The GALEX/S⁴G Surface Brightness and Color Profiles Catalog. I. Surface Photometry and Color Gradients of Galaxies

The S⁴G galaxy sample is a deep infrared survey of a (mainly) volume-limited sample of nearby galaxies within d < 40 Mpc observed at 3.6 and 4.5 μm with the IRAC (Fazio et al. 2004; see Sheth et al. 2010 for a full description of the survey). Additional selection criteria are size-limited with D₂₅ > 1', magnitude-limited in B-band (Vega) < 15.5 mag, and above and below the Galactic plane $| b| \gt 30\,^\circ$. The total sample size is 2352 galaxies. A follow-up survey was done to include more ETGs, but those data are not included in this catalog.

A multiwavelength analysis of the S⁴G sample has since been carried out as part of the Detailed Anatomy of Galaxies (DAGAL) project, and it is now complemented with FUV and NUV data from GALEX (see also Zaritsky et al. 2014b, 2015 and Bouquin et al. 2015 for preliminary analyses of the UV-observed sample), ugriz images from SDSS, and various other data, such as H i data cubes (see Ponomareva et al. 2016) and Hα images (e.g., Knapen et al. 2004; Erroz-Ferrer et al. 2012). Additional analyses and catalogs, such as a classical morphological classification (Buta et al. 2015), bulge/disk decomposition (from the S⁴G P4 pipeline; Salo et al. 2015), catalog of morphological features (Herrera-Endoqui et al. 2015), and stellar mass catalog (P5; Querejeta et al. 2015), have also been produced and are publicly available online.¹⁰ Much more detailed analyses of specific subsamples within S⁴G are also available elsewhere, such as a catalog of structural parameters from BUDDA decomposition (de Souza et al. 2004; Gadotti 2008) of 3.6 μm images (Kim et al. 2016) and Hα kinematic studies of the inner regions (Erroz-Ferrer et al. 2016).

In this paper, we have used the surface photometry at 3.6 μm (IRAC1) measurements from the output of pipeline 3 (P3) of the S⁴G sample (see Muñoz-Mateos et al. 2015 for a detailed description of the S⁴G P3 treatment). We have collected these data from the IRSA database¹¹ via their dedicated website. We only used the 3.6 μm surface photometry performed with a fixed aperture geometry (file names of the form ∗.1fx2a_noclean_fin.dat) where the center, position angle, and ellipticity are all kept fixed and only the aperture radius is increased by radial increments of 2'' along the semimajor axis. Subsequent mentions of μ_[3.6] correspond to the aperture-corrected surface brightness (columns SB_COR and its error ESB_COR, as well as the cumulative magnitude TMAG_COR and its error ETMAG_COR) found in these publicly available data. Since our GALEX photometry is performed every 6'' in major-axis radius steps, we only use the data outputs obtained at the same step values for the 3.6 μm photometry.

Table 1 shows the first galaxies of our GALEX/S⁴G sample sorted by R.A. and lists the FUV and NUV asymptotic magnitudes obtained for our sample along the 3.6 μm asymptotic magnitudes obtained by Muñoz-Mateos et al. (2015). The complete table, with additional columns such as which GALEX tiles were used, is publicly available online through VizieR (Ochsenbein et al. 2000).

We gathered all available GALEX FUV and NUV images and related data products for 1931 S⁴G galaxies that had been observed in at least one of these two UV bands. Over 200 galaxies do not have GALEX data at all. We obtained the original GALEX data using the GALEXview¹² tool. Priority was given to galaxies that have both FUV and NUV images, with the longest FUV exposure time. If this condition was met for several product tiles (including a very similar exposure time to the NUV in the FUV), we chose the one where the target galaxy was best centered in the field-of-view (FOV). We collected imaging data from all kinds of surveys, such as the All-sky Imaging Survey, Medium Imaging Survey, Deep Imaging Survey, and Nearby Galaxy Survey, as well as from Guest Investigator (GIs/GIIs) Programs.

The collected data, once processed, yielded a total of 1931 galaxies with both FUV and NUV photometry available. We call this sample, derived from the S⁴G and having FUV, NUV, and IRAC1 3.6 μm photometry, the GALEX/S⁴G sample. We compare the S⁴G sample and the GALEX/S⁴G sample in Figure 1. The distributions of distances, apparent B-band magnitudes, and morphological types of the two samples and the distribution of the integrated (FUV − NUV) colors of the final GALEX/S⁴G sample are shown. Demographics are shown in Table 2. Our GALEX/S⁴G sample is clearly representative of the whole S⁴G sample with only minor differences in the case of the absolute magnitude distribution. Note that every S⁴G galaxy targeted with GALEX was detected and its UV fluxes measured.

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We also subdivided the GALEX/S⁴G sample into three subsamples. This was done according to the preliminary analysis of the UV-to-IR photometry of Bouquin et al. (2015), where we presented our sample of 1931 galaxies with their asymptotic magnitudes plotted on an (FUV − NUV) versus (NUV − [3.6]) color–color diagram. From this integrated color–color diagram, we were able to select three subsamples of galaxies, namely the GBS, GRS, and GALEX Green Valley (GGV) galaxies, which were defined as follows:

$$\begin{eqnarray}&&\mathrm{GBS}:0.12x+0.16-2{\sigma }_{\mathrm{GBS}}\leqslant y\leqslant 0.12x+0.16+2{\sigma }_{\mathrm{GBS}},\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&\mathrm{GRS}:-0.23y+5.63-1{\sigma }_{\mathrm{GRS}}\leqslant x\leqslant -0.23y\\ &&\qquad +5.63+1{\sigma }_{\mathrm{GRS}},\end{eqnarray} \tag{ 2 }$$

and

$$\begin{eqnarray}\mathrm{GGV}:y\gt 0.12x & + & 0.16+2{\sigma }_{\mathrm{GBS}}\mathrm{and}x\lt -0.23y\\ & + & 5.63-1{\sigma }_{\mathrm{GRS}},\end{eqnarray} \tag{ 3 }$$

where x = (NUV − [3.6]), y = (FUV − NUV), σ_GBS = 0.20, and σ_GRS = 0.45. Both the GBS and GRS are defined to be stripes defined between two parallel lines (Equations (1) and (2)). Note that the GRS equations are expressed in the yx space. The GGV is the region bluer in (NUV − [3.6]) than the GRS but redder in (FUV − NUV) than the GBS (Equation (3)).

The GBS is populated by star-forming galaxies and mostly late-type galaxies, while the GRS is populated by redder systems that lack star formation (quiescent) and are passively evolving or where only low levels of residual star formation are present (e.g., Boselli et al. 2005; Yıldız et al. 2017) and that are, morphologically speaking, mostly ETGs. The GGV galaxies are found between the GBS and the GRS in this UV-to-IR color–color plane, and they are special in the sense that these galaxies can be seen to have decreased star formation activity in recent epochs. Hence, their (FUV − NUV) colors are redder than in GBS galaxies, and their (NUV − [3.6]) colors are bluer than in GRS galaxies. However, it should be noted that we do not exclude the possibility that this GGV population could represent GRS galaxies that are being rejuvenated, thus showing a bluing (FUV − NUV) color. The important point here is that the quick response of the (FUV − NUV) color to even small amounts of recent star formation, coupled with the tightness of the GBS, allows identifying galaxies that are just starting to experience these quenching or rejuvenating events. See Bouquin et al. (2015) for further details.

We obtained spatially resolved FUV and NUV surface photometry, as well as asymptotic magnitudes, for the 1931 galaxies in our GALEX/S⁴G sample. Three types of GALEX data products were collected from the database:

• 1.  
  the intensity maps in FUV (*fd-int.fits) and NUV (*nd-int.fits),
• 2.  
  the high-resolution relative response maps in FUV (*fd-rrhr.fits) and NUV (*nd-rrhr.fits), and
• 3.  
  the object masks in FUV (*fd-objmask.fits) and NUV (*nd-objmask.fits).

Once all data were gathered, we proceeded to reduce and analyze our GALEX UV sample in the same manner as in Gil de Paz et al. (2007).

First, a sky value was measured from the surroundings of the target galaxy. This was followed by the preparation of a mask in two steps. In the first step of the masking process, we masked automatically unresolved sources that had (FUV − NUV) colors redder than 1 mag, which masks out most foreground stars. This was followed by careful visual checks verifying each and every single galaxy and carefully editing the masks one by one by manually adding or removing masks, since the automatization could (a) falsely detect bulges, (b) fail to select companions, and (c) foreground blue stars, all for the benefit of preserving very blue star-forming regions, especially those in the outskirts of disk galaxies. We unmasked all affected bulges and tried to include as many star-forming regions that were falsely masked, while foreground stars were masked out as much as possible. In the process, we also generated FUV+NUV red giant branch (RGB) images for each galaxy that were used during the manual masking process in order to have an educated guess on any potential masking failure encountered. Although great care had been taken during this masking process, it should be noted that in some cases (e.g., merging galaxies, galaxies with bright stars nearby, objects at the edge of the FOV, bad image quality) difficult choices had to be made. We acknowledge that in those cases (less than a few percent) the values obtained may differ from those obtained by other authors (our masks can be provided on demand). Errors associated with these effects cannot be accounted for and are not included in Table 1.

Then, surface brightnesses were measured by averaging over annuli with the same position angle (PA) and ellipticity () as those used in the analysis of the S⁴G sample IRAC data. We used a step in major-axis radius of 6'' and integrated over a width of ±3'', also in major-axis radius. The total uncertainty in the surface brightness does take into account the contribution of both local and large-scale background errors (Gil de Paz et al. 2007).

In Figure 2, we show the FUV+NUV RGB postage-stamp images. The resulting products, also shown in this figure, include the surface brightness radial profiles in both FUV and NUV in mag arcsec⁻², (FUV − NUV) color profiles in mag arcsec⁻², and asymptotic magnitudes (in mag) for each galaxy. The obtained values are corrected for extinction due to the Milky Way (MW). This foreground Galactic extinction was obtained following the UV extinction law of Cardelli et al. (1989), assuming a total-to-selective extinction ratio R_V = A_V/E(B − V) = 3.1, giving the attenuation values of A_FUV = 7.9 E(B − V) and A_NUV = 8.0 E(B − V), where the reddening E(B − V) from Galactic dust is obtained from the map of Schlegel et al. (1998). The surface photometry of the sample is not corrected for internal dust attenuation nor inclination of the host galaxy. A partial table including FUV and NUV surface photometry for 192 ETGs was first released by Zaritsky et al. (2015) and is also available in the VizieR online database (Ochsenbein et al. 2000).

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In Table 3, examples of the values we obtained are shown. The graphical rendering of the data is shown in Figure 3 and is explained in the next subsection.

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Figure 3 shows the FUV, NUV, and 3.6 μm surface brightness profiles μ_FUV, μ_NUV, and μ_[3.6] in units of mag arcsec⁻² plotted against the radius in kpc in one case (left panels) and normalized in units of R/R80 in the other (right panels).

We devised the distance unit R/R80 based on the radius (i.e., semimajor axis of ellipse) that encloses 80% of the total 3.6 μm light and that we call R80. The innermost measurement is at 6'' semimajor axis radius, and the rest of the measurements radially outward in the disk are represented as small dots for each 6'' step. The very center is excluded because it could be affected by differences in the PSF among the three bands and by the contribution of an active galactic nucleus (AGN). The surface brightness (SB) measurements are taken up to 3 × D25; however, for the analysis, we select only measurements having errors less than 0.2 mag arcsec⁻². These errors include the total measurement uncertainties, dominated by Poisson noise in the centers and sky uncertainties in the outskirts, but exclude any systematic zero-point uncertainty. Color-coding is based on the numerical morphological types and is as follows: E is red, E-S0 is orange, S0 is yellow, S0-a is pink, Sa is light green, Sb is dark green, Sc is cyan, Sd is light blue, Sm is dark blue, and Irr is purple. Numerical morphological types were obtained from HyperLeda (Makarov et al. 2014) and follow the RC2 classification scheme: −5 ≤ E ≤ −3.5, −3.5 < E-S0 ≤ −2.5, −2.5 < S0 ≤ −1.5, −1.5 < S0-a ≤ 0.5, 0.5 < Sa ≤ 2.5, 2.5 < Sb ≤ 4.5, 4.5 < Sc ≤ 7.5, 7.5 < Sd ≤ 8.5, 8.5 < Sm ≤ 9.5, and 9.5 < Irr ≤ 999. Galaxies with unknown morphological types are assigned the numerical type 999 and are included in the irregular galaxies (Irr) bin, as these are, in the vast majority of cases, systems with ill-defined morphology. We list the ranges of R80 and maximum radial distances observed at 3.6 μm, and their respective average values per morphological type, in Table 8.

The right column of Figure 3 shows each galaxy's spatially resolved radial color profiles in (FUV − NUV), (FUV − [3.6]), and (NUV − [3.6]) as a function of galactocentric distance both in kpc and in R/R80 units. Each plot shows the corresponding color profile distribution for each galaxy, color-coded by morphological type. As mentioned above, measurements are taken every 6'' from the center of each galaxy, and each profile reaches the galactocentric distance where the error in either FUV, NUV, or 3.6 μm surface brightness becomes 0.2 mag arcsec⁻² or larger, thus rejecting the data that follow. It should be noted that measurements are available up to 3 × D25 but are more dominated by sky uncertainties as we move radially outward.

Figure 4 shows the average surface brightnesses and colors per R/R80 bin of width 0.5, as well as the range of the scatter from the mean value in each bin and per morphological type. It should be noted that the range appears to diminish as we move radially outward, but this is due to reaching the observation limits in each band.

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Disks are known to have an exponential profile and are therefore close to a straight line in a surface brightness (a logarithm) versus galactocentric radius plot, at least in their inner regions. In the very outer regions, these single exponential profiles commonly bend (see Marino et al. 2016 and references therein). It should be noted in this context, however, that the level of either downbending or upbending in the surface brightness profiles of galaxy disks is usually minimized at near-infrared wavelengths (e.g., Muñoz-Mateos et al. 2011; see also Bakos et al. 2008 for a comparison of these bending profiles at different wavelengths and in stellar mass).

In order to isolate the disk component in a coherent and reproducible way among all 1884 disk galaxies (S0 and beyond) and to derive their multiwavelength properties, we have made use of the 3.6 μm surface brightness profiles of our sample and performed an error-weighted fit to our data points in μ_[3.6] versus galactocentric radius in kpc. Prior to this fitting, the surface brightnesses were corrected for geometrical inclination effects by adding $-2.5{\mathrm{log}}_{10}(b/a)$ (mag arcsec⁻²), where a and b are the semimajor and semiminor axes in the B band, to each data point. No internal dust attenuation correction is applied. This has the effect of dimming the surface brightness for inclined systems (Graham & Worley 2008). See Section 5 on how this inclination correction affects the comparison with the models. Then, we identified the position beyond which the profile starts to be best described by an exponential law at these wavelengths. In order to exclude the bulge (i.e., either the region where the Sérsic index is significantly larger than unity or the steepening associated with a pseudo-bulge), and given that we have in hand R80 measurements (major-axis radius where 80% of the IR light is enclosed) for the entire sample, we remove the inner part of the profile up to some factor of R80 to perform different sets of fits. For this analysis, we explored R/R80 cutoff factors of 0, 0.25, 0.50, 0.75, 1.00, and 1.25 and evaluated how far we should go from the galaxy center in each case to have good linear fits, as given by the corresponding sample-averaged reduced χ² values (see below). We combined this inner cutoff in R/R80 with cutoffs in surface brightness magnitude in the range μ_[3.6] = 21.5–24 mag arcsec⁻², so only points fainter than the corresponding cutoff would be considered for the fit.

The rationale for using a combination of the two parameters is that we should normalize to the size of the objects to (1) do a first-order separation between bulges and disks and (2) take into account the fact that early-type systems usually have large, massive bulges with brighter near-infrared surface brightnesses than the disks of late-type spirals. Thus, when we cut in surface brightness we exclude larger regions in massive early-type systems and only the very central regions of very late-type spirals (see Figure 3, bottom right panel). However, we should certainly add a quality-of-fit criterion here to determine the goodness of these criteria.

In order to determine the reducedχ² for each fit, the number of degrees of freedom is computed as the number of data points that remain after applying the corresponding cutoffs minus the number P of free parameters, where P = 2 in our linear fitting case (see Andrae et al. 2010 for a discussion). Average reduced χ² values are computed for each combination of cutoffs, and the results are shown in Table 4.

Table 4.  Average Reduced χ² of the Linear Fit with μ_[3.6] and R/R80 Cuts

R/R80 Cutoffs
		0.00		0.25		0.50		0.75		1.00		1.25
		$\langle {\chi }^{2}\rangle$	Na	$\langle {\chi }^{2}\rangle$	N	$\langle {\chi }^{2}\rangle$	N	$\langle {\chi }^{2}\rangle$	N	$\langle {\chi }^{2}\rangle$	N	$\langle {\chi }^{2}\rangle$	N
μ[3.6] cutoffs	21.5	26.20	(1577)	20.84	(1554)	15.72	(1451)	9.68	(1240)	4.04	(794)	2.87	(535)
	22	10.64	(1489)	8.63	(1474)	6.97	(1387)	5.85	(1191)	3.26	(781)	2.48	(530)
	22.5	4.89	(1384)	4.28	(1375)	3.54	(1298)	3.11	(1126)	2.02	(756)	1.62	(518)
	23	2.34	(1232)	2.17	(1228)	1.81	(1165)	1.63	(1014)	1.14	(693)	0.98	(482)
	23.5	1.37	(1034)	1.28	(1033)	1.12	(987)	0.96	(863)	0.68	(591)	0.56	(419)
	24	0.78	(755)	0.77	(754)	0.73	(723)	0.67	(630)	0.40	(426)	0.35	(296)

Note.

^aN is the number of galaxies remaining after applying the cutoffs and on which the linear fitting is performed.

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When doing these fits, we excluded elliptical galaxies (T ≤ −3.5) in all cases. It should be noted that as we move toward higher values in both the R/R80 and μ_[3.6] cutoffs, the number of points used for the linear fit decreases, and the number of galaxies that can be analyzed becomes smaller. This is because some galaxy profiles do not reach beyond the cutoffs, or only one data point is beyond them. Besides, eventually the reducedχ² goes below unity, telling us that we are overfitting the data. This is in part due to the effect of correlated errors associated with the uncertainties in the sky subtraction in the very outer surface brightness measurements. We find that the best set of R/R80 and μ_[3.6] cutoffs, i.e., the one that yields an average reduced χ² ∼ 1 with still a large number of galaxies, is at R/R80 = 0.5 and μ_[3.6] = 23.5 mag arcsec⁻², where 〈χ²〉 = 1.12 and the number of galaxies is 987 (∼51% of the GALEX/S⁴G sample; see Figure 5).

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We also apply oblique cuts in the μ_[3.6] versus R/R80 plane instead of a combination of vertical and horizontal cuts. Table 5 shows the resulting average reducedχ² and the number of galaxies for a combination of cutoff slopes a and cutoff y intercepts b. We tried all the combinations of slopes ranging from −7 to −1 (in units of mag arcsec⁻²/(R/R80)) and y intercepts between 20 and 30 mag arcsec⁻². The best compromise between the average reduced χ² and number of galaxies is for slope and y-intercept values of a = −1 and b = 24 mag arcsec⁻², where the average reduced χ² = 2.07 and the number of galaxies is 1233 (∼64% of the GALEX/S⁴G sample; see Figure 5). Graphical representations of the slopes and yintercepts at these best cutoffs are shown in Figure 6.

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Table 5.  Average Reduced χ² of the Linear Fit in the μ_[3.6] vs. R/R80 Plane with Oblique Cuts

Slope (a) Cutoff
		−6		−5		−4		−3		−2		−1
		$\langle {\chi }^{2}\rangle$	N	$\langle {\chi }^{2}\rangle$	N	$\langle {\chi }^{2}\rangle$	N	$\langle {\chi }^{2}\rangle$	N	$\langle {\chi }^{2}\rangle$	N	$\langle {\chi }^{2}\rangle$	N
y intercept (b) cutoff	20	777.55	(1717)	649.14	(1716)	569.63	(1713)	469.68	(1712)	393.01	(1707)	304.54	(1699)
	22	205.61	(1697)	158.46	(1691)	129.09	(1684)	88.95	(1668)	52.78	(1644)	27.10	(1592)
	24	61.96	(1633)	44.50	(1607)	28.48	(1563)	13.20	(1528)	5.58	(1412)	2.07	(1233)
	25	33.19	(1578)	23.64	(1540)	11.19	(1482)	6.19	(1375)	2.21	(1202)	0.78	(831)
	26	20.87	(1516)	10.53	(1445)	6.24	(1339)	2.50	(1166)	0.96	(845)	0.44	(219)
	28	6.20	(1260)	3.12	(1090)	1.74	(838)	0.89	(471)	0.79	(127)	0.72	(5)
	30	2.46	(858)	1.56	(596)	0.87	(322)	1.27	(103)	1.04	(8)	...	(0)

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The relatively good isolation of the disk component by some of these sets of criteria opens the door to statistical studies of the photometric properties of disks in thousands or millions of galaxies using existing data (SDSS) or data from future facilities and missions, such as the Large Synoptic Survey Telescope (LSST) or EUCLID.

In Figure 7, we plot the FUV surface brightness μ_FUV versus the 3.6 μm surface brightness μ_[3.6] for galaxies belonging to the GBS, GGV, and GRS subsamples based on their integrated colors. Both axes are expressed in mag arcsec⁻².

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This figure can also be seen as a comparison between the observed SFR (i.e., not corrected for internal dust extinction) and the stellar mass surface densities (see Appendix A), except for those cases where the FUV emission is not due to young massive stars. In that regard, this point is equivalent to the star formation main sequence (SFMS) but in surface brightness (see Cano-Díaz et al. 2016).

Each data point is the averaged value within fixed-inclination elliptical ring apertures of 6'' width. The innermost ring has a semimajor axis length of 6'' with a width of 6'', defined by an inner ellipse with a major axis of 3'' from the center and an outer ellipse with a semimajor axis of 9'' from the center. The initial ring does not cover the center of the galaxy, as this could be affected by differences in the PSF among the three bands and by the contribution of an AGN. Subsequent rings increase in size in 6'' steps, i.e., they have semimajor axis radii of 12'', 18'', 24'', and so on.

For early-type GRS galaxies, the FUV and 3.6 μm surface brightnesses show a pretty tight correlation, which indicates that the 3.6 μm emission traces not only the stellar mass but also the bulk of the stars dominating the FUV emission in these objects, mainly main-sequence turnoff or extreme horizontal branch (EHB) stars, depending on the strength of the UV upturn. Despite the large scatter of the GRS found in Bouquin et al. (2015), the use of spatially resolved data with the 3.6 μm surface brightness as normalizing parameter leads now to a very tight GRS in this SB–SB plane (or a very small range in FUV − [3.6] color). The comparison of these profiles with those of the GGV galaxies shows that in the latter case the central stellar mass surface density is 1.5–2 mag fainter than in the former and that most GGV galaxies (all except the few very late-type GGVs) have (outer) disks that follow a trend similar to that followed by the outer regions of GRS galaxies. Finally, late-type galaxies in the GBS span a large range of values in both μ_FUV and μ_[3.6]. Irregular, Sm, and Sd galaxies have the highest SFR surface densities (for a given stellar mass surface density) among the GBS subsample.

Despite the large scatter of GBS galaxies, they can be clearly distinguished from the ETGs of the GRS and even GGV galaxies by looking at the (observed) sSFR values in their disks. Thus, while GBS disks have sSFR values that are higher than 10^−11.5 yr⁻¹, the outer regions of GGV and GRS galaxies are in the majority of cases (all in the case of the GRS) below this value. This value could be used to easily discriminate between star-forming and quiescent regions within galaxies.

GBS galaxies define a well-separated sequence, and with the spatial information now available, we can see what parts of the galaxies are now just leaving the GBS, that is, have their star formation suppressed or exhausted. While a few GGV galaxies show a decrease in the sSFR of their inner regions, most of these galaxies are within the locus of the GBS in the inner parts but approach the sequence marked by the GRS profiles in their outer regions. In other words, the fact that these galaxies were identified as leaving the GBS in Bouquin et al. (2015) is mainly due to their outer parts, likely caused by the disks of GGV galaxies undergoing either an outside-in star formation quenching or an inside-out rebirth.

It is worth emphasizing here that only the combined use of FUV, NUV, and 3.6 μm allows for properly separating the "classical blue cloud" (now blue sequence) and "classical red sequence" and determining which galaxies are now leaving (or entering) the GBS and what regions within the galaxies are responsible for it.

We mark in Figure 7 the μ_[3.6] value that corresponds to the surface stellar mass density of Σ_⋆ = 3 × 10⁸ M_⊙ kpc⁻² = 300 M_⊙ pc⁻² (${\mu }_{[3.6]}=20.89$ mag arcsec⁻²) proposed by Kauffmann et al. (2006) to separate the bulge-dominated and disk-dominated objects.

In the case of our GBS galaxies, this stellar mass surface density indicates the region inside which the SFR surface density flattens relative to the stellar mass surface density, i.e., when the (FUV − [3.6]) color becomes significantly redder (see Figure 9). A similar change is observed when using the light-weighted age of the stellar population in galaxies instead (González Delgado et al. 2014).

The sSFR of the outer parts (beyond μ_[3.6] = 20.89 mag arcsec⁻²) is shown in Figure 8 for GBS, GGV, and GRS galaxies. This is done simply by calculating the linear scale sSFR of one galaxy at each point that is in the outer parts and averaging these sSFR values (not light/mass-weighted) in order to get a single sSFR value per galaxy (and expressing them in the logarithmic scale at the end). We find the following sSFR density ranges: −12.5 < log₁₀(sSFR) < −9.5 for GBS galaxies, −12.4 < log₁₀(sSFR) < −9.8 for GGV galaxies, and −12.6 <log₁₀(sSFR) < −11.7 for GRS galaxies. Since we do not correct for internal dust attenuation, these values should be viewed as lower limits of the true sSFR. Previous studies of the impact of dust on the (FUV − [3.6]) colors (Muñoz-Mateos et al. 2007, 2009a, 2009b) have shown that dust attenuation A_FUV decreases as we move outward in the disks, although the dust content differs from one morphological type bin to another; for example, Sb-Sbc galaxies have higher A_FUV at all radii than the other types, whereas Sdm-Irr have relatively very low dust content. It should be noted, however, that besides dust, the reddening in the outer parts of quiescent galaxies is due to their older stars. There is a clear difference between the outer parts of GRS galaxies having low sSFR and a narrow range of values and those of GBS galaxies with a wide range of sSFR but in general not as low as the outer parts of the GRS. For our sample, we have a distribution in outer disk sSFR with the mean at −10.6 and σ = 0.5 dex (rms) for GBS, −11.5 and σ = 0.7 dex for GGV, and −12.3 and σ = 0.2 dex for GRS galaxies. The sSFR of the outer parts of the GGV galaxies in our sample covers a wider range of values but is not as high as that of some GBS galaxies and not as low as that of some GRS galaxies. Note that in the case of the GRS galaxies, the UV emission might not be due to recent star formation but to the light from low-mass evolved stars.

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Figure 9 shows the GRS (top), GGV (middle), and GBS (bottom) galaxies' (FUV − [3.6]) color profiles versus 3.6 μm surface brightness μ_[3.6], with the same color-coding per morphological type as in previous plots. Again, the 3.6 μm surface brightness corresponds to the stellar mass per area (see Equation (14) in Appendix A), and the (FUV − [3.6]) color is equivalent to the observed (not corrected for internal extinction) sSFR (units yr⁻¹; see Equation (20) in Appendix B).

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The yellow star symbol corresponds to the radial measurement where the cumulative magnitude at 3.6 μm reaches 80% of the enclosed light at this wavelength.

The (FUV − [3.6]) color profiles are very different for the GRS, GGV, and GBS subsamples. In the case of GRS galaxies, which are mostly early-type but not exclusively, the color is tightly constrained within a range from 6 to 8 mag but gets a bit bluer to the outer regions, especially for GRS galaxies of S0, Sa, Sb, and Sc morphological types.

On the other hand, in the case of GBS galaxies, their (FUV − [3.6]) color ranges from −1 to 10 mag, corresponding to an sSFR value ranging from 10⁻¹⁰ to 10⁻¹³ yr⁻¹. Regarding the differences in the color profiles for each galaxy type, Sa, Sb, and Sc galaxies go from red to blue from the inside out, while Sd, Sm, and Irregulars are much bluer than Sa, Sb, and Sc at a given stellar mass surface density but their color gradients are somewhat flatter. Again, it should be noted that we are not correcting for dust and that the effect of dust is to redden the (FUV − [3.6]) color (Muñoz-Mateos et al. 2007) and therefore yields a lower limit to the sSFR.

The fact that most profiles of GBS galaxies become bluer from the inside out indicates that the lower the surface stellar mass density (the greater the galactocentric distance), the greater the sSFR, i.e., the higher the SFR for a given surface stellar mass density, the more stars are born in the outskirts. Correcting for internal dust extinction, assuming that dust extinction and reddening effects are stronger in the inner regions than in the outer parts, would yield bluer centers compared to the outer disk. This has the effect of increasing the slope of the gradient, where negative color gradients would become flatter and positive color gradients even more positive. Such an effect would translate to a less-pronounced degree of inside-out growth. It should be noted that while the internal dust correction would affect the color profiles of the galaxies, it is not enough to explain why most galaxies are becoming bluer from the inside out (see Figure 2 in Muñoz-Mateos et al. 2007). Studies by Muñoz-Mateos et al. (2007, 2011) and Pezzulli et al. (2015) on nearby galaxy samples have shown that mass and radial growth of nearby spiral disks growing from the inside out have timescales on the order of ∼10 and 30 Gyr, respectively. Isolating a few galaxies actively forming stars in their outer regions reveals that their outer regions indeed fall near log₁₀(sSFR) ∼ −10 yr⁻¹, or ∼10 Gyr, in agreement with the above work (see GBS plot in Figure 9). In the case of profiles reddening in the outskirts, the lower Σ_⋆ becomes, the smaller the sSFR.

Remarkably, a clear color flattening is observed in the outer parts of the profiles of most GBS galaxies when Σ_⋆ < 300 M_⊙ pc⁻². Applying a weighted linear fit to the left-hand and right-hand sides of μ_[3.6] = 20.89 mag arcsec⁻², we get (FUV − [3.6]) = (−0.395 ± 0.023) · μ_[3.6] + (11.537 ± 0.453) and $(-0.438\pm 0.009)\cdot {\mu }_{[3.6]}+(12.210\pm 0.193)$, respectively. These are shown in Figure 9 as solid blue lines for the mean value accompanied by parallel dashed blue lines corresponding to the 1σ uncertainty.

The galaxies falling into the GGV category globally are also clearly distinct from the GBS ones in terms of their spatially resolved properties. They show flat or even inverted color (and sSFR) profiles as a function of stellar mass surface density (hardly due to radial variations in the amount of dust reddening; see Muñoz-Mateos et al. 2007), which indicates either a decline in the observed SFR (oblique lines in Figure 9) in their outskirts, or alternatively, a recent enhancement of the SFR in the inner regions of an otherwise passively evolving system. In the latter case, the low fraction of intermediate-type spirals in the GRS (compared to the GGV) suggests that this rebirth should be accompanied by a morphological transformation from ETGs toward later galaxy types. There are, indeed, post-starburst (E+A) or (K+A) galaxies that are in the classical Green Valley (French et al. 2015) that did have centrally concentrated star formation (Norton et al. 2001).

In the more likely case of a decline of the SFR in the outer disks of GGV intermediate-type spirals, we should invoke the presence of a quenching (or, at least, damping) mechanism for the star formation acting primarily in these regions.

Table 6.  Color and Surface Brightness Gradients from Radial Profiles Normalized to R80 (Except for μ_[3.6])

	FUV − NUV		FUV − [3.6]		NUV − [3.6]		μ[3.6]
Unit	mag/(R/R80)		mag/(R/R80)		mag/(R/R80)		mag kpc−1
Namea	ab	bc	a	b	a	b	a	b
ESO 293-034	−0.03 ± 0.06	0.48 ± 0.07	−1.31 ± 0.12	4.30 ± 0.13	−1.37 ± 0.09	3.91 ± 0.09	0.55 ± 0.02	21.41 ± 0.14
NGC 0007	0.15 ± 0.42	0.21 ± 0.34	−0.11 ± 0.48	1.64 ± 0.39	−0.25 ± 0.14	1.42 ± 0.11	... ± ...	... ± ...
IC 1532	−0.76 ± 0.92	0.96 ± 0.66	−0.12 ± 0.95	2.44 ± 0.67	0.63 ± 0.01	1.48 ± 0.01	... ± ...	... ± ...
NGC 0024	0.00 ± 0.02	0.34 ± 0.02	−0.54 ± 0.05	3.04 ± 0.04	−0.58 ± 0.05	2.74 ± 0.04	1.04 ± 0.03	20.81 ± 0.12
ESO 293-045	0.05 ± 0.07	0.08 ± 0.06	−0.83 ± 0.41	1.20 ± 0.33	−0.92 ± 0.36	1.15 ± 0.29	0.64 ± 0.03	23.15 ± 0.12
UGC 00122	1.01 ± 0.21	−0.63 ± 0.16	1.16 ± 0.30	−0.23 ± 0.23	0.15 ± 0.25	0.40 ± 0.19	0.81 ± 0.04	24.24 ± 0.10
NGC 0059	0.09 ± 0.11	1.60 ± 0.09	0.18 ± 0.11	4.82 ± 0.09	0.10 ± 0.05	3.21 ± 0.04	2.23 ± 0.07	21.38 ± 0.09
ESO 539-007	−1.11 ± 1.14	0.97 ± 0.90	−5.36 ± 0.44	4.58 ± 0.33	−3.73 ± 0.71	3.22 ± 0.50	0.24 ± 0.04	24.37 ± 0.14
ESO 150-005	−0.27 ± 0.18	0.36 ± 0.14	−0.77 ± 0.50	1.89 ± 0.35	−0.56 ± 0.40	1.57 ± 0.28	0.24 ± 0.04	24.19 ± 0.14
NGC 0100	0.87 ± 0.18	0.02 ± 0.12	−1.15 ± 0.85	4.10 ± 0.57	−2.05 ± 0.68	4.10 ± 0.45	... ± ...	... ± ...
NGC 0115	0.06 ± 0.04	0.16 ± 0.04	−0.48 ± 0.13	1.83 ± 0.11	−0.51 ± 0.13	1.63 ± 0.11	0.52 ± 0.03	21.27 ± 0.17
UGC 00260	0.04 ± 0.07	0.29 ± 0.09	−1.29 ± 0.13	3.76 ± 0.16	−1.43 ± 0.14	3.57 ± 0.16	0.27 ± 0.02	22.96 ± 0.26
NGC 0131	0.11 ± 0.08	0.34 ± 0.08	0.00 ± 0.12	2.86 ± 0.10	−0.15 ± 0.08	2.55 ± 0.06	... ± ...	... ± ...
UGC 00320	0.12 ± 0.17	0.20 ± 0.15	0.15 ± 0.46	1.61 ± 0.36	−0.01 ± 0.31	1.44 ± 0.23	0.50 ± 0.03	22.88 ± 0.17
...
Totald	1541		1541		1541		992

Notes.

^aSame nomenclature as the S⁴G. ^bSlope of linear fit and 1σ uncertainty obtained with thescipy.optimize.curve package. We applied the cutoffs at R/R80 = 0.5 and μ_[3.6] = 23.5 mag arcsec⁻² only to the linear fit to the μ_[3.6] versus kpc data. In the case of colors, only the radial cutoff at R/R80 = 0.5 is applied. We also applied a simple inclination correction to the data by adding $-2.5{\mathrm{log}}_{10}(b/a)$, where a and b are the semimajor and semiminor axes, respectively. ^c The y intercept of the linear fit with uncertainty. ^dTotal number of successful fits for each column. There are three galaxies with T < −3.5 (E galaxies, namely ESO 548-023, NGC 4278, and NGC 5173) that are included in the μ_[3.6] versus kpc column, bringing the total to 992 galaxies, but they are removed from the subsample for further analysis.

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

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Figure 10 shows the color profiles of (FUV − NUV), (FUV − [3.6]), and (NUV − [3.6]) versus μ_[3.6] surface brightness. Linear fits to these color profiles were performed for each individual galaxy and are included in Table 7. The fits were performed for SB fainter than μ_[3.6] = 20.89 mag arcsec⁻² in these cases.

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While a positive gradient seems to be more pronounced in (FUV − NUV) color compared to the other two, it is not clear what is driving it. Since dust reddening is rarely increasing toward the outer parts, those objects with positive (FUV − NUV) color gradients are likely suffering changes in the recent star formation history of their outer regions. The dominant morphological types of positive (FUV − NUV) color gradient galaxies are S0-a galaxies.

Table 8.  GALEX/S⁴G Sample Radial Ranges at 3.6 μm

Morpha	Nb	R80 rangec	max ranged	$\langle R80\rangle$ e	$\langle \max \rangle$ f
		kpc	kpc	kpc	kpc
E	24	1.86–18.79	6.51–55.39	6.51	23.77
E-S0	23	0.94–12.2	3.23–42.98	3.60	14.00
S0	51	1.01–12.22	3.71–45.47	3.98	16.57
S0-a	103	1.43–15.14	5.44–51.54	4.67	18.26
Sa	175	1.14–17.31	6.33–57.03	5.26	21.38
Sb	340	0.97–17.21	4.2–90.17	5.77	22.27
Sc	669	0.88–19.57	2.25–81.73	6.22	19.21
Sd	168	1.24–15.68	2.48–39.79	5.53	13.55
Sm	192	0.18–12.54	0.32–36.04	4.94	11.68
Irr	186	0.19–17.59	0.31–28.86	4.01	8.61
Total	1931

Notes.

^aRC2 morphological types. ^bNumber of galaxies. ^cSmallest and largest R80 distance in kiloparsec. ^dSmallest and largest maximum size of galaxies in kiloparsec. ^eAverage R80. ^fAverage maximum.

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The comparison between the (NUV − [3.6]) and (FUV − [3.6]) color profiles (both shown in Figure 10) is also important to determine whether the UV emission is coming from newly formed O and B stars or from evolved UV-upturn sources (likely associated with EHB stars for the latter case, which mainly contribute to the FUV band; O'Connell 1999; see also Section 4.4).

From the colors measured above, we formed three color–color diagrams, namely (FUV − NUV) versus (NUV − [3.6]) (Figure 11), (FUV − NUV) versus (FUV − [3.6]) (Figure 12), and (FUV − [3.6]) versus (NUV − [3.6]) (not shown). The color–color diagrams presented here show the galaxies separated into nine panels of separate morphological type.

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Comparing the (FUV − NUV) versus (NUV − [3.6]) and the (FUV − NUV) versus (FUV − [3.6]) color–color diagrams, we can see that the two sequences are more distinguishable in the former. This is mainly caused by the fact that the GRS is orthogonal to the GBS in the case of the (FUV − NUV) versus (NUV − [3.6]) diagram. This is due to the fact that the strength of the UV upturn also increases with the stellar mass surface density. This is also the case when considering the total galaxy mass (Boselli et al. 2005). We cannot determine here whether this is due to the stellar populations at high stellar mass surface densities hosting either an important helium rich or metal-poor horizontal branch (HB) population (Yi et al. 2005, 2011) or whether it is related to changes in the IMF (as suggested by Zaritsky et al. 2014b, 2015).

The (FUV − NUV) versus (NUV − [3.6]) color–color diagram is where we defined the GBS, GRS, and GGV subsamples from the galaxies' integrated (asymptotic) magnitudes by visually separating the distribution into two regions and fitting an error-weighted least-squares line to each region (Bouquin et al. 2015). With our current spatially resolved data, we can see the spatially resolved (radially, at least) color evolution of galaxies in these three categories. While ETGs such as E, E-S0, S0, S0-a, and Sa galaxies span both the GBS and GRS regions, LTGs such as Sb, Sc, Sd, Sm, and Irregular galaxies have this color much more constrained and their entire profile mostly located within the GBS region (mean ±2σ).

In the panels for the E, E-S0, S0, and S0-a types (top row) of the (FUV − NUV) versus (NUV − [3.6]) (Figure 11) and (FUV − NUV) versus (FUV − [3.6]) (Figure 12) color-color diagrams, the galaxies are distributed into two regions: the bottom left (blue-blue) and the top right (red-red) parts in both color-color diagrams. The galaxies with the bluest central region have redder disks in (FUV − NUV), (NUV − [3.6]) and (FUV − [3.6]) colors. The galaxies with the reddest central region also have redder disks in (FUV − NUV), but not much in (NUV − [3.6]) nor in (FUV − [3.6]). In both cases, their central regions (triangles) are bluer in (FUV − NUV) color than their outer parts. If the bluing were caused by residual star formation (RSF), which contributes in both FUV and NUV, the observed data points would be bluer in all three colors. This is indeed the case for the ETGs seen in the bottom left (well within the GBS) in both color–color diagrams, where RSF is more prominent in their central regions. Note that the innermost 6'' (in semimajor axis, i.e., 12'' in major axis) are excluded, so the potential contribution of AGNs should not affect these results in a direct way.

For the ETGs in the top right of these plots, there is a difference between the (NUV − [3.6]) and (FUV − [3.6]) colors. While in the (FUV − NUV) versus (NUV − [3.6]) color–color diagram the distribution of these reddest systems has a negative slope (which provides a better isolation of the GRS), it has a positive slope in the (FUV − NUV) versus (FUV − [3.6]) color–color diagram. The central regions of these galaxies are bluer in (FUV − [3.6]) than in (NUV − [3.6]), which is the sign of a weaker contribution from the emitter of the UV radiation in these systems in the NUV than in the FUV compared to GBS galaxies. This can probably be attributed to evolved (UV-upturn) stars.

Our color–color diagrams are, thus, able to segregate and allow us to extract the properties of a whole range of galaxies, from star-forming LTGs to ETGs with and without RSF. For ETGs, they allow us to directly see the effect of UV-upturn stars, which can only be done in the UV-to-IR colors. In this regard, we find that RSF in ETGs seems to be concentrated in the center and the UV upturn is also stronger as we move to the inner regions of red (in NUV − [3.6]) ETGs. However, it should be noted that a recent study by Yıldız et al. (2017) showed that a not-insignificant fraction, 20%, of field (non-Virgo) nearby galaxies have disks or rings of H i gas around them, and that their UV profiles are closely tied to their H i gas reservoir.

This color–color diagram does not allow us to clearly determine whether the UV upturn is also present in the bulges of early-type spiral galaxies as they are located in a position similar to that expected for turnoff stars in these bulges. We can nevertheless conclude that in galaxies with morphological types later than Sc, the light from HB stars is clearly overshone by these turnoff stars of progressively higher masses (statistically speaking) as we move to later types.

A subsample of 70 GGV galaxies was identified in the (FUV − NUV) versus (NUV − [3.6]) integrated color–color diagram by Bouquin et al. (2015).

As already pointed out in that paper, these objects can be interpreted as galaxies that have either left the GBS and are "transitioning" to eventually reach the GRS or were previously in the GRS and are now experiencing a modest rebirth or rejuvenation (in terms of the light-weighted ages of their stellar populations) and are evolving back to the GBS.

In the former scenario, star formation would have been suppressed (or at least damped) by starvation from having used up all the gas, ram-pressure stripping, or quenching due to the perturbations induced from AGNs, merger events, or some other gas-heating process. OB stars would not form any longer, and the FUV and NUV emissions would decrease, with the FUV emission evolving faster than the NUV because of the shorter lifespan of the most massive stars, resulting in a progressive reddening of their (FUV − NUV) color.

In the case of the latter (rejuvenation) scenario, these galaxies would have started to form stars on top of relatively passively evolving galaxies either by the accretion of new gas or by cooling gas that was already present in the galaxy in a hotter phase.

The results presented above provide another fundamental piece of evidence for the origin of these transitioning objects. In particular, we have shown that the outer parts of most GGV galaxies are redder than their inner parts and that this reddening is progressive (see, e.g., Figure 13). In the case of the quenching scenario, this implies that the mechanism responsible for the quenching is acting in an outside-in fashion. Should the rejuvenation scenario be happening, these galaxies would be starting to form stars from the inside out. As the associated blue colors are not limited to the very central regions, this would likely imply the growth of a disk, again, in an inside-out fashion.

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With regard to the mechanism(s) that could potentially lead to the suppression of star formation in the outskirts, we showed in Bouquin et al. (2015) that the GGV has the highest fraction of Virgo cluster galaxies, with 20 (out of 70) GGV objects in the Virgo cluster, i.e., ∼29%, in comparison to a fraction of Virgo cluster galaxies in the GBS of only ∼7% (124/1753) and in the GRS of ∼18% (14/79). For example, one ram-pressure model in Virgo (Boselli et al. 2006) creates an inverted color gradient compared to late-type field galaxies, with redder outer disks and bluer inner parts.

We also analyze whether the GGV objects are mainly located in groups where environmental effects might start to occur (in particular, strangulation; Kawata & Mulchaey 2008). Among the 70 GGV galaxies of our sample, 28 (40%) are field galaxies and 42 (60%) are in groups or clusters. We see that the fraction of field galaxies decreases to 30%, while the fraction of group galaxies increases to 70% (56/79) in the case of GRS galaxies. In contrast, the fraction of field/group galaxies is 51%/49% in the case of GBS galaxies, and that of the overall sample is 50%/50%. That is, we see an increase in the fraction of galaxies belonging to groups as we go from the GBS to the GRS. This result hints that the disk reddening that we see in GGV galaxies is likely due to a mechanism that is favored in dense environments. We note that this result does not exclude rejuvenation scenarios, as many ETGs with extended star formation are now being identified (Fang et al. 2012; Salim et al. 2012; Yıldız et al. 2017).

In this study, we use the disk models of BP00 as in the version presented in Muñoz-Mateos et al. (2011) but increasing the sampling and range spanned by the model parameters, namely circular velocity v_c and spin λ. As mentioned above, these are bulgeless, disk-only models that naturally grow inside-out from gas infall and are left to run for T = 13.5 Gyr to the present. They include scaling laws so that mass scales as v³ and scale length as λ × v (Mo et al. 1998). As can be seen in Figure 14, an increase in circular velocity v_c leads to an increase in both the total stellar mass and the disk scale length, whereas increasing the spin parameter λ only increases the scale length. Correcting our observed galaxies for inclination (see Section 4.1) leads to a dimming in surface brightness at all radii and thus eventually would yield a lower circular velocity and a larger spin than when not applying the correction.

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These models aimed to reproduce the multiwavelength SB profile by varying only those two parameters. Other assumptions were calibrated in the MW model (BP99) and in nearby disks (BP00). Predictions for disks with different spins and velocities are based on ΛCDM scaling laws. Disk models were generated for various spin parameters and circular velocity combinations: the spin ranges from 0.002 to 0.15, inclusively, and varying by a step of 0.001, i.e., 149 different spins, while the velocity ranges from 20 to 430 km s⁻¹, inclusively, and varying by a step of 10 km s⁻¹, i.e., 42 different velocities. The total number of models generated is 6258. We fit these models with an error-weighted linear fit (in surface brightness scale) in a similar manner to what we do with our data points. It is, however, necessary to insert an uncertainty on the data point of each model in order to compute the reduced χ² of the fit and to determine whether an exponential law also properly describes the radial distribution of the UV through near-infrared light in these models. A reasonable assumption in this regard is 0.10–0.15 mag (see, e.g., Muñoz-Mateos et al. 2011). Indeed, a value of 0.15 mag yields a reduced χ² close to unity for most of the models.

Figure 15 shows the slopes and y intercepts obtained from the fits to the IR surface brightness profiles (corrected for inclination) of our galaxy sample plotted along with the grid of slopes and y intercept obtained from fits to the BP00 models described above. Data error bars are coming from the slope and y-intercept fitting errors obtained from the weighted fits to our surface brightness profiles. The error bars in the slopes and y intercepts of the models are omitted for simplicity. They are separated by morphological type.

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This approach allows us to assign to a given galaxy disk a specific 3.6 μm central surface brightness and scale length along with the corresponding closest model. That way, we are able to deduce circular velocities and spin parameters for the entire S⁴G sample. In Figure 16, we show the circular velocity and spin distributions and the comparison between both parameters for the entire sample. We split these parameters by morphological type.

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For each pair of best-fitting slope (i.e., scale-length) and y-intercept (i.e., central surface brightness) measurements, we generated 1000 random points using elliptical 2D Gaussian probability distribution functions with 1σ being the uncertainties in these measurements and obtained the closest model for each Monte Carlo particle. Thus, for each data point (i.e., for each galaxy), we obtained a distribution in best-fitting circular velocity and spin parameter. Typical distributions of circular velocities from the sampling of 1000 points are shown in Figure 17. This figure also shows the distribution of the individual 1000 points in the circular velocity versus spin diagram for three example galaxies. There is a mild degeneracy between the two parameters (although we show galaxies with very skewed distributions) in some of these objects that is in the same direction as the correlation seen in Figure 16 for late-type galaxies. Note, however, that such a correlation is not driving the whole distribution of points in Figure 16 and that the latter spans a wider range of spins and circular velocities than the 1σ errors found for the individual galaxies. Thus, although the degeneracy between the two parameters certainly contributes to the morphology of the different panels of Figure 16, it also reflects the bona fide distribution of the physical properties of the disks of galaxies in the local universe.

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We see that this method of sampling produces circular velocity distributions with long tails toward high v_c. These asymmetric distributions, for which the median or mode (rather than the mean) gives a better estimate of the peak of the distribution for the corresponding parameter, are a consequence of the nonregularity of the coverage of the model grid in Figure 15. In this work, we make use of the mode values and the percentiles obtained from these distributions to get the data points and average error bars in Figure 16. We also list the results obtained in Table 9.

Table 9.  GALEX/S⁴G Sample Circular Velocity and Spin Obtained from a Grid of BP00 Disk Models

Galaxy Namea	vcb	λc	Td
ESO 293-034	${130}_{-28}^{+40}$	${0.041}_{-0.007}^{+0.008}$	6.2
NGC 0024	${110}_{-27}^{+13}$	${0.027}_{-0.006}^{+0.003}$	5.1
ESO 293-045	${90}_{-16}^{+24}$	${0.066}_{-0.009}^{+0.009}$	7.8
UGC 00122	${70}_{-25}^{+15}$	${0.067}_{-0.007}^{+0.008}$	9.6
NGC 0059	${50}_{-\ldots }^{+\ldots }$	${0.032}_{-0.004}^{+0.004}$	−2.9
ESO 539-007	${110}_{-45}^{+25}$	${0.150}_{-0.029}^{+\ldots }$	8.7
ESO 150-005	${110}_{-35}^{+45}$	${0.150}_{-0.033}^{+\ldots }$	7.8
NGC 0115	${130}_{-29}^{+41}$	${0.044}_{-0.007}^{+0.010}$	3.9
UGC 00260	${430}_{-288}^{+\ldots }$	${0.070}_{-0.012}^{+0.023}$	5.8
...

Notes. The v_c and spin are obtained from BP00.

^aSame as the S⁴G nomenclature. ^bCircular velocity (mode) v_c plus–minus 1σ uncertainty in km s⁻¹. ^cSpin parameter (mode) λ plus 1σ uncertainty. ^dNumerical morphological type.

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

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We then compare our values with the observed values of the circular velocity for galaxies for which we have data (see Figure 18). We obtained the inclination-corrected maximum rotational (i.e., circular) velocity and its associated uncertainty from HyperLeda, vrot and e_vrot. These observed values are computed from the apparent maximum rotation velocity obtained from the width of the 21 cm line at various levels or from Hα rotation curves. They are homogenized using a large sample (>50,000) of measurements and are corrected for inclination (Paturel et al. 2003). We do not aim here to provide a fully coherent set of circular velocity measurements but to see whether or not the values that we obtain from our method are similar to the observed ones. In the case of our "best" χ² fit with cutoffs of R/R80 ≃ 0.5 and μ_[3.6] ≃ 23.5 mag arcsec⁻², 976 galaxies when using the median and 978 when using the mode out of 987 have actual measurements in HyperLeda. In the case of the mode, we quantify the 1σ (68.269%) distribution range to the left (right) of the mode by counting only the bins on the left-hand side (right-hand side) distribution starting from the bin of the mode but excluding it from the counts. Also, in case of multimodal distributions, we choose the bin with the smallest associated value. When we compare the two, we see that most of our values are larger than the observed ones but rarely above twice the observed rotational velocity. This effect comes partly from the accuracy of extracting the peak value over the skewed distributions of the circular velocities and spin parameters that we obtained from our method, as can be seen in Figure 18. When the distribution is skewed to the left, the mean is systematically larger than the median and the median is larger than the mode. It is vice versa when the skew is to the right: then the mean is smaller than the median and the median is smaller than the mode. This comes from our grid of models (Figure 15) and the sampling that we use to extract the best model. For given observational uncertainties and as the slope flattens out, higher circular velocity models that match the observations largely increase. The same holds true for larger values for the y intercept (i.e., fainter): the higher the spin, the more models that match the observations. Hence, the sampling distributions show a tail toward larger circular velocities and spin parameters. Using either the median or the mode gives similar results. This is shown in Figure 18, where using the median yields a similar scatter as when using the mode.

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Our values are consistent with the observed values within a factor of 0.5–2, especially if the very large uncertainties present are taken into account. The distributions given in Figure 16 provide powerful tools to test the predictions for numerical simulations of disks in a cosmological context.

Finally, we compare the color gradients (the slopes) obtained in the (FUV − NUV), (FUV − [3.6]), and (NUV − [3.6]) color profiles (with a cutoff at R/R80 = 0.5 but no cutoff in SB; see Table 6) against the mode circular velocities, mode spins that we derived with the method described in Section 5.1, and stellar masses calculated from the 3.6 μm SB. This is shown in Figure 19. The panels showing the circular velocity and spin comprise 987 galaxies, whereas the panels showing the stellar mass comprise 1541 galaxies. For the mode circular velocities, a large scatter is seen, especially for low-mass systems, in all three colors. In the case of the mode spin parameters, the scatter is very much the same throughout the entire range of spins for all morphological types and all three colors. Then, the color gradient versus the stellar mass plots show a large scatter for low-mass galaxies with stellar mass of around 10⁸–10⁹ M_⊙. On average, there is a trend toward a more negative gradient as we move to larger masses, therefore indicating bluer outer disks. However, most low-mass galaxies and a nonnegligible fraction of massive galaxies show positive color gradients.

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The results shown in Section 5 show that it is possible to derive (albeit with relatively large uncertainties in specific cases) the statistical distribution of the circular velocity (total mass) and spin (specific angular momentum) of galaxies from the analysis of deep near-infrared photometry of their disks. Besides, the fact that we can impose some simple criteria to isolate the disk component of the profiles makes this kind of analysis a very powerful tool for application to upcoming surface photometry data from LSST, EUCLID, or WFIRST.

Our analysis reveals that up to the current surface brightness detection limits (we note that all S⁴G galaxies are detected by Spitzer but many low surface brightness objects might still be missing from the catalogs), nearby galaxies show a wide distribution in spin with a maximum at λ ∼ 0.06 and a relatively high fraction (24%) of galaxies with λ > 0.08 (see top right panel of Figure 16).

The comparison of these values with those derived for the SINGS sample (Kennicutt et al. 2003) by Muñoz-Mateos et al. (2011) using a similar method and a similar set of models indicates a larger number of high-λ systems in our sample, in terms of the mean, median, and mode of the distribution. This is expected in the case of the SINGS sample, as this is biased toward high surface brightness systems with low angular momentum content relative to their mass. In addition, the SINGS sample (75 galaxies) was constructed to sample physical parameters (morphological type, luminosity, and FIR/optical luminosity ratio) and, therefore, is not representative in numbers of different kinds of galaxies. With respect to the predictions of semi-analytic models (e.g., Mo et al. 1998), we find a median value that is displaced toward larger spins (0.06) relative to recent simulations (∼0.036, quite independently of the galaxy mass and method of determining λ; Rodríguez-Puebla et al. 2016). To quantify this distribution, for the S⁴G sample, we derive mean (with 1σ distribution width) and median values of 0.062 ± 0.037 and ${0.054}_{-0.024}^{+0.030}$, respectively, while for MW mass halos, the models of Rodríguez-Puebla et al. (2016) yield a mean of 0.036 with a dispersion of 0.24 dex (for the spin parameter λ_P of Peebles 1969).

With regard to the circular velocities, we find a relatively narrow mode distribution peaking at $120\sim {v}_{{\rm{c}}}\sim 149\,\mathrm{km}\,{{\rm{s}}}^{-1}$ (ignoring the outliers; top left panel of Figure 16). This indicates a lack of low-mass (dwarf) systems, which is probably occurring both at the high surface brightness (because of our diameter selection for S⁴G) and low surface brightness (because of the limiting central surface brightness present in the catalogs of nearby galaxies) ends. Determining a volume- and diameter-corrected circular velocity (i.e., halo mass) function is beyond the scope of this paper. It could, however, be an interesting test for the models complementary to the halo mass functions derived from dynamical masses obtained from the modeling of 21 cm velocity maps and line profiles (de Blok et al. 2008; Papastergis et al. 2013; see also Zaritsky et al. 2014a, which connected the kinematics to the baryon fractions using the S⁴G).

Finally, the distribution of circular velocity versus spin (bottom panel of Figure 16) shows a larger dependence of the spin on the circular velocity than that found by Rodríguez-Puebla et al. (2016). In those cases where a significant portion of the input probability distribution of the y intercept and slope of the 1000 sampled points are outside of the grid, the mode is biased toward the most extreme value model in spin or circular velocity, or both. We then use the central value (if the central value is within the grid) instead of the mode. If the central value is not in the grid, we ignore it. These are shown as open circles. The percentages are the fractions of outliers in circular velocity (top left) and spin parameter (bottom right). Outliers in both parameters are included in both fractions. Uncertainties for the outliers are not included in the average uncertainty. The lack of objects of high spin and low circular velocity could be due to the surface brightness limit involved in defining our sample. However, this would make our distribution even wider toward high-λ values (see also Mo et al. 1998). Besides, the lack of low-mass, low-spin galaxies (high surface brightness dwarfs) is attributable to our diameter selection (>1), as these would be very compact dwarf systems.

Thus, we conclude that the strong dependence of the spin on the circular velocity and, in particular, the lack of low-mass galaxies at both extremes of the distribution in spin might be due to selection effects in the S⁴G survey (at least, we cannot conclude otherwise). The relatively flat distribution of spin values in the range λ = 0.03–0.11, which would be even more extended toward high-λ values, used to pose a challenge to current models of galaxy formation. However, Amorisco & Loeb (2016) recently showed that the properties and abundances in clusters of large, ultra-diffuse galaxies (UDGs) can be reproduced from within a standard cosmological framework and classical disk-formation models. It will be interesting to see, once catalogs of low surface brightness disk galaxies are available (including UDGs such as those found by Koda et al. 2015 in Coma), how they are distributed in terms of spin and circular velocity.

The UV emission found in the 1931 galaxies within the S⁴G sample is clearly aligned in two sequences of UV-to-IR colors. These two sequences, which are called the GRS and GBS and are best isolated in the (FUV − NUV) and (NUV − 3.6 μm) color–color diagram and when galaxies are previously split by morphological type (see Figure 11), each correspond to a different mechanism responsible for the UV emission. In the case of the GRS, the big change in (FUV − NUV) color (∼1.5 mag) with a change in (NUV − 3.6 μm) of <1 mag can only be attributed to the UV-upturn phenomenon (O'Connell 1999), which is believed to be caused by very hot EHB stars (see Zaritsky et al. 2015 and references therein).

On the other hand, the GBS has a slope of 0.12 (see Equation (1)), which implies a change of only 1.2 mag in the (FUV − NUV) color for a change of 10 mag in (NUV − 3.6 μm). As shown in Bouquin et al. (2015), this slope agrees well with the color correlation predicted by spectrophotometric models for the evolution of galaxy disks (see, e.g., BP00), so the UV emission of these objects can be interpreted as due to emission from relatively massive stars in the turnoff of the main sequence.

The GRS is mainly populated by E, E-S0, S0, and S0-a morphological types, and it is clearly isolated in its (FUV − NUV) blue end only in ETGs, i.e., E, E-S0, and S0 galaxies. This isolation is possible thanks to the dichotomy in the (NUV − 3.6 μm) colors of the central regions of ETGs (triangles in Figure 11). They are either very blue, indicating (residual) star formation in these innermost regions, or very red, which points toward a very old (light-weighted) stellar population. The fact that these very old populations in the centers of ETGs are also the ones showing the strongest UV upturn is something that has been explained in the past as being related to either the older age or higher metal (helium, at least) abundance of the horizontal-branch stars responsible for the UV emission in these regions (Boselli et al. 2005), but it may also be tied to the observations supporting differences in IMF (e.g., Cappellari et al. 2012, 2013a, 2013b; Conroy & van Dokkum 2012).

In early-to-intermediate spirals (S0-a through Sc), the central regions of many galaxies appear in the locus where the GBS and GRS overlap. Besides, the entire GBS is well populated by measurements obtained in both the inner and outer regions of galaxies. Thus, these colors are of no use to determine whether the UV emission from the bulges of these galaxies is dominated by emission from young massive or evolved low-mass EHB stars or a combination of both. Both the outer parts of early-to-intermediate spirals (except for regions populating the GGV; see below) and the late-type spirals (Sd and beyond) at all radii follow a narrow GBS. According to the color profiles shown in Figure 3, the majority of the galaxies that are found to populate the GBS show negative color gradients, which is in agreement with the global scenario of inside-out formation of their disks. The study of the most extreme cases of inside-out disk formation will be the subject of a future communication. At the surface brightness levels reached by our data, we do not find clear signs of color upbending, at least in the bands considered in this work (see Bakos et al. 2008 and Marino et al. 2016 for studies of reversed optical color profiles and ionized-gas chemical abundance gradients in outer disks).

Finally, it is also worth mentioning that the central regions of galaxies (despite having the highest signal-to-noise ratios) show the widest dispersion in all three (FUV − NUV), (FUV − 3.6 μm), and (NUV − 3.6 μm) colors among galaxy types and, as a whole, covering ∼10 mag in the case of the latter two colors. This, of course, indicates that nuclear regions are the least homogeneous within the population of local galaxies in terms of their stellar population and dust content.

Here we focus on discussing the properties of those galaxies that were identified in Bouquin et al. (2015) as being globally included in the so-called GGV and of those regions within galaxies that are now found to be located in the GGV even though they are part of the GBS or GRS when considered as a whole.

In Figures 7 and 8, we showed that galaxies that belong (globally) to the GGV are mainly lenticulars and early-type spirals (S0-a through Sb) showing a relatively narrow distribution of (observed) sSFR around 10⁻¹² yr⁻¹. Furthermore, Figure 9 shows that the outer regions of GGV galaxies behave differently from the outer regions of most GBS systems, with the FUV−3.6 μm color getting redder as we move progressively toward their outer disks. This clearly indicates that the reason these objects are in the GGV is that their disks are redder, for the same morphological type and surface brightness, than those of most GBS galaxies. Exploration of Figure 9 in the case of the GBS shows that the region of red disks is populated by a number of ETGs with profiles similar in shape to those found in the GRS, but that they probably show a very blue nucleus that places them in the GBS when considered as a whole.

A small fraction of GBS galaxies (mainly early-type spirals, but only a fraction of them) have disks that also redden with radius. These are objects that are likely to evolve into GGV galaxies or objects that GGV galaxies will evolve into, depending on whether GGV galaxies are quenching their star formation or regrowing a disk.

Our analysis shows that the fraction of galaxies belonging to dense environments is higher for GGV galaxies than for GBS galaxies but less than for the GRS. This result, combined with the fact that GGV galaxies have redder outer disks, hints at the direction of the evolution, from GBS to GRS, that favors star formation quenching due to environmental effects. Similar results have been obtained in the analysis of galaxies in clusters (see Bamford et al. 2009; Wolf et al. 2009; Cibinel et al. 2013; Head et al. 2014).

Moreover, a study of galaxies in transition in different environments (Vulcani et al. 2015) shows that galaxies in groups have a higher quenching efficiency than field galaxies. These results show that color transformation is due to the overall decrease in SFR, both in bulges and disks, while maintaining the morphology. They also show that morphological transformation is due to an increase in bulge-to-disk ratio because of disk removal, not because of the growth of the bulge, in disagreement with a bulge enhancement and absence of a disk-fading scenario (Christlein & Zabludoff 2004). What is presented in Section 4 is in agreement with the former, where disk fading occurs, resulting in an increase in the bulge-to-disk ratio.

In this work, we make use of the stellar mass surface density Σ_⋆ (M_⊙ pc^–2) distribution that is obtained from the 3.6 μm surface brightness (AB mag arcsec^–2) radial profiles. We start from the definition of absolute magnitude,

$$\begin{eqnarray}&&{M}_{[3.6],\star }={M}_{[3.6],\odot }-2.5{\mathrm{log}}_{10}\left(\displaystyle \frac{{L}_{[3.6],\star }}{{L}_{[3.6],\odot }}\right),\end{eqnarray} \tag{ 7 }$$

where M_[3.6],⋆ and L_[3.6],⋆ are the 3.6 μm absolute magnitude (AB) and luminosity (in erg s⁻¹ Hz⁻¹) of the galaxy and ${M}_{[3.6],\odot }$ and L_[3.6],⊙ are the solar 3.6 μm absolute magnitude and luminosity.

We also need the following expression for the mass-to-light ratio:

$$\begin{eqnarray}&&\displaystyle \frac{{M}_{\star }}{{L}_{[3.6],\star }}={{\rm{\Upsilon }}}_{[3.6]},\end{eqnarray} \tag{ 8 }$$

where the mass-to-light ratio of the Sun (M_⊙/L_[3.6],⊙) is unity and M_⋆ is the stellar mass of the galaxy, ${L}_{[3.6],\star }$ is the luminosity at 3.6 μm, M_⊙ is solar mass, and L_⊙,3.6 is the solar luminosity at 3.6 μm. Here ϒ_[3.6] is the mass-to-light ratio at 3.6 μm as obtained by Meidt et al. (2014) and is equal to 0.6 (assuming a Chabrier IMF).

Rearranging Equation (7), we have

$$\begin{eqnarray}&&\displaystyle \frac{{L}_{[3.6],\star }}{{L}_{[3.6],\odot }}={10}^{-0.4({M}_{[3.6],\star }-{M}_{[3.6],\odot })}.\end{eqnarray} \tag{ 9 }$$

Rearranging Equation (8) and adding the conversion factor a_IMF for the transformation from a Chabrier IMF (Chabrier 2003) to Kroupa IMF (Kroupa 2001), we get

$$\begin{eqnarray}&&\displaystyle \frac{{M}_{\star }}{{M}_{\odot }}=\displaystyle \frac{{L}_{[3.6],\star }}{{L}_{[3.6],\odot }}\cdot {{\rm{\Upsilon }}}_{[3.6]}\cdot {a}_{\mathrm{IMF}},\end{eqnarray} \tag{ 10 }$$

where we use, in our case, ${a}_{\mathrm{IMF}}=\tfrac{{\text{}}M/L(\mathrm{Kroupa})}{{\text{}}M/L(\mathrm{Chabrier})}=1.034$ (conversion factors from Madau & Dickinson 2014).

We then take the log of Equation (10), combined with Equation (9):

$$\begin{eqnarray}&&{\mathrm{log}}_{10}\left(\displaystyle \frac{{M}_{\star }}{{M}_{\odot }}\right)={\mathrm{log}}_{10}\left(\displaystyle \frac{{L}_{[3.6],\star }}{{L}_{[3.6],\odot }}\right)+{\mathrm{log}}_{10}({{\rm{\Upsilon }}}_{[3.6]}\cdot {a}_{\mathrm{IMF}}),\end{eqnarray} \tag{ 11 }$$

i.e.,

$$\begin{eqnarray}&&{\mathrm{log}}_{10}\left(\displaystyle \frac{{M}_{\star }}{{M}_{\odot }}\right)=0.4({M}_{[3.6],\odot }-{M}_{[3.6],\star })+{\mathrm{log}}_{10}({{\rm{\Upsilon }}}_{[3.6]}\cdot {a}_{\mathrm{IMF}}).\end{eqnarray} \tag{ 12 }$$

Finally, changing M_[3.6],⋆ to ${\mu }_{[3.6]}({\rm{AB}}\,\mathrm{mag}\,{\mathrm{arcsec}}^{-2})\,+5-5{\mathrm{log}}_{10}d(\mathrm{pc})$ and converting arcsec⁻² to pc⁻² gives

$$\begin{eqnarray}{{\rm{\Sigma }}}_{\star }({M}_{\odot }\,{\mathrm{pc}}^{-2}) & = & {{\rm{\Upsilon }}}_{[3.6]}\cdot {a}_{\mathrm{IMF}}\cdot {10}^{0.4{M}_{[3.6],\odot }}\\ & & \cdot {10}^{-0.4\cdot ({\mu }_{[3.6]}+5-5{\mathrm{log}}_{10}d)}\cdot {\left(\displaystyle \frac{206265}{d}\right)}^{2},\end{eqnarray} \tag{ 13 }$$

where M_[3.6],⊙ is the Sun's 3.6 μm absolute AB magnitude, which is taken to be 6.03 mag (converted to AB scale from the Vega magnitude value, M_{⊙,3.6, Vega} = 3.24, given by Equation (13) in Oh et al. 2008).

This corresponds to a stellar mass surface density M_⋆/area = 1.045 M_⊙ pc⁻² at a 3.6 μm surface brightness μ_[3.6] = 27 mag arcsec⁻² in the case of a Chabrier IMF and M_⋆/area = 1.080 M_⊙ pc⁻² in the case of a Kroupa IMF. The equation, then, simplifies to the following:

$$\begin{eqnarray}&&{\mathrm{log}}_{10}({{\rm{\Sigma }}}_{\star }({M}_{\odot }\,{\mathrm{pc}}^{-2}))=10.819-0.4{\mu }_{[3.6]}+{\mathrm{log}}_{10}{a}_{\mathrm{IMF}},\end{eqnarray} \tag{ 14 }$$

where the term log₁₀ a_IMF = 0 for a Chabrier IMF, 0.015 for a Kroupa IMF, and 0.215 for a Salpeter IMF.

We start with the SFR (UV), assuming a Salpeter IMF (Salpeter 1955) and using a calibration by Madau et al. (1998), as provided by Kennicutt (1998), which we can convert to the expression for a Kroupa IMF by multiplying by b_IMF = 0.67 or by b_IMF = 0.63 for a Chabrier IMF, as reviewed and prescribed in Kennicutt & Evans (2012) and Madau & Dickinson (2014),

$$\begin{eqnarray}&&\mathrm{SFR}({M}_{\odot }\,{\mathrm{yr}}^{-1})=1.4\times {10}^{-28}\cdot {b}_{\mathrm{IMF}}\cdot {L}_{\nu }\,(\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{Hz}}^{-1}),\end{eqnarray} \tag{ 15 }$$

and with the following expression of luminosity:

$$\begin{eqnarray}{L}_{\nu } & = & 4\pi {(d(\mathrm{cm}))}^{2}{f}_{\nu }\\ {L}_{\nu } & = & 4\pi {[d(\mathrm{pc})\cdot 3.086\times {10}^{18}(\mathrm{cm}/\mathrm{pc})]}^{2}{10}^{-0.4(\mathrm{FUV}+48.6)}.\end{eqnarray} \tag{ 16 }$$

Combining the two equations above gives

$$\begin{eqnarray}{\mathrm{log}}_{10}(\mathrm{SFR})({M}_{\odot }\,{\mathrm{yr}}^{-1}) & = & 2{\mathrm{log}}_{10}d(\mathrm{pc})-0.4\,\mathrm{FUV}\\ & & -9.216+{\mathrm{log}}_{10}{b}_{\mathrm{IMF}},\end{eqnarray} \tag{ 17 }$$

where FUV is in AB magnitudes, the distance d is in pc, and log₁₀ b_IMF = 0, −0.174, and −0.201 for a Salpeter, Kroupa, and Chabrier IMF, respectively.

Second, we need to introduce the distance modulus $m-M=5-5{\mathrm{log}}_{10}d(\mathrm{pc})$ into Equation (12), so this becomes

$$\begin{eqnarray}{\mathrm{log}}_{10}\left(\displaystyle \frac{{M}_{\star }}{{M}_{\odot }}\right) & = & {\mathrm{log}}_{10}({{\rm{\Upsilon }}}_{3.6}\cdot {a}_{\mathrm{IMF}})\\ & & -0.4([3.6]+5-5{\mathrm{log}}_{10}d-6.03),\end{eqnarray} \tag{ 18 }$$

where [3.6] is the apparent AB magnitude at 3.6 μm, d is the distance in pc, and M_⊙,3.6,AB = 6.03 (see Appendix A).

Finally, we combine Equations (17) and (18):

$$\begin{eqnarray}&&{\mathrm{log}}_{10}(\mathrm{sSFR})={\mathrm{log}}_{10}\left(\displaystyle \frac{\mathrm{SFR}}{{M}_{\star }}\right)={\mathrm{log}}_{10}(\mathrm{SFR})-{\mathrm{log}}_{10}({M}_{\star }).\end{eqnarray} \tag{ 19 }$$

It thus becomes

$$\begin{eqnarray}{\mathrm{log}}_{10}(\mathrm{sSFR}) & = & -0.4(\mathrm{FUV}-[3.6])-9.628+{\mathrm{log}}_{10}{b}_{\mathrm{IMF}}\\ & & -{\mathrm{log}}_{10}({{\rm{\Upsilon }}}_{3.6}\cdot {a}_{\mathrm{IMF}}).\end{eqnarray} \tag{ 20 }$$

We can thus obtain the logarithm of the sSFR (in units of yr⁻¹) from the (FUV − [3.6]) (AB mag) color. We emphasize that these quantities would not be corrected for extinction.