RADIAL STAR FORMATION HISTORIES IN 15 NEARBY GALAXIES

For the EDGES sample we constructed large mosaics based on Spitzer Space Telescope imaging that trace 3.6 and 4.5 μm substructures out to at least five times the optical radius a₂₅. Compared to most Spitzer/IRAC imaging campaigns of nearby galaxies, the EDGES near-infrared image mosaics are quite deep; the 1800 s integration per position obtained for EDGES targets is 7.5 times longer than what was obtained for the SINGS (Kennicutt et al. 2003), LVL (Dale et al. 2009), and S⁴G (Sheth et al. 2010) surveys, and 12–30 times longer compared to the IRAC GTO project (Pahre et al. 2004). We reach a 1σ per pixel sensitivity of 2 kJy sr⁻¹, and averaging over several square arcminutes can reach down to below 0.4 kJy sr⁻¹ (fainter than 29 mag arcsec⁻² AB), a level necessary for securely detecting faint stellar streams associated with nearby galaxies (Krick et al. 2011; Barnes et al. 2014; Staudaher et al. 2015). For comparison, WISE achieves a 3.4 μm diffuse sensitivity larger than 1 kJy sr⁻¹ over a ${5}^{\prime }\times \;$ ${5}^{\prime }$ area (Wright et al. 2010). The photometric accuracy is taken to be 5% (see also Reach et al. 2005).

Archival ultraviolet and infrared data were gathered from the GALEX, Spitzer, WISE, and Herschel Space Observatory archives. In all instances, priority was given to longer-exposure data, where available. As such, the ultraviolet data for only two galaxies (see Table 2) stem exclusively from the shallow All-Sky Imaging Survey for which the integrations are ∼0.1 ks (Martin et al. 2005); the majority of the GALEX imaging utilized here arises from integrations longer than 1 ks. For these longer integrations the limiting surface brightnesses are ∼32.5 and 32.0 mag arcsec⁻² AB, respectively for the far-ultraviolet and near-ultraviolet channels, based on the standard deviations in the median sky values for a set of sky apertures placed beyond the galaxy emission (see Section 4); for the small set of shorter integration ultraviolet images, the surface brightness limits are about 1–2 mag arcsec⁻² shallower. Likewise, most of the infrared data on warm dust emission derives from WISE 12 μm (Wright et al. 2010) and Spitzer 24 μm imaging (Dale et al. 2009), with WISE 22 μm and Herschel 70 μm used to fill in any gaps in the Spitzer 24 μm archives. The surface brightness sensitivity of the infrared data is approximately 26.7 AB mag arcsec⁻² at 12 μm, 25.0 mag arcsec⁻² at 22 μm, 26.0 mag arcsec⁻² at 24 μm, and 19.5 mag arcsec⁻² at 70 μm(see also Wright et al. 2010; Dale et al. 2012). The GALEX photometric accuracy is estimated at 0.05 mag (Gil de Paz et al. 2007; Morrissey et al. 2007) and the infrared calibrations are known to ∼10%, 10%, 7%, and 5% at 12, 22, 24, and 70 μm, respectively (Dale et al. 2007, 2012; Wright et al. 2010). These ancillary/archival data sets have angular resolutions of ∼5''–6''.

Table 2.  Imaging Integrations

Galaxy	GALEX	GALEX	WIRO	WIRO	WIRO	Spitzer	WISE	Spitzer
	FUV	NUV	${u}^{\prime }$	${g}^{\prime }$	${r}^{\prime }$	3.6 μm	12 μm	24 μm
NGC 4220	12101	12101	3600	3600	3600	1800	72	10
UGC 7301	13756	13757	3600	3600	3600	1800	72	72a
NGC 4242	1683	3282	3600	3600	3600	1800	72	160
NGC 4485	1587	2810	3600	3600	3600	1800	72	160
NGC 4490	1587	2810	3600	3600	3600	1800	72	160
NGC 4618	3242	3259	3600	3600	3600	1800	72	160
NGC 4625	3259	3259	3600	3600	3600	1800	72	160
NGC 4707	1664	1664	3600	3600	3600	1800	72	160
UGC 8303	205	1623	3600	3600	3600	1800	72	72a
UGC 8320	1576	3116	⋯	3600	3600	1800	72	160
NGC 5055	3002	3754	⋯	3600	3600	1800	72	160
NGC 5229	2757	2757	3600	3600	3600	1800	72	160
NGC 5273	1659	1659	3600	3600	3600	1800	72	282b
NGC 5523	96	96	3600	3600	3600	1800	72	72a
NGC 5608	105	105	3600	3600	3600	1800	72	72a

Notes. Integrations are in seconds per position on the sky. The post-processing images utilized here have resolutions of ≈ 6'' (GALEX, WISE 12 μm, Spitzer 24 μm, Herschel 70 μm), 17 (Spitzer 3.6 μm), and 20 (WIRO).

^aWISE 22 μm. ^bHerschel 70 μm.

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New deep ucloseup-->${}^{\prime }$closeup-->gcloseup-->${}^{\prime }$closeup-->rcloseup-->${}^{\prime }$closeup--> imaging was obtained on the WIRO 2.3 m telescope with the WIROPrime camera (Pierce & Nations 2002) over the course of the summer of 2014 (Figure 1). For each galaxy and each filter 12 individual 300 s frames were taken. Individual frames were randomly dithered with small offsets for enhanced pixel sampling. Each night a series of zero second bias frames were obtained in addition to a series of twilight sky flats within each filter.

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The optical images were processed with standard procedures, including subtraction of a master bias image and removal of pixel-to-pixel sensitivity variations through flatfield corrections. Typically the sky flat was constructed from flats taken on the same night, but occasionally flats from multiple consecutive nights were utilized. The 12 dithered 300 s frames for a galaxy taken in one filter were aligned and stacked, resulting in images with integrations equivalent to one hour. The astrometric solutions and flux zeropoints were calibrated using positions and photometry extracted from Sloan Digital Sky Survey (SDSS; York et al. 2000) imaging on several foreground stars spread across each image stack. Scattered light from Galactic dust is fortunately not an issue for these observations, as all 15 targets lie north of $b\;=\;+66^\circ$. The uncertainties in the zeropoint calibrations were typically 3%. The 5σ ucloseup-->${}^{\prime }$closeup-->gcloseup-->${}^{\prime }$closeup-->rcloseup-->${}^{\prime }$closeup--> point source sensitivities are ∼23.0, 24.0, 23.4 mag AB for 28 diameter apertures (twice the seeing FWHM), about 1–1.8 mag deeper than SDSS (e.g., sdss.org/dr12/scope; Cook et al. 2014). The stacked images are flat to 1% or better on 10' scales. The limiting ucloseup-->$^{\prime}$closeup-->gcloseup-->$^{\prime}$closeup-->rcloseup-->$^{\prime}$closeup--> surface brightnesses are ∼28.2, 28.4, and 28.0 mag arcsec⁻² AB, based on the standard deviations in the median sky values for a set of sky apertures placed beyond the galaxy emission (see Section 4), about 1 mag arcsec⁻² deeper than SDSS (Pohlen & Trujillo 2006; D'Souza et al. 2014). Similar to what was done for the imaging at all other wavelengths studied here, foreground stars and background galaxies were removed from each optical image using IRAF/IMEDIT and a local sky interpolation. This editing typically reached down to sources of several microJanskys (∼21–22 mag AB). Of particular note is the bright foreground star superposed on the nucleus of NGC 4707. This star was edited in the ucloseup-->${}^{\prime }$closeup-->gcloseup-->${}^{\prime }$closeup-->rcloseup-->${}^{\prime }$closeup--> and 3.6 μm images. Additionally, the overlap region between NGC 4485 and NGC 4490 was edited. Fortunately this region is fractionally small compared to the total areas within the outermost elliptical annuli: approximately $\frac{1}{4}$ for NGC 4485 and $\frac{1}{8}$ for NGC 4490.

Photometry was obtained for each galaxy using IRAF/IMCNTS and a series of elliptical annuli covering semimajor axis a ranges of 0 < $\frac{a}{{a}_{25}}$ < 0.25, 0.25 < $\frac{a}{{a}_{25}}\;$ < 0.5, 0.5 < $\frac{a}{{a}_{25}}$ < 0.75, 0.75 < $\frac{a}{{a}_{25}}$ < 1, 1 < $\frac{a}{{a}_{25}}$ < 1.25, and 1.25 < $\frac{a}{{a}_{25}}\;$ < 1.5. For the range of galaxy angular sizes in our sample, these $\frac{1}{4}{a}_{25}$ annular widths correspond to a range of values between 14'' (for UGC 7301) and 94'' (for NGC 5055). Traditional surface brightness analyses typically rely on a finer set of annular widths, but any radial analysis that requires a full panchromatic data set (e.g., SED fitting) is necessarily limited by the wavelength for which the detected extent of the emission is smallest. Our choice of coarsely spaced annular apertures provides less spatial information but allows for more robust signal-to-noise in the galaxy outskirts where the emission is weakest. All annuli for a given galaxy used the same (NED-based) centroids, position angles, and ellipticities. Photometric uncertainties ${\epsilon }_{{\rm{total}}}$ are computed by summing in quadrature the calibration error ${\epsilon }_{{\rm{cal}}}$ and two uncertainties ${\epsilon }_{{\rm{sky,local}}}$ and ${\epsilon }_{{\rm{sky,global}}}$ based on the measured sky fluctuations, i.e.,

$$\begin{eqnarray}&&{\epsilon }_{{\rm{total}}}=\sqrt{{\epsilon }_{{\rm{cal}}}^{2}+{\epsilon }_{{\rm{sky,local}}}^{2}+{\epsilon }_{{\rm{sky,global}}}^{2}}\end{eqnarray} \tag{ 1 }$$

with

$$\begin{eqnarray}&&{\epsilon }_{{\rm{sky,local}}}={\sigma }_{{\rm{sky,local}}}{{\rm{\Omega }}}_{{\rm{pix}}}\sqrt{{N}_{{\rm{pix}}}}\end{eqnarray} \tag{ 2 }$$

and

$$\begin{eqnarray}&&{\epsilon }_{{\rm{sky,global}}}={\sigma }_{{\rm{sky,global}}}{{\rm{\Omega }}}_{{\rm{pix}}}{N}_{{\rm{pix}}}\end{eqnarray} \tag{ 3 }$$

where ${\sigma }_{{\rm{sky,local}}}$ is the standard deviation of the sky values in the combined set of sky apertures, ${\sigma }_{{\rm{sky,global}}}$ is the standard deviation of the median sky values for the set of sky apertures, ${{\rm{\Omega }}}_{{\rm{pix}}}$ is the solid angle subtended per pixel, and ${N}_{{\rm{pix}}}$ is the number of pixels in an annulus. Following Boselli et al. (2003) and Ciesla et al. (2012), ${\sigma }_{{\rm{sky,local}}}$ accounts for random error contributions from small-scale sky fluctuations (e.g., faint background sources) whereas ${\sigma }_{{\rm{sky,global}}}$ represents large-scale deviations in the sky value such as errors due to flat-fielding. All fluxes were corrected for Galactic extinction (Schlafly & Finkbeiner 2011) assuming ${A}_{V}/E(B-V)\approx 3.1$ and the reddening curve of Draine (2003).

The full ultraviolet–infrared SEDs were fitted using the Bayesian-based CIGALE software package (Noll et al. 2009; D. Burgarella 2015, in preparation; Boquien 2015). This package allows the user to estimate fundamental parameters such as stellar mass, star formation rate, and the characteristic epoch of star formation and its decay rate using an energy-balanced approach whereby the diminution of ultraviolet/optical light via dust extinction is accounted for in equal amounts in the infrared via dust emission. In our SED fitting we adopt the stellar and dust emission libraries of Bruzual & Charlot (2003) and Dale et al. (2014), respectively, the Chabrier (2003) stellar initial mass function, and a dust attenuation curve based on the work of Calzetti et al. (2000) and Leitherer et al. (2002). The fit parameters include metallicity, extinction, attenuation curve modifier,¹¹ and characteristics of the major star-forming events. For example, an exponential decreasing star formation history (also known as the "τ model") beginning at time t₁ with e-folding time ${\tau }_{1}$ and amplitude ${{\mathcal{A}}}_{1}$ would be expressed as

$$\begin{eqnarray}&&\mathrm{SFR}(t)\propto {{\mathcal{A}}}_{1}{e}^{-(t-{t}_{1})/{\tau }_{1}},\ \ \ \ {{\mathcal{A}}}_{1}(t-{t}_{1}\lt 0)=0\end{eqnarray} \tag{ 4 }$$

(Papovich et al. 2001; Borch et al. 2006; Gawiser et al. 2007; Lee et al. 2009). Another form of star formation history we utilize here is the so-called delayed star formation history model (Lee et al. 2010, 2011; Schaerer et al. 2013), i.e.,

$$\begin{eqnarray}&&\mathrm{SFR}(t)\propto {{\mathcal{A}}}_{0}{{te}}^{-(t-{t}_{0})/{\tau }_{0}},\ \ \ {{\mathcal{A}}}_{0}(t-{t}_{0}\lt 0)=0.\end{eqnarray} \tag{ 5 }$$

Unlike the decreasing exponential star formation history for which the maximum occurs at $t-{t}_{1}=0,$ in this formulation the maximum star formation rate occurs at the value of the e-folding rate after the onset of star formation: $t-{t}_{0}={\tau }_{0}.$ Figure 3 shows the characteristics of four example delayed star formation models in addition to an example of an exponential decreasing model. Note how smaller values of ${\tau }_{0}$ correspond to more sharply defined and earlier characteristic epochs of star formation. Both the delayed and decreasing exponential models for star formation histories are utilized in this work since they are common, simple prescriptions that rely on a small number of parameters. CIGALE-based simulations show that the delayed star formation model provides superior accuracy in recovering galaxy stellar masses and star formation rates (Buat et al. 2014; Ciesla et al. 2015). However, Noll et al. (2009) caution that the degeneracies inherent to the models result in less than well-constrained τ values for fits based on broad-band photometry of nearby galaxies; in such cases τ values can only typically be characterized as "rather high" or "rather low" (see also Hayward & Smith 2015; Smith & Hayward 2015)

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The input parameter ranges are provided in Table 3. The main output physical parameters (e.g., ${M}_{*},$τ, A_V) are computed based on a probability distribution function (PDF) analysis: the SED fit ${\chi }^{2}$ is derived for each combination of input parameters, a PDF is constructed for each parameter based on the ${\chi }^{2}$ for the best fit models, and the probability-weighted means and standard deviations of the PDFs are adopted as the values and associated uncertainties of the output physical parameters (see Section 2.2 of Noll et al. 2009 for details of the process).

Table 3.  Fit Parameters

Parameter	Notation	Allowed Values
Metallicity	Z	0.008, 0.02, 0.05
IMF		Chabrier
Color excess: young stars	$E(B-V{)}_{*}^{{\rm{y}}}$	0.0, 0.025, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.4
Color excess: old stars	$E(B-V{)}_{*}^{{\rm{o}}}$	$0.44E(B-V{)}_{*}^{{\rm{y}}}$
Dust emission template	α	0.5, 1.0, 1.25, 1.50, 1.75, 2.0, 2.25, 2.50, 3.00
Slope of power law that modifies attenuation curve	δ	−0.5, −0.4, −0.3, −0.2, −0.1, 0
Delayed Star Formation History
SFR e-folding time (Gyr)	${\tau }_{0}$	0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7, 7.5, 8, 10
Age of oldest stars (Gyr ago)	t0	11
Single Exponential Decreasing Star Formation History
SFR e-folding time (Gyr)	${\tau }_{1}$	0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7, 7.5, 8, 10
Age of oldest stars (Gyr ago)	t1	11

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Table 4 provides the integrated fluxes arising from within the $2{a}_{25}\times 2{b}_{25}$ apertures. For the subset of the sample that has published data, spanning nine galaxies and seven wavelengths, these fluxes agree quite well with published values: the average ratio of these fluxes to literature fluxes is 0.98 ± 0.02. Two notable exceptions are for the GALEX measurements of NGC 4625, a galaxy with known extended ultraviolet emission (Thilker et al. 2007).

Table 4.  Integrated Fluxes

Galaxy	GALEX	GALEX	WIRO	WIRO	WIRO	Spitzer	WISE	Spitzer
	FUV	NUV	${u}^{\prime }$	${g}^{\prime }$	${r}^{\prime }$	3.6 μm	12 μm	24 μm
NGC 4220	494±050E−3	142±014E−2	154±008E−1	712±035E−1	143±007E+0	196±009E+0	138±014E+0	147±017E+0
UGC 7301	415±041E−3	567±056E−3	129±007E−2	344±017E−2	518±026E−2	311±015E−2	⋯	⋯
NGC 4242	891±089E−2	140±014E−1	422±051E−1	123±006E+0	159±008E+0	120±006E+0	847±106E−1	109±017E+0
NGC 4485	124±012E−1	163±016E−1	284±014E−1	571±028E−1	979±049E−1	419±021E−1	961±097E−1	201±015E+0
NGC 4490	550±056E−1	875±087E−1	203±010E+0	449±022E+0	807±040E+0	519±026E+0	152±015E+1	428±030E+1
NGC 4618	261±026E−1	333±033E−1	632±038E−1	158±008E+0	213±011E+0	167±008E+0	258±026E+0	397±030E+0
NGC 4625a	409±043E−2	594±059E−2	135±013E−1	344±017E−1	535±030E−1	493±024E−1	101±010E+0	127±009E+0
NGC 4707	329±033E−2	374±039E−2	599±040E−2	136±009E−1	187±011E−1	115±006E−1	⋯	⋯
UGC 8303	351±035E−2	423±042E−2	691±062E−2	174±013E−1	219±011E−1	137±007E−1	134±024E−1	511±075E−1b
UGC 8320	533±053E−2	707±071E−2	⋯	281±014E−1	364±019E−1	188±009E−1	272±041E−2	112±022E−1
NGC 5055a	364±036E−1	663±067E−1	⋯	108±005E+1	187±009E+1	254±012E+1	498±050E+1	574±040E+1
NGC 5229	182±018E−2	251±025E−2	536±031E−2	122±006E−1	184±009E−1	117±006E−1	444±115E−2	131±016E−1
NGC 5273	223±024E−3	104±015E−2	155±008E−1	648±032E−1	127±006E+0	124±006E+0	416±054E−1	294±031E+1c
NGC 5523	402±040E−2	587±059E−2	149±008E−1	395±020E−1	616±031E−1	542±027E−1	749±075E−1	136±015E+0b
NGC 5608	321±032E−2	387±038E−2	660±039E−2	147±007E−1	200±010E−1	109±005E−1	295±042E−2	607±064E−2b

Notes. Fluxes (in mJy) are derived using $2{a}_{25}\;\times \;2{b}_{25}$ elliptical apertures. The compact table entry format TUV ± WXYEZ implies (T.UV ± W.XY)$\;\times \;{10}^{{\rm{Z}}}.$ All fluxes were corrected for Galactic extinction (Schlafly & Finkbeiner 2011) assuming ${A}_{V}/E(B-V)\approx 3.1$ and the reddening curve of Draine (2003). The uncertainties include both statistical and systematic effects.

^aUltraviolet emission extends beyond the aperture (Thilker et al. 2007). ^bWISE 22 μm. ^cHerschel 70 μm.

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Figure 4 displays the surface brightness profiles for the eight different wavelengths observed for each galaxy. The profiles generally fall with radius, though for a few galaxies the peak of the warm dust emission (usually traced by MIPS 24 μm) is significantly spatially displaced from the galaxy centers; the warm dust emission does not spatially mimic the stellar emission for NGC 4242, NGC 4485, UGC 8303, and NGC 5523. The dust emission surface brightness profile is also one of two profiles that is not systematically detected sample-wide out to the last annular region of 1.25 < $a/{a}_{25}$ < 1.50; the (detection of the) dust emission is truncated for NGC 4420, NGC 4242, NGC 4625, UGC 8320, NGC 5273, and NGC 5608 (the far-ultraviolet is also undetected for the last annular region of NGC 4220). Many galaxies show fairly consistent profile shapes in the ultraviolet/optical/near-infrared, but we note that the two most inclined galaxies in our sample, UGC 7301 ($b/a=0.13$) and NGC 5229 ($b/a=0.17$), exhibit the smallest scatters in the surface brightness profile (log-linear) slopes $m(\lambda )={\rm{\Delta }}\mathrm{log}{I}_{\nu }(\lambda )/{\rm{\Delta }}(a/{a}_{25}),$ with $\sigma (m)=0.10$ dex and 0.08 dex for UGC 7301 and NGC 5229, respectively. This similarity in slopes across wavelengths for the more inclined systems is not the result of reddening effects, since the internal extinctions derived in the SED fitting (Section 4.2) are not unusually large for UGC 7301 and NGC 5229. Rather, the similarity is more likely due to the projected mixing of inner and outer disk regions for the central annular apertures. The less inclined galaxies show nuanced differences in their multi-wavelength surface brightness profiles, which in turn lead to variations in the color profiles and in the interpreted star formation histories, as discussed below.

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Pohlen & Trujillo (2006) studied the ${g}^{\prime }$ and ${r}^{\prime }$ surface brightness profiles of 85 moderately inclined, late-type spiral galaxies from SDSS. Martín-Navarro et al. (2012) carried out a similar study for 34 inclined galaxies using SDSS and Spitzer 3.6 μm images. Pohlen & Trujillo (2006) found that 60% (30%) of their systems displayed exponential disks followed by downbending (upbending) surface brightness profiles; Martín-Navarro et al. (2012) found generally similar results. They saw downbending features primarily for later-type spiral galaxies and upbending for earlier-type spirals. Our relatively coarse annular sampling may not yield surface brightness profiles as detailed as those studied by Pohlen & Trujillo (2006), but we can explore any trends near the galaxy outskirts with higher signal-to-noise, especially since our images go significantly deeper (Section 3.3). Our multi-wavelength collection of surface brightness profiles in Figure 4 exhibits all three types of profiles. However, only two of our targets satisfy the Pohlen & Trujillo (2006) joint criteria of late-type spiral morphology ($3\leqslant T\leqslant 8$) and moderately inclined ($b/a\gt 0.5$), so no strong conclusions based on going significantly deeper than SDSS can be drawn here.

On the other hand, stacking the images of many galaxies can yield exquisitely sensitive surface brightness profiles (e.g., Zibetti et al. 2004; Tal & van Dokkum 2011). Though such analyses cannot provide insight on individual systems, they do inform us about the broad brush characteristics for large ensembles of galaxies. D'Souza et al. (2014) stack the $g^{\prime}$ and $r^{\prime}$ SDSS images for over 45,000 isolated galaxies at redshifts $0.05\leqslant z\leqslant 0.1.$ Binned according to global galaxy stellar mass, their stacks probe down to an effective surface brightness of $\mu (r)\sim 32$ mag arcsec⁻² (compared to 27 mag arcsec⁻² for Pohlen & Trujillo 2006). They find that the outer portions, which they refer to as the stellar halos, are redder than the main disk for all systems with ${M}_{*}\lt {10}^{11}\;{L}_{\odot },$ and that the detected halo mass fraction rises with increasing galaxy mass. This reddening feature is not due to effects of dust attenuation since galaxy dust mass surface densities are minimal for larger radii (Muñoz-Mateos et al. 2009; Aniano et al. 2012). Figure 5 presents a compilation of the radial g' − r' trends for our sample. Our galaxies exhibit a similar range in g' − r' color as seen in the SDSS stacks (see also West et al. 2009; Tortora et al. 2010). Considered as a whole, our sample shows an outward reddening color trend (upper panel of Figure 6); on average, our galaxies are redder at $a=1.38{a}_{25}$ by 0.08 mag in g' − r' compared to the value at $a=0.63{a}_{25}.$ D'Souza et al. (2014) suggest such peripheral reddening implies accretion of old stars into the stellar halo. However, given the typical color uncertainties in the outskirts, this average reddening is modest and is clearly seen for only a few individual galaxies (e.g., NGC 4490, NGC 4618, NGC 4707, NGC 5608). There is a considerable diversity in the galaxy color profiles, with some galaxies exhibiting flat (NGC 5055, UGC 7301) or even blue trends (NGC 5273, NGC 5523), and so caution must be taken when analyzing sample-wide averages.

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It has been shown that the extended wings of the point-spread function (PSF) can lead to artificially red optical colors for observations utilizing thinned CCDs (Michard 2002). This so-called "red halo" effect stems from increased instrumental scattering at longer wavelengths for radial distances greater than ∼15'', leading some authors to ignore SDSS i band data when studying galaxy colors: the effect is much less pronounced for the shorter-wavelength SDSS filters while the SDSS z band data are taken with unthinned CCDs and thus do not suffer from this effect (Wu et al. 2005; Liu et al. 2009). Though the WIROPrime camera utilizes a thinned detector, i band data were not utilized in this analysis. A second potential PSF-related issue is that each line of sight contains emission from a range of galacto-centric distances for inclined galaxies, and the impact is of course largest for edge-on galaxies. We investigate the potential impact of both inclination and the red halo effect for UGC 7301, the smallest and most inclined galaxy in the sample. Figure 7 provides a comparison of g' − r' colors for our annuli and for a series of 9''-diameter apertures placed along the major axis, an arrangement that promotes a more PSF-independent radial analysis. No obvious differences appear between the two color trends, and so annular smearing is expected to be negligible in this work. To enable further interpretation of the observed colors, we turn to SED fitting of the complete collection of panchromatic surface brightness profiles.

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An example of our SED fitting results is displayed in Figure 8 for NGC 4618, a galaxy for which dust emission is detected throughout the six annular regions studied. As described in Section 4.2, multiple parameters are involved in such fits. Figure 9 presents for each galaxy the e-folding timescale radial trends for a delayed star formation history. We experimented with allowing t₀, the age of the oldest stars, to be a free parameter with a range of 6–13 Gyr ago. Since the radial trends for ${\tau }_{0}$ were essentially unchanged for different values of t₀, we adopted a fixed value of ${t}_{0}=11\;{\rm{Gyr}}$ ago in order to minimize the number of free parameters in the fits. As a result of fixing t₀, any differences in ${\tau }_{0}$ directly correspond to differences in the timing of the peak of the star formation histories (see Figure 3 and the corresponding discussion in Section 4.2). The error bars seen in Figure 9 are generally larger for larger values of ${\tau }_{0},$ which can be visually deciphered from inspection of Figure 3: the profile of the delayed star formation model is broader for larger ${\tau }_{0}$ and thus naturally leads to a less well constrained epoch for the peak in the star formation history.

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When all the ${\tau }_{0}$ values are presented in a single plot (lower panel of Figure 6), the sample overall shows older stellar populations stemming from more sharply defined epochs of star formation at both the galaxy centers and galaxy outskirts compared to the stellar populations at mid-galacto-centric distances. On average, our galaxies' characteristic epoch of star formation is ∼1–2 Gyr earlier at $r=0.13{a}_{25}$ and $1.38{a}_{25}$ compared to the value at $r=0.63{a}_{25}.$ Similar results are seen for the e-folding time ${\tau }_{1}$ when a decreasing exponential decreasing star formation history is considered (crosses in Figure 6). Nonetheless, there is a large diversity in the individual profiles, similar to what is seen for the g' − r' colors; for some galaxies the ${\tau }_{0}$ trend is essentially flat, for others it is mildly falling, there are galaxies that show rising-then-falling radial trends, etc. Thus, it is perhaps more illuminating to note the sample diversity than any average trend that may be unduly influenced by outliers, especially in light of the range of morphologies represented in the sample. The two S0 galaxies, NGC 4220 and NGC 5273, are notable in this presentation since they show the smallest and most constant values for ${\tau }_{0}.$ The implication is that the bulk of their stars formed spatially more uniformly across the disk, and with an earlier and more sharply defined epoch of star formation, than the stellar populations in the 13 other galaxies in the sample.

About half of the sample exhibits trends suggesting older on both the inside and the outside, consistent with being redder in those locations (provided our constraints on dust reddening and metallicity are reasonable). This scenario echoes that seen observationally for M33 and other nearby galaxies: an inside-out formation process for the main galaxy disk where the stars are younger and the colors increasingly blue with radius (e.g., González Delgado et al. 2014), followed by a redder and older stellar population in the galaxy peripheries or halos (Williams et al. 2009; Gogarten et al. 2010; Barker et al. 2011). Bullock & Johnston (2005) find in their simulations of galaxy stellar halo formation that the bulk of the mass in halos derives from the remnants of accreted satellites merger tidal debris that occurred on average 9 Gyr ago. During the time that has passed since those accretion events, the stars have passively evolved to provide an old, red present-day appearance for the spiral galaxy halos. Alternatively, Roškar et al. (2008) and Sánchez-Blázquez et al. (2009) predict that radial migration, a process whereby the influence of passing spiral arms can transport stars outwards, results in a conspicuous old–young–old mean radial age profile, in essence creating a red stellar periphery through internal dynamical processes. Though there is ample evidence that the outer disks of many galaxies possess pockets of active star formation (Gil de Paz et al. 2005; Thilker et al. 2007; Dong et al. 2008; Alberts et al. 2011), there are not enough OB stars in galaxy peripheries to result in overall blue stellar halos.

While we are mainly interested in the e-folding timescales inferred from the SED fitting, it is important to verify that the other output physical parameters derived are reasonable, as a check on the overall fit reliability. The fitted metallicities range from half-solar to slightly super-solar, with higher values preferentially found near the galaxy optical centers. The extinction range is 0.1–1.1 mag in ${A}_{V}\approx 3.1E(B-V{)}_{*}^{y}$ and again the average value peaks, as expected, for the innermost annular regions. Figure 10 shows a comparison between the global star formation rates output from the CIGALE fits and those independently derived from a combination of the global Hα and 24 μm data, taking care to ensure that both estimates use the same galaxy distances and initial mass function prescriptions (e.g., Equations (1) and (16) of Kennicutt et al. 2008). The average ratio of the two types of star formation rates is 0.95, with a dispersion of 0.4 and peak-to-peak variations within a factor of ∼2 from unity. Detailed studies have also been carried out that compare simulated input parameters for a sample of mock galaxies with the output parameters extracted from CIGALE SED fitting (Giovannoli et al. 2011; Boquien et al. 2012; Ciesla et al. 2015). Ciesla et al. (2015), for example, find that CIGALE returns stellar masses and star formation rates that are systematically low by 5%–10% (for decreasing exponential and delayed star formation histories), while Giovannoli et al. (2011) and Boquien et al. (2012) respectively find that the shape of the dust SED and the slope of the power law that modifies the attenuation curve (α and δ in Table 3) are the least accurate parameters returned. To help further assess the validity of the SED fit parameters, we have carried out a series of Monte Carlo simulations. In each simulation a random flux offset was added to each flux, with the flux offset for a given wavelength and radial position derived from a Gaussian distribution with σ scaled according to the measured uncertainty at that same wavelength and radial position. For each of these simulations the same SED fitting and Bayesian-based analysis described above was carried out. Figure 11 presents a comparison between the standard fit parameters and those from the Monte Carlo analysis. The standard deviation of the difference between the canonical and simulated e-folding time is about 700 Myr, a reasonable value given the estimated uncertainties. The output parameters with the broadest distributions in Figure 11 are the dust model power-law parameter α (see Dale et al. 2014) and the stellar metallicity Z: the simulated values for these parameters disperse noticeably more from the standard values, with standard deviations in each distribution of ∼0.2.

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