The Blue Compact Dwarf Galaxy VCC 848 Formed by Dwarf–Dwarf Merging

In order to better visualize faint substructures, we mask out bright foreground stars or background galaxies in the g image, and then use the adaptive smoothing code adaptsmooth (Zibetti et al. 2009) to adaptively smooth the masked g-band image to a minimum signal-to-noise ratio (S/N) of 5 pixel⁻¹. The smoothed image is shown in Figure 2. One can notice three extended shell-like structures around the bright stellar main body. These shell structures are largely aligned along the east–west direction, and the innermost one is brighter and has sharper edges than the two at larger radii. Moving toward smaller radii, there is a circularly edged stream-like feature wrapping nearly 180° around the stellar main body to the southeast. Last, there is a straight stream-like narrow feature that extends to the southwest and is largely parallel to the orientation of the stellar main body.

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To quantify the stellar light distribution, we perform surface photometry in the original g- and i-band images with the IRAF task ellipse. Our isophotal fitting is carried out in an iterative manner in order to find the photometric center, which is constant with radius, and the ellipticity and position angle (PA) that vary with radius. The results are shown in Figure 3.

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The stellar main body of VCC 848 has twisted isophotes, with the PA varying from ≃ 32° near the center to 42° at a major axis radius ${R}_{\mathrm{maj}}$ ≃ 28'' (∼2.2 kpc) where boxy distortion of the isophotes reaches the maximum (ellipse B4 coefficient ≃ −0.3; bottom right panel of Figure 3). Beyond the central ∼30'' (i.e., the stellar main body) are the above-described tidal streams and shells, which apparently drive the abrupt decrease of isophotal ellipticities at large radii (${R}_{\mathrm{maj}}$ ≳ 40''). Photometry integrated over the area enclosed by the 27.3 and 28.3 mag arcsec⁻² g-band brightness contours is shown as red open square symbols in Figure 3.

The (g − i) colors become redder at larger radii. The obscured star formation traced by Herschel far-infrared photometry accounts for merely 9% of the SFR budget of VCC 848 (Section 1). So the radial color trend primarily reflects an increasingly older stellar population toward larger radii. The shell-dominated region reaches g−i ≃ 0.6–0.7 mag that, for single stellar populations (SSPs) at one-fifth solar metallicity (i.e., the nebular gas abundance measured by Vilchez & Iglesias-Paramo 2003), would correspond to stellar ages of 2–3 Gyr.

The radial surface brightness distribution at ${R}_{\mathrm{maj}}$ ≲ 28'' follows an exponential profile, suggesting a disk structure that is presumably dominated by the primary progenitor of this merging system. The best-fit exponential profile for the disk-dominated radial range is overplotted as a blue straight line in Figure 3. To make an estimate of the respective stellar luminosities of the primary and secondary galaxies of the merging system, we assume that the region within ${R}_{\mathrm{maj}}$ = 28'' is contributed exclusively by the primary, while the region beyond has significant contribution from both the primary and secondary. The total luminosity of the primary is a sum of the luminosity directly measured in the images within ${R}_{\mathrm{maj}}$ = 28'' and an exponential extrapolation beyond by using the average ellipse geometric parameters at 26'' < ${R}_{\mathrm{maj}}$ < 28''. The luminosity of the secondary is calculated by subtracting the luminosity of the primary from the total luminosity enclosed within the 28.3 mag arcsec⁻² contour.

The above exercise of decomposing the merging system gives a g-band absolute magnitude M_g of −16.28 and a (g − i) color of 0.45 for the primary, and an M_g of −14.39 and a (g − i) color of 0.53 for the secondary. To estimate the stellar mass, we first transform our MegaCam magnitude to the Sloan Digital Sky Survey (SDSS) magnitude using the relation: (g − i)_SDSS = 1.1 × (g − i)_MegaCam and i_SDSS = i_MegaCam + 0.005 × (g − i)_MegaCam,¹³ and then obtain mass-to-light ratios using the color–mass-to-light relation calibrated for Local Group dwarf galaxies by Zhang et al. (2017) based on the Flexible Stellar Population Synthesis (FSPS) stellar population models (Conroy et al. 2009). The resultant stellar masses are 1.7 × 10⁸ M_⊙ and 3.8 × 10⁷ M_⊙ for the primary and secondary, respectively, leading to a 4.5: 1 primary-to-secondary stellar mass ratio. By adopting the stellar-to-dark matter halo mass relation from Guo et al. (2010), the corresponding dark matter halo masses for the primary and secondary are 5.6 × 10¹⁰ and 3.4 × 10¹⁰ M_⊙, respectively, giving a halo mass ratio of 1.6:1. The mass ratio estimated here is likely an upper limit if allowing for a nonnegligible contribution of the secondary to the central exponential part of the system.

The fact that we observe mostly extended stellar shells, rather than tidal tails, around the merging system favors a nearly radial encounter (Quinn 1984). The overall alignment of the stellar shells suggests that the collision was largely along the east–west direction. Because we do not see any distinct stellar concentrations other than the main body, the secondary progenitor has been almost entirely disrupted, leaving behind the observed stellar shells.

We use SExtractor (Bertin & Arnouts 1996) to detect star cluster candidates in the original i-band image, which has the highest spatial resolution among our images. Ordinary star clusters (r_eff ∼ 2−10 pc; e.g., Portegies Zwart et al. 2010) at the distance of VCC 848 are expected to be pointlike or marginally resolved sources at our i-band resolution (e.g., Durrell et al. 2014). We run SExtractor with a BACK_SIZE parameter of 9 pixels and a detection threshold of 3 times the rms noise. A total of 1994 sources are detected in a 72 × 112 cutout image centered around VCC 848. By following the routine procedure of completeness estimation based on artificial star tests (e.g., Munoz et al. 2014), we find that our detection reaches a 90% completeness limit at i = 23.5 mag. 1078 of the 1994 sources have i ≤ 23.5 mag.

We perform i-band aperture photometry for the detected sources with a 5 pixel (093) diameter aperture size. The aperture size is chosen to contain more than half of the total flux expected for a point source and at the same time to reduce as much as possible the contamination from neighboring sources. Local background for each source is determined using a 4 pixel wide background annulus, with an inner radius of 6 pixels. We apply a multiplicative correction factor of 1.8 to the background-subtracted aperture photometry to recover the expected total flux for i-band point sources. To determine the colors, we smooth the g, i, z images to match the u-band spatial resolution, and follow the same procedure described above to obtain u, g, i, z photometry based on the resolution-matched images.

We select star cluster candidates taking advantage of both the shape and color information. In particular, we use the criteria of ELLIPTICITY < 0.2 and FWHM < 4.5 pixels to pick out pointlike or marginally resolved objects with i < 23.5 mag. The SExtractor shape parameter measurements are subject to large uncertainties in regions with a steep background gradient, so we relax the requirement for shape parameters if a source in question is spatially coincident with an H ii region visible in the Hα image of Gil de Paz et al. (2003). The above selection criteria leave us with 526 sources to be considered for further selection with colors.

The right panel of Figure 4 shows the (u − g) versus (g − i) distribution of the above-selected 526 sources. The sources occupy two distinct branches. The upper branch is identified to be background galaxies, while the lower branch is largely occupied by star clusters and foreground stars. We draw a polygon to delineate a region in the color–color space to single out the most probable star cluster candidates (116 in total). Last, we require that the VCC 848 star cluster candidates be located within a 12 radius circular region, approximately matching the area enclosed by the 27.3 mag arcsec⁻² g-band brightness contour. This last step leaves us with a final sample of 37 star cluster candidates.

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The average number density of the 79 (116–37) color-selected candidates located outside of the 12 radius circular region around VCC 848 is ≃ 1.0 arcmin⁻². Therefore, we expect an average of ≃ 4.5 contaminants for the 12 radius circular region, giving a ≃ 88% purity for our star cluster sample. We note, however, that 33 of the 37 candidates are concentrated within the central 30'', implying a 98% purity.

We estimate stellar ages and masses of our star cluster candidates by fitting the FSPS SSP models to u, g, i, z photometry. Considering the age–metallicity degeneracies, we perform two sets of extinction-free stellar population fitting. One imposes a Gaussian prior constraint on metallicities, with a mean of −0.88 dex (chosen to be 0.2 dex lower than the abundance measurements for H ii regions by Vilchez & Iglesias-Paramo 2003) and a standard deviation of 0.3 dex, while the other one does not impose prior constraints on metallicities. An upper limit of one-third solar metallicity is adopted for both sets of fitting. We will show that the two sets of spectral energy distribution (SED) fitting give statistically similar age–metallicity distributions. With the best-fit age and metallicity of each cluster, we infer the stellar mass at birth by correcting the present-day mass for mass loss due to stellar evolution, based on the FSPS models. As we will show in Figure 5(c), mass loss caused by dynamical evaporation is not expected to be important for our cluster sample.

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The stellar masses at birth are plotted against ages of our star cluster candidates in Figure 5(c). The lower limit of cluster mass increases with age, which is jointly driven by the luminosity-limited detection efficiency, evolutionary fading, and dynamical evaporation. The maximum cluster mass also varies with age, which may be driven by the size-of-sample effect, a time-dependent cluster formation rate (CFR), or cluster mass function (CMF). CMF of young star clusters observed in nearby galaxies can always be described by a power-law dN/dM ∝ M^α, where α ≃ −2 ± 0.2 (see Krumholz et al. 2019 and references therein). For a constant CFR and α = −2 power-law CMF, the maximum cluster mass per logarithmic time interval scales linearly with age due to the size-of-sample effect (e.g., Hunter et al. 2003). Such a linear M−age relation is illustrated in Figure 5(c).

Given that dynamical evaporation and tidal shocking are not expected to significantly influence star clusters with M_⋆ > 10⁵ M_⊙ (Reina-Campos et al. 2018), the CFR of VCC 848 has been significantly enhanced during the past ∼1.0 Gyr, because the observed maximum cluster masses above 10⁵ M_⊙ do not rise steadily with lookback time, which would otherwise be expected for the size-of-sample effect. However, during the last ∼20–30 Myr, the CFR appears to have started declining. The brightest star cluster of VCC 848, with a V-band absolute magnitude ${M}_{V}^{\mathrm{brightest}}$ = −11.15 mag (derived based on the best-fit model SED), is >3σ above the average ${M}_{V}^{\mathrm{brightest}}$−SFR relation for nearby galaxies (Figure 5(b)), in line with a recent decline of SFR (Bastian 2008).

Our cluster sample is ≳90% complete at M_⋆ ≥ 10^5.25 M_⊙ across nearly the whole age range. Figure 5(d) shows the average number of clusters with M_⋆ > 10^5.25 M_⊙ over age intervals of 0−1 Gyr and 1−13 Gyr. The average CFR in the last 1 Gyr is ∼7–10 times that at earlier times. If the mass fraction of stars born in star clusters is independent of SFR, as suggested by recent studies (e.g., Chandar et al. 2017), the trend for CFR would be approximately equivalent to that for SFR.

The two most massive young star clusters (<1 Gyr), which have ages ≳0.3 Gyr and M_⋆ ≃ ${10}^{5.4}$ M_⊙, are near the galactic center, while the youngest star clusters (≲30 Myr), which have M_⋆ < 10^5.0 M_⊙, are at large distances (≥10'') from the center (Figure 5(a)). This suggests that the most intense merging-induced star formation happened near the galactic center a few hundred Myr ago, after which active star-forming activities have shifted to larger radii. Star clusters with ages >1 Gyr appear to avoid the central disk region and might be regarded as (globular) clusters formed in the progenitor galaxies.