odot}$, and $\alpha=0.97\pm 0.05$ for $M_{200}>10^{12}~{}M_{\odot}$. If we include two Hickson compact groups (HCGs) with lower mass ($5\times 10^{11}~{}M_{\odot}<M_{200}<10^{12}~{}M_{\odot}$), we derive a slightly smaller value, $\alpha=0.92\pm 0.05$. It is noted that we selected UDGs in the literature samples using the same selection criteria as used in this study.

We compare our results with those in the previous studies, as shown in Figure 13 in the following. van der Burg et al. (2016) suggested $\alpha=0.93\pm 0.16$ from UDGs in eight MENeaCS galaxy clusters at $z=0.044-0.063$. Later, adding the stacked numbers of UDGs in galaxy groups from KiDS+GAMA fields, van der Burg et al. (2017) derived $\alpha=1.11\pm 0.07$. Lee et al. (2017) added the data for UDGs in two massive clusters (Abell S1063 and Abell 2744) to the previous sample, and obtained $\alpha=1.05\pm 0.09$ for the systems with $M_{200}>10^{13}M_{\odot}$. Recently, Mancera Piña et al. (2018) suggested $\alpha=0.96\pm 0.11$ for $M_{200}=10^{12}-5\times 10^{14}~{}M_{\odot}$, using the samples in 8 clusters from the KIWICS and applying homogeneous selection criteria of UDGs. These values are all close to one, being consistent with the results in this study.

On the other hand, a few studies presented slightly lower values of $\alpha$. Román & Trujillo (2017b) added UDGs in HCGs ($5\times 10^{11}M_{\odot}<M_{200}<10^{13}M_{\odot}$) to the sample and derived $\alpha=0.85\pm 0.05$. Mancera Piña et al. (2018) also presented $\alpha=0.77\pm 0.06$, if they include two Hickson compact groups with lower mass ($10^{11}~{}M_{\odot}<M_{200}<10^{12}~{}M_{\odot}$). Our value for the sample including lower mass systems, $\alpha=0.92\pm 0.05$, is larger than these values. However, it is noted that the upper virial mass limit for the samples in Román & Trujillo (2017b) and Mancera Piña et al. (2018), $M_{200}=5\times 10^{14}~{}M_{\odot}$, is much smaller than the value in this study ($M_{200}=3\times 10^{15}~{}M_{\odot}$).

There are three main scenarios proposed to explain the formation of UDGs in the literature: 1) the failed galaxies scenario, 2) the extended dwarf galaxies scenario, and 3) the interaction scenario (Amorisco & Loeb, 2016; van Dokkum et al., 2016; Di Cintio et al., 2017; Bennet et al., 2018).

The first scenario is applicable to UDG progenitors undergoing early accretion to galaxy clusters. Yozin & Bekki (2015) used $N$-body simulation to show how star formation in UDG progenitors could be quenched by ram-pressure stripping in cluster environments. There are two variations of this scenario depending on the range of halo masses: a “failed $L^{*}$ galaxies” scenario and a “failed dwarf galaxies” scenario. UDGs from “failed $L^{*}$ galaxies” have comparable halo masses to that of the MW ($M_{200}>10^{11}$ $M_{\odot}$), whereas “failed dwarf galaxies” have halo masses less than those of the Large Magellanic Cloud ($M_{200}<10^{11}$ $M_{\odot}$). Observationally, some Coma UDGs like DF44 or DFX1, which have red colors and massive dark matter (DM) halos ($M_{200}>10^{11}$ $M_{\odot}$), are consistent with the “failed $L^{*}$ galaxies” scenario (van Dokkum et al., 2016, 2017). On the other hand, less massive UDGs with red colors such as DF17 or VCC 1287 ($M_{200}<10^{11}$ $M_{\odot}$) can be explained by the “failed dwarf galaxies” scenario (Beasley et al., 2016; Beasley & Trujillo, 2016; Peng & Lim, 2016).

In the “extended dwarf galaxies” scenario, UDG progenitors could be extended by internal processes. This scenario does not require high density environments or massive DM halos to produce UDGs. Amorisco & Loeb (2016) and Rong et al. (2017) suggested that the high spin parameters of DM halos of UDGs could produce extended dwarf galaxies, and concluded that UDGs are the high-spin tails of normal dwarf galaxies. In contrast, Di Cintio et al. (2017) and Chan et al. (2018) suggested that strong gas outflows from stellar feedback could affect the gravitational potential of the DM halo and eventually extend the stellar content of UDG progenitors. Blue isolated UDGs such as UGC 2162 (Trujillo et al., 2017), LSBG-750 (Greco et al., 2018b), and the UDGs in HCGs (Román & Trujillo, 2017b; Spekkens & Karunakaran, 2018) have lower virial masses of $M_{\rm vir}\lesssim 10^{11}$ $M_{\odot}$, which can be explained by this scenario. Moreover, Leisman et al. (2017) used HI observations and showed that UDGs in low-density environments tend to have relatively higher spin parameters than normal gas-rich galaxies.

In the third scenario, UDGs are created by tidal interactions with neighboring massive galaxies. This scenario is supported by the presence of UDGs close to massive galaxies. Several studies of UDG morphology provided observational evidence supporting this scenario: CenA-MM-Dw3 (Crnojević et al., 2016), DF4 near NGC 5485 (Merritt et al., 2016), Scl-MM-Dw2 near NGC 253 (Toloba et al., 2016), VLSB-A and VLSB-D in the Virgo cluster (Mihos et al., 2015; Toloba et al., 2018), NGC 2708-Dw1, and NGC 5631-Dw1 (Bennet et al., 2018). Baushev (2018) suggested that UDGs could be also generated via head-on collisions between two gas-rich galaxies which remove a large amount of gas in UDG progenitors.

Recent studies tend to suggest mixed formation scenarios to explain the diversity in the UDG populations in various environments by combining the individual scenarios (Lee et al., 2017; Papastergis et al., 2017; Alabi et al., 2018; Ferré-Mateu et al., 2018; Lim et al., 2018; Pandya et al., 2018). These studies revealed the presence of diverse UDGs through various methods: 1) the total number of GCs in UDGs, 2) optical spectroscopy, 3) SED fitting, and 4) HI observation.

First, the total number of GCs in UDGs has been used as a proxy to estimate the UDG halo mass. van Dokkum et al. (2017) presented that UDGs have, on average, a significantly larger number of GCs (by a factor of $\sim 7$) than other galaxies with similar luminosity and stellar mass, using HST/ACS data of 16 Coma UDGs. In their work, DF44 and DFX1 in Coma are good examples of UDGs with rich GC populations. This implies that those UDGs are hosted by massive halos like the MW, but they failed to form as many stars as bright galaxies with similar dynamical masses. From this, van Dokkum et al. (2017) concluded that their results support the failed $L^{*}$ galaxy scenario. However, Amorisco et al. (2018) presented the opposite conclusion, using GCs in 54 Coma LSBs including 18 UDGs ($R_{\rm eff}>1.5$ $\rm kpc$). They found that most of Coma UDGs in their sample have dwarf-like halos with $M_{\rm vir}<10^{11}$ $M_{\odot}$ with the 90% confidence level, and only three UDGs are hosted by massive halos ($M_{\rm vir}>10^{11}$ $M_{\odot}$). Later, Lim et al. (2018) studied the GC populations of 48 Coma UDGs. They divided their UDG samples into two populations according to their GC specific frequency ($S_{N}$): high-$S_{N}$ UDGs and low-$S_{N}$ UDGs. They revealed that high-$S_{N}$ UDGs (27 in total) have $M_{\rm halo}\sim 10^{11}$ $M_{\odot}$ on average, whereas the remaining low-$S_{N}$ UDGs have significantly lower halo mass ($<10^{11}$ $M_{\odot}$). This result is intermediate between van Dokkum et al. (2017) and Amorisco et al. (2018) and implies that UDGs have two populations generated by multiple formation routes. Lim et al. (2018) concluded that UDGs have two populations formed by different routes. Likewise, Toloba et al. (2018) applied a similar method to three Virgo UDGs. They suggested that there are two types of UDGs: one is a smooth and DM-dominated system with a massive halo ($M_{200}\sim 10^{12}$ $M_{\odot}$), and the other is a tidally perturbed system with significant rotation and a less massive halo ($M_{200}<10^{11}$ $M_{\odot}$).

Second, optical spectroscopy has been used to study kinematics and stellar populations of UDGs. Alabi et al. (2018) obtained spectra of Coma UDGs using Keck/DEIMOS and derived the clustercentric radial velocities of the UDGs. They suggested that Coma UDGs are divided into two different types in their velocity phase-space diagram (Fig 9. in their study). One is ‘recent infall’ UDGs ($\sim 2$ $\rm Gyr$ ago) with high relative line-of-sight velocities and relatively bluer colors, and the other is early accreted ‘primordial’ UDGs ($\sim 8$ $\rm Gyr$ ago) with low relative line-of-sight velocities and redder colors. Ferré-Mateu et al. (2018) presented the results of stellar population analysis based on the same spectra as used in Alabi et al. (2018). They derived the stellar parameters such as age, metallicity, and SFH, and showed that most UDGs have similar SFH, mass-age, and mass-metallicity relations to those of dwarf galaxies rather than to those of bright galaxies. This supports that most UDGs have a dwarf-like nature. However, a few UDGs like DF07 and DF44 in Coma show a ‘primordial’ nature with low metallicities, old ages, and early quenching SFHs (Kadowaki et al., 2017; Gu et al., 2018). Chilingarian et al. (2019) derived kinematic and stellar parameters of 9 Coma UDGs/LSB dwarfs, using the MMT/Binospec spectrograph. They suggested that UDGs and LSB dwarfs are of the same population and they have a wide range of age and metallicity due to a diversity of formation scenarios. All these spectroscopic results imply that UDGs have multiple populations originated from different formation processes.

Third, SED fitting is also useful to reveal the multiple nature of UDGs. Applying prospector (a fully Bayesian SED fitting package) to optical-NIR SEDs, Pandya et al. (2018) studied two UDGs residing in different environments: VCC 1287 in the Virgo cluster, and DGSAT-I in the field environment. They found that VCC 1287 shows a redder color ($g-i\sim 0.7$), an older age ($\sim 8$ $\rm Gyr$), a lower metallicity ($[Z/Z_{\odot}]\sim-1.0$), and a less extended SFH than DGSAT-I. In contrast, DGSAT-I has a bluer color ($V-I\sim 0.3$), a younger age ($\sim 3$ $\rm Gyr$), a relatively metal-rich SED ($[Z/Z_{\odot}]\sim-0.6$), and an extended SFH. Although there have been not many studies of SEDs of UDGs, this implies that UDGs have a multiple formation scenario.

Fourth, recent HI observations of UDGs provided evidence of multiple populations of UDGs. Papastergis et al. (2017) presented the HI properties of four isolated UDGs. Three UDGs (DGSAT I, R-127-1, and M161-1) are gas-deficient ($M_{\rm HI}/M_{*}\lesssim 0.6$) and quiescent galaxies, while one UDG (SdI-2) is a gas-rich ($M_{\rm HI}/M_{*}>20$) dwarf galaxy. Considering that isolated UDGs such as UGC 2162 (Trujillo et al., 2017) and SdI-1 (Bellazzini et al., 2017) have high gas fractions ($M_{\rm HI}/M_{*}>10$), UDGs in the low density environment can be distinguished as two types according to their gas fractions.

In a similar context, our study of UDGs in massive clusters shows diverse types of UDGs. A majority of UDGs are dwarf galaxies in terms of thier RDPs and dynamical masses. Considering most UDGs have red colors and no star-forming features, they can be failed dwarf galaxies. However, UDG-C22 in Abell 370 is so large ($R_{\rm eff,c}=6.16$ $\rm kpc$) and massive ($M_{200}>10^{11}$ $M_{\odot}$) that it can be considered as an example of a primodal failed $L^{*}$ galaxy. Interestingly, UDG-C02 in Abell 370 can be an extended dwarf galaxy due to its remarkably blue color. There are also a few tidally interacting UDGs. This diversity of UDGs is consistently shown in the UDGs in other HFF clusters. Thus, we conclude that UDGs in massive HFF clusters can be explained by multiple formation scenarios.