Low Metallicities and Old Ages for Three Ultra-diffuse Galaxies in the Coma Cluster

We make use of data obtained by the MaNGA Survey (Mapping Nearby Galaxies at Apache Point Observatory, Bundy et al. 2015; Drory et al. 2015; Yan et al. 2016a). MaNGA is a large, optical integral field spectroscopy survey with 17 deployable integral field units (IFUs; ranging from 12'' to 32'' in diameter), and one of the fourth-generation Sloan Digital Sky Survey (SDSS-IV) programs (Blanton et al. 2017). The primary goal of MaNGA is to obtain an integral field spectroscopy of ∼10,000 nearby galaxies.

Our data comes from one of MaNGA's ancillary programs, the Deep Coma program.¹⁹ The goal of the Deep Coma program is to study the stellar populations of various targets in the Coma Cluster and its surrounding area through long integration spectroscopy. Our targets include two brightest cluster galaxies (BCG), several additional massive elliptical galaxies, dwarf galaxies, intracluster light regions, and three UDGs: DF 44, DF 17, and DF 7.

MaNGA makes use of IFU fiber bundles to feed two dual-beam Baryonic Oscillation Spectroscopic Survey (BOSS) spectrographs (Smee et al. 2013; Drory et al. 2015) that are on the SDSS 2.5 m telescope (Gunn et al. 2006). The spectrographs have 1423 fibers in total that are bundled into different size IFUs. The diameter of each fiber is 198 on the sky. The wavelength coverage of the spectrographs is 3622–10354 Å with a ∼400 Å overlap from ∼5900 Å to ∼6300 Å . The spectral resolution is 1560–2650.

The Deep Coma project consists of six plates designed to observe selected targets in the Coma cluster. The centers of all plates are at R.A. = 12^h58^m3558, decl. = 27^d36^m12744. This position was carefully chosen to optimize the IFU bundle mapping of desired targets. The first two plates were observed in Spring, 2015. The third to fifth plates were observed in Spring, 2016. The sixth plate was observed in Spring, 2017. The total on-source exposure time in each plate is 2.25 hr. To evaluate the impact on low surface brightness targets from systematic residuals (see Section 2.3), we have shuffled the IFU bundles used for the same target among different plates. The most frequently used IFU bundles for UDGs are 61-fiber bundles, but 37-fiber bundles and 91-fiber bundles have been used to observe them as well. The stacked spectra in our analyses are from the inner 19 fibers of each bundle for the optimum integrated signal-to-noise ratio (S/N). The locations of the stacked region for the three UDGs analyzed in this paper are shown in Figure 1. The diameter of each stacked region on the sky is 125. The positions, central surface brightness, and effective radii of the two UDGs are shown in Table 1. The stacked regions sample roughly the inner 0.7 effective radii of the three UDGs.

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Table 1.  UDG Properties

Target	DF 7	DF 44	DF 17
α	12h57m017	13h00m580	13h01m583
δ	28°23'25''	26°58'35''	27°50'11''
μ0,g (mag/arcsec−2)	24.4 ± 0.5	24.5 ± 0.5	25.1 ± 0.5
Mg (mag)	$-{16.0}_{-0.2}^{+0.2}$	$-{15.7}_{-0.2}^{+0.2}$	$-{15.2}_{-0.2}^{+0.3}$
Reff (kpc)	${4.3}_{-0.8}^{+1.4}$	${4.6}_{-0.8}^{+1.5}$	${4.4}_{-0.9}^{+1.5}$
S/N (4500–5000 Å)	9.5 Å−1	7.9 Å−1	5.0 Å−1
Constraints from Spectra
Velocity (km s−1)	${6600}_{-26}^{+40}$	${6402}_{-38}^{+41}$	${8311}_{-43}^{+43}$
log(age/Gyr)	${0.93}_{-0.18}^{+0.17}$	${1.02}_{-0.24}^{+0.11}$	${0.88}_{-0.42}^{+0.22}$
[Fe/H]	$-{1.03}_{-0.34}^{+0.31}$	$-{1.25}_{-0.39}^{+0.33}$	$-{0.83}_{-0.51}^{+0.56}$
(M/L)r	${1.63}_{-0.29}^{+0.55}$	${1.86}_{-0.56}^{+0.39}$	${1.54}_{-0.52}^{+0.71}$
$\mathrm{log}({M}_{\star }/{M}_{\odot })$	${8.74}_{-0.11}^{+0.17}$	${8.66}_{-0.15}^{+0.12}$	${8.42}_{-0.19}^{+0.22}$
Combined Constraints from Spectra and Photometry
Velocity (km s−1)	${6599}_{-25}^{+40}$	${6402}_{-39}^{+41}$	${8315}_{-43}^{+43}$
log(age/Gyr)	${0.90}_{-0.16}^{+0.17}$	${0.95}_{-0.20}^{+0.17}$	${0.96}_{-0.40}^{+0.16}$
[Fe/H]	$-{1.04}_{-0.36}^{+0.32}$	$-{1.25}_{-0.41}^{+0.35}$	$-{0.80}_{-0.47}^{+0.49}$
(M/L)r	${1.56}_{-0.28}^{+0.47}$	${1.64}_{-0.38}^{+0.54}$	${1.80}_{-0.66}^{+0.51}$
$\mathrm{log}({M}_{\star }/{M}_{\odot })$	${8.72}_{-0.13}^{+0.17}$	${8.61}_{-0.11}^{+0.16}$	${8.49}_{-0.20}^{+0.15}$

Note. We adopt the locations, central g-band surface brightness, absolute g-band magnitude and effective radii from van Dokkum et al. (2015a). Stellar population properties are derived from the central 19 fibers.

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To probe low surface brightness regions, excellent sky subtraction is required. In the Deep Coma plates, the locations of the reference sky fibers are carefully selected using images from the Dragonfly Telephoto Array. The expected g-band surface brightness of all-sky fiber locations (∼3 arcsec around each fiber) based on the Dragonfly imaging are >27.8 mag arcsec⁻². In addition to the 92 single fibers used to construct the model sky spectrum for ordinary MaNGA plates, we also devote three IFU bundles (two 19-fiber bundles, one 37-fiber bundle) to additional measurements of the sky. These additional sky fibers enable us to reach fainter surface brightness limits for stacked spectra than the regular MaNGA survey. The 1σ limiting surface brightness we are able to detect is calculated from the 1σ rms in the wavelength range of 4000–5500 Å, and is 27.6 mag arcsec⁻² for the Deep Coma plates.

To further improve the accuracy of the background estimate and to mitigate systematics, we adopt an on-and-off nodding strategy. The goal is to obtain reference "all-sky" exposures by shifting the whole field approximately 20' away, so that most of the sky fibers and science IFUs will sample the blank sky. We searched for the ideal locations for the shifts using images from the Dragonfly Telephoto Array to optimize the fraction of both the science and sky fibers on the low surface brightness region. Each of the first two plates includes nine 5-minute nodding exposures at nine different locations between the normal science exposures. Each of the last four plates includes four 15-minute nodding exposures at four different locations.

We processed our data using version 2_2_0 of the MaNGA Data Reduction Pipeline (DRP; Law et al. 2015, 2016). This version is similar to v2_1_2 released in 2017 July as SDSS DR14 (Abolfathi et al. 2018), but incorporates a number of custom modifications made specifically for the Deep Coma program. The baseline DRP first removes detector overscan regions and quadrant-dependent bias and extracts the spectrum of each fiber using an optimal profile-fitting technique. It next uses the sky fibers to create a super-sampled model for the background sky spectrum and subtracts this model spectrum from each of the science fibers. Flux calibration is then performed on individual exposures using 12 seven-fiber IFUs targeting spectrophotometric standard stars (Yan et al. 2016b). Fiber spectra from the blue and red cameras are then combined together onto a common logarithmic wavelength solution using a cubic b-spline fit. These "mgCFrame" files thus represent spectra of all 1423 MaNGA fibers from a single exposure in a row-stacked format, where each row corresponds to an individual one-dimensional fiber spectrum. The logarithmic wavelength grid runs from $\mathrm{log}\lambda$(Å) = 3.5589 to $\mathrm{log}\lambda$(Å) = 4.0151, which corresponds to 4563 spectral elements from 3621.5960 to 10353.805 Å. We do not utilize the 3D stage DRP (which combines fiber spectra into three-dimensional data cubes), and restrict our analysis to the mgCFrame row-stacked spectra.

A number of custom modifications were made to the DRP in v2_2_0 to optimize performance for observations of low surface brightness regions in the Coma cluster. First, the DRP was modified to use the 167 total sky fibers (92 single fibers plus 3 IFU fiber bundles) to construct the model sky spectrum. second, analysis of our nodded all-sky observations showed evidence for low-level systematics in the detector electronics. We added a step in the pipeline to measure and remove a 0.5 e-/pixel offset in bias between the light-sensitive detector pixels and the overscan region, compensating at the same time for a seasonally dependent 0.1 electron/pixel drift in the difference. Additionally, we found that the amplifier-dependent gain values tended to drift from one exposure to the next away from nominal at the ∼0.1% level; we added procedures to measure and correct for this effect empirically using the sky fibers in each exposure. Finally, we modified the DRP to be able to apply the flux calibration vector from the nearest (in time) ordinary science exposure to the nod exposures (for which there are no calibration stars in the 7-fiber mini bundles).

Additionally, performance analysis of early observations in the Deep Coma program revealed that scattered light and the extended (>100 pixel) profile wings of bright galaxies targeted by the Coma program were contaminating the spectra of fainter objects. We therefore redesigned our observing program to consolidate all bright targets (central and dE galaxies) onto one of the two BOSS spectrographs, and all faint targets (UDGs and intracluster light) onto the other so that these targets never share a detector.

Although these modifications substantially improve performance for the Deep Coma program relative to the DR14 baseline DRP, we find that the final stacked science spectra are nonetheless still limited by systematic residuals over large wavelength scales (>100 Å). These residuals are consistent between stacked science and nodded sky spectra within each plate, possibly due to cartridge-dependent uncertainties in fiber alignment and the detector point-spread function. For example, in the fifth plate, the stacked science spectrum for DF 17 is systematically negative in flux, but the nodded sky spectrum is systematically more negative, and the offset ranges from 0 to 10⁻¹⁸ erg s⁻¹ cm⁻² Å⁻¹. In the last four plates, we mitigate the impact of these systematics by fitting the stacked spectra of the sky subtracted nodded sky exposures with a tenth degree polynomial from 3836 to 5873 Å in the observed frame and subtracting the result from the corresponding science exposures prior to stacking science spectra. The amplitude of polynomial correction ranges from 10⁻¹⁹ to 10⁻¹⁸ erg s⁻¹ cm⁻² Å⁻¹ in the continuum and represents an important correction to the baseline flux level for extremely faint targets. We manage to match the continuum levels of stacked spectra from different plates via subtracting the above polynomial continuum before we derive any science result.

The mean S/N we achieved after all of these steps was 9.5 Å⁻¹ for DF 7, 7.9 Å⁻¹ for DF 44, and 5.0 Å⁻¹ for DF 17 in the observed wavelength range of 4500–5000 Å. This corresponds to a total integration time on source of 13.5 hr, and a total integration time on nod exposures of 4 hr.

Our main tool for modeling spectra of galaxies and UDGs in our sample is the absorption line fitter (alf; Conroy & van Dokkum 2012a; Conroy et al. 2014, 2017). alf enables stellar population modeling of the full spectrum for stellar ages >1 Gyr and for metallicities from approximately −2.0 to +0.25. With alf, we explore the parameter space using a Markov Chain Monte Carlo algorithm (emcee, Foreman-Mackey et al. 2013). The program now adopts the MIST stellar isochrones (Choi et al. 2016) and utilizes a new spectral library that includes continuous wavelength coverage from 0.35 to 2.4 μm over a wide range in metallicity. This new library, described in Villaume et al. (2017), is the result of obtaining new IRTF NIR spectra for stars in the MILES optical spectral library (Sánchez-Blázquez et al. 2006). Finally, theoretical response functions, which tabulate the effect on the spectrum of enhancing each of the 18 individual elements, were computed using the ATLAS and SYNTHE programs (Kurucz 1970, 1993). Further details of these updates to alf are described in Conroy et al. (2018). With alf, we are able to fit a two burst star formation history, the redshift, velocity dispersion, overall metallicity ([Z/H]), 18 individual element abundances, several IMF parameters, and a variety of "nuisance" parameters.

Throughout this paper, we use alf in a simplified mode. Not all the parameters are included, but only the recession velocity, age, overall metallicity [Z/H] and abundances of Fe, C,  N,  O,  Mg,  Si,  Ca,  Ti, and Na. The IMF is fixed to the Kroupa (2001) form. Instead of adopting a two burst star formation history in the standard model, the simplified mode adopts only a single-age component. We adopt this approach due to the limited S/N of the data. The intrinsic velocity dispersions of UDGs (van Dokkum et al. 2016) are assumed to be lower than both the instrumental resolution (Law et al. 2016) and the resolution of models. Therefore, we smoothed each spectrum based on the instrumental resolution of the corresponding fiber. The desired velocity resolutions (σ_D) are chosen based on the maximum instrumental resolution (maximum σ_i) and are different among three galaxies. The desired velocity resolutions are 110 km s⁻¹ for DF 7, 125 km s⁻¹ for DF 44, and 135 km s⁻¹ for DF 17. Each spectrum is smoothed to the desired velocity resolution by convolving a wavelength dependent Gaussian kernel with $\sigma =\sqrt{{{\sigma }_{D}}^{2}-{{\sigma }_{i}}^{2}}$. With alf, we fit for the velocity dispersion of the smoothed spectra and describe this property below as "resolution." We adopt flat priors from 500 to 10,500 km s⁻¹ for recession velocity, 10–500 km s⁻¹ for resolution, 1.0–14 Gyr for age, and −1.8 − +0.3 for [Fe/H]. The priors are zero outside of these ranges. For each spectrum, we fit a continuum in the form of a polynomial to the ratio between model and data. The polynomial order is (λ_max − λ_min)/100 Å. During each likelihood call, the polynomial divided input spectrum and model are matched. For computational convenience, the continuum normalization occurs in two separate wavelength intervals, 3800–4700 Å and 4700–5700 Å (Conroy & van Dokkum 2012b). In this paper, we only use the data taken by the blue spectrograph. This allows us to avoid additional issues associated with the numerous bright atmospheric OH features in the red. Pixels near bright sky lines in the blue were masked prior to the fitting.

In this section, we examine how well the recession velocity, age, and [Fe/H] can be recovered with alf. We have constructed a mock spectra data set with 20 realizations at a range of S/Ns from 5 to 50 Å⁻¹. We assume that the mock spectra have a true recession velocity of 7200 km s⁻¹, a velocity dispersion of 50 km s⁻¹ and a metallicity of [Fe/H] = −0.8. We test a set of mock spectra with ages of 10 Gyr and the other with ages of 3 Gyr. The data are fit over two wavelength ranges, 3800–4700 Å and 4700–5700 Å. The fitting ranges are the same as what we apply to the UDG spectra. In addition, the mock spectra are convolved by a 100 km s⁻¹ Gaussian kernel since we need to smooth the UDG spectra. The results are shown in Figure 2 as a function of S/N.

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The S/N of our UDG spectra lie between 5 and 10. From the mock test of the old stellar population, we estimate that their recession velocities, log(age/Gyr), and [Fe/H] can be reliably measured with an uncertainty of 14–29 km s⁻¹, 0.14–0.22, and 0.21–0.39 dex, respectively. From the mock test of the 3 Gyr stellar population, we estimate that their recession velocities, log(age/Gyr), and [Fe/H] can be reliably measured with an uncertainty of 16–36 km s⁻¹, 0.14–0.23, and 0.31–0.52 dex, respectively. The recession velocity can be recovered at a good accuracy for mock spectra at all S/Ns. The bias in the recovered parameter is small even at low S/N: for log(age/Gyr) and [Fe/H], the bias is of the order of 0.01–0.04 and 0.05–0.12 dex, well within the statistical uncertainties.

In this section, we present our constraints on the redshift, age, and metallicity for DF 7 (Figures 3 and 4), DF 44 (Figures 5 and 6), and DF 17 (Figures 7 and 8). For each parameter, we present the median values and the 16th and 84th percentile of the posterior distributions. Top panels of Figures 3, 5, and 7 show the normalized median stacked spectra of DF 7, DF 44, and DF 17 with the inner 19 fibers over all exposures in black, and our best-fit model spectra in red. The best-fit model spectra are generated with parameters at the minimum χ².

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The bottom panels of Figures 3, 5, and 7 show the fractional residuals in black, compared with flux uncertainty in the yellow shaded regions. The comparison between the residual and data uncertainty indicates that the fitting results for all three UDGs are successful, as the residuals are all consistent with the flux uncertainty. For DF 7 and DF 44, several prominent absorption line features that are well-known for estimating stellar age and metallicity, such as Hδ, Hγ, Hβ, Mg b, and the G-band at ∼4300 Å are all well described by the best-fit model. The Ca ii H and K lines are very prominent as well. The spectrum for DF 17 has a much lower S/N, but key features such as Hγ and Hβ are all clearly visible and well described by the best-fit model.

In Figures 4, 6, and 8, we show the projections of posteriors for several parameters we fit in alf, including the recession velocity, log(age/Gyr), and [Fe/H] (Foreman-Mackey 2016). As described in Section 2, the input spectra have been smoothed to the desired velocity resolutions, which are 110 km s⁻¹ for DF 7, 125 km s⁻¹ for DF 44, and 135 km s⁻¹ for DF 17. Therefore, when we fit the spectra with alf, the velocity dispersion of our model spectra cannot be taken as a description of the intrinsic velocity dispersion of our targets. To avoid confusion, we describe this property as "resolution" in Figures 4, 6, and 8. Although we do not attempt to derive reliable velocity dispersion from the smoothed spectra, it is reassuring to see that the resolution we derive is roughly consistent with the sum in quadrature of the measured velocity dispersion from van Dokkum et al. (2016) and the desired resolution. For all derived parameters, the values of parameters at 16th, 50th, and 84th percentiles of posteriors are shown as dashed lines in the 1D histograms and contours in the 2D histograms. Outliers are shown as dots. The blue lines in the 2D histograms mark the values of parameters at minimum χ².

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We find that the recession velocities of DF 7, DF 44, and DF 17 are ${6600}_{-26}^{+40}$ km s⁻¹, ${6402}_{-39}^{+41}$ km s⁻¹, and ${8311}_{-43}^{+43}$ km s⁻¹. The uncertainties are consistent with the mock data tests. For DF 44, our result is consistent with the recession velocity measured by van Dokkum et al. (2016, 2017). They measured the kinematics of DF 44 using a 33.5 hr integration spectra observed by the DEIMOS spectrograph on the Keck II telescope, and obtained a recession velocity of ${6398}_{-6}^{+6}$ km s⁻¹ for DF 44. The recession velocity of DF 7 is consistent with the measurement by Kadowaki et al. (2017, cz = 6587 ± 33 km s⁻¹). The derived recession velocities confirm that all of the three UDGs are members of the Coma cluster.

The ages of DF 7, DF 44, and DF 17 are ${8.57}_{-2.93}^{+4.11}$ Gyr, ${10.50}_{-4.39}^{+3.00}$ Gyr, and ${7.61}_{-4.72}^{+5.09}$ Gyr. The iron abundances, [Fe/H], are $-{1.03}_{-0.34}^{+0.31}$, $-{1.25}_{-0.39}^{+0.33}$, and $-{0.83}_{-0.51}^{+0.56}$, respectively. The uncertainties of both log(age/Gyr) and [Fe/H] are similar to what was derived from the mock tests. From the 2D posterior distributions in Figures 4, 6, and 8, one can see that there are no strong degeneracies between the resolution and age or metallicity. There is a modest degeneracy between age and metallicity, as expected (Worthey 1994). The age posteriors are not perfectly Gaussian, but the local maximum in the marginalized age posteriors are all in the old age regime. The probabilities that the stellar populations are young are very low. The 16th percentiles of age posteriors are 5.6, 6.0, and 2.9 Gyr, and the 2.5th percentiles of age posteriors are 2.6, 2.7, and 1.4 Gyr for DF 7, DF 44, and DF 17, respectively. In addition, the mock test shows that alf is able to recover the true ages for young (3 Gyr) stellar populations. The primary result of this paper is that all three UDGs are old and metal-poor.

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In this section, we add the g–r color as an additional constraint to our stellar population parameters. We measure the color from the Dragonfly data within an aperture of 6'', which is similar to the regions of our stacked spectra. The measured g–r colors are 0.57 ± 0.05 mag, 0.53 ± 0.05 mag, and 0.65 ± 0.06 mag, respectively. In Figure 9, the normalized 1D posterior distributions of the g–r color derived from fitting the continuum-normalized spectra are shown in the top panels in black. We assume the probability density of the observed g–r colors to be a normal distribution and take the measured color and uncertainty as the mean and standard deviation of this normal distribution. The top panels show that the differences between the observed color and the inferred color from the models are no more than 0.02 mag for both DF 7 and DF 44. The good agreement between the inference from fitting spectra and the observed colors suggests that reddening is low in both UDGs, and therefore their gas and dust content is likely low. For DF 17, the color from photometry is slightly redder than the color from the spectral models, but the difference is smaller than 1σ uncertainty. Near-infrared photometry would be helpful to confirm whether DF 17 is dust reddened.

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We use the observed g–r color to further constrain the model space. We re-weight the MCMC chains based on the probability density of the broadband g–r color, and generate new posterior distributions by bootstrap resampling. The middle and bottom panels of Figure 9 show the joint posterior distributions of log(age/Gyr) and [Fe/H] in red, respectively. Compared with the posterior distributions obtained from spectroscopy alone, we find that the inclusion of photometry results in slightly tighter constraints for DF 44 and DF 7. This is at least partially due to the relatively large errors on the observed colors—more precise colors would likely result in stronger constraints on the age and metallicity. The results from these joint constraints are also shown in Table 1. For DF 17, an additional constraint from photometry provides us with a slightly older and less metal-poor stellar population.

We calculate the stellar mass using the g-band total integrated magnitude from van Dokkum et al. (2014). The g-band integrated magnitudes for DF 7, DF 44, and DF 17 are $-{16.0}_{-0.2}^{+0.2}$ mag, $-{15.7}_{-0.2}^{+0.2}$ mag, and $-{15.2}_{-0.2}^{+0.3}$ mag. The g–r color within 6''  from the galaxy centers are 0.57 ± 0.05 mag, 0.53 ± 0.05 mag, and 0.65 ± 0.06 mag. We adopt the r-band solar absolute magnitude as 4.76 from Blanton et al. (2003). r-band K-corrections are calculated based on the best-fit model spectra, and K_r ∼ −0.02. The rest-frame r-band mass-to-light ratio for DF 7, DF 44, and DF 17 are taken from the results constrained jointly by spectra and photometry within a radius of 6'', and they are ${1.56}_{-0.28}^{+0.47}$ M_⊙/L_⊙, ${1.64}_{-0.38}^{+0.54}$ M_⊙/L_⊙, and ${1.80}_{-0.66}^{+0.51}$ M_⊙/L_⊙. Therefore, the stellar masses for the three UDGs are ${5.24}_{-1.22}^{+2.27}\times {10}^{8}$M_⊙, ${4.03}_{-1.05}^{+1.87}\times {10}^{8}$M_⊙, and ${3.11}_{-1.15}^{+1.28}\times {10}^{8}$M_⊙, respectively. van Dokkum et al. (2016) has calculated the stellar mass for DF 44 using its i-band luminosity and g–i color. Our result is consistent with theirs (M_* ≈ 3 × 10⁸ M_⊙).