SDSS-IV MaNGA: The MaNGA Dwarf Galaxy Sample Presentation

Here, we describe the fitting process to the SB profiles of the MaNDala galaxies.

As it is often in the literature, we assume that the SB profiles of the galaxies are well-described by a Sérsic (1963) function:

$$\begin{eqnarray}&&I(R)={I}_{e}\exp \left(-{b}_{n}\left[{\left(\displaystyle \frac{R}{{R}_{e}}\right)}^{1/n}-1\right]\right),\end{eqnarray} \tag{ 2 }$$

where R_e is effective radius, n is the Sérsic index, I_e is the amplitude of the SB at R_e , and b_n is such that γ(2n, b_n ) = Γ(2n)/2 (where Γ and γ are respectively the complete and incomplete gamma functions). In this paper, we use the analytical approximation for b_n reported in Ciotti & Bertin (1999), which we assume to be valid for 0.5 ≤ n ≤ 10. We note that, in this paper, the variable R refers to the radius along the semimajor axis of the SB profiles. Therefore, the effective radius, R_e , reported here will refer to the effective radius along the semimajor axis.

The effects of seeing on the SB profiles of MaNDala galaxies are introduced by assuming that the PSF from the DESI images are well-described by a Moffat (1969) function with β = 2.480, 2.229, and 1.999 for the g, r, and z bands, respectively, (DESI help desk and Imaging Survey Experts, private communication). Thus, here we convolve the Sérsic profile, Equation (2), by a Moffat PSF (for a discussion, see Trujillo et al. 2001); we will denote the above by I_conv. That is, assuming that the 1D profile is in elliptical coordinates $(x,y)=(\xi \cos \theta ,\xi (1-\epsilon )\sin \theta )$, then the convolved SB along the semimajor axis, θ = 0, is given by

$$\begin{eqnarray}&&{I}_{\mathrm{conv}}(\xi )=(1-\epsilon )\int \int \mathrm{PSF}(\xi ^{\prime} ,\theta ^{\prime} ,\xi )I(\xi ^{\prime} )\xi ^{\prime} d\xi ^{\prime} d\theta ^{\prime} .\end{eqnarray} \tag{ 3 }$$

Here, is the ellipticity, which for simplicity we assume to be constant and equal to its average value for each galaxy.

The methodology to determine the best-fit parameters of Equation (2) for every galaxy in the MaNDala sample is as follows:

• 1.  
  As an initial guess, we use the R_e from the photometric analysis described in a previous subsection and compute ${\mu }_{e}(=-2.5\mathrm{log}{I}_{e})$ from the observed SB profiles. Initially, we assume that all galaxies have a Sérsic index of n = 2.5. ²⁰
• 2.  
  We sample the best-fit parameters that minimize the likelihood function $L\propto {e}^{{\chi }^{2}/2}$ by using the Markov Chain Monte Carlo method (described in Rodríguez-Puebla et al. 2013) and the initial values described in the previous item. We run 10 chains consisting of 10⁴ elements each, and χ² is given by

  $$\begin{eqnarray}&&{\chi }^{2}=\sum _{i=1}^{{N}_{\mathrm{bin}}}{\left(\displaystyle \frac{{\mu }_{i,\mathrm{model}}-{\mu }_{i,\mathrm{obs}}}{{\sigma }_{i,\mathrm{obs}}}\right)}^{2},\end{eqnarray} \tag{ 4 }$$

  where N_bin is the number of radial bins in the observed SB profiles μ_i,obs of each galaxy and σ_i,obs is its corresponding error, and μ_i,model represents the SB profiles given by Equation (2). As a result, we find the best-fit parameters to μ_e , n, and R_e that minimize Equation (2).
• 3.  
  Next, we use the best-fitting parameters and the covariance matrix constrained above as the initial guess for finding the best-fit parameters of the convolved Sérsic profile, I_conv(R). We do so by replacing in Equation (4) μ_model by μ_conv−model. Here, we sample three chains consisting of 500 elements each. ²¹

The best-fitting parameters described here are fitted to each band independently. That is, we do not make any assumption on the wavelength dependence of the Sérsic profile parameters. The bottom right panel of Figure 3 shows an example of the best-fit Sérsic profiles for the observed SB profiles of MaNGA-8145-3702 galaxy. The inset in the same panel shows the reduced χ² defined as χ²/(d. o. f), where d. o. f = N_bin − 3.

pyPipe3D subtracts the fitted stellar population models from the original data cube to create a cube comprising only the ionized gas emission lines (and the noise). Individual nebular emission line fluxes are then calculated segment-by-segment using a weighted momentum analysis based on the kinematics of H α (Sánchez et al. 2022; Lacerda et al. 2022). From the obtained emission line maps, we integrate the ionized gas line fluxes within the two apertures mentioned above, R_e and the FoV of each galaxy. To avoid contamination of any nearby star within our apertures, we used a set of star masks derived from the GAIA star positions. These star masks are described in Sánchez et al. (2022). The nebular emission lines used in this work are: H β, H α, [O iii]λ5007, [N ii]λ6584, [S ii]λ6716, [S ii]λ6731, and [O i]λ6300. We estimate the total equivalent widths (EW) of H α within a given aperture by dividing the total emission line flux by the integrated stellar continuum within the same aperture.

To ensure that our photometric analysis is consistent with previous results, here we present a series of comparisons between our results and those available in the NSA Catalog. We recall that our analysis is based on the photometry from the DESI Legacy Imaging Surveys, while in the NSA Catalog, the shallower SDSS photometry has been used.

In the upper panels of Figure 5, we show the comparisons of the Sérsic index and R_e ²⁵ derived from our photometric analysis and Sérsic fit in the r-band versus those given in the NSA Catalog. ²⁶ In both plots, we see a good agreement with the NSA results. However, in both cases, when reaching the largest values, the dispersion in the points becomes larger. In the case of the index n, it is noticeable that, for the largest values reported by the NSA (n_r > 2), we find smaller values, mostly between 1 and 2, which are more consistent with smaller and LTG galaxies. The opposite occurs in the case of R_e , for which, in general, our estimations seem to be larger than those reported in the NSA. These panels both exhibit some outliers. We checked if the large differences between the Sérsic indices and R_e derived by us and those reported in the NSA Catalogue for those objects may be due to bad fits of the SB profiles; however, the majority of them have χ² values below 3 for both plots. A possible source of the differences could be the fact that the NSA fits use an extrapolation while ours use only observed points with the SB profiles.

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In the two bottom panels of Figure 5, we show the comparisons between our estimations of the apparent magnitudes in the g, r, and z bands versus those from the NSA Catalog. The NSA apparent magnitudes were derived using the absolute ones retrieved directly from their catalog. In all panels, we also include the Pearson correlation coefficient (r). As in the previous plots, in general there is a good agreement, in particular in the g and r bands, while for the z band, the dispersion seems larger, which is also visible in its low r value.

Also, Arora et al. (2021) recently performed a photometric analysis for 4585 MaNGA galaxies using DESI data. For the 71 galaxies that we have in common with their sample, we performed comparisons for some global properties provided by them, such as apparent magnitudes, R_e , and μ_eff, and our results are consistent with theirs (Pearson coefficients of ∼0.9 for the first two and ∼0.8 for the last one). It is important to mention that the results given by Arora et al. (2021) are not based on Sérsic fits; instead, they are taken directly from the photometric analysis, meaning that these comparisons are not direct.

In the left panels of Figure 6, we show the individual SB profiles for all the galaxies in our sample in the g, r, and z bands (for each band, the radii are normalized to their corresponding R_e derived from the Sérsic fit). On top of them, an average profile is shown for each band. In dashed lines and shaded areas, the mean depth limits for each band of the MaNDala sample and the standard deviations are shown, respectively (see Section 4.2 for the details of their derivations). For comparison, the red solid line shows the SDSS depth limit in the r band at 24.5 mag arcsec⁻² (see, for example, Strauss et al. 2002), which emphasizes the difference in photometric depth achieved by DESI and SDSS image data. These plots give an idea of the difference between the photometric depths of the DESI data in the three bands. We can see that the flattening of the average profile rises to brighter SB values when moving from the g to the z band. This is relevant because the flattening of these profiles is related to the radius of the galaxies in which the brightness of the sky is starting to dominate in the data. For the g band, we are able to obtain the best SB profiles, as on average, they arrive out to ∼5 R_e before the profiles start to flatten. The flattening moves to inner regions of the galaxies when moving to redder bands, as it occurs at ∼4.5 R_e and ∼3.5 R_e in the g and z bands, respectively (note that, as shown in Figure 7 below, the measured effective radii are roughly similar in the three bands). It is also important to mention that NSA SB profiles for these galaxies can extend to larger radii, beyond the photometric depth limits of the SDSS images (see middle left panel of Figure 6). In contrast, the profiles from our analysis naturally extend beyond the SDSS depths up to the DESI limits, showing the shapes of the profiles obtained at those radii.

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In order to make evident any systematic difference provided by the morphology, in the top right panel of Figure 6, we reproduce the profiles in the r band of the top left panel of the same figure, but color-coded according to the morphology: red and blue for the early and late types, respectively. In a second panel, we also show the individual color g − r profiles for our sample, color-coded in the same way as in the previous panel. On top of both panels, a median profile is shown in magenta for the early-type galaxies and in dark blue for the late ones. These general profiles are derived binning the early and late types' distributions with a bin size of 0.4 in units of R_e and calculating the median value for each one. The error bars correspond to the 16th–84th percentiles of the distributions within each bin.

According to the right panel of Figure 6, the r-band SB profiles of the dwarf LTGs are less scattered than those of the dwarf ETGs (note that the distributions of magnitudes or masses of both subsamples are roughly similar, and given that LTGs are much more numerous than ETGs, the greater dispersion of the latter with respect to the former is hardly an effect of sample size). On average, the ETGs have slightly higher SB at all radii than the LTGs. As for the g − r color gradients, they fluctuate with radius but around a fixed value; that is, they tend to be flat or slightly positive, both for dwarf LTGs and ETGs. As expected, the latter are redder than the former.

Making use of our photometric results, we can now perform a basic characterization of the MaNDala sample, such as identifying its limits, and even testing if all the objects are consistent with the expected behavior for DGs.

Histograms of the Sérsic index, effective radius, apparent and absolute magnitudes, central SB, central color, and color gradients for the three DESI photometric bands used in this work for our sample are shown in Figure 7. Color gradients are defined as

$$\begin{eqnarray}&&{\rm{\nabla }}({\lambda }_{1}-{\lambda }_{2})=\displaystyle \frac{{\rm{\Delta }}({\lambda }_{1}-{\lambda }_{2})(R)}{{\rm{\Delta }}(\mathrm{log}R)}.\end{eqnarray} \tag{ 7 }$$

We evaluate ∇(λ₁ − λ₂) at 0.1 and 1 R_e . All of these properties are results of the Sérsic fits explained in Section 4.2.1. These distributions show the natural limits of the sample in brightness, which are summarized in Table 1, along with other relevant characteristics. In general, we can see that the MaNDala sample is indeed biased toward bright DGs, as suggested by the M_* distribution shown in Figure 1. Moreover, the dashed magenta line in the absolute magnitude histogram represents the limit imposed to select the galaxies in our sample (NSA M_g > −18.5). It is noticeable that a few of our galaxies surpass this limit while using the results derived with the DESI photometry and with our Sérsic fits, and as shown in the previous section, some galaxies tend to give brighter magnitudes when compared with those available in the NSA Catalog.

Table 1. Statistical Parameters of the Photometric Properties in the r Band of the MaNDala Sample and for the g − r Colors and Color Gradients ^a

	Max	Min	Mean	Median	σ
Full sample
nr	8.30	0.50	1.64	1.25	1.22
${R}_{{e}_{r}}$ [kpc]	12.49	0.15	2.71	2.45	1.76
mr [mag]	17.61	12.28	16.18	16.27	0.87
Mr [mag]	−10.63	−19.27	−17.38	−17.48	1.05
${\mu }_{{0}_{r}}$ [mag arcsec−2]	22.20	6.30	19.29	19.98	2.58
g-r [mag]	1.61	−0.27	0.46	0.44	0.16
∇(g − r) [mag dex−1]	0.66	−1.67	−0.05	−0.06	0.25
Early Types
nr	8.30	1.18	2.77	2.50	1.60
${R}_{{e}_{r}}$ [kpc]	6.02	0.48	1.93	1.33	1.46
mr [mag]	17.61	15.16	16.44	16.32	0.59
Mr [mag]	−16.52	−18.69	−17.40	−17.26	0.57
${\mu }_{{0}_{r}}$ [mag arcsec−2]	21.71	6.64	16.63	16.98	3.15
g − r [mag]	1.61	0.27	0.59	0.57	0.24
∇(g − r) [mag dex−1]	0.38	−0.47	−0.05	−0.07	0.20
Late Types
nr	8.15	0.50	1.38	1.15	0.94
${R}_{{e}_{r}}$ [arcsec]	12.49	0.15	2.91	2.58	1.79
mr [mag]	17.51	12.28	16.14	16.24	0.88
Mr [mag]	−10.63	−19.27	−17.42	−17.53	1.02
${\mu }_{{0}_{r}}$ [mag arcsec−2]	22.20	6.30	19.89	20.23	2.00
g − r [mag]	0.71	0.20	0.44	0.44	0.10
∇(g − r) [mag dex−1]	0.66	−1.67	−0.06	−0.06	0.26

Note.

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From Figure 7, we see that the Sérsic index of dwarf ETGs tends to be higher and with a greater spread than for LTGs (there is also a small trend of lower n values as the band is redder, especially for ETGs). As reported in Table 1, the medians of n_r for ETGs and LTGs are 2.50 and 1.15, and the 1σ scatters are 1.60 and 0.94, respectively. A similar trend is observed for μ₀: ETGs tend to have higher central SBs and a greater spread than LTGs (median μ_0,r of 16.98 and 20.23 mag arcsec⁻², respectively. Regarding the sizes, R_e depends little on the photometric band and tends to be smaller for the ETGs than for the LTGs (note that the absolute magnitude distributions are similar for both groups): the median R_e,r are 1.33 and 2.58 kpc, respectively. In general and as expected, the dwarf ETGs are significantly more compact than the dwarf LTGs; the ratio of the median r-band luminosity to the median effective radius for ETGs is ≈1.7 times higher than for LTGs. As for the colors, ETGs are redder on average than LTGs (medians of g − r of 0.57 and 0.44 mag, respectively) but with a broader distribution. Finally, the g − r color gradients of the MaNDala galaxies oscillate around 0, meaning that the gradients are nearly flat.

Using the ellipticity profiles derived from our analysis, we can interpolate the value at any radius in the r band. In particular, we can also interpolate an approximation of the radius that contains 90% of the light (r₉₀), using the cumulative flux profiles for each galaxy (upper right panel in Figure 3), and then interpolate the at that radius for all the galaxies in the sample. Assuming these values as the overall ellipticities for the galaxies, they can be converted into inclinations ($\cos i=b/a$). The MaNDala sample has galaxies with various inclinations, with a mean of 5383 (_mean = 0.43): 18 galaxies (∼13% of the sample) are highly inclined, i > 70° ( ∼ 0.66 ), while 14 (∼10% of the sample) exhibit low inclinations, i < 30° ( ∼ 0.13). Recall that cuts were applied to derive all the profiles, including the cumulative flux one, which means that the r₉₀ may be underestimated.

In Figure 8, we show the relation between the mean effective SB (Graham & Driver 2005), which is defined as

$$\begin{eqnarray}&&\langle {\mu }_{e}\rangle =m+2.5{\mathrm{log}}_{10}(2\pi {R}_{e}^{2}),\end{eqnarray} \tag{ 8 }$$

and the g − r color and the color gradient ∇(g − r) as well. To calculate 〈μ_e 〉_g , we use our estimations of the Sérsic apparent magnitude in g, and the R_e estimated in the g band. There is no significant trend of the g − r color with 〈μ_e 〉_g , neither for ETGs nor for LTGs. We use crosses and diamonds to indicate field and group dwarfs, respectively. There is no clear segregation in this plot, due to environmental characterization; however, the highest-SB dwarfs in the sample are all ETGs in denser environments, D_host ≤ 1 Mpc. Regarding the g − r gradient, for the dwarfs with 〈μ_e 〉_g < 22 (high SBs), positive gradients are more common, while for those with lower SBs, flat or negative gradients are more more common. There is no clear segregation due to environment.

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A classical way to characterize dwarfs is using the so-called Kormendy relations (Kormendy 1977, 1985), which relate galaxy parameters that can be inferred by a Sérsic fit. In Figure 9, we show one of these relations, which compares the absolute magnitude in the g band and R_e in the same band. In this plot, we aim to locate the MaNDala sample within a summary similar to the one presented by Poulain et al. (2021), which compares several DG samples (Poulain et al. 2021; Ferrarese et al. 2020; Carlsten et al. 2020; Eigenthaler et al. 2018), and some Ultra Diffuse Galaxy (UDGs) samples (Lim et al. 2020; van Dokkum et al. 2015). Along with these samples, we present results for normal (giant) early- and late-type galaxies represented with solid red and blue lines. Effective radii were obtained from the Meert et al. (2013, 2016) catalogs based on the SDSS DR7 and the morphologies from the Huertas-Company et al. (2011) catalog. We compute these relations for galaxies with spectroscopic redshifts z ≤ 0.07 in order to avoid biases due to the PSF resolution of the SDSS. The g-band magnitudes were K-corrected and evolution-corrected to z = 0 following Dragomir et al. (2018) and Rodríguez-Puebla et al. (2020b). We see that our sample populates the brighter end of the distribution for DGs, indicating that these objects are indeed bright DGs, with the exception of a few galaxies that fall below and within the cloud of DGs for magnitudes fainter than −16. For a given M_g , the radii of our early-type dwarfs agree with the low-luminosity end of the Meert et al. (2013, 2016) catalogs of normal ETGs, though the former have a very large scatter. For our late-type dwarfs, they tend, on average, to have larger radii than the low-luminosity end of normal LTGs. In particular, there is a fraction of MaNDala galaxies with very large radii, R_e > 3 kpc, for their luminosities. They appear as an extension to higher magnitudes of the UDCs depicted in this figure. In general, our results show that the R_e − M_g relation tends to flatten, especially for LTGs, in the range −19 ≤ M_g < −15, though with a large scatter.

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In Figure 10, we present the full Kormendy diagrams for the g band. For the purpose of comparison, we present along with the MaNDala sample the ones described in Habas et al. (2020) and Poulain et al. (2021), with gray dots. In the upper panels, the relations between 〈μ_e 〉 and absolute magnitude M_g (left panel) and R_e (right panel) are presented. In the left plot, in general terms, the mean SB increases for brighter galaxies, which is visible as our sample continues the tendency drawn by the Poulain et al. (2021) sample. However, those low-SB galaxies with 〈μ_e,g 〉 ≳ 24.5 mag arcsec⁻² are outliers in this relation. These galaxies may be so-called UDGs, ²⁷ and we have already noticed them in the R_e − 〈μ_e 〉 diagram shown in Figure 9. Note also that our dwarf ETGs have, on average, smaller radii and higher mean effective SBs than the dwarf LTGs, while their magnitudes are similar. As for the right-side plot, most of the MaNDala galaxies lie in a diagonal band, where for larger R_e , the 〈μ_e,g 〉 becomes lower. According to Equation (8), this is due to the short range in absolute magnitudes of our sample. However, comparing the MaNDala sample against a larger and less luminous sample, such as the one given by Poulain et al. (2021), makes it easier to understand that MaNDala is an extension of this sample to larger/brighter dwarfs. In any case, there are dwarfs that seem to be outliers from the main trend, i.e., those with 〈μ_e,g 〉 ≳ 24.5 mag arcsec⁻² and R_e ≳ 1.5 kpc (these are roughly the criteria to define UDGs; see Poulain et al. 2021; van Dokkum et al. 2015). These galaxies also seem to be outliers in the M_g − 〈μ_e 〉 and M_g − R_e diagrams, and as mentioned above, they may be UDG candidates. Note also that there are a few MaNDala galaxies that strongly deviate from the main trend, but at the other extreme, there are those with high SBs and small radii for their luminosity, i.e., very compact objects. These are mainly ETG dwarfs.

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We can analyze the details of the individual galaxies that lay in the two already identified outlier groups. Starting with the UDG candidates, we find 12 galaxies that fulfill the aforementioned conditions (〈μ_e,g 〉 ≳ 24.5 mag arcsec⁻² and R_e ≳ 1.5 kpc). However, five of them have reduced χ² values for their g-band Sérsic fit larger than 2.5; this leads to think that their location in the Kormendy diagram may be inaccurate. Another galaxy of this group exhibits a small χ² value of its g-band fit (of 0.6), which may also indicate that this fit may not be optimal. The remaining six galaxies could be considered as UDG candidates. Four of them, manga-8487-9101, manga-9494-6103, manga-9876-12704, and manga-10517–12704, exhibit early-type morphologies; however, the last two show a clearly bright center. The other two, manga-10221-12704 and manga-10841-12705, have late-type morphologies. However, the last one shows signs of interaction. On the other hand, to select the MaNDala galaxies with large 〈μ_e 〉 values and small radii, we impose an arbitrary limit of 〈μ_e 〉 ≤ 20 mag arcsec⁻². Only three galaxies surpass this limit; however, one of them also have χ² values for their g-band Sérsic fit larger than 2.5. For the remaining two (manga-8727-3702 and manga 9495-1901), their χ² values are close to unity (∼0.8) and we can assume they are indeed very compact and bright DGs.

The lower panel of Figure 10 is similar to Figure 9, but indicating now the field/group information for our sample. As can be seen, there is not a clear segregation of the MaNDala galaxies by this environmental characterization in the M_g − R_e diagram. We have verified that this segregation does not appear in the other diagrams either. We also do not observe a notable segregation between central and satellite dwarfs.

Finally, in Figure 11, we locate the MaNDala galaxies in the M_*–R_e diagram, shown as stars (color-coded according to their morphological type as in Figures 9 and 10), along with all the DGs in the NSA Catalog, selected with the same criteria as the ones in our sample. The resulting 25,998 NSA galaxies are traced by gray contours. The vast majority of the MaNDala galaxies are within the 1σ distribution of the NSA Catalog. In solid lines, we show two of the mass–size relation fits reported by Nedkova et al. (2021), corresponding to quiescent and star-forming galaxies in red and blue respectively (in Section 5.4, we will show that almost all the LTG dwarfs are star-forming). Both fits were derived for galaxies in a redshift range of 0.2 < z < 0.5, and for the entire range of M_* considered in their sample (10⁷ M_⊙ < M_* < 10^11.6 M_⊙). We also show the fits provided by Lange et al. (2015) for ETGs and LTGs from the GAMA local survey, using their morphology cut, in red and blue dashed lines, respectively. In addition, we compare to the M_* – R_e relationship derived from the effective radii reported in Meert et al. (2013, 2016) catalogs (as in Figure 9) and the stellar masses for this survey as derived in Rodríguez-Puebla et al. (2020b). All the plotted mean relations agree well with our results for the MaNDala galaxies, both for LTGs and ETGs. On average, the former are larger than the latter at a given stellar mass.

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In Figure 12, we present the Baldwin–Philips–Terlevich N ii diagram (BPT; Baldwin et al. 1981) for the MaNDAla galaxies, using the corresponding emission line fluxes integrated within the FoV of each galaxy. The BPT diagram, as well as other line diagnostic diagrams (Veilleux & Osterbrock 1987; Kewley et al. 2001), are used to distinguish the ionization mechanisms of nebular gas, which can be associated with active galactic nuclei (AGN), SF, or hot old stars. Based on the BPT-N ii diagram and on the H α EW, we attempt a classification of the SF activity level of MaNDala galaxies, following the criteria discussed in Sánchez et al. (2014), Cano-Díaz et al. (2016), and Cano-Díaz et al. (2019). Three types of galaxies are defined:

• 1.  
  Star-forming (SFg), those with EW(H α) > 6 Å and below the Kewley line (black solid line in Figure 12; Kewley et al. 2001);
• 2.  
  Passive (P; also referred to as quiescent, quenched, or retired), those with EW(H α)<3 Å independently of their position in the BPT diagram; and
• 3.  
  Transitioning (T), those with 3 Å ≤ EW(H α) ≤ 6 Å.

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Applying the above criteria, we find that 115 galaxies (92%) are SFg, five are P galaxies (4%), and five are T (4%). The blue, red, and green symbols in Figure 12 show the SFg, P, and T galaxies, respectively, while closed circles and open triangles are for the LTG and ETG dwarfs, respectively. In Figure 12, only two P galaxies are plotted. This is because the Hα and [O iii] lines of the other three P galaxies are very low, such that the line ratios for them are well outside the ranges of the axes. It can be definitively stated that the great majority of our DGs in the MaNGA sample have signatures of being SFg. Among the dwarf LTGs, 96% are SFg, 2% are T, and 2% are P. For the dwarf ETGs, these fractions are 75%, 12.5%, and 12.5%, accordingly. Thus, even for the ETGs, most of the dwarfs are SFg galaxies. On the other hand, we did not find significant signatures of AGN in any MaNDala galaxy when using the BPT diagram; however, further and more detailed analysis is required in order to exclude the possibility of finding nuclear activity in any MaNDala galaxy, as previous studies of dwarf galaxies observed in MaNGA have found AGN signatures (Mezcua & Domínguez Sánchez 2020; Penny et al. 2018, with samples selected to have galaxies with: M_* < 3 and 5 ×10⁹ M_⊙, respectively). In summary, most of dwarf galaxies in the MaNGA survey are SFg without signatures of AGN contribution. In Section 5.4.3, we will explore the SFR-M_* relationship and show that our DG sample is a low-mass extension of the main sequence of SFg galaxies.

We use the (mass- and luminosity-weighted) stellar age and metallicity maps based on the SPS analysis from pyPipe3D described in Section 4.3 to estimate the respective (mass- and luminosity-weighted) integrated ages and metallicities: Age_mw, Age_lw, Z_⋆,mw, and Z_⋆,lw, for each MaNDala galaxy. We also use the index maps to obtain the integrated D4000 index, defined as the ratio between the continuum flux within 4050–4250 Å and 3750–3950 Å (Sánchez et al. 2016b). In the VAC, the above quantities are reported within the FOV and R_e for each individual galaxy, but in the present work, unless otherwise specified, we present these results within the FOV.

The two upper left panels of Figure 13 show Age_mw and Age_lw versus M_*, respectively, for our DG sample (averaging of the SSPs' ages is logarithmic, see Section 4.3). The colors and symbols are as in Figure 12. The isodensity contours in the same figure present the results for the whole MaNGA sample. As for M_*, we use the masses from the NSA catalog. The masses calculated with pyPipe3D from the MaNGA data cubes are, on average, slightly lower than those from the NSA catalog, after passing to the Chabrier IMF; this may be due to aperture effects. For a more detailed discussion, see Sánchez et al. (2022).

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According to the left panels in Figure 13, low-mass galaxies, and dwarfs in particular, show a wide range of mass-weighted ages, the latter with a median of 6.2 Gyr and 16th–84th percentiles of 7.1–4.2 Gyr; see the right panel for the full distribution. On average, these ages are slightly lower than those of the massive galaxies in the MaNGA survey. The situation is different for the light-weighted age: dwarfs have much lower ages than massive galaxies, and with a small scatter. The median and 16th–84th percentiles of Age_lw are 0.4 and 0.6–0.3 Gyrs, respectively. The few dwarfs with Age_lw > 1 Gyr are passive or in transition. Unlike Age_mw, which has a similar distribution for dwarf LTGs and ETGs, the values of Age_lw for dwarf ETGs tend to be larger than those for dwarf LTGs. The lower left panel of Figure 13 shows the logarithmic differences of the mass- and light-weighted ages for the MaNDala and the whole MaNGA samples. For massive galaxies, this difference is on average small, with a median of 0.18 dex. For the dwarfs, however, the differences are very large, with a median of 1.15 dex, and with a large scatter; see the right panel for the full distribution. The differences are smaller on average for dwarf ETGs than for the LTG ones. The mass-weighted age is biased toward older stellar populations, which informs us about when a significant fraction of the stellar mass was formed, while the light-weighted age is more sensitive to late episodes of SF. Therefore, the difference between Age_lw and Age_mw can be indicative of how coeval or dispersed in time the SFH of a galaxy was, or it can also indicate the presence of very recent bursts of SF, as is the case of poststarburst galaxies (Plauchu-Frayn et al. 2012; Lacerna et al. 2020; Ge et al. 2021). If the difference is very large, it indicates that there are two markedly different populations in the SSP decomposition of the observed spectrum: one that formed early and is dominant in the total stellar mass, and another associated with late SF episodes, with a low contribution to the total mass. With age differences as large as factors of 3–30, this seems to be the case for the MaNGA dwarfs.

In the right panels of Figure 13, we show the stellar mass–metallicity relationships, both for Z_⋆,mw and Z_⋆,lw, for the dwarf and whole MaNGA samples; the right panels show the respective metallicity distributions. Both the mass- and light-weighted stellar metallicities of dwarfs are significantly lower than those of massive galaxies, as many previous works have shown (e.g., Ikuta & Arimoto 2002; Hidalgo 2017; McQuinn et al. 2020); the medians (16th and 84th percentiles) of $\mathrm{log}({Z}_{\star ,\mathrm{lw}}/{Z}_{\odot })$ and $\mathrm{log}({Z}_{\star ,\mathrm{mw}}/{Z}_{\odot })$ are −0.82 (−0.54, −1.17) and −0.67 (−0.47, −0.84), respectively. This points to a decrease in the chemical enrichment with a decrease in the stellar mass of the galaxies. DGs also show a large scatter in stellar metallicities, especially in the mass-weighed one. There is a weak preference for higher metallicities in dwarf ETGs than dwarf LTGs. It is interesting that, on average, Z_⋆,lw is larger than Z_⋆,mw for dwarfs (though with a large scatter, including even some galaxies with an inverse result), while for the massive galaxies, Z_⋆,lw is mostly slightly smaller than Z_⋆,mw. The median (16th and 84th percentiles) of log(Z_⋆,mw/Z_⋆,lw) for dwarfs is −0.15 (0.03, −0.34) dex. The above results suggest that the young stellar populations of most of the dwarfs formed from gas that underwent more chemical enrichment (this probably is reaccreted gas) than the pristine gas from which the old populations formed. In contrast, the opposite is true for massive galaxies; that is, their younger stellar populations were formed from less metallic gas, probably because these systems have accreted significant amounts of mostly pristine gas over their lifetimes and their old populations were significantly enriched by early SF.

In the middle right panel of Figure 13, we plot several previous measures of Z_⋆,lw for dwarf and normal galaxies. When necessary, we homogenize to our adopted value of Z_⊙ = 0.019. The solid black line and gray shaded area show the mean relation and its scatter obtained by Kirby et al. (2013) from observations of resolved stars in Local Group dwarfs, both spheroidals and irregulars. The red crosses also correspond to determinations from the spectra of resolved stars—in this case, in local normal galaxies and DGs (Kudritzki et al. 2016, and more references therein). The works of Gallazzi et al. (2005; solid orange line) and Panter et al. (2008; solid red line) used spectral information from the SDSS and applied different analysis techniques and SPS methods for determining Z_⋆,lw. In the case of Zahid et al. (2017; blue crosses), stacked spectra of only SFg were used. In general, the MaNGA Z_⋆,lw–M_* relation obtained with pyPipe3D is in rough agreement with previous studies. As for the dwarfs, our Z_⋆,lw determinations are on average higher than those of Kirby et al. (2013) and in good agreement with those of Zahid et al. (2017) and Kudritzki et al. (2016).

In Figure 14, we show the relationship between the Age_mw/Age_lw and Z_⋆,mw/Z_⋆,lw ratios for the dwarf and whole MaNGA samples. The loci of DGs in this diagram clearly differ from the loci of the most massive galaxies. As discussed above, for dwarfs, on average, Age_mw > > Age_lw and Z_⋆,mw < Z_⋆,lw, such that they tend to lie in the lower right side of this diagram, but with a large scatter. The trend seen in Figure 14 suggests a diversity of stellar populations for dwarfs, but in most of the cases they are characterized by a dominant old population with low metallicity and the presence of late, chemically enriched populations. The above points to a diversity of (bursty) SFHs, but characterized, on average, by an intense early phase of transformation of low-metallicity gas into stars and late episodes of SF from chemically enriched gas (the latter suggests a poor or absent contribution of pristine gas accretion during the late evolution of dwarfs). The larger the time interval between early and late bursts of SF episodes, the more enriched is, on average, the gas from which the young populations form.

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For massive galaxies, the small values of the Age_mw/Age_lw and Z_⋆,mw/Z_⋆,lw ratios point to more continuous and homogeneous SFHs, and the fact that Z_⋆,mw/Z_⋆,lw tends to be slightly larger than unity suggests that most of the gas out of which form younger stellar populations is of cosmological origin, i.e., it is accreted from the poorly enriched intergalactic medium as the dark matter halo grows. As is well-known, within the ΛCDM cosmogony, the more massive the halos, the later their mass growth occurs (see, e.g., Mo et al. 2010; Rodríguez-Puebla et al. 2016), including the accretion of baryons. Following this trend, the growth of low-mass halos that host DGs is very slow at late epochs. Therefore, most of the gas out of which young populations form in dwarfs galaxies is expected to come from inside the same halo or galaxy; it is (enriched) gas that was likely heated/ejected by early SF in the galaxy that later cools and falls back again. The results presented above agree with this general picture.

Finally, we have explored whether the age– and metallicity–mass relations of our DGs are segregated by being central or satellites or being at distances D_host larger or smaller than 1 Mpc. We do not find any clear trend in either case.

The SPS analysis of the MaNGA galaxies allows us to reconstruct their full global/local SF, stellar mass, and chemical enrichment histories (see, e.g., Ibarra-Medel et al. 2016; Goddard et al. 2017; Rowlands et al. 2018; Sánchez et al. 2019; Peterken et al. 2021). In a forthcoming paper, we will present and discuss results related to these histories for the DGs. By using the global stellar mass growth history of each galaxy, we report in the VAC the stellar ages when 50% (T₅₀) and 90% (T₉₀) of the final stellar mass were formed, respectively. Since most of the targets in the MaNDAla catalog are at very low redshifts z < 0.03 (look-back time less than 0.4 Gyr for the cosmology adopted here), the stellar ages mentioned above differ from the respective cosmic look-back times only by small amounts of time. In any case, we calculate the look-back time at which each galaxy formed a given fraction of its M_* by adding to the respective stellar age (e.g., T₅₀) the look-back time of observation, ${T}_{{z}_{\mathrm{obs}}}$. Figure 15 presents the differential and cumulative histograms of the look-back times (for the cosmology adopted here) at which the MaNGA DGs formed 50%, 80%, and 90% of their stellar masses. From the distributions, we see that most of the dwarfs formed half of their stars at very early epochs. For 50% (70%) of them, these epochs correspond to look-back times larger than ≈10 (8) Gyr, i.e., z ≳ 1.9 (z ≳ 1.1). On the other hand, the formation of the last 20% or 10% of stars in the MaNGA dwarfs happened at late cosmic times. The medians of the look-back times corresponding to 80% and 90% of the formed stars are 3.7 and 1.8 Gyr, respectively, i.e., half of the dwarfs formed the last 20% (10%) of their stars at z ≲ 0.33 (z ≲ 0.14). The above results are in rough agreement with those of Zhou et al. (2020), who also analyzed a sample of MaNGA low-mass galaxies by using a Bayesian spectrum parametric fitting.

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An interesting question, related to the shape of the SFHs, is how different are the look-back times at which two different stellar mass fractions were formed. In Figure 16, we show the look-back times corresponding to 50% and 80% of the formed stars for the dwarfs. The color indicates the mass-weighted age of each galaxy. First, as expected, there is a good correlation between Age_mw and the half-mass formation time, though the former tends to be shorter than the latter by 1–3 Gyr, on average, for ages greater than ∼4 Gyr. According to Figure 16, the dwarfs that formed 50% of their stars late (≈2–5 Gyr ago or Age_mw ≈ 1–4 Gyr), formed the last 20% of stars very late, i.e., 1–1.5 Gyr ago. For the oldest galaxies, there is a weak trend for the last 20% of stars to form earlier, the earlier the first half of the stars form. The galaxies with higher differences between the formation of the 50% and 80% of their stellar masses (>6 Gyr) are those with intermediate ages, Age_mw ≈ 5–8 Gyr. The dwarfs classified as passive, P (triangles), present small differences (2–4 Gyr) between the formation of 50% and 80% of their stellar masses. Since these galaxies are retired, they are not expected to have late SF events able to contribute to the late growth of the last 20% of stellar mass.

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Finally, in the upper panel of Figure 17, we present the global SFR versus M_* relationship for the MaNDala and the whole MaNGA samples. We have calculated the SFR from the dust-corrected H α line integrated within the FoV of each galaxy, using the Kennicutt conversion factor corrected to the Chabrier (2003) IMF. In addition, we introduce here a nebular metallicity-dependent correction to this factor. For this, we follow Shin et al. (2021) and use the pyPipe3D nebular metallicity calculated for each MaNDala galaxy. We also apply a correction to our H α-based SFR, which for dwarfs is systematically underpredicted with respect to the FUV-based SFR (Lee et al. 2009). This is likely because, at low SFRs, statistically sampling the IMF does not produce enough massive OB stars, resulting in a deficit for H α measurements (Weidner et al. 2013). This correction is applied following Shin et al. (2021), and it is actually very small for most of our dwarfs.

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Dwarf SFgs (blue circles) follow roughly the trend toward low masses of the main sequence of galaxies of the whole sample, though with a large scatter. The few dwarfs classified as P and T (red and green colors, respectively), as expected, lie far below the SF main sequence. The lower panel of Figure 17 shows the sSFR (=SFR/M_*) versus M_*. The data at lower masses are scarce but they hint at a bending in the specific SFR − M_* relation at masses around 10⁹ M_⊙, in accordance with some previous observations and empirical inferences (e.g., Skibba et al. 2011; McGaugh et al. 2017; Rodríguez-Puebla et al. 2020a). The local SF main sequence inferred by the latter authors from a large set of observations from the FUV to the FIR (obeying volume completeness) is overplotted in the lower panel of Figure 17. Despite the large differences in the methodologies, and taking into account that the isocontours plotted in Figure 17 are not corrected by volume completeness, the agreement here is reasonable, including its extension to dwarfs.