RADIAL DISTRIBUTION OF STARS, GAS AND DUST IN SINGS GALAXIES. I. SURFACE PHOTOMETRY AND MORPHOLOGY

The IRAC surface brightness profiles required being corrected for aperture effects to account for the diffuse scattering of incoming photons throughout the IRAC array.¹⁶ While usual aperture corrections account for the extended wings of the PSF due to the diffraction of light through the telescope optics, the ones considered here correct for the diffraction of light through the detector substrate (Reach et al. 2005).

In order to properly correct our radial profiles, we first computed the growth curve, thus getting the accumulated flux up to each given radius. We then applied the proper extended source aperture corrections to each elliptical aperture, and then recomputed μ by subtracting the flux of adjacent apertures.

For the 70 μm image, prior to measuring the profiles, we applied the preliminary correction for nonlinearity effects quoted in Dale et al. (2007), which is derived from data presented by Gordon et al. (2007).

The asymptotic magnitudes—that is, the ones that would be obtained by measuring with a hypothetically infinite aperture—can be derived by means of the growth curve (see, e.g., Cairós et al. 2001). The procedure is depicted in Figure 3. We computed the radial gradient in the accumulated magnitude at each radius, which typically exhibits a linear behavior when plotted against the accumulated magnitude. We then applied a weighted linear fit to the points within a suitable outer spatial range, with the asymptotic magnitude being the y-intercept of this fit, that is, the extrapolation toward a zero gradient. The resulting values are shown in Tables 5–7. The uncertainties were estimated with the classical statistical formulae, from the residual dispersion of the data points with respect to the fitting line. However, these errors do not include calibration uncertainties (see Section 2).

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From the growth curve at each wavelength, we computed the concentration indices C₃₁ (de Vaucouleurs 1977) and C₄₂ (Kent 1985), defined as

$$\begin{equation} C_{31}=\frac{r_{75}}{r_{25}} \end{equation} \tag{ 10 }$$

$$\begin{equation} C_{42}=5 \log \left(\frac{r_{80}}{r_{20}}\right), \end{equation} \tag{ 11 }$$

where r_x are the radii along the semi-major axis encompassing x% of the total flux of the galaxy at each band, the latter computed from the asymptotic magnitude. Note that since we are dealing with elliptical apertures, a correction for inclination needs not to be applied. For the remainder of the analysis presented here, we will focus on C₄₂ only, since both indices are tightly correlated.¹⁷

The resulting values of C₄₂ are quoted in Table 8. We have flagged as unreliable those values in which the inner radius r₂₀ is smaller than the innermost point of our profiles (6'' at 24 μm and 12'' at 70 μm and 160 μm, the latter two oversampling the PSF, see Section 3.2). In these cases, the quoted values are then just lower limits. Taking into account the shape and spatial extent of the PSF is necessary in order not to overinterpret concentration indices in unresolved sources. This is specially critical in the MIPS bands, given the broad and strong Airy rings of the corresponding PSFs. We measured the concentration index C₄₂ on model images of the MIPS PSFs, resulting in values of 3.7, 3.5, and 3.6 at 24 μm, 70 μm, and 160 μm, respectively. We also found that r₂₀ ≃ 2'', 6'', and 12'' at those bands, which lie below or close to the smallest radius used in the galaxy profiles, so the corresponding values of C₄₂ have been flagged when necessary as explained above.

Table 8. Nonparametrical Morphological Estimators

Galaxy		FUV	NUV	B	V	R	I	u	g	r	i	z	J	H	KS	3.6 μm	4.5 μm	5.8 μm	8.0 μm	24 μm	70 μm	160 μm
NGC 0925	C42	2.55	2.63	2.84	2.90	2.99	3.14	...	...	...	...	...	3.07	3.02	3.05	3.27	3.25	3.40	3.51	3.14	3.01	2.52
SAB(s)d	A	0.404	0.350	0.176	0.109	0.133	0.095	...	...	...	...	...	0.015	0.010	0.000	0.149	0.123	0.134	0.260	0.309	0.224†	0.205†
T = 7	G	0.648	0.619	0.551	0.516	0.550	0.530	...	...	...	...	...	0.516	0.482	0.467	0.600	0.599	0.616	0.676	0.692	0.615†	0.509†
	$\overline{M}_{20}$	−0.90	−0.95	−1.21	−1.41	−1.42	−1.64	...	...	...	...	...	−1.75	−1.75	−1.58	−1.56	−1.41	−1.27	−1.28	−0.85	−1.15†	−1.62†
NGC 2841	C42	2.28	2.36	3.77	3.93	3.93	3.89	3.33	3.84	3.92	3.91	3.96	3.84	3.84	3.84	3.95	3.83	3.12	2.00	1.82	1.90	2.15
SA(r)b	A	0.289	0.213	0.107	0.082	0.065	0.052	0.084	0.098	0.070	0.054	0.031	0.009	0.008	0.000	0.027	0.018	0.022	0.086	0.084	0.041†	0.081†
T = 3	G	0.586	0.586	0.595	0.606	0.610	0.605	0.566	0.611	0.626	0.629	0.647	0.666	0.662	0.667	0.648	0.645	0.633	0.601	0.612	0.610†	0.444†
	$\overline{M}_{20}$	−1.02	−1.15	−2.42	−2.47	−2.45	−2.51	−2.16	−2.48	−2.53	−2.55	−2.61	−2.58	−2.55	−2.57	−2.56	−2.54	−2.03	−1.09	−0.99	−1.02†	−1.04†
NGC 3190	C42	2.95	3.16	3.70	3.99	4.20	4.14	3.90	4.00	4.15	4.13	4.11	4.12	4.10	4.21	4.44	4.40	4.11	3.85	3.62	2.93	3.05
SA(s)a pec	A	0.171†	0.226†	0.260	0.213	0.180	0.148	0.178	0.247	0.211	0.172	0.119	0.062	0.052	0.043	0.080	0.064	0.073	0.131	0.160	0.202†	0.227†
T = 1	G	0.486†	0.592†	0.675	0.693	0.701	0.714	0.621	0.688	0.710	0.723	0.746	0.758	0.769	0.762	0.773	0.769	0.755	0.808	0.788	0.706†	0.479†
	$\overline{M}_{20}$	−1.58†	−1.92†	−2.67	−2.73	−2.71	−2.70	−2.45	−2.74	−2.73	−2.77	−2.80	−2.77	−2.57	−2.68	−2.75	−2.58	−2.54	−2.00	−2.28	−2.07†	−1.69†
NGC 3184	C42	1.73	1.78	2.22	2.35	2.44	2.56	2.03	2.27	2.41	2.51	2.56	2.62	2.70	2.63	2.55	2.51	2.03	1.89	2.06	2.05	2.12
SAB(rs)cd	A	0.537	0.400	0.163	0.104	0.093	0.068	0.153	0.143	0.121	0.089	0.042	0.026	0.011	0.008	0.137	0.125	0.186	0.293	0.294	0.200†	0.085†
T = 6	G	0.771	0.598	0.490	0.492	0.513	0.520	0.509	0.510	0.525	0.531	0.532	0.518	0.496	0.483	0.553	0.562	0.591	0.640	0.662	0.592†	0.486†
	$\overline{M}_{20}$	−0.84	−0.90	−1.26	−1.43	−1.50	−1.62	−0.94	−1.31	−1.45	−1.59	−1.62	−1.73	−1.72	−1.60	−1.47	−1.39	−0.98	−0.94	−0.98	−1.14†	−1.45†
NGC 4125	C42	...	4.48	4.12	4.30	4.34	4.32	4.21	4.63	4.71	4.75	4.78	4.40	4.38	4.36	5.17	5.10	5.00	5.10	5.18	>2.92	>1.86
E6 pec	A	... †	0.104†	0.106	0.098	0.087	0.172	0.000	0.016	0.015	0.011	0.000	0.030	0.023	0.025	0.036	0.033	0.000	0.000	0.025†	0.108†	0.162†
T = −5	G	... †	0.610†	0.713	0.701	0.712	0.723	0.629	0.659	0.672	0.672	0.696	0.727	0.726	0.711	0.686	0.684	0.650	0.696	0.652†	0.741†	0.625†
	$\overline{M}_{20}$	... †	−2.32†	−2.52	−2.58	−2.60	−1.56	−2.47	−2.55	−2.60	−2.59	−2.65	−2.48	−2.48	−2.53	−2.67	−2.67	−2.58	−2.62	−2.43†	−2.36†	−1.77†

Notes. Concentration index (C₄₂), asymmetry (A), Gini coefficient (G) and normalized second-order moment of the brightest 20% to the total galaxy flux ($\overline{M}_{20}$) at different wavelengths. When the inner radius r₂₀ needed to compute C₄₂ is smaller than the innermost point in our profiles (or the PSF size, in the case of the 70 μm and 160 μm bands), the quoted values are just lower limits for the actual concentration indices. Values of A, G, and $\overline{M}_{20}$ marked with a dagger (†) should be taken with caution, since at the particular distance of each galaxy, the FWHM of the PSF of the affected bands does not allow resolving structures smaller than 0.5 kpc.

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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Although when measuring C₄₂ we rely on the centers given in the RC3 catalog, for the asymmetry and the second-order moment we follow an iterative process to find the center (see below). We have checked that offsets ≲3'' have a negligible impact on C₄₂. In most cases, the differences between the resulting values are just ∼0.01–0.001. Only in highly concentrated objects with small values of r₂₀ do the discrepancies amount to ∼0.3–0.1.

Several mathematical definitions for computing the asymmetry can be found in the literature (Schade et al. 1995; Abraham et al. 1996b; Kuchinski et al. 2000, Conselice et al. 2000), although the philosophy behind all of them is essentially the same. It involves comparing the original image of a galaxy with its rotated counterpart, the rotation angle being usually 180° (although other angles can also yield useful information, see Conselice et al. 2000).

Here we adopt the definition of the asymmetry given by Abraham et al. (1996b):

$$\begin{equation} A=\frac{1}{2}\left[\frac{\sum {| I_{180\mbox{$^\circ $}}-I_0 |}}{\sum {| I_0 |}}-\frac{\sum {| B_{180\mbox{$^\circ $}}-B_0 |}}{\sum {| I_0 |}}\right]. \end{equation} \tag{ 12 }$$

I₀ and $I_{180\mbox{$^\circ $}}$ are the intensities of the original and rotated images, respectively, and B₀ and $B_{180\mbox{$^\circ $}}$ are the intensities of background pixels and their rotationally symmetric counterparts. The sum is carried out over all pixels within a certain aperture (see below). By taking the absolute value, the sky noise introduces a certain positive signal in A that has to be subtracted in order to get the asymmetry of the galaxy itself. In principle, this can be done by computing the asymmetry within a reasonably large patch of sky, free from emission coming from the galaxy (hence the second term in Equation (12)). However, this is not always possible in many images of our very extended sources, and it also tends to increase the computation time. Lauger et al. (2005) demonstrate that the noise asymmetry can be estimated by assuming Poissonian statistics for the sky:

$$\begin{equation} \sum {| B_{180\mbox{$^\circ $}}-B_0 |}=\frac{2}{\sqrt{\pi }}\sigma _{\mathrm{sky}}N_{\mathrm{pix,}} \end{equation} \tag{ 13 }$$

where σ_sky is the sky noise, measured as explained in Section 3.2, and N_pix is the number of pixels within the aperture used to derive the asymmetry in the galaxy. We verified that Equation (13) is indeed valid for our images.

The asymmetry was measured within elliptical apertures with position angles, diameters, and axis ratios equal to those of the μ_B = 25 mag arcsec⁻² isophotes from the RC3 or NED, and the resulting values are shown in Table 8. The use of isophotal radius is discouraged when comparing galaxies within large redshift intervals, since they might be affected by cosmological surface brightness dimming, k-correction, evolution, and zero-point offsets. The use of the Petrosian η-function (Petrosian 1976) is usually more convenient in these cases (Bershady et al. 2000). It is defined as¹⁸ η(r) = I(r)/〈I(r)〉, i.e., the local surface brightness at a given radius r divided by the average surface brightness inside r. By definition, η(r) is equal to 1 at r = 0 and approaches 0 at larger radii. The Petrosian radius r_P is such that η(r_P) is equal to a certain value, usually 0.2. We found that the Petrosian radius often misses significant emission from the outer regions of many galaxies. Since the SINGS galaxies do not suffer from the cosmological issues listed above, the choice of employing the RC3 apertures is probably more justified in our case. While these apertures encompass more light than those derived from the η-function, they still miss some light of the very outer regions of the galaxies. Increasing the aperture size would introduce more sky in the less spatially extended bands, thus making the subtraction of the noise asymmetry more critical. The choice of the RC3 ellipses constitutes a compromise solution; as long as A is computed consistently in all bands, the trends with wavelength should remain essentially correct.

In any case, for the sake of comparison, we have also computed A within ellipses whose semi-major axis was set equal to the Petrosian radius, such that η(r_P) = 0.2 (see Table 1). Considering all bands together, we find that the difference between the asymmetries computed with both apertures is negligible, with $\langle A_{R25}-A_{r_P} \rangle =-0.005$ and a scatter of ±0.009. This holds true on a band-by-band basis as well, except in those with poorer S/N ratios (like the u, z, J, H, and K_S bands) where the offsets, while still smaller than the scatter, seem to be statistically significant. Those slight discrepancies are most likely due to the subtraction of the sky asymmetry being more delicate in those cases. Conselice et al. (2000) computed A both within r_P and 1.5r_P (incidentally, R25 ∼ 1.5r_P on average for the SINGS galaxies). We have checked from their published data that the difference between both cases is also negligible, with a scatter similar to ours.

The center of rotation was determined by minimizing the asymmetry. Starting from the central positions quoted in the RC3, we computed the asymmetry over a grid of (x, y) positions, recentering and repeating the process until a minimum value was found. To account for differences in the astrometrical calibration and resolution of the images, we allowed a maximum difference of 3 '' from the initial central coordinates. Objects requiring larger offsets are intrinsically asymmetric, the centers minimizing A probably not being the actual centers of the galaxy.

It should be noted that since A is computed on a pixel-by-pixel basis, the precise final values may depend on several parameters, such as the signal-to-noise ratio (S/N) and the spatial resolution. Conselice et al. (2000) showed that A drops when one is unable to resolve structures smaller than 0.5 kpc, although for large galaxies asymmetries with a resolution of ∼1 kpc may be still acceptable. Bendo et al. (2007) found that A_3.6 μm does not strongly depend on the distance in the SINGS galaxies, but A_24 μm does, thus implying that other bands also showing inherently clumpy structures might be affected as well. We opt for a conservative approach and flag those values of A in which the spatial resolution at each particular band does not allow resolving structures smaller than 0.5 kpc. This mainly affects the 70 μm and 160 μm bands and, in galaxies further than 17 Mpc, the GALEX and 24 μm images too.

The S/N ratio can also bias the derived values of A (Lotz et al. 2004; Lauger et al. 2005). All in all, an accurate determination of the asymmetry as a function of wavelength would require setting all images to a common PSF size, plate scale, and depth, which is beyond the scope of this paper. Note, however, that differences in these parameters within the SINGS imagery are not that large anyway (except at 70 μm and 160 μm in terms of resolution, and also the 2MASS bands regarding the S/N ratio). The aforementioned corrections, therefore, are not as critical as when analyzing the morphology of galaxies in cosmological surveys (see, e.g., López-Sanjuan et al. 2009 and references therein). Nevertheless, the results presented here should be treated cautiously, as our intention is simply to depict broad general trends.

The Gini coefficient (Gini 1912) is a statistical parameter widely used in econometrics to determine how wealth is distributed in a given population. It was adapted by Abraham et al. (2003) for galaxy morphology classification as a proxy for the relative contribution of bright and faint pixels to the total galaxy flux. Here we follow the prescriptions given by Lotz et al. (2004) to compute G. We first order the sky-subtracted pixels from the lowest absolute pixel intensity to the highest one. The Gini coefficient can be then computed as

$$\begin{equation} G=\frac{1}{\overline{\left|f\right|}n(n-1)}\sum _{i=1}^n (2i-n-1)\left|f_i\right|, \end{equation} \tag{ 14 }$$

where n is the number of pixels, $\overline{\left|f\right|}$ is the average absolute pixel intensity, and f_i is the value of the pixel i once the pixels have been ranked by their absolute brightness. The possible values of G range from 0 to 1. A galaxy where the total flux is equally distributed among all pixels would have G = 0, and G = 1 would be found if one pixel was responsible of the total galaxy flux. Generally speaking, high values of G mean that most of the galaxy flux is localized in a few pixels, whereas low values are indicative of a more even distribution.

Although sophisticated methods like segmentation maps can be used to define pixels belonging to the galaxy (Lotz et al. 2004), here we simply measure G within the R25 elliptical apertures from the RC3 or NED in all bands. While a precise centering is a delicate point when computing the asymmetry, as explained in Section 3.3.2, the Gini coefficient is not affected by this issue. However, this is a double-edged sword, since G only tells us about the relative contribution of pixels with different intensities to the total flux, regardless of their spatial distribution within the galaxy. In other words, objects with entirely different morphologies may yield very similar values of G (see, e.g., Figure 2 in Abraham et al. 2003). While the usefulness of G as a standalone morphological parameter might be somewhat limited depending on the rest-frame wavelength of observation, its real power emerges when comparing it with other estimators, as we will see later.

As with the asymmetry, we have analyzed the impact on G of using the Petrosian radius instead of the R25 one. As explained in Lotz et al. (2004), including too many sky pixels in the aperture will tend to increase G, while leaving out emission from the outer parts of the galaxy will systematically decrease it. We have found that, on average, $\langle G_{R25}-G_{r_P} \rangle =0.11$, with a typical scatter of ±0.10. Since G ∼ 0.6 for our galaxies (see Figure 8), such an offset represents a relative difference of ∼18%. By visually inspecting the images with the R25 and Petrosian ellipses over-plotted, we have verified that the Petrosian radius usually leaves out significant emission from the outer regions of galaxies. The amount of missed light depends strongly on the radial light profile, and indeed increases monotonically with light concentration and/or the Sérsic index (Graham et al. 2005). While r_P usually encloses almost all the emission in late-type spirals, prominent bulges and bright inner arms in earlier ones tend to decrease r_P, and with it G as well. Performing the measurements within n times the Petrosian radius would not help, as it would probably introduce too many sky pixels in late-type spirals where r_P alone is already a sufficiently large aperture.

Perhaps the most flagrant case in our sample is NGC 4736, a Sab spiral with a small bright inner ring that dominates the overall emission at all wavelengths. The Petrosian radius at η = 0.2 is 60'', which is precisely the radius of the inner ring. Having a Gini coefficient of ∼0.5 within r_P, this galaxy would hardly qualify as being particularly concentrated. However, the emission actually extends much further out, with clearly visible structures lying 350'' away from the center at all wavelengths. The R25 ellipse comfortably includes all this emission, and yields G>0.8, which reflects more faithfully the true nature of this object.

Since the dependence of r_P on light concentration may bias the resulting values of G as a function of Hubble type, and in order to properly handle objects like NGC 4736, we have opted to keep the R25 ellipses as our measurement apertures.

The derived values of the Gini coefficient can be seen in Table 8. We have flagged values of G as unreliable when the FWHM at a given band is larger than 0.5 kpc at the particular distance of each galaxy, as we did for the asymmetry. The Gini coefficient is expected to decrease at very low S/N ratios, so the values of G measured on the 2MASS images should be taken with care, as they could be underestimated.

The total second-order moment of the light in a galaxy is defined as

$$\begin{equation} M_{\mathrm{tot}}=\sum _{i=1}^n M_i=\sum _{i=1}^n f_i [(x_i-x_c)^2+(y_i-y_c)^2], \end{equation} \tag{ 15 }$$

where f_i is the flux of the pixel located at (x_i, y_i), and (x_c, y_c) are the coordinates of the galaxy's center. Lotz et al. (2004) suggest using the normalized second-order moment of the pixels responsible of the brightest 20% of the total galaxy flux:

$$\begin{equation} \overline{M}_{20}=\log \left(M_{20}/M_{\mathrm{tot}}\right), \end{equation} \tag{ 16 }$$

where M₂₀ is computed by ranking the pixels in order of decreasing intensity, and then summing M_i over the brightest pixels until ∑f_i = 0.2f_tot.

The values of $\overline{M}_{20}$ are always negative. Centralized emission yields lower (i.e., more negative) values than more extended emission. The advantage of $\overline{M}_{20}$ over the concentration index C₄₂ is that since $\overline{M}_{20}$ depends on the squared distance to the galaxy's center, it is more sensitive to the spatial distribution of bright regions than C₄₂, which is usually heavily influenced by the bulge. We measured $\overline{M}_{20}$ within the RC3 elliptical apertures, whose centers were iteratively shifted in order to minimize M_tot, as suggested by Lotz et al. (2004). These authors also found that $\overline{M}_{20}$ can be unreliable at poor spatial resolutions, so we again impose the same limit of 0.5 kpc for the physical resolution.

When comparing the values of $\overline{M}_{20}$ measured inside the optical ellipses with those obtained within the Petrosian ellipses, we find that $\langle \overline{M}_{20,R25} - \overline{M}_{20,r_P} \rangle =-0.15$, with an rms of ±0.22. Considering that the second-order moment typically ranges between −1 and −4 for the SINGS galaxies (see Figure 8), this offset translates into a relative difference of just a few percent. The fact that $\overline{M}_{20}$ is slightly smaller when measured inside the optical ellipses is expected, since the outer regions of galaxies between r_P and R25 will contribute to increase M_tot but not necessarily M₂₀, thus decreasing the normalized moment $\overline{M}_{20}$.

Concentration Index. In Figure 7, we show how C₄₂ varies with wavelength for galaxies of different morphological types. Dashed lines are used when r₂₀ is smaller than the innermost point of our profiles (6'' at 24 μm and 12'' at 70 μm and 160 μm). In order to detect possible biases due to the spatial resolution, we show red (blue) lines with the median values for the galaxies further (closer) than the median distance of the galaxies within each morphological bin. These median distances were individually computed for each bin of Hubble types, since late-type galaxies in the sample are closer on average than early-type ones. The values are 17 Mpc (E-S0), 17 Mpc (S0/a–Sab), 15 Mpc (Sb–Sbc), 9 Mpc (Sc–Sd), and 4 Mpc (Sdm–Irr).

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Ellipticals and lenticulars exhibit C₄₂ ≳ 3 at all wavelengths, but spirals present a much more varied behavior. Their concentration indices typically lie below 3 in the UV due to the contribution of young stars spread across the disk. Then it suddenly rises in the optical, as the bulge dominates the overall light concentration longward of the Balmer break (λ ∼ 0.36 μm). Early-type spirals usually show central depletions in their UV emission, with inner-truncated disks, while in the optical and near-IR the bulge is more prominent, hence the large discontinuity between C₄₂(UV) and C₄₂(opt). Such a jump can be enhanced by the presence of rings (Lauger et al. 2005). The difference becomes progressively less pronounced in later Hubble types, as the transition from the central bulge (or pseudobulge) and the disk becomes more gradual.

The concentration index rises slowly from the optical to the near-IR and then drops again at 5.8 μm and 8.0 μm, since these bands probe the spatial distribution of PAHs. The amplitude of this "break" in C₄₂ decreases in late-type spirals, but is still sharper than the one between the UV and the optical bands. While Sc spirals and later usually exhibit low values of C₄₂, typically below ∼3, there is much more dispersion in galaxies or earlier types toward larger concentration indices. By analyzing the 24 μm morphologies of the SINGS galaxies, Bendo et al. (2007) suggested that bars might increase light concentration at 24 μm by enhancing nuclear star formation activity, although the statistical evidence was not compelling.

There are some galaxies in each panel having significantly larger infrared concentration indices than the remaining galaxies of the same morphological type. This is the case of NGC 1291 (S0/a), NGC 1512 (Sa), NGC 1097 (Sb), NGC 3351 (Sb), and NGC 4536 (Sbc). These galaxies exhibit signs of very intense nuclear and/or circumnuclear emission when inspected at 8 μm and 24 μm, hence their unusually large concentrations. Note that although NGC 1291 has an outer ring, the nuclear emission dominates the total luminosity at 24 μm and 70 μm, hence the large values of C₄₂ at these bands.

The galaxy exhibiting high values of C₄₂ in the panel for Sc–Sd spirals is NGC 5033. Unlike the galaxies mentioned above, which depart from the general trends only in the infrared, NGC 5033 is above all Sc–Sd galaxies already in the optical. A visual inspection shows no sign of any intense nuclear emission, but reveals however a rather prominent bulge for an Sc spiral. The multiband radial profiles show indeed that the light distribution of this galaxy has a non-negligible contribution from the central bulge, which is absent in other galaxies of the same morphological bin. The fact that this is a Seyfert galaxy might contribute to its high concentration in the infrared.

The results presented here agree with those presented in other papers in the literature. As an example, Taylor-Mager et al. (2007) performed a quantitative analysis of the rest-frame UV and optical morphology of 199 nearby galaxies, using imagery from GALEX, HST and ground-based telescopes. They found that ellipticals and lenticulars typically have C₄₂ ≃ 4, the same average value obtained here. Although these authors noted a drop-off in C₄₂ shortward of the Balmer break in E-S0 galaxies—a feature that is absent here—they warned against overinterpreting this feature, given the low S/N of those red galaxies in the UV. They do find a clear trend with wavelength in Sa–Sc spirals, with C₄₂ rising from ∼2 in the FUV to ∼3 in the I band. The trend we observe is fully consistent with theirs, although our finer bins in morphological types reveal that the wavelength dependence of C₄₂ actually varies within Sa–Sc galaxies, being less pronounced in later types. Our typical concentration indices for irregulars agree well with those of Taylor-Mager et al. (2007; roughly 2.5). While these authors study in great detail the morphology of mergers, such an analysis is not possible here, since there are not major mergers in our sample, and the few galaxies with low mass companions have those objects deliberately masked out.

Asymmetry. In Figure 7, we also show the dependence of the asymmetry on wavelength. Dashed lines indicate that the FWHM at a given wavelength corresponds to a physical size larger than 0.5 kpc at the distance of each galaxy. As expected, ellipticals and lenticulars exhibit low asymmetries at all wavelengths, typically below 0.15. In S0/a galaxies and later there is a clear trend with wavelength: A reaches a maximum in the FUV, where the emission is dominated by recent star formation. As we move toward longer wavelengths in the optical and near-IR, the intermediate-age and old stars from the bulge and halo—which are more smoothly distributed across the disk than young ones—progressively decrease the global asymmetry of the galaxies. PAHs make their appearance at 5.8 μm and 8.0 μm, increasing the asymmetry again. Hot dust associated with clumps of star formation tend to increase A even more at 24 μm. This U-like shape of the A_λ distribution is enhanced as we progress along the Hubble sequence: intermediate- and late-type spirals become progressively more asymmetric in the UV–optical range, as well as in the mid-IR. Note that the increase in asymmetry in the UV and mid-IR bands is the opposite of what would be expected from the degradation of the PSF, thus reassuring that these changes in A are real. However, the drop-off seen at 70 μm and 160 μm for some galaxies is most likely the result of the poorer resolution.

The outlier in the panel for Sc–Sd galaxies is NGC 5474. This companion of M 101 (Drozdovsky & Karachentsev 2000) shows a strongly disturbed morphology, with a large plateau shifted southward with respect to the bright central disk, hence its large asymmetry. Interestingly, NGC 5474 looks like a normal spiral when viewed in the UV, thus not showing much departure from the typical asymmetries in that spectral range.

Our multi-wavelength asymmetries seem to be consistent with other published values for nearby galaxies. We take again as an example the work of Taylor-Mager et al. (2007). As expected, they also conclude that E-S0 galaxies exhibit the lowest asymmetries. In Sa–Sc spirals, their asymmetries decrease from ∼0.8 in the FUV to ∼0.2 in the I band. Once divided by 2, since these authors do not include the 1/2 factor when computing the asymmetry, these values nicely match the ones we have derived. The agreement is not as good as in very late-type spirals and irregulars, our UV asymmetries being a bit larger in the UV, although with considerable dispersion.

Most galaxies show a small bump in the asymmetry at 3.6 μm and 4.5 μm. This feature becomes more evident in the latest Hubble types, and is most likely due to the large number of background sources detected in these bands. While our masking procedure eliminates sources that could potentially contaminate our profiles and magnitudes (see Section 3.1 and Figure 2), these ubiquitous faint sources may still have a substantial impact on the asymmetry. This effect is expected to become more noticeable in galaxies with lower average surface brightness within the aperture used to compute the asymmetry (usually late-type ones). We do observe indeed a marked correlation between A_{3.6, 4.5 μm} and the average surface brightness at those bands, a correlation that is not seen at other wavelengths (not shown).

Gini Coefficient. In Figure 8, we show how the Gini coefficient (and also $\overline{M}_{20}$) varies with wavelength and morphological type. As with the asymmetry, dashed lines are used when the FWHM does not allow resolving structures smaller than 0.5 kpc at the distance of each galaxy. In general, G tends to decrease from early- to late-type galaxies, especially in the optical and near-IR bands. However, the scatter is large, and the overlap between the values of G between adjacent bins of T type is considerable. No clear trend with wavelength can be inferred for galaxies earlier than Sab, but Sb spirals, and later G apparently exhibits a mild wavelength dependence, in the sense that it seems to be larger in the UV and mid-IR (especially at 24 μm) than in the optical and near-IR.¹⁹ What is the reason behind this modest trend with wavelength, despite the evident change in morphology among the bands considered here? In the optical and near-IR, pixels in the bulge contribute to a relatively large fraction of the total galaxy luminosity, the Gini coefficient being largest in early-type galaxies than in late-type ones. The morphology in the UV and the mid-IR is considerably different, yet the total galaxy luminosity can still be dominated by emission arising from a few pixels, but this time localized mainly in star-forming regions. As a result, G can reach values similar to or even larger than those in the optical and near-IR. Therefore, G is only expected to be correlated with central light concentration in the optical and near-IR (see Section 4.3.2).

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Our Gini coefficients seem to be consistent with those in the literature. At 3.6 μm and 24 μm, the agreement between our values and those derived in Bendo et al. (2007) is excellent.²⁰ The average offset 〈G_Bendo − G_ours〉 is just −0.03 at 3.6 μm and 0.008 at 24 μm, the scatter being ∼0.03 in both cases. In the optical, for the galaxies, we have in common with Lotz et al. (2004) our values of G are, on average, ∼15% larger. This is most likely attributable to differences in the sizes of the regions used to perform the measurements. Lotz et al. compute G within segmentation maps whose extent depends on the Petrosian radius at η = 0.2, while we do it within the R25 ellipses, including emission that is missed by the Petrosian aperture. As discussed in Section 3.3.3, this can easily lead to systematic differences of 15%–20% in the resulting values of G.

Second-order Moment. Not surprisingly, the behavior of $\overline{M}_{20}$ is remarkably similar to that of C₄₂ (see Figure 7). Ellipticals and lenticulars exhibit $\overline{M}_{20}\sim -2.5$ across the whole wavelength range, which is indicative of highly concentrated light distributions. In contrast, most Sdm galaxies and irregulars tend to have $\overline{M}_{20} \gtrsim -1$. In spirals, $\overline{M}_{20}$ remains high in the UV, where most of the emission emerges from star-forming regions distributed across the disk. Longward of the Balmer break, $\overline{M}_{20}$ decreases abruptly, the decrement being more pronounced in early-type spirals than in late-type ones due to the larger B/D ratios of the former. A second break happens in the mid-IR, where $\overline{M}_{20}$ increases again due to the emission of PAHs at 5.8 and 8.0 μm, and hot dust at 24 μm.

Our values of $\overline{M}_{20}$ agree well with published ones, both in the optical for the galaxies in common with Lotz et al. (2004), and at 3.6 μm and 24 μm in the study by Bendo et al. (2007).

It is apparent from Figures 7 and 8 that the most dramatic changes in C₄₂ and $\overline{M}_{20}$ with Hubble type take place at the optical and near-IR. An obvious correlation shows up when plotting these morphological estimators at 3.6 μm against the morphological type (Figures 9(a) and (c)). In Figure 9(b), we plot the concentration index as a function of the absolute magnitude in that band, which is a proxy for the stellar mass of the galaxies. While both parameters are correlated for galaxies fainter than −21 mags, the trend breaks down at larger luminosities, since galaxies with M_3.6 μm ∼ −22 are ellipticals, lenticulars, and early-type spirals, the former being typically more concentrated than spirals with similar stellar masses. A very similar result was obtained by Boselli et al. (1997) for Virgo galaxies. These authors found a somewhat tighter trend between C₄₂ and the K-band magnitude at the low luminosity regime, since their sample better probed that luminosity range. While the SINGS galaxies are quite homogeneously distributed in terms of morphological types, the distribution in near-IR luminosity is more peaked around relatively bright objects. The trend between $\overline{M}_{20}$ and the absolute magnitude does not exhibit the upward bending seen in panel (b) with the concentration index, since both parameters are not linearly correlated, as we shall see below.

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In Figure 10, we can see that at 3.6 μm, and also in the optical bands, C₄₂ and $\overline{M}_{20}$ are very tightly correlated, the slope of the trend increasing from late- to early-type spirals. We have used the boundary-fitting code of Cardiel (2009) to fit third-order polynomials to the upper and lower envelopes of the data-point distribution at 3.6 μm. These curves are replicated in all panels for the ease of comparison. The trend presents an elbow located at $\overline{M}_{20} \sim -2, C_{42} \sim 3$, in good agreement with other works in the literature (Lotz et al. 2004; Scarlata et al. 2007). The different slopes at both sides of the elbow can be attributed to the varying contribution of the bulge and disk to the overall light distribution (Scarlata et al. 2007). Indeed, most points leftward of the elbow correspond to Sc spirals and later, whereas those at larger concentration values correspond to Sbc spirals and earlier. Since this trend is shaped by the varying B/D ratio, it also holds in the optical bands, which still trace the underlying stellar population, but it breaks down in the UV and the mid-IR, which trace recent star formation. Both indicators show that at these wavelengths galaxies exhibit much more extended light distributions.

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In Figure 11, we compare the Gini coefficient and $\overline{M}_{20}$. We have fitted two straight lines to the boundaries of the data-point distribution at 3.6 μm. A clear correlation is seen in the optical and near-IR, in agreement with previous studies (Abraham et al. 2003; Lotz et al. 2004). The interpretation of G as a proxy for light concentration is valid in these bands simply because bright pixels are mainly located in the bulge. Therefore, to first order the relative contribution of bright pixels to the total luminosity closely depends on the B/D ratio, which in turn is correlated with central light concentration. But this is no longer valid as soon as we peer into the UV and mid-IR regimes, where galaxies usually have larger values of G and $\overline{M}_{20}$. This time, most bright pixels are associated with star-forming regions, so G is no longer correlated with central concentration.

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Interestingly, when viewed at 24 μm normal galaxies occupy the same region in the G–$\overline{M}_{20}$ plane as the ultraluminous infrared galaxies (ULIRGs) of Lotz et al. (2004) in the R band. This was already noted by Bendo et al. (2007), and we confirm that this also occurs in the FUV and 8 μm, although to a lesser extent. The same behavior is seen in the G–A plane (not shown), where normal galaxies exhibit high asymmetries and Gini coefficients at 24 μm, similar to those of ULIRGs in the optical. However, this should not be blindly generalized. For instance, the R-band data for ULIRGS in Lotz et al. (2004) fill the upper-left region of the C₄₂–$\overline{M}_{20}$ plane, but our normal galaxies occupy a different area of the plot when observed at 24 μm (Figure 10).

The relation between the concentration index and the asymmetry is presented in Figure 12. The dynamic range in C₄₂ and A is largest in the FUV, where different morphological types clearly delineate a sequence in the C₄₂–A plane, although with a certain overlap. In the optical and near-IR bands, not only the dynamic range is smaller, but also the relative arrangement of data points differs. For instance, Sb–Sbc spirals appear to be of later Hubble types when viewed in the FUV, but merge with S0/a–Sab galaxies at longer wavelengths. Note that, as stated above, the systematic upward shift in the asymmetries of Sdm–Irr galaxies at 3.6 μm is likely due to background sources. In the mid-IR the C₄₂–A sequence lengthens again, the main difference with respect to the FUV being the presence of sources with high central concentrations, due to intense (circum)nuclear emission.

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Unlike in the previous diagrams, where galaxies shift to an entirely different locus in the parameter space when observed in the UV or mid-IR, in the C₄₂–A plane they apparently move along roughly the same diagonal sequence. At 24 μm, there are a few points with slightly larger asymmetries at fixed C₄₂ in comparison with the optical bands, but in general the displacement takes place diagonally. In Figure 13, we have plotted all data points for different bands simultaneously. Besides the six bands shown in Figure 12, we have added the NUV as well for a better wavelength sampling. The bulk of the data points lie within the boundaries delineated by the dashed lines, regardless of the wavelength. Many ULIRGs would probably lie in the upper-right region of the plot.

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