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A&A 535, A13 (2011) DOI: 10.1051/0004-6361/201116872
c ESO 2011

Astronomy & Astrophysics

The Herschel Virgo Cluster Survey
IX. Dust-to-gas mass ratio and metallicity gradients in four Virgo spiral galaxies
L. Magrini1 ,S.Bianchi1 , E. Corbelli1 , L. Cortese3 ,L.Hunt1 , M. Smith2 ,C.Vlahakis4 ,J. Davies2 ,G. J.Bendo5 , M. Baes6 ,A.Boselli7 , M. Clemens8 , V. Casasola9 , I. De Looze6 , J. Fritz6 ,C.Giovanardi1 , M. Grossi10 , T. Hughes11 , S. Madden12 , C. Pappalardo1 , M. Pohlen2 , S. di Serego Alighieri1 , and J. Verstappen6
1 2 3 4 5 6 7 8 9 10 11 12

INAF ­ Osservatorio Astrofisico di Arcetri, Largo E. Fermi, 5, 50125 Firenze, Italy e-mail: laura@arcetri.astro.it Department of Physics and Astronomy, Cardiff University, The Parade, Cardiff, CF24 3AA, UK European Southern Observatory, Karl-Schwarzschild-Strasse 2, 85748 Garching bei MЭnchen, Germany Departamento de Astronomia, Universidad de Chile, Casilla 36-D, Santiago, Chile Jodrell Bank Centre for Astrophysics, Alan Turing Building, School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281 S9, 9000 Gent, Belgium Laboratoire d'Astrophysique de Marseille, UMR 6110 CNRS, 38 rue F. Joliot-Curie, 13388 Marseille, France Osservatorio Astronomico di Padova, Vicolo dell'Osservatorio 5, 35122 Padova, Italy INAF ­ Istituto di Radioastronomia, via P. Gobetti 101, 40129 Bologna, Italy CAAUL, Observatorio Astronomico de Lisboa, Universidade de Lisboa, Tapada de Ajuda, 1349-018 Lisboa, Portugal The Kavli Institute for Astronomy & Astrophysics, Peking University, Beijing 100871, PR China Service d'Astrophysique, CEA/Saclay, l'Orme des Merisiers, 91191 Gif-sur-Yvette, France

Received 11 March 2011 / Accepted 3 June 2011
ABSTRACT

Context. Using Herschel data from the open time key project the Herschel Virgo Cluster Survey (HeViCS), we investigated the relationship between the metallicity gradients expressed by metal abundances in the gas phase as traced by the chemical composition of HII regions, and in the solid phase, as traced by the dust-to-gas mass ratio. Aims. We derived the radial gradient of the dust-to-gas mass ratio for all galaxies observed by HeViCS whose metallicity gradients are available in the literature. They are all late type Sbc galaxies, namely NGC 4254, NGC 4303, NGC 4321, and NGC 4501. Methods. We fitted PACS and SPIRE observations with a single-temperature modified blackbody, inferred the dust mass, and calculated two dimensional maps of the dust-to-gas mass ratio, with the total mass of gas from available HI and CO maps. HI moment1 maps were used to derive the geometric parameters of the galaxies and extract the radial profiles. We examined different dependencies on metallicity of the CO-to-H2 conversion factor (XCO ), used to transform the 12 CO observations into the amount of molecular hydrogen. Results. We found that in these galaxies the dust-to-gas mass ratio radial profile is extremely sensitive to choice of the XCO value, since the molecular gas is the dominant component in the inner parts. We found that for three galaxies of our sample, namely NGC 4254, NGC 4321, and NGC 4501, the slopes of the oxygen and of the dust-to-gas radial gradients agree up to 0.6-0.7 R25 using XCO values in the range 1/3-1/2 Galactic XCO . For NGC 4303 a lower value of XCO 0.1 в 1020 is necessary. Conclusions. We suggest that such low XCO values might be due to a metallicity dependence of XCO (from close to linear for NGC 4254, NGC 4321, and NGC 4501 to superlinear for NGC 4303), especially in the radial regions RG < 0.6-0.7 R25 where the molecular gas dominates. On the other hand, the outer regions, where the atomic gas component is dominant, are less affected by the choice of XCO , and thus we cannot put constraints on its value there.
Key words. galaxies: spiral ­ galaxies: abundances ­ submillimeter: galaxies ­ galaxies: ISM ­ dust, extinction

1. Introduction
Virgo is one of the best studied galaxy clusters, being the richest cluster nearest to our own Galaxy (17 Mpc, Gavazzi et al. 1999). It is a relatively populous system, consisting of more than 1000 confirmed members (Binggeli et al. 1985). Galaxies in clusters such as Virgo differ significantly from their field counterparts since interactions with the hostile environment remove gas, quenching the star formation (cf., Boselli & Gavazzi 2006). A galaxy's metallicity is closely related to the star formation (SF) history by which the interstellar medium (ISM) is enriched with the end-products of stellar evolution, and to the infall

process that dilutes the ISM and triggers new SF. As a consequence of their star formation histories, gas stripping and infall events, modified by the cluster environment, galaxies in clusters are expected also to differ in metal content relatively to isolated galaxies. A fundamental tool with which tracing the chemical evolution of a galaxy is the study of its radial metallicity gradient. The metallicity gradient tracks indeed the star formation history of galaxies, integrated over time, together with infall and/or outflow events. The first pioneering work in Virgo was done by Skillman et al. (1996), who analyzed nine spiral galaxies with the aim of seeking correlations among their gas content, locations in the A13, page 1 of 13

Article published by EDP Sciences


A&A 535, A13 (2011)

cluster, metallicities and radial gradients, and comparing them with field spirals. Skillman et al. (1996) found weak evidence of shallower gradients in cluster galaxies deficient in HI than gradients in galaxies with a normal HI content. The situation is however very complex because galaxy interactions affect the star formation history and the gas content across the disk, producing metallicity gradients which differ from those measured in isolated galaxies of the same morphological type. Rupke et al. (2010) have shown that gradients in strongly interacting galaxies are flatter than in similar isolated galaxies; on the other hand, the metallicity gradient of M 81, the largest member of a small group of galaxies, is steeper than in an isolated counterpart due to gas removal in the outskirts (Stanghellini et al. 2010). A direct correlation between gas metallicity and the dust-togas mass ratio is naturally expected since approximatively half of the metals in the ISM reside in dust grains; thus the dust-togas ratio should scale with metal abundance. Such a trend has been obtained theoretically by models computing consistently the evolution of metals and dust, despite the large uncertainties in the yields of both (Dwek 1998; Inoue 2003). The relation of the global dust-to-gas mass ratio with metallicity was investigated by, e.g., James et al. (2002); Draine et al. (2007); Hirashita et al. (2008); Lisenfeld & Ferrara (1998). The radial variation of the dust-to-gas mass ratio was first investigated by Issa et al. (1990) in our Galaxy and in other nearby galaxies (LMC, SMC, M 31, M 33, and M 51) who found evidence for a correlation, with dust-to-gas mass ratio and metallicity decreasing at roughly the same rate with increasing galactocentric radius. More recently, Boissier et al. (2004, 2005) and Thilker et al. (2007) found a clear relationship between metallicity and extinction, thus dust, in several nearby galaxies, suggesting that the variation in extinction is associated with the metallicity gradient. MuЯoz-Mateos et al. (2009) found a good correlation between dust-to-gas and metallicity gradients in the Spitzer Infrared Nearby Galaxies Survey (SINGS; Kennicutt et al. 2003). Finally, Bendo et al. (2010a) compared the dustto-gas ratio and metallicity gradients in NGC 2403, finding a similar decreasing behavior with radius. We have recently obtained observations of the Virgo galaxies with the Herschel Space Observatory (Pilbratt et al. 2010), within the open time key project HeViCS (Herschel Virgo Cluster Survey) (Davies et al. 2010). HeViCS maps a wide area over the Virgo Cluster at wavelengths from 100 to 500 m. This spectral range covers the peak of the thermal emission from cold dust (T < 30 K) which enables the detection of the bulk of the dust emission in galaxies. Also, Herschel gives an unprecedented resolution at these wavelengths (ranging from about 10 to 36 , equivalent to 1-3 kpc for Virgo galaxies). Atomic and molecular gas maps are available in the literature at a comparable resolution (Chung et al. 2009a; Kuno et al. 2007), thus providing resolved maps and the possibility of deriving radial gradients of dust-to-gas mass ratios. In the present paper we assessed the validity of using HeViCS observations to obtain metallicity gradients from radial profiles of the dust-to-gas mass ratio. We investigated the hypothesis that the local dust-to-gas mass ratio is proportional to metallicity, starting from the four spiral galaxy in the Virgo cluster (NGC 4254, NGC 4303, NGC 4321, and NGC 4501) whose metallicity gradients are available in the literature. We studied the relation between radial profiles of metallicity and dust-to-gas mass ratios, and how this can be used to constrain the CO-to-H2 conversion factor (XCO ) and its dependence on metallicity.
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The paper is structured as follows: in Sect. 2 we describe the new HeViCS observations, and the observations of atomic and molecular gas. We also derive the oxygen abundance and its radial gradient in each galaxy. Section 3 discusses the fits to the observed Herschel dust spectral energy distributions (SEDs), how the radial profiles are derived, and how we calculate dust and gas masses. In Sect. 4 we develop the method by which we constrain XCO , and Sect. 5 gives our conclusions.

2. Data
2.1. The sample

In the HeViCS field there are four galaxies for which the oxygen gradient has been well determined in the literature (e.g., Skillman et al. 1996; Moustakas et al. 2010). They are NGC 4254 (M 99), NGC 4303 (M 61), NGC 4321 (M 100), and NGC 4501 (M 88), all Sbc late-type galaxies. NGC 4254 is a bright spiral galaxy located at the periphery of the Virgo cluster, at a projected distance of 1 Mpc from the cluster center. Optical images show that this galaxy has onearmed structure, also seen in the HI gas distribution (Phookun et al. 1993; Chung et al. 2009a). Such an asymmetric spiral pattern is often observed in tidally galaxies, but there is no apparently massive companion near NGC 4254 (Sofue et al. 2003). NGC 4321 is located at a distance of 1.1 Mpc form M 87, and has an HI disk that is slightly larger than the optical disk. NGC 4501 is the closest galaxy of our sample to M 87, being located at a distance of 0.5 Mpc. It is weakly HI-deficient, following the definition of Chung et al. (2009a). Comparisons with simulations suggest that NGC 4501 is in an early stage of ram pressure stripping (Vollmer et al. 2008), entering the highdensity region of the cluster for the first time. NGC 4303 is the most isolated galaxy in our sample. It is a barred spiral galaxy with face-on geometry located in the outskirts of the Virgo cluster. We assume for all the galaxies the distance of 17 Mpc (Gavazzi et al. 1999).
2.2. Herschel observations

The HeViCS program consists of Herschel observations of an area of about 60 sq. deg over the denser parts of the Virgo Cluster. The total area is made of 4 overlapping fields, which are observed in parallel scanning mode (fast scan rate: 60 /s) with both the PACS and SPIRE instruments, yielding data simultaneously in 5 spectral bands, at 100 and 160 m (from PACS) and at 250, 350, and 500 m (from SPIRE). At the completion of the program, each field will be covered with 8 scans done in two perpendicular scan directions. The full width half maximum (FWHM) of the beams is 6. 98 в 12. 7 and 11. 64 в 15. 65 in the two PACS bands (PACS observer's manual, 2010), and 18. 2, 24. 9, 36. 3 in the three SPIRE bands (SPIRE observer's manual, 2010). At the time of writing, each field has been observed with at least two scans. In this paper, we use this dataset, whose data reduction and analysis is described in details in Paper VIII, Davies et al. (2011). Some papers presenting Herschel observations for these galaxies have been already published. Eales et al. (2010) and Sauvage et al. (2010) analyzed the SPIRE maps of NGC 4254 (M 99) and NGC 4321 (M 100) observed within the Herschel Reference Survey (Boselli et al. 2010) to map the ISM using dust emission. Adding these data to archival Spitzer, HI, and CO maps, Pohlen et al. (2010) investigated the spatial distribution of gas and dust in these same galaxies. They also present


L. Magrini et al.: Dust and metal gradients in Virgo spirals. IX.

12+log(O/H)

as a preliminary result, the ratio of the total gas mass (HI + H2 ) to 500 m flux, an approximation of the dust mass for the two galaxies. They found a decreasing dust-to-gas mass ratio with radius, consistent with results by, e.g., Bendo et al. (2010a) in NGC 2403. With the present-time availability of the PACS data the dust SED fitting can be better defined allowing to measure the exact shape of the radial dust-to-gas mass gradient. Finally, Smith et al. (2010) presented a resolved dust analysis of three of the largest (in angular size) spiral galaxies in HeViCS, among them NGC 4501.
2.3. The calibration of metallicity and the abundance gradients

NGC4254 9.4 9.2 9.0 8.8 8.6 8.4 8.2 8.0 0.0 0.2 0.4 0.6 R/R25 0.8 1.0

The metallicity measurements of these galaxies are available in the literature from optical spectroscopy of their HII regions. The most direct method to derive the oxygen abundance is to measure the electron temperature (T e ) of the ionized gas using the intensity (relative to a hydrogen recombination line) of one or more temperature-sensitive auroral lines such as [O III] 4363 е, [N II] 5755 е, [S III] 6312 е, and [O II] 7325 е, as summarized by Moustakas et al. (2010). However, measurements of the electron temperature were not available from the spectroscopic observations in the original papers of McCall et al. (1985), Shields et al. (1991), Henry et al. (1994), and Skillman et al. (1996). The temperature diagnostic lines are indeed intrinsically faint in metal-rich HII regions. Therefore, oxygen abundance has been derived using the strong-line abundance calibrations which relate the metallicity to one or more line ratios involving the strongest recombination and forbidden lines. In particular, the oxygen excitation index R23 = ([OII]+[OIII])/H is one of the most often adopted calibrators to estimate the nebular abundances. As discussed by Moustakas et al. (2010), the principal advantage of R23 as an oxygen abundance diagnostic is that it is directly proportional to both principal ionization states of oxygen, whereas one of the major disadvantages is that the relation between R23 and metallicity is degenerate for low and high metallicity. However, the calibrations of the metallicity by means of the strong-line ratios are not unique. They can be divided in three main categories: those calibrated with photoionization models (e.g., McGaugh 1991; Zaritsky et al. 1994; Kewley & Dopita 2002; Kobulnicky & Kewley 2004); those calibrated directly with the electron temperature, called empirical methods (e.g., Pilyugin 2001; Pettini & Pagel 2004; Pilyugin & Thuan 2005); and those combining both methods (e.g., DenicolС et al. 2002). As discussed widely in Kewley & Ellison (2008), the abundances derived with different methods do not have a common absolute oxygen abundance scale. The oxygen abundances derived using the theoretical calibration are up to a factor of 4 higher than those based on the empirical calibration. However, despite the significant zero-point offset in the abundance scales, to first order the slope of the abundance gradients agrees when calculated with different calibrators (see Moustakas et al. 2010). We have tested the effect of several metallicity calibrators in NGC 4254, the galaxy with the best sampled metallicity gradient. Starting with the abundance estimates from Moustakas et al. (2010), based on literature spectroscopy calibrated with the Kobulnicky & Kewley (2004, hereafter KK04) formula, we used the relationships provided by Kewley & Ellison (2008) to convert to other abundance scales. The relationships of Kewley & Ellison (2008) are obtained for limited oxygen abundance ranges, corresponding to the ranges where they could perform

Fig. 1. The oxygen abundance gradient of NGC 4254 obtained with several metallicity calibrations: Kobulnicky & Kewley (2004) (magenta circles), Pilyugin & Thuan (2005) (yellow squares), Zaritsky et al. (1994) (cyan triangles), McGaugh (1991) (blue stars), Kewley & Dopita (2002) (empty squares), Tremonti et al. (2004) (green asterisks), and Pettini & Pagel (2004) (violet diamond).

a polynomial fit to transform one abundance scale to another. Because of this, from the abundances of KK04 we were unable to recover the oxygen determination of Pettini & Pagel (2004) and Pilyugin & Thuan (2005). For these cases, we recomputed the oxygen abundance from the original spectra (McCall et al. 1985; Shields et al. 1991; Henry et al. 1994). In Fig. 1, we show the result of our test: while the slope of the gradient is almost invariant with different calibrations, the zero-point depends on the choice of the calibration. In Fig. 3 we show the radial variation of dust temperature. In particular, the empirical calibrations of Pettini & Pagel (2004) and Pilyugin & Thuan (2005) show values of the oxygen abundances roughly 0.5-0.8 dex lower than the other determinations. These two latter empirical calibrations were obtained for HII regions with available electron temperature in a relatively low metallicity regime. They could not be valid for metal rich environments, as the galaxies of our sample. In Sect. 4.1 we will discuss how the dust-to-gas ratio might help in setting a lower limit to the metallicity and to discriminate among different calibrations.
2.4. HI and CO maps

The radial profile of the gas, including both atomic and molecular components, is necessary to derive the dust-to-gas mass ratio gradient. For NGC 4254, NGC 4321, and NGC 4501, we use the moment-0 HI maps obtained with VLA Imaging survey of Virgo galaxies in Atomic gas (VIVA) survey by Chung et al. (2009a). VIVA observations reach a column density sensitivity of 3-5 в 1019 cm-2 . The comparison of their total HI fluxes with values in the literature from single dish observations gives a good agreement especially for the large galaxies, indicating no loss of flux in the interferometric observations (see Fig. 5 in Chung et al. 2009a). The beam sizes are: 30. 86 в 28. 07 for NGC 4254, 15. 90 в 14. 66 for NGC 4321, and 16. 83 в 16. 41 for NGC 4501. The HI radial profile of NGC 4303 is available from Warmels (1988) and Cayatte et al. (1990). We adopt the combined radial profile of the two, shown in Fig. 3 of Skillman et al. (1996).
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Maps of molecular gas were available thanks to the CO ( J = 1-0) mapping survey of 40 nearby spiral galaxies, performed with the Nobeyama 45 m telescope by Kuno et al. (2007).

3. Analysis
3.1. The mass and temperature of dust

Maps of the dust temperature and mass surface density were obtained as in Smith et al. (2010). The images of the galaxies from the five PACS (100 and 160 m) and SPIRE (250, 350, and 500 m) bands were all convolved and re-gridded to the lower resolution (FWHM = 36. 9, 3 kpc) and pixel size (14. 0, 1.1 kpc) of the 500 m observations. We used only pixels with S /N > 10 at 500 m (the rms of our maps in this band is about 0.3 MJy/sr, see Davies et al. 2011). The selection of these high surface-brightness pixels was necessary to limit the uncertainties due to background subtraction and avoid the artefacts caused by the high-pass filtering in the PACS data reduction. Despite this limit, we were able to study the dust and gas properties up to at least 0.7 R25 1 in all galaxies. For each galaxy we thus considered approximately 150-200 pixels covering about 1/2of the optically defined area. We estimated the error on the surface brightness on a pixel by pixel basis by comparing galaxy images from the two scan data used in this paper with those relative to other two scans recently taken by Herschel which cover only part of the HeViCS field. We found errors very similar to those estimated on the total fluxes (see Davies et al. 2011). Including a calibration error of 15% for PACS (PACS ICC, priv. comm.) and 7% for SPIRE (SPIRE observer's manual, 2010), the total error is 30%, 20%, 10%, 10%, and 15% of the flux at 100, 160, 250, 350, and 500 m, respectively. The SED for each pixel was fitted with a single modified blackbody, using a power law dust emissivity = 0 (0 /) , with spectral index = 2 and emissivity 0 = 0.192 m2 kg-1 at 0 = 350 m. These values reproduce the average emissivity of models of the Milky Way dust in the FIR-submm (Draine 2003). The fit was obtained with a standard 2 minimization technique. In the pipeline calibration, the flux density observed by the various instruments, i.e. weighted over each filter passband, is converted into a monochromatic flux density assuming F -1 . Before fitting a modified blackbody, a color correction should be applied to the data, to account for the real spectral slope of the source. Alternatively, the conversion implemented into the pipeline calibration can be removed from the data (in SPIRE parlance this is equivalent to dividing the pipeline flux densities by the K4 factor; SPIRE observer's manual, 2010); the passband weighted flux thus obtained should then be compared with the mean of the model flux density over the spectral response function for each of the bands. We adopted this second technique, using the appropriate response functions for the PACS and SPIRE bands (for SPIRE, we used the response functions for extended emission). However, color corrections are small for the adopted emissivity and the temperature range derived here (see Davies et al. 2011). In Fig. 2 we show typical SEDs and graybody fits for three positions of different dust temperature in NGC 4254. As shown by the figure, a single temperature modified blackbody with
1 R25 is the radius of the galaxy measured to a B surface brightness of 25 mag arcsec-2 , and is an indication of the size of the galaxy; R25 were obtained from NED; 0.7 R25 is equivalent to the solar radius in our Galaxy.

Fig. 2. Typical SEDs on three different positions (pixels) on NGC 4254. Blue dots are the measured (color-corrected) fluxes and the red (solid) + curves are the modified blackbody fits. The three SED correspond to minimum (21 K), mean (23.5 K), and maximum (26 K) temperature in the galaxy (see Fig. 3). The green (dashed) curves show the fit of the Draine & Li (2007) model to the data, for IRSFs of intensities 2, 4 and 8 times the Local ISRF (see their paper for details).

= 2 is sufficient to obtain reasonable fits of the SED over the wavelength range considered here (see also Davies et al. 2011). When data at shorter wavelength than PACS 100 m is available, one might want to consider a two-component model, to include emission from warmer dust that might significantly contribute at least to the 100 m flux. This was done, for example, by Bendo et al. (2010b), who used Herschel data, and by Smith et al. (2010) who used 70 m data from the Spitzer satellite. However, they found that the inclusion of a warmer temperature component, thought necessary to fit the 70 m data, improves the fit at > 100 m only slightly, and does not modify significantly the estimate of the temperature and mass surface density of cold dust.
3.2. Sources of uncer tainty in mass and temperature of dust

When only the errors on photometry are considered, the uncertainty in the determination of the temperature is about 2 K, and thus 20% on the dust mass surface density. In principle, fitting the dust SED with a single thermalequilibrium temperature component could result in larger uncertainties in the dust mass estimates: grains of a given size and material could be exposed to different intensities of the interstellar radiation field (ISRF) and thus attain different equilibrium temperatures which will contribute differently to the SED; conversely, for the same radiation field the SED could depend on the dust distribution, because it results from the emission of a mixture of grains of different size and composition, each with its own equilibrium temperature. We found neither of these to have a strong effects on our mass estimates. In fact, by fitting the SED pixel by pixel, we already take into account the gradients due to the diffuse ISRF, which is more prominent in the radial direction than in the vertical directions (i.e. along the line of sight, for non edge-on disks; Bianchi et al. 2000). However, the temperature radial gradients found here (see Sect. 3.3) would not produce very large uncertainties, even when the global SED is fitted with a single temperature model. For our targets, the differences between the sum of the dust mass in each pixel, and the dust mass obtained by fitting the sum of

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L. Magrini et al.: Dust and metal gradients in Virgo spirals. IX.

the flux densities in each pixel, is smaller than the fit error. The insensitivity of the global dust SED fitting on the shallow diffuse ISRF gradient is clearly shown in the analysis of the the FIR/submm SED of late type galaxies of Draine et al. (2007): though the more complex fitting procedure includes a dust grain model and a range of ISRF intensities (see also Draine & Li 2007), the global SED at 100 m is found to be fitted by a dust component that accounts for most of the dust mass (a part from a few percents), heated by an IRSF of constant intensity. We evaluated the effects of a complex dust mixture by fitting the model of Draine & Li (2007) to our pixel-by-pixel SED. Following Draine et al. (2007), we used a single value of the ISRF for emission at 100 m. An example can be seen in Fig. 2. The SED from the dust grain mixtures and our single temperature model fit equally well the data. The dust mass obtained by using the procedure of Draine et al. (2007) is higher by about 10%, that is, within the error we quoted. Thus, the dust mass derived from a simple averaged emissivity, and a single IRSF ­ or temperature ­, is not severely underestimated. Larger uncertainties can come also from the assumption for the emissivity. For example, the value of the emissivity derived by James et al. (2002) from SCUBA observations of galaxies is equivalent to 0 = 0.41 m2 kg-1 , a factor of two larger than the value we adopted. Adopting this emissivity would result in dust surface densities a factor of two smaller than what we found in this paper. Also, dust emissivity has been reported to increase by about a factor two in grains associated to denser environments (see, e.g., Bianchi et al. 2003). However, this might be the case for extreme environments and not representative of the bulk of the diffuse dust mass: in the Milky Way, recent results from the Planck satellite show no emissivity variation between dust associated with HI and CO emission, nor emissivity variations with the galactocentric radius (Planck Collaboration et al. 2011). In Sect. 4.1 we will discuss how the uncertainty on 0 might affect our discussion. The limited wavelength coverage does not allow us to investigate in details the effect of variation of the emissivity spectral index. In any case, the modified = 2 blackbody provides good fits for all the SEDs analised here, as well as for the global SEDs in a larger sample of HeViCS objects (Davies et al. 2011). Local variations of the dust emissivity index with temperature, as those reported by Paradis et al. (2010) cannot be easily verified in our dataset. Variation of from 1.7 to 2.2, as those measured at a reference temperature of 20 K, would result in an underestimate and overestimate of the dust mass of the same order as the quoted errors, respectively. Lower values, as those found for dust at higher temperatures, will not be able to provide good fits to our SEDs in the central part of the galaxies. Maps of the temperature and dust mass surface density for NGC 4501 have been presented in Smith et al. (2010). For the other galaxies, they will be presented in Vlahakis et al. (in prep.).
3.3. Radial profiles

28 26 24

T (K)

22 20 18 16 0.0 0.2 0.4 R/R25 0.6 0.8 1.0

Fig. 3. Radial variation of dust temperature in NGC 4254 (red dotdashed curve), NGC 4303 (green dashed line), NGC 4321 (blue dotted curve), and NGC 4501 (black solid curve).

The galaxies in our sample are disturbed by tidal interactions, thus we consider more reliable the determination of the geometric parameters of the galactic disks from kinematics rather than from photometry (see, for example, the discrepancy between parameters derived with the two methods for the case of NGC 4321 in Chung et al. 2009a). The task ROTCUR of the package NEMO (Teuben 1995) was used to fit a tilted ring model to the 21-cm moment-1 maps from the VIVA dataset. We

obtained values for the rotational velocity, the inclination and the position angle, as a function of the galactocentric radius. The radial variations of i and PA are shown in Fig. 4. The average values are indicated with solid lines. For NGC 4321 and NGC 4501, i and PA are quite constant with radius and thus we use the average parameters in the whole radial range. For NGC 4254, which is a one-armed spiral, the variations of PA and i are important due to its asymmetric shape. Since in our comparison between metallicity and dust-to-gas mass ratio gradients we are interested mostly in the inner regions where the metallicity data are available, for NGC 4254 we used i and PA averaged in the regions with galactocentric radius RG < R25 (dashed line in Fig. 4, top panels) where the variations are small. Pohlen et al. (2010) also found different ellipse parameters for the outer parts and for the inner parts of NGC 4254. For NGC 4303, for which VIVA maps are not available, we adopted the parameters by Koda & Sofue (2006). The final values are shown in Table 1:in Col.1 we show the galaxy name, in Cols. 2 and 3 the mean i and PA, in Col. 4 the optical diameter Dopt in arcmin, in Cols. 6-8 the slope of the metallicity gradient, the metallicity at the equivalent solar radius 0.7 R25 , and their reference. For NGC 4254 we report the value we adopt, i.e. the average within the optical radius, and in square brackets the average in the whole radial range. Between square brackets, for all galaxies, we report also inclinations and position angles from the literature, which are generally in good agreement with our values in the radial range considered. The atomic and molecular gas maps were convolved to the same resolution of the SPIRE 50