INTEGRAL FIELD SPECTROSCOPY AND MULTI-WAVELENGTH IMAGING OF THE NEARBY SPIRAL GALAXY NGC 5668^*: AN UNUSUAL FLATTENING IN METALLICITY GRADIENT

We have observed the nearly face-on spiral galaxy NGC 5668 with the PPAK IFU of PMAS at the CAHA observatory 3.5 m telescope (Kelz et al. 2006). The observations were carried out on 2007 June 22–24. We used the PPAK mode that yields a total field of view of 74'' × 65'' (hexagonal packed) for each pointing. We covered a total area of roughly 2 × 3 arcmin² with a mosaic of six PPAK pointings (see Figure 1). We used for the V300 grating covering a wavelength range of 3700–7100 Å(10 Å FWHM, corresponding to σ ∼ 300 km s⁻¹ at Hβ). With this spectral configuration, we covered all the optical strong emission lines in which we are interested. A total of 112 individual images were taken during the observing run. These images include 19 on-source frames for the 6 pointings obtained in NGC 5668 (see Table 2 for a summary of the science observations), bias frames (22 in total), sky flats (19), focus images (6), HgCdHe arcs (14), tungsten-lamp flats (14), observations of the spectrophotometric standard star Hz44 (3), and dome flats (6). The spatial sampling is determined by a hexagonal array of 331 densely packed optical fibers for the object (science fibers), 36 fibers for the sky, and 15 calibration fibers. Each fiber has a diameter of 268 and a pitch of 3458 with a high filling factor in one single pointing (65%). For a more exhaustive description of the instrument, see Kelz et al. (2006).

The reduction procedure applied to NGC 5668 follows the techniques described in Sánchez (2006) using R3D. This is a software package developed specifically for the reduction of fiber-based IFS data, which has been extensively used for the reduction of PMAS data, in combination with IRAF⁹ packages and Euro3D software (Sánchez 2004). Six pointings were observed for NCG 5668, leading to total covered area of 2 × 3 arcmin². Each pointing results from the combination of three or four images, each one with an exposure time of 1000 s. Our combined raw mosaic includes a total of 2292 spectra (1982+310 science+internal calibration spectra) covering the spectral range 3700–7131 Å. The pre-reduction of the IFS data consists of all standard corrections applied to the CCD that are common to the reduction of any CCD-based data.

• 1.  
  Bias subtraction. A master bias frame was created by averaging all the bias frames observed during the night and subtracted from the science frames.
• 2.  
  Cosmic-ray rejection. We median combined different exposures (at least three) of the same pointing. This procedure is able to remove 95% of all cosmic-ray events from each pointing.

After these corrections, the IFS data reduction consists of

• 1.  
  Spectra extraction. We identified the position of the spectra on the detector for each pixel along the dispersion axis. We then co-added the flux within an aperture of 5 pixels around the trace of the spectra and we extracted the flux corresponding to the different spectra at each pixel along the dispersion axis. Finally, the one-dimensional extracted spectra are stored in a row-staked-spectra (RSS) file.
• 2.  
  Wavelength calibration. We corrected for all distortions and determined the wavelength solution by using an arc calibration lamp exposure. Calibration data cubes were taken at the beginning and at the end of the night by illuminating the instrument with an HgCdHe lamp. The V300 wavelength calibration was performed using 14 lines in the considered spectral range. The rms of the best-fitting polynomial (order 4) was 0.45 Å (i.e., FWHM/20).
• 3.  
  Fiber-to-fiber transmission. We corrected the differences in fiber-to-fiber transmission by using twilight sky exposures from which a Fiber-Flat frame was computed.
• 4.  
  Sky emission subtraction. For each pointing, a sky image of 300 s (shifted +5' in decl.) was taken. We median combined the different sky images to create a sky frame, which was then subtracted from the science data frame.
• 5.  
  Relative flux calibration. We relative flux calibrated our data using observations of the spectrophotometric standard star Hz44 (α(2000) = 13^h23^m3537, δ(2000) = +36°08'000, Oke 1990) obtained during the night with the same instrumental setup as for the object. We applied all of the previous steps to the calibration star frame and extracted the standard star spectrum from the brightest 27 wide PPAK fiber centered on the star. Finally, we derived the ratio between counts per second and flux. In this way we obtained the instrumental response, which was applied to the science frames in order to flux calibrate them. Note that although this procedure also provides an absolute calibration for the data, this is uncertain due to potential flux loses during the observation of the standard star and variations in the transparency throughout the night.
• 6.  
  Differential atmospheric refraction (DAR) correction. We calculated a total theoretical DAR value using a Calar Alto public tool, obtaining a value of 1'' (the mean value of air mass used is 1.3). In this case the DAR can be considered negligible compared with the fiber size (27 in diameter). Therefore, we considered the DAR correction not to be required for this data cube. In any case, we never obtained any flux measurements from regions with less than five adjacent fibers in size.
• 7.  
  Locating the spectra in the sky. A position table that relates each spectrum to a certain fiber gives the location of the spectra in the sky.
• 8.  
  Mosaic reconstruction. We built a single RSS file for the whole mosaic by adding pointings previously normalized to a reference ("master") pointing. The "master" pointing is that having the best sky subtraction and most optimal observing conditions regardless of the geometric position of the pointing in the mosaic. In our case this "master" pointing was number 5 (offsets (0,−60); see Figure 1). This procedure makes use of the overlapping fibers between different pointings (11 fibers in total) to re-scale each new added pointing using the flux ratio in the continuum region 5869–5893 Å between the two pointings (the newly added and the "master" one).
• 9.  
  Absolute flux re-calibration. We also computed an absolute flux re-calibration based on SDSS photometry. Only two of the five filters of SDSS (g and r, λ_eff = 4694  and 6178 Å, respectively) are used because these are the ones for which their passbands are fully covered by our spectra. We convolved the whole data cube of NGC 5668 with the SDSS g- and r-filter passbands to derive the absolute spectrophotometry. First, we measured the AB magnitude within the footprint of the entire PPAK mosaic and in seven concentric annuli for both PPAK and SDSS images. Then, these magnitudes were converted to fluxes using the prescription in the SDSS documentation¹⁰ in order to calculate the flux ratio in both bands. The resulting average scaling factor found is 0.9 for the two data pairs. This result implies a factor of 0.04 in magnitude. Note that the error in SDSS photometry alone is estimated to be 2% mag. In our case, we have an uncertainty of 5% in fluxes, so the total absolute error associated with line fluxes is 8%. Obviously, relative measurements are more precise. All results shown in the following analysis (and in Table 3) are re-calibrated based on these SDSS photometry measurements.

In order to complement the IFS data of NGC 5668 presented here, we have also compiled multi-wavelength broadband images acquired with different facilities: UV imaging data from GALEX, optical data from SDSS, and near-IR data from Spitzer (see Figure 2). The GALEX telescope (Martin et al. 2005) observed NGC 5668 as part of its Medium-deep Imaging Survey. Images at both the FUV (λ_eff = 151.6 nm) and NUV (λ_eff = 226.7 nm) bands are available for this galaxy. The final pixel scale is 15 pixel⁻¹, and the point-spread function (PSF) has an FWHM of ∼5''–6''  in both bands (Morrissey et al. 2007). At the distance of NGC 5668, this corresponds to a physical scale of ∼700 pc. The uncertainty of the zero point, which is calibrated against white dwarfs, is estimated to be less than 0.15 mag (Gil de Paz et al. 2007).

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Optical images in the ugriz bands were retrieved from the SDSS (York et al. 2000) Data Release 7 (DR7) archive (Abazajian et al. 2009). The two different scans on which NGC 5668 lies were flux-matched and mosaicked together using a custom-built task in IRAF. We applied the photometric calibration specified in the SDSS DR7 Flux Calibration Guide,¹¹ relying on the calibration factors of the scan used as reference when creating the mosaic. According to the information provided by the SDSS project, the photometric relative errors are of the order of 2%–3%. The plate scale is 0396 pixel⁻¹ with a PSF FWHM of 14 (170 pc at the distance of the galaxy).

Near-IR images at 3.6 μm and 4.5 μm were taken by Spitzer (Werner et al. 2004) using the IRAC instrument (Fazio et al. 2004). The corresponding Post Basic Calibrated Data were downloaded from the Spitzer archive.¹² These images are already flux calibrated and delivered in units of MJy sr⁻¹. The pixel scale is 06 pixel⁻¹, and the PSF has an FWHM of 17 in both channels, probing a spatial extent of 200 pc (Reach et al. 2005). The photometric error (∼2%) is dominated by the aperture corrections that need to be applied to account for the scattered light on the array. This total uncertainty is estimated to be around 10%¹³ in this case.

Many important topics in astrophysics involve the physics of ionized gases and the interpretation of their emission-line spectra. Powerful constraints on theories of galactic chemical evolution and on the star formation histories (SFHs) of galaxies can be derived from the accurate determination of chemical abundances either in individual star-forming regions or distributed across galaxies or even in galaxies as a whole. In this sense, chemical abundance is a fossil record of star formation history (SFH). In addition, the distribution of H ii regions is an excellent tracer of recent massive star formation in spiral galaxies. The previous evolutionary history of the gas and the local ionization, density, and temperature are important features for understanding the physical conditions prevailing in the regions where they are emitted.

For all these reasons, our first aim is to identify H ii regions in our target, or at least H ii complexes (see Figure 3).¹⁴ We extract from the PPAK data cube the emission-line fluxes corresponding to each of these regions. Furthermore, we also compute two-dimensional maps of the flux of strong emission lines, such as [O ii] λλ3726, 3729¹⁵; [O iii] λλ4959, 5007; Hβ; [N ii] λ6548; Hα; [N ii] λ6583; and [S ii] λλ6717, 6731.

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4.1.1. Region Selection

4.1.2. Emission-line Fluxes

The radiation emitted by each element of volume in a region depends upon the abundance of the elements, determined by the previous evolutionary history of the galaxy, and the local ionization, density, and temperature. The most prominent spectral features are emission lines, many of which are collisionally excited lines. In the V300 grating setup, the main emission lines observed are [O ii] λ3727 doublet; [O iii] λλ4959, 5007; Hβ; [N ii] λ6548; Hα; [N ii] λ6583; and [S ii] λλ6717, 6731.

We identified two different types of regions according to the intensity of the continuum: (1) regions where the continuum was bright enough so some absorption features were clearly visible and, therefore, the spectrum of the underlying stellar population could be fit using stellar population synthesis models, and (2) regions with fainter and/or noisier continua where no spectral absorption features could be identified.¹⁶

We refer to Section 4.1.3 for a description of the procedure followed to fit the underlying continuum in the case of the former regions; here we discuss the procedure followed to derive accurate emission-line fluxes in regions with negligible or noisy continua. Initially, we have identified 73 H ii regions in our synthetic Hα image but we excluded some of these regions because of their low signal-to-noise ratio (S/N) or because they were later identified as bad columns or field stars.

We first masked out the main emission lines and used a third-order polynomial function to fit the continuum. We then selected two spectral ranges excluding emission lines in three different wavelength ranges [O ii] λ3727, Hβ, and Hα regions, and measured the continuum level in each of these ranges. In a second step, we averaged the two continua and subtracted the result from each emission-line spectra in order to obtain a decontaminated flux. We analyzed the spectra using the IRAF package onedspec and stsdas. For well-isolated emission lines, such as [O ii] λ3727, Hδ, Hγ,¹⁷ [O iii] λ5007, we fit the emission-line profile to a single Gaussian function. For partially blended emission lines, such as the [N ii] λ6548; Hα; [N ii] λ6583 triplet, and [S ii] λλ6717, 6731 doublet, we used the task ngaussfit that fits simultaneously multiple Gaussian functions. We calculated the typical S/N of our data. In the case of [O ii] λ3727, the S/N ranges are between 3.4 and 23. In the case of Hβ, we obtain similar S/N values, ranging between 2.5 and 23. For the part of our spectra where the Hα emission line is located, the S/N values vary between 6 and 67.

Before analyzing the data in terms of chemical abundances or SFR, the observed emission-line fluxes must be corrected for various effects. For example, the presence of dust between the zone of the emission and the observer or the possible underlying stellar absorption in the case of the hydrogen recombination lines can alter considerably the intrinsic emission-line fluxes. We correct for underlying stellar absorption in the hydrogen Balmer lines using the values obtained from the analysis of the ring spectra (see Section 4.1.3 for fitting details). These best-fitting equivalent widths in absorption show very little variation with a radius ranging between −1.9 and −2.3 Å in Hβ and −1.7 and −1.8 Å in Hα. We apply an average correction of −2 and −1.7 Å, respectively, for Hβ and Hα, to the spectra of the 58 H ii regions where the continuum emission was too faint for carrying out a full spectral fitting. The emission fluxes were then corrected for reddening using the Hα/Hβ Balmer decrements after adopting an intrinsic ratio of 2.86 (Osterbrock & Ferland 2006). Additionally, we verified that in the case of regions with a high equivalent width in emission (typically no less than 5 Å  in Hβ), the corrected Hβ/Hγ ratios were consistent with the predictions for the case B recombination value at a typical T_e of ∼10⁴ K. In Table 3, we present the results obtained from the analysis of H ii regions and concentric annuli in NGC 5668.

Following a similar analysis on a pixel-by-pixel basis, we also generate maps of ionized-gas extinction, radial velocity, emission-line fluxes, and stellar-absorption equivalent width. In Figure 4, we present the maps of the Hα line flux, [O ii] λ3727 doublet flux, Hα continuum intensity, and the equivalent width (EW). Note that while the EW(Hα) in emission gets locally higher as we move toward the outer parts of the disk, this is mainly due to the decrease in the intensity of the adjacent underlying (R-band) continuum. Indeed, when we compute the azimuthally averaged EW(Hα) from the ring spectra, this changes less dramatically, with values ranging from 20 to 50 Å in all cases except for the very outer rings (see Table 4). The very high EW(Hα) values measured in the rings beyond ∼70'' are likely due to strong Hα emission associated with the bright H ii complex located in the galaxy Northern spiral arm. Note that in the very outer disk, where the total SFR is low, stochasticity in the number and luminosity of H ii regions might lead to significant fluctuations in the EW(Hα) compared with values averaged over timescales of a few hundred Myr or even a rotation period.

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Table 4. Hα Equivalent Widths in Emission from the Ring Spectra

Ring	EWemHα	Radius	Ring	EWemHα	Radius
	(Å)	('')		(Å)	('')
1	a	1	9	38.34	40
2	8.75	5	10	37.85	45
3	18.65	10	11	36.5	50
4	29.32	15	12	24.04	55
5	25.56	20	13	34.98	60
6	39.18	25	14	50.18	65
7	44.97	30	15	100.1	70
8	44.00	35	16	128.5	75b

Notes. These values are not corrected for underlying stellar absorption. ^aNo line emission was detected. ^bIn this table, we present the value for ring 16 that it is not shown in any of the other tables in the paper since only the Hα line could be detected in the spectrum and its flux (and EW) measured.

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4.1.3. Stellar-absorption Correction

As discussed above, for the rings and some H ii regions the continuum is sufficiently strong enough to allow us to clearly identify absorption features in their spectra. In this way we can fit the absorption and emission components in the spectra simultaneously. The spectra of the 18 concentric annuli are plotted in Figure 5. In this case, we made use of an IDL script that finds the best-fitting stellar population synthesis model among the ones in libraries by Bruzual & Charlot (2003, hereafter BC03) and Sánchez-Blázquez et al. (2006, also known as MILES). This procedure allowed us to measure intensities for the emission lines already corrected for stellar continuum absorption (nebular continuum emission is negligible at the EW(Hα) measured anywhere in this object). Both libraries yield good fits to our spectra, yet the analysis presented here is based on the results obtained using the BC03 library since this provides a good coverage of physical parameters and good spectral resolution and has been more extensively tested than MILES. We explore the whole range in age and metallicity in the BC03 library for simple stellar populations (SSPs) with a spectral resolution of 3 Å  across the whole wavelength range from 3200 Å  to 9500 Å . These templates have 11 values in age (5, 25, 100, 290, 640, 900 Myr, and 1.4, 2.5, 11, 13, 17 Gyr) and each of them has six different metallicity values: z = 0.0001, 0.0004, 0.004, 0.008, 0.02, 0.05. Our fitting program is able to find the model that best fits the underlying stellar population (stellar continuum) in this BC03 stellar library by minimizing the residuals between the model and observed spectra for a set of input parameters. The program finds the best-fitting parameters for the recession velocity, velocity dispersion, normalization factor, and stellar continuum attenuation in the V band for each region.

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In order to attenuate the stellar continuum as a function of wavelength, we adopt a dependence of the optical depth with a wavelength of the form λ^−0.7, which, according to the results of Charlot & Fall (2000), is a good approximation to the extinction law in star-forming galaxies at these wavelengths. This analysis provides us with the best-fitting SSP model for each spectrum along with best-fitting values for the recession (tropocentric) velocity, velocity dispersion, normalization factor, and continuum dust attenuation.

Note that the age and metallicities derived are, in general, highly uncertain, but, on the other hand, the Hα and Hβ equivalent widths in absorption are much more precise (see Mármol-Queraltó et al. 2011 for a detailed description on the feasibility in the derivation of the properties of the underlying stellar population). The residual spectrum obtained after the subtraction of the best-fitting SSP model is then used for the subsequent analysis of the emission-line fluxes.

We calculate the errors in all line fluxes from the rms in the spectra (in the region adjacent to each emission feature) after the best-fitting stellar synthesis model has been subtracted. We assume that these rms measurements were due mainly to photon noise and to sky subtraction. These errors were scaled to those spectra for which the fainter continuum emission prevented carrying out a full spectral fitting. Finally, we used the errors in the continuum to calculate the errors associated with the line fluxes.¹⁸

Some advantages of using IFUs are that all the spectra are obtained simultaneously and that we can use the IFU as a large-aperture spectrograph. From our data cube, we add up the spectra of all the fibers to create an integrated spectrum of NGC 5668 (see Figure 6). In this figure, we also compare this spectrum with the corresponding fluxes derived from the SDSS photometry. Note that the g' and r' bands overlap completely with our spectral range. Since the spectroscopy data were not taken under photometric conditions and given that some flux losses are expected as part of the PPAK observations of our spectrophotometric standard star, an 8% difference was found between the two data sets. This offset, which is wavelength independent, has already been applied to the spectrum shown in Figure 6, although it was not applied to our spectral data cube and the line fluxes measured hereafter. Similar wavelength-independent offsets are also found in other works based on PPAK spectroscopic observations (Rosales-Ortega et al. 2010, 2011). In any case, this does not have any impact on the physical properties derived (dust attenuation, oxygen abundance, and electron density) as these are determined by the ratio of emission-line fluxes alone. In Table 3 (last row), we present the emission-line flux ratios found for the integrated fiber spectrum of NGC 5668.

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Prior to the measurement of the surface brightness profiles in NGC 5668, foreground stars, background galaxies, and cosmetic artifacts had to be masked out from our multi-wavelength imaging data. Radial profiles were obtained using the IRAF task ellipse. We measured the mean intensity within concentric circular annuli centered on the galaxy's nucleus, using a radial increment of 6'' between adjacent annuli. Photometric errors were derived as explained in Gil de Paz & Madore (2005) and Muñoz-Mateos et al. (2009b). The uncertainty of the mean intensity at a given radius is computed as the quadratic sum of two terms: the Poissonian noise of the galaxy's light and the error in the sky level. The latter was the result of the combination of both pixel-to-pixel variations and large-scale background errors.

More than 80 years have passed since Trumpler's discovery of color excesses provided the first definitive proof of the existence of interstellar dust (Trumpler 1930). However, the nature of interstellar dust still remains unclear and how dust both reddens and attenuates the light from the stars is one of the least understood of the physical phenomena which take place in galaxies.

The dust content of galaxies is a critical issue given its important impact on the observational properties of galaxies (mainly in the optical and UV). The extinction in a galaxy depends first on the amount of dust and its composition, and also on the distribution of dust relative to the light sources (Calzetti 2001). For instance, some authors favor a foreground screen dust geometry model (Calzetti et al. 1994, 1996), while others propose hybrid models with the dust partially distributed in a foreground screen and partially concentrated in the star-forming regions (Charlot & Fall 2000). In this subsection, we discuss the methods used to estimate dust attenuation. We calculate the attenuation of the stellar continuum from the UV data available on NGC 5668 and these estimates are then compared with the ionized-gas attenuation derived from the Balmer decrement in both individual H ii regions and concentric annuli.

5.1.1. UV-continuum Attenuation

In this case, we estimate the attenuation of the stellar continuum using UV data alone. Because the UV radiation is preferentially emitted by young stars (∼100 Myr) and because the dust is most efficient in attenuating UV light, rest-frame UV observations can lead to incomplete and/or biased reconstructions of the recent star formation activity and SFH of galaxies where dust absorption is expected to be significant, unless proper corrections are applied. Radiative transfer models suggest that the total-IR (TIR; 3–1100 μm) to UV luminosity ratio method (i.e., Buat 1992; Xu & Buat 1995; Meurer et al. 1995, 1999) is the most reliable estimator of the dust attenuation in star-forming galaxies because it is almost completely independent of the extinction mechanisms (i.e., dust/star geometry, extinction law; see Xu & Buat 1995; Meurer et al. 1999; Gordon et al. 2000; Witt & Gordon 2000). However, this would require having both far-infrared data at the same resolution as the UV data. In the case of galaxies at the distance of NGC 5668, this would provide very little spatial information on the radial variation of the dust attenuation even if data from state-of-the-art infrared facilities such as Herschel would be available. Even though IRAC and MIPS images for NGC 5668 are available in the Spitzer archive, and we can theoretically obtain profiles in 8, 24, 70, and 160 μm, the poor resolution at 160 μm (38'') would yield a TIR profile with just a couple of data points. Under certain circumstances, the UV attenuation can be indirectly estimated using the slope of the UV spectrum (denoted as β), in the sense that redder UV colors are indicative of larger attenuations. This so-called infrared excess (IRX)–β relation has been widely used in starburst galaxies, where most of the UV light comes from newly born stars (Calzetti et al. 1994; Heckman et al. 1995; Meurer et al. 1999). In normal star-forming spirals, more evolved stars can also contribute to the UV flux, shifting the IRX–β relation to redder UV colors and increasing the overall scatter (Bell 2002; Buat et al. 2005; Seibert et al. 2005; Cortese et al. 2006; Gil de Paz et al. 2007; Dale et al. 2007). The use of radial profiles instead of integrated measurements seems to reduce the global scatter (Boissier et al. 2007; Muñoz-Mateos et al. 2009a).

Here, we apply the IRX–β relation provided by Muñoz-Mateos et al. (2009a) to FUV–NUV measurements obtained from the GALEX images of NGC 5668. This relationship was specifically calibrated for normal nearby spirals, so it should be applicable to NGC 5668 as well. However, before applying this technique to subregions, we checked this assumption using the total galaxy IR luminosity of NGC 5668 from the IRAS fluxes quoted by Wang & Rowan-Robinson (2009) leading to a TIR flux of log (F_TIR) = 13.64 × 10⁻²³ (erg s⁻¹ cm⁻²). This value combined with the FUV flux obtained from our GALEX FUV image leads to log (TIR/FUV) ∼ 0.18. On the other hand, for a global UV color of FUV–NUV = 0.27, the IRX–β yields log (TIR/FUV) ∼ 0.39. This is somewhat larger than the observed value, but still lies within the 1σ scatter around the IRX–β relation of Muñoz-Mateos et al. (2009b). Thus, using the radial profiles described in Section 4.3, we determined the radial variation of the FUV–NUV color in steps of 6''. The UV color was then used to obtain profiles of TIR/FUV and TIR/NUV ratios using the prescriptions of Muñoz-Mateos et al. (2009b). These values were then transformed into dust attenuation in the FUV (A_FUV) and NUV (A_NUV) by means of the recipes by Cortese et al. (2008), which take into account the IR excess associated with the extra dust heating due to the light from old stars. The resulting attenuation profiles are shown in Table 5. Note that the absolute uncertainty in the TIR/FUV ratio from the FUV–NUV is larger than the relative change in such a ratio across the galaxy (see Muñoz-Mateos et al. 2009b).

Table 5. UV-continuum Attenuation Results

Radius	AFUV	ANUV	E(B − V)Cardelli	AV, Cardelli	E(B − V)Calzetti	AV, Calzetti
('')	(mag)	(mag)	(mag)	(mag)	(mag)	(mag)
(1)	(2)	(3)	(4)	(5)	(6)	(7)
6	1.98	1.40	0.18	0.54	0.17	0.69
12	1.51	1.13	0.14	0.44	0.14	0.56
18	1.33	1.03	0.13	0.40	0.12	0.51
24	1.20	0.95	0.12	0.37	0.12	0.47
30	1.04	0.87	0.11	0.34	0.11	0.43
36	0.90	0.80	0.10	0.31	0.10	0.39
42	1.01	0.86	0.11	0.33	0.10	0.42
48	1.04	0.87	0.11	0.34	0.11	0.43
54	1.23	0.97	0.12	0.38	0.12	0.48
60	1.20	0.96	0.12	0.37	0.12	0.47
66	0.95	0.83	0.10	0.32	0.10	0.41
72	0.84	0.77	0.10	0.30	0.09	0.38
78	0.84	0.77	0.10	0.30	0.09	0.38
84	0.93	0.82	0.10	0.32	0.10	0.40
90	0.75	0.73	0.09	0.28	0.09	0.36
96	0.40	0.59	0.07	0.23	0.07	0.29
102	0.62	0.67	0.08	0.26	0.08	0.33
108	0.58	0.66	0.08	0.26	0.08	0.32
114	0.90	0.80	0.10	0.31	0.10	0.40

Notes. (1) Radius in arcsec. (2) Far-UV attenuation values in magnitudes. (3) Near-UV attenuation values in magnitudes. (4) and (5) Galactic color excess from UV data and attenuation values calculated via Cardelli law, (E(B − V) = A_NUV/8.0) R_V = 3.1, expressed in magnitudes. (6) and (7) Galactic color excess from UV data and attenuation values calculated via Calzetti law, (E(B − V) = A_NUV/8.22) R_V = 4.05, expressed in magnitudes.

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Now that we have derived the extinction in the UV, we can calculate the extinction in other bands using an attenuation curve. Such reddening corrections have normally been undertaken using a number of extinction curves, including those of Seaton (1979; in the UV), Cardelli et al. (1989), Savage & Mathis (1979), Ardeberg & Virdefors (1982), and Fitzpatrick (1999). These "standard" curves are often used interchangeably, on the understanding that they should give broadly similar results. The parameterized curve by Cardelli et al. (1989) is commonly used to fit the extinction data both for diffuse and dense interstellar medium (ISM). In our case, the continuum attenuation is obtained using at different wavelengths two different extinction laws (Cardelli et al. 1989; Calzetti 2001). We based our calculation on the NUV data, adopting the relation with the color excess E(B − V) given by Cardelli et al. (1989), E(B − V) = A_NUV/8.0, and for Calzetti et al. (1994), E(B − V) = A_NUV/8.22 (Gil de Paz et al. 2007). We then adopt the average values of R_{V, Cardelli} = 3.1 and R_{V, Calzetti} = 4.05. For sake of clarity, Figure 7 plots only the results obtained in the case of the Calzetti extinction law as the two curves are consistent within the errors (but offset by −0.09 mag in the case of the Cardelli law).

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5.1.2. Ionized-gas Emission-line Attenuation

5.1.3. Optical-continuum Attenuation

The electron density, N_e, is one of the key physical parameters that characterize gaseous nebulae. Most of the density estimates found in the literature are based on measurements of a sensitive emission-line ratio. In the presence of internal variations of electron density, however, these single line ratio measurements may not be representative of all ionizing zones. The measurements are based on the fact that a relation exists between the collisional de-excitation of atoms and electron density (Osterbrock & Ferland 2006). If an ion emits similar amounts of energy from different energy levels at nearby wavelengths, then the ratio of the emission-line intensities can be used to obtain an estimate of the electron density and there are two line ratios that can be used: [O ii] λλ3726, 3729 or [S ii] λλ6717, 6731. In our case, we make use of the [S ii] λλ6717, 6731 line ratio and the electron density of the region responsible for the [S ii] emission can be determined as

$$\begin{equation} R([{\rm S\,\mathsc{ii}}])=\frac{I([{\rm S\,\mathsc{ii}}]\,\lambda 6717)}{I([{\rm S\,\mathsc{ii}}]\,\lambda 6731)}\simeq 1.49\left(\frac{1+3.77x}{1+12.8x}\right), \end{equation} \tag{ 1 }$$

where x, the density parameter, is defined as x = 10⁻⁴ · n_e · t^−1/2. Solving this equation for the density parameter, we can obtain N_e by assuming T_e = T_[S ii]/10⁴, where T_[S ii] is the electron temperature of the region responsible for the [S ii] emission (McCall et al. 1985). Thus, in order to properly estimate this electron density, a previous knowledge of the electron temperature of the region responsible for the [S ii] emission lines is required. Assuming the calibration of T[N ii] as a function of the R₂₃ line ratio (see Equation (2)) given by Thurston et al. (1996) and an average difference of 3000 K between T[N ii] and T[S ii] (with the former being lower; Garnett 1992), we estimated T_[S ii] in the equation above. Note that although this estimate for the temperature is not very precise (as it does not rely on the use of temperature-sensitive line ratios), it is accurate enough for correcting the densities obtained from the [S ii] λλ6717, 6731 line ratio for temperature effects. The large uncertainties associated with the determination of T[S ii] prevent us from extracting further conclusions from the density measurement derived. Despite that, we find a mean value for N_e of 190 cm⁻³ for the H ii regions in agreement with the typical value densities in H ii regions (N_e ∼ 10² cm⁻³; Osterbrock & Ferland 2006).

H ii regions identify the sites of recent massive star formations in galaxies. The rapid evolution of these stars, ending in SNe explosions, and the subsequent recycling of nucleosynthesis products into the ISM, make H ii regions essential probes for the present-day chemical composition of star-forming galaxies across the universe. The study of nebular abundances is therefore crucial for understanding the chemical evolution of galaxies. Obtaining a direct measurement of chemical abundances in H ii regions requires a good estimate of the electron temperature. Unfortunately, this implies detecting very faint auroral lines such as [O iii] λ4363 or [N ii] λ5755, that are very faint at the abundance levels of most spiral disks. Thus, we must use instead calibrations based on the predictions of photoionization models or on empirical measurements for strong lines. Among the various strong-line methods, the R₂₃ indicator originally proposed by Pagel et al. (1979) stands out as arguably the most popular:

$$\begin{equation} R_{23}=\frac{f([{\rm O\,\mathsc{iii}}]\, \lambda \lambda 4959, 5007)+f([{\rm O\,\mathsc{ii}}]\, \lambda \lambda 3726, 3729)}{f({\rm H}\beta)}. \end{equation} \tag{ 2 }$$

Like all strong-line diagnostics, R₂₃ as an abundance indicator has a statistical value, based on the fact that the hardness of the ionizing radiation correlates with metallicity. Numerous calibrations of R₂₃ in terms of the nebular chemical composition can be found in the literature. We choose as the best set of values for the oxygen abundance those given by the Kewley & Dopita (2002) recipe, which basically adopts a calibration of the [N ii]/[O ii] ratio for oxygen abundances above half-solar and their own calibration of R₂₃ for abundances below that value.¹⁹ The R₂₃ abundance diagnostic depends strongly on the ionization parameter, for this reason we also calculated it following the indications given in Kewley & Dopita (2002). These authors used a combination of stellar population synthesis and photoionization models to develop a set of ionization parameter and abundance diagnostics based only on the use of strong optical emission lines. These techniques are applicable to all metallicities. In particular, for metallicities above half-solar, the ratio [N ii]/[O ii] provides a very reliable diagnostic since it is an independent ionization parameter and does not have a local maximum. This ratio has not been used historically because of concerns about reddening corrections. However, the use of classical reddening curves is sufficient to allow this [N ii]/[O ii] diagnostic to be used with confidence as a reliable abundance indicator. Note that the calibration of the [N ii]/[O ii] line ratio as a diagnostic of 12 + log (O/H) relies on the dependence of the (N/O) abundance ratio on the oxygen abundance. Thus, no attempt has been made to derive the nitrogen abundance in this work.

The iterative method used as part of this recipe allows both these parameters to be obtained without the need of using temperature-sensitive line ratios involving very faint emission lines that are particularly elusive in the case of spiral disks. One drawback of using R₂₃ (and many other emission-line abundance diagnostics; see Pérez-Montero & Díaz 2005) is that it depends also on the ionization parameter q defined here as q = S_H0/n, where S_H0 is the ionizing photon flux through a unit area and n is the local number density of hydrogen atoms. Some calibrations have attempted to take this into account (e.g., McGaugh 1991), but others do not (e.g., Zaritsky et al. 1994). Another difficulty in the use of R₂₃ and many other emission-line abundance diagnostics is that they are double valued in terms of the abundance (12 + log (O/H)). Thus, one of the main difficulties in its adoption is related to the necessity of locating which of two branches (upper and lower) a given H ii region belongs to, since R₂₃ is degenerate (Bresolin et al. 2009a). This is because at a low abundance the intensity of the forbidden lines scales roughly with the chemical abundance while at high abundance the nebular cooling is dominated by the infrared fine structure lines and the electron temperature becomes too low to collisionally excite the optical forbidden lines. When only double-valued diagnostics are available, an iterative approach that explicitly solves for the ionization parameter, as the one used here that is based on the Kewley and Dopita logical flow diagram, helps to resolve the abundance ambiguities. In Tables 6 and 7, we present, the results respectively, derived for the abundance gradient Fits and the values obtained for both H ii regions and concentric annuli. The metallicity values vary between 12 + log (O/H) = 8.15 and 12 + log (O/H) = 8.7 (i.e., from approximately 1/3 the solar oxygen abundance to nearly the solar value). The lack of some regions in this table is due to the poor signal to noise or simply non-detection of Hβ emission (12 regions).

Simulations of the line flux errors were carried out in order to derive the errors in the oxygen abundances. These simulations assumed a Gaussian probability distribution for each line flux and that these were not correlated between the different lines. The resulting errors, which are shown in Table 7, could then be considered as upper limits to the actual line flux errors (where a contribution of correlated errors is expected).

In order to quantify the abundance gradient, we have carried out three linear regressions to the data points, the first one is a fit to all points weighted by their errors (χ²_red = 1.45); the gradient has a value of −0.035 dex kpc⁻¹ (−0.0042 dex arcsec⁻¹). The second and the third fits are double fits to the data with a free parameter, the radius of break, but one is weighted by the errors (black solid line) and the other is unweighted (black dashed line; yield both χ²_red = 0.54).

The Kewley & Dopita recipe allows us to make use of the most optimal abundance indicator among [N ii]/[O ii], [N ii]/Hα, and R₂₃. We find that the three abundance diagnostics (shown in the bottom panel of Figure 8 with different colors) are homogeneously mixed, as shown in Figure 8. Thus, the [N ii]/Hα and R₂₃-based abundance values are well mixed and can be derived at almost any galaxy radius, while the [N ii]/[O ii] indicator is lost in some H ii regions, mostly at large radii. This is, as pointed out in Kewley & Dopita (2002), because nitrogen is predominantly a primary nucleosynthesis element in the range 12 + log (O/H) ⩽ 8.6 (see also Figure 3 in Kewley & Dopita 2002) and the calibration of the (N/O) abundance ratio and the [N ii]/[O ii] line ratio is not sensitive to the oxygen abundance under these circumstances.

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The results are summarized in Table 6 and Figure 8 where we plot the three gradients as a function of the de-projected galactocentric radius. We find that inward r ∼36'' (∼4.4 kpc) the O/H ratio follows an exponential profile with a slope of 0.140 ± 0.016 (dex kpc⁻¹) and 12 + log (O/H)_{r = 0} ≃ 8.9, similar to the normalized radial gradient found in other spiral disks. The outer abundance trend flattens out to an approximately constant value of 12 + log (O/H)_{r = 0} ≃ 8.27 (with a slight gradient of 0.002 ± 0.019 (dex kpc⁻¹)) and could even reverse (see Section 6 for a discussion on the possible causes for such flattening). The abundance gradient derived, −0.035 dex kpc⁻¹ (−0.0042 dex arcsec⁻¹), is somewhat shallower than the one for the MW (−0.08 dex kpc⁻¹; Boissier & Prantzos 1999 and references therein). A similar trend was found from the analysis of the spectra of the concentric annuli. The analysis of these spectra was limited to the innermost nine annuli, because beyond this ring both the continuum and line emission become too faint to derive reliable emission-line fluxes. In Figure 8, we plot the change in abundance for all annuli with a solid black line (bottom panel) where the uncertainties associated are represented by the gray shaded area. The blue dashed line represents the metallicity profile predicted by the best-fitting model of Boissier & Prantzos (1999, 2000, hereafter BP2000 models). This profile has been shifted by 1 dex to match the metallicity scale derived from our spectroscopic data. Note that this kind of zero-point offsets in metallicity are not unexpected due to the significant uncertainties in the yields used in the disk evolution models (see discussion in Muñoz-Mateos et al. 2011); besides, even the empirical oxygen abundances can be subject to large systematic offsets (Moustakas et al. 2010). The relative changes in metal abundances and therefore their radial profiles, on the other hand, are much more robust to these unknowns.

In order to gain further insight into the evolution of NGC 5668, we have fitted its multi-wavelength surface brightness profiles with the BP2000 models. These models describe the chemical and spectrophotometric evolution of spiral disks as a function of only two variables: the dimensionless spin parameter, λ, and the circular velocity in the flat regime of the rotation curve, V_C. Within these models, galactic disks are simulated as a set of concentric rings that evolve independently from each other (for simplicity, radial mass or energy flows are not considered). The gas infall rate at each radius decreases exponentially with time, with a timescale that depends on both the total mass of the galaxy and the local mass surface density at that radius. Once in the disk, gas is transformed into stars following a Kennicutt–Schmidt law multiplied by a dynamical term, which accounts for the periodic passage of spiral density waves. The mass distribution of each new generation of stars follows a Kroupa (2001) initial mass function (IMF). The finite lifetimes of stars of different masses is taken into account; when they die, they inject metals into the ISM, thus affecting the metallicity of subsequent stars. The local metallicity at the time of formation is taken into account when determining the lifetimes, yields, evolutionary tracks, and spectra of each generation of stars. The model was first calibrated against several observables in the MW (see Boissier & Prantzos 1999) and then extended to other galaxies with different values of λ and V_C (BP2000), using several scaling laws derived from the Λ-Cold Dark Matter framework of galaxy formation (Mo et al. 1998).

For each pair of values of λ and V_C, the model outputs radial profiles at different wavelengths, which can then be compared to the actual profiles of our Galaxy. In order to probe the spatial location of stars of different ages—and therefore better constrain the model predictions—we measured surface brightness profiles at all GALEX FUV and NUV bands, the ugriz bands from SDSS, and the 3.6 and 4.5 μm Spitzer bands. The radial variation of internal extinction in the UV was estimated indirectly from the FUV−NUV color profiles, as explained in Section 5.1.1. The UV extinction was then extrapolated to the optical and near-IR bands, assuming a MW extinction curve, convolved with a sandwich model to account for the relative geometry of stars and dust (see Muñoz-Mateos et al. 2011 for details).

We compared these extinction-free profiles with the model predictions for a grid of values of λ and V_C, and used an χ² minimization algorithm to find the best-fitting values. The results of the fit are shown in Figure 9, and in Figure 10 we present the residuals. Each panel corresponds to a different wavelength. The gray profiles are only corrected for foreground MW extinction, whereas the black ones are corrected for internal extinction as well. The red and blue dashed lines bracket the region of the profile used for the fit. On the one hand, starlight inside r ≃ 20'' is dominated by emission coming from the bulge and the oval. On the other hand, beyond r ≃ 125'' the S/N becomes very low, and contamination from background sources could be an issue. The model that best reproduces simultaneously all multi-wavelength profiles is shown with a red line. The shaded band encompasses all models whose χ² is less than twice the χ² of the best model (χ²_min  ≃  0.8).²⁰ The resulting χ² of the fitting model is obtained after a two-stage-fitting procedure because, as one would expect, this model does not reproduce the very small-scale variations of the surface brightness profiles of our disk. So in a first run of the fitting procedure we assume that the total uncertainty for each point is due to the quadratic sum of the zero-point and photometric errors, plus an extra uncertainty in the model predictions of 10%. These values represent the initial guess for the intrinsic error of the model and in this stage the χ² is ∼5. In the second step, we calculate the rms of the best-fitting model with respect to the galaxy profiles and we pass these error profiles to the code as initial uncertainties to start the second run. In this way the new reduced χ² values are close to unity. In principle, when we fit a set of data points with a given model, it is often implicitly assumed that deviations between the observed data points and the model are due to the measured uncertainties of the former. However, in practice one also has to account for the fact that the models themselves are not a perfect representation of nature and have their own "uncertainties." The model yields smooth profiles that, by construction, cannot reproduce the fine structure of the actual profiles. In order to account for this, we performed this fit for NGC 5668 in a two-stage fashion (see also Section 5 of Muñoz-Mateos et al. (2011) for a detailed discussion). When fitting the multi-wavelength profiles, we should not ignore the internal degeneracy in the determination of the λ and V_C values as these are not completely independent parameters. For this reason in Figure 11, we show the two-dimensional χ² distribution obtained for NGC 5668 in the case of fitting all bands simultaneously and in the case of each band separately. The corresponding best-fitting values are λ = 0.053^+0.016_−0.015 and V_C = 167⁺¹²₋₈ km s⁻¹. Where the errors are those expected when one is interested in deriving each of the two quantities separately.

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In general, all bands are successfully reproduced by the BP2000 models, but the fit is not equally good at all wavelengths. For example, we can appreciate in the top panels of Figure 10 that in the cases of FUV, NUV, and u-band data the quality of the fit is not so good because these bands are more sensitive to the recent variations in the SFH and on the recipe used to calculate the extinction (or even limitations intrinsic to the models in order to reproduce the UV part of the spectrum at certain metallicities, as explained in Figure 9 of Muñoz-Mateos et al. 2011). The deviations in UV bands from the BP2000 models are compatible with the typical range of errors, as pointed out in Muñoz-Mateos et al. (2011).

While the BP2000 models provide a good fit to the overall shape of the surface brightness profiles of NGC 5668 (see Figure 9), the analysis of the deviations from these otherwise idealized models could give important clues on the details of the SFH of this galaxy (e.g., gas and/or stellar radial transfers). In this regard, Figure 12 shows that while the best-fitting model predicts a systematic bluing in the colors toward the outer parts of the disks, the measured colors flatten or even get redder beyond ∼30''–40''. This radius interestingly coincides with the position where the slope of the metallicity gradient changes sign. We also find small offsets (⩽0.2 mag) between the observed and predicted colors. This is partially due to uncertainties in the model predictions for some of these colors.

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The model has to reproduce at the same time the shape of the observed surface brightness profiles in all bands simultaneously and in addition it has to reproduce the "average" level of surface brightness. This kind of fitting introduces some limits in the range of the model parameters in a way that the colors of these models are located in a relatively narrow range as a consequence of the high degeneration within those model (surface brightness) profiles that match the data at all wavelengths simultaneously.²¹

Small variations of a few tenths of a magnitude will not have a significant impact on the overall shape of the surface brightness profiles, but will reveal themselves more clearly in the color profiles (see Muñoz-Mateos et al. 2011). On the other hand, the SFHs of the different annuli in the model are tied to one another (due to the analytical way in which we implement radial changes) but the actual SFH within the galaxy will exhibit more complex radial variations from one ring to the next.

The re-distribution of stars, gas, and dust in galaxies can have important consequences in the metallicity distribution and, in particular, in deviations of the chemical and photometric properties of disks with respect to the predictions of static disk evolution models. In this regard, radial changes (up- or down-bending) in the slope of the abundance gradient of nearby spiral galaxies (Vílchez & Esteban 1996) are detected and are often related to gaseous and stellar radial mixing processes (Spitzer & Schwarzschild 1953; Barbanis & Woltjer 1967; Shaver et al. 1983; Fuchs 2001; Sellwood & Binney 2002; Roškar et al. 2008; Haywood 2008; Bresolin et al. 2009b; Vlajić et al. 2009).

The existence of this kind of bimodal gradients are often proposed to have been induced by the presence of a bar-like potential (Díaz et al. 1990; Vila-Costas & Edmunds 1992; Edmunds & Roy 1993; Zaritsky et al. 1994). Indeed, in the case of strong-barred galaxies a change from a shallow to a steep metallicity profile is commonly observed and explained in the context of radial mixing of the gas induced by the bar (Martin & Roy 1995; Roy & Walsh 1997). On the other hand, bars can also lead to a steepening of the metallicity profile toward the inner disk if the gas transfer results in significant star formation in situ (Friedli et al. 1994; Martin & Roy 1995; Roy et al. 1996; Roy & Walsh 1997).

This latter behavior has been found in dynamical simulations of the formation of bars (Friedli et al. 1994; Friedli & Benz 1995). In these simulations, the presence of a steep-shallow break in the metallicity profile is the result of an intense chemical enrichment by star formation in the bar combined with the dilution effect of the outward flow beyond the break. According to these models the presence of such a break indicates that the bar has recently formed, i.e., in the last Gyr. Observationally, the metallicity distribution of a number of galaxies hosting young bars has been successfully reproduced by this or a similar scenario (Roy & Walsh 1997; Considère et al. 2000).

However, other mechanisms have been also proposed to explain bimodal metallicity distributions. Thus, in the context of the spiral density wave theory, star formation is expected to be proportional to Ω − Ω_p (Oort & Peixóto 1974). In Jensen et al. (1976), this prediction was successfully tested against the metallicity gradients measured in a number of grand-design spirals. Should this scenario be valid, one would expect to find a minimum in the chemical abundance at the position of the corotation radius (see also the recent works by Acharova et al. 2005; Scarano 2010), especially in the case of galaxies where the spiral structure is long-lived and quasi-stationary (McCall 1986; Acharova et al. 2005). This is to the fact that Ω − Ω_p is null (by definition) at corotation and, therefore, star formation should be less efficient resulting in a lesser degree of metal enrichment. In this scenario, a maximum in the colors should also be observed at the approximate position of the corotation radius as the optical–near-infrared colors would be dominated by those of the underlying stellar population since the current day SFR is expected to be low.

Finally, a flattening of the outer color and metallicity profiles is believed to be also caused by the increasing contribution of old migrated stars to the stellar content of disks (Zaritsky et al. 1994; Binney 2001; Sellwood & Binney 2002; Roškar et al. 2008; more recently, Minchev et al. 2011; Roškar et al. 2011). In this case, as we move further out into the outer disk we find progressively older stars, which have been migrating for a longer period of time, leading to a positive age and color gradient in these regions. With regard to the metal abundance and according to the simulations of Roškar et al. (2008), radial migration leads to the mixing of the old stellar populations, which results in flatter gradients at early times and in the very outer regions of the present-day disks as these regions are primarily populated by migrated stars. In the few observational and theoretical studies on the luminosity-weighted age profiles of the disks, a similar flattening or even an up-bending is found (Bakos et al. 2008; Sánchez-Blázquez et al. 2009, 2012; Yoachim et al. 2010). While some authors favor stellar migration as the main driver of the shaping of these age profiles (Yoachim et al. 2010), some others indicate that this might be due to a decrease in the star formation in the external parts of the disk with time caused by a reduction of the volume density of the gas in these regions (Sánchez-Blázquez et al. 2009).

The different scenarios proposed above to explain a steep-shallow break in the metallicity gradient of galaxies, namely, a young bar, reduced star formation at the corotation radius, stellar migration, or evolution of the star formation threshold with redshift have different imprints not only on the specific shape of the metallicity gradient but also on other properties such as the colors. In the case of NGC 5668, the change in the shape of the metallicity gradient takes place at a radius of ∼36'' (4.4 kpc or 2.8 disk-scale lengths), well within the region where in situ star formation takes place in the disk, at an approximate surface brightness of ∼22 mag arcsec⁻² (3.6 μm Spitzer band). At this radius the contribution of migrated stars to either the colors, luminosity-weighted age, or chemical abundance is expected to be negligible compared with that from stars formed in situ (see Bakos et al. 2008; Vlajić et al. 2009). Again, as this brake takes place well within the star-forming disk of NGC 5668, changes in the color and metallicity gradients associated with a possible evolution of the star formation threshold with redshift is highly unlikely. With respect to the possibility that the minimum in the metal abundance profile of NGC 5668 could be due to the presence of the corotation radius at this break, two things can be said. First, NGC 5668 is a rather flocculent spiral,²² where spiral density waves are expected to be weak or absent and, consequently, the effects of the spiral arms on the radial distribution of the star formation should be minimal (if any; McCall 1986). Second, the color profiles in (u − g) and (g − r) show a minimum at the position of the metallicity break, which is the opposite to what we would expect if that position corresponds to the corotation radius.

The only scenario that remains to be analyzed in detail is the possibility that the deviations of the metallicity and color profiles from those predicted by the best-fitting BP2000 model of NGC 5668 are due to the presence of a nascent bar and the effects associated with it. It is well known that one of the most important drivers in the evolution of galaxies are bars (or non-axisymmetric central light distributions or ovals; Athanassoula 1994). Bars exist in about two-thirds of disk galaxies (Sellwood & Wilkinson 1993) and isolated galaxies are known to be able to develop a barred morphology spontaneously from internal instabilities caused by cooling processes (Miller & Prendergast 1968; Kalnajs 1978; Binney & Tremaine 1987; Sellwood & Wilkinson 1993). These gravitational instabilities are commonly the result of enhanced gas accretion in the disk (Lindblad et al. 1996). Some of the observational properties of NGC 5668 already reveal a potential active gas-accretion phase in this galaxy, such as the presence of both HVCs and HRVCs (Jiménez-Vicente & Battaner 2000 and references therein) and the high total SFR in this object.

In this regard, another relevant parameter is the H i content of NGC 5668 compared with objects of similar total mass and morphological type. In order to find out whether the H i content NGC 5668 is particularly high or low, we resort to the so-called H i deficiency parameter. This quantity, defined by Haynes & Giovanelli (1984), compares—in logarithmic scale—the observed H i mass of a given galaxy and the typical H i mass of isolated galaxies of similar morphological types and linear sizes. The difference between both values is performed in such a way that positive H i deficiencies correspond to galaxies with less gas than similar field galaxies, and vice versa. Following the prescriptions of Haynes & Giovanelli (1984), we find that an Sd galaxy with the same optical diameter as NGC 5668 is expected to have log(M_H i) = 9.66. Solanes et al. (1996) extended the work of Haynes & Giovanelli (1984) to a larger sample of galaxies. While they only include Sa-Sc galaxies in their sample, we can safely apply the fitting coefficients of Sc's to our Sd spiral (Solanes et al. 2001). By doing so we obtain a reference H i mass of log(M_H i) = 9.64, completely consistent with the previous estimation. According to Schulman et al. (1996), the actual H i mass of NGC 5668 is log(M_H i) = 10, which implies a negative H i deficiency of ∼ − 0.35. Considering that the usual 1σ scatter of the H i mass for a given type and size is 0.2–0.3 dex (including all types of galaxies), we conclude that our Galaxy is roughly 1σ–2σ gas richer than its normal counterparts. While this difference might not be significant, it shows that, if anything, NGC 5668 has a larger H i content than the average of the spiral galaxy population of its type. Schulman et al. (1994) found in NGC 5668 a weak bar or oval inner structure of 12'' size visible in both optical and near-infrared images. Athanassoula (1994) found that in spiral galaxies having oval structures or weak bars, star formation can occur prolifically along them, especially in the central parts and at the two ends of the bar region. This would result in bluer colors in these regions. The presence of a local minimum in color at a galactocentric distance of ∼30–40 arcsec seems to favor this scenario for NGC 5668. Note, however, that the oval seen in its images is significantly smaller than the radius where the minimum in color and metallicity is found. One possible explanation for this difference might come from the fact that while the light from the superposition of x₁ orbits that shape the oval is only clearly seen in the central 12'', the instabilities associated with it could take place further out, where the superposition of these orbits is not yet significant enough for being detected via photometry only (Debattista et al. 2006).

Another possible explanation for the existence of the oval distortion in NGC 5668 is the possible interaction of NGC 5668 with UGC9380 (Schulman et al. 1996). This is a dwarf galaxy at a relative distance of 200 kpc to the southeast of NGC 5668, with a systemic velocity of 1690 km s⁻¹ and a relative velocity of ∼108 km s⁻¹. A recent or ongoing tidal interaction between these two galaxies could have produced the high-velocity features in NGC 5668 and triggered the formation of both the oval and the incipient bar, as reported by N-body simulations of minor mergers (Eliche-Moral et al. 2006, 2011).

The fact that these blue colors do not extend all the way from this galactocentric distance to the center of the galaxy is likely due to a combination of different effects. First, the secular inside-out model for the evolution of the disk of NGC 5668 predicts a reddening of ∼0.2 mag (0.15 mag) in u − g (g − r) from 36''to 6'' (see Figure 12). Moreover, the reddening in the (FUV − NUV) color indicates a change of ∼0.09 mag in the B − V color purely due to dust attenuation [E(B − V)] within this same radial range. Finally, the light contribution of the bulge in the center, despite being small, can also lead to relatively red colors. These three effects are superimposed on the change in colors induced by star formation in the bar region and whose effects on the colors appear to be noticeable only at both its ends.

Regarding the age of this young bar, in the case of the barred galaxy NGC 3359, Martin & Roy (1995) calculated the age of the bar by using the equation of turbulent transport in a shear flow (Roy & Kunth 1995). Below we repeat this exercise for the case of NGC 5668. If we consider a Cartesian coordinate system centered in the galaxy center and we take x₂ as the radial direction of the local circular orbit (we do not take in account perpendicular effects), l  ∼  300 pc as the mean free path of clouds between collisions (Roberts & Hausman 1984), we can then calculate the time for the gas to diffuse in a length Δx₂ in the radial direction as

$$\begin{equation} \tau _{x_{2}}=\frac{\Delta {x_{2}}^{2} }{v l}. \end{equation} \tag{ 3 }$$

In our case Δx₂ = 4.4 kpc, which coincides with r_BREAK which is the radius at which we detect the flattening of the metallicity gradient and the minimum in the color profiles. From the radial velocity map kindly provided by J. Jiménez-Vicente (2010, private communication; see also Jiménez-Vicente & Battaner 2000), we determine the maximum of the non-circular motions to be v = 10 km s⁻¹. This yields $\tau _{x_{2}}\sim \,10^{9}$ yr, which can be considered as an upper limit to the bar age since the radial transport induced by a bar is a stationary flow. The lower limit is given by a simple division of Δx₂/v. The best estimate for the age of the young bar in NGC 5668 is then $10^{8}{\rm yr} \le \tau _{x_{2}} \le 10^{9}$ yr.

In summary, while the overall observational properties of NGC 5668 are well fitted by the inside-out scenario of disk formation, the deviations in the color and metallicity profiles are best interpreted in the context of the presence of a nascent bar where significant in situ star formation is (or have been recently) taking place. The formation of the bar is believed to be due to instabilities in the gas-rich inner disk of NGC 5668, possibly helped in the interaction with a companion. This scenario is compatible with the relatively large H i content and SFR of NGC 5668 and with the presence of HVCs and HRVCs in its velocity field, evidence of significant non-rotational gas motions in the disk.