© ESO, 2014

1. Introduction

In the interstellar medium (ISM), dust holds a major role: a) it acts as a catalyst in the transformation of atomic hydrogen into molecular hydrogen from which stars form (Wolfire et al. 1995); b) it allows gas to cool and condense to form new stars by absorbing the ultraviolet (UV) emission of surrounding young stars (Draine 1978; Dwek 1986; Hollenbach & Tielens 1997); and c) it reemits the absorbed energy in the infrared domain (IR), where the thermal emission by dust grains dominates the spectral energy distribution (SED) of galaxies between ≈10 and 1000 μm. Dust is thus an important tracer of star formation activity. Formed by the aggregation of metals injected into the ISM by stars through stellar winds and supernovae explosions, its composition still remains uncertain. The most popular models assume that dust consists of a mixture of silicate and graphite grains (Mathis et al. 1977; Draine & Lee 1984; Kim et al. 1994), and are extended by adding the contribution of the polycyclic aromatic hydrocarbons (PAH), producing the broad spectral features seen in the mid-IR (MIR), such as in models by Siebenmorgen & Kruegel (1992), Li & Draine (2001), Weingartner & Draine (2001), and Draine & Li (2007).

Because of the important role of dust in the ISM and its tight link with the other components of galaxies, the study of dust emission is mandatory to have a better understanding of all of the processes at play. IRAS (Infrared Astronomical Satellite, Neugebauer et al. 1984), COBE (Cosmic Background Explorer, 1989), ISO (Infrared Space Observatory, Kessler et al. 1996), Spitzer (Werner et al. 2004), and AKARI (Murakami 2008) allowed us to study dust emission up to 240 μm. While these telescopes sampled well the dust properties from the MIR to around the peak of the dust SED, going to longer submillimeter (submm) wavelengths, well beyond the peak, is crucial for modeling the distribution of the dust size, temperature, and composition. In this way, the inventory of the bulk of the dust mass in galaxies, manifested in the submm, is also not missed (Devereux & Young 1990; Gordon et al. 2010). Ground-based facilities, such as SCUBA (Submillimeter Common-User Bolometer Array, Holland et al. 1999), provide us with submm data, but observations of large samples of normal galaxies are still prohibitive due to the long integration times needed for these instruments, which suffer from limited sensitivity.. Furthermore, a large part of the far-IR (FIR) and submm domains are not accessible from the ground. The Herschel Space Observatory (Pilbratt et al. 2010) opened a new window on the FIR/submm spectral domain (55 to 672 μm), allowing us to probe the cold dust component in a large number of nearby objects.

We now have a global view of the emission from all of thermal dust components, covering a broad range of temperatures and the different heating mechanisms for these components. Before Herschel, it was already evident that a significant part of the IR SEDs of galaxies potentially includes cold (17 to 20 K) diffuse cirrus components heated by the diffuse interstellar radiation field from the total stellar population, and not just the light from star forming regions (e.g., Helou 1986; Xu & Helou 1996; Li & Draine 2002; Boselli et al. 2004; Komugi et al. 2011; Totani et al. 2011). However, the emission for these colder components often appears intermixed with emission from warmer dust heated by star forming regions at λ lower than ≈240 μm, and in many cases, the emission is poorly constrained. Multiple authors using Herschel, including Bendo et al. (2010, 2012b), Boquien et al. (2011), Groves et al. (2012), and Smith et al. (2012b), have used comparisons of FIR colors to NIR emission from the evolved stellar population to demonstrate that the cirrus component is often the primary source of >250 μm emission and also contributes at shorter wavelengths.

Understanding the heating processes of the dust is of paramount importance to provide physical models than can reproduce the FIR/submm SED of galaxies. Multiwavelength radiative transfer modeling of galaxies is a powerful tool to analyze the properties of dust in galaxies in a self-consistent way (e.g., Xilouris et al. 1999; Popescu et al. 2000, 2011; de Looze et al. 2012b; Alton et al. 2004; Bianchi 2008; Baes et al. 2010; MacLachlan et al. 2011; de Looze et al. 2012a). However, assumptions regarding the geometry of the dust need to be made, and these codes require large computational resources, especially for a large sample of galaxies. Therefore, models, as well as empirical templates, are widely used to extract information about galaxies from their IR SED (Chary & Elbaz 2001; Dale & Helou 2002; Boselli et al. 2003a; Draine & Li 2007, hereafter CE01, DH02, B03, and DL07). The pre-Herschel empirical libraries of templates (CE01, DH02) were calibrated on FIR observations and detections of galaxies up to ≈200 μm, and were constructed from local normal and IR luminous star forming galaxies. Recent studies, making use of the new Herschel data, provided new IR templates for low- and high-redshift objects (Elbaz et al. 2011; Smith et al. 2012a; Magdis et al. 2012). However, there is a lack of templates representative of the broad variety of nearby normal galaxies, reference of the z = 0 Universe.

The Herschel Reference Survey (HRS, Boselli et al. 2010b) is composed of 322 nearby galaxies spanning the entire range of morphological types and environment. The aim of this volume-limited, K-band selected sample is to investigate the dust properties of galaxies for which a wealth of ancillary data are available, both photometric (from UV to radio, Bendo et al. 2012a; Boselli et al. 2010b, 2011; Ciesla et al. 2012; Cortese et al. 2012b, 2014) as well as spectroscopic (Boselli et al. 2013, 2014; Hughes et al. 2013). With this set of data, the HRS is one of the best samples to study the dust properties of nearby galaxies versus parameters such as the stellar mass, the metallicity, the star formation rate (SFR), etc., giving us a better understanding of its role in the ISM and the interplay with the stellar radiation field.

In this work, we derive the physical properties of the dust by fitting the integrated IR SED of the HRS galaxies with the models of DL07. Although these models are physical, they have been mainly tested on FIR data (Draine et al. 2007), and recently, using Herschel data (Dale et al. 2012; Aniano et al. 2012; Draine et al. 2014). We thus discuss the ability of these models to reproduce the submm observations of our galaxies. For a subsample of gas-rich galaxies, we then investigate the relations between the derived output parameters and the integrated galaxy properties (stellar mass, SFR, birthrate parameter, metallicity, FUV attenuation, Hα surface brightness, and H-band effective surface brightness). Based on this analysis, we derive a set of SED templates, binned according to those parameters that better characterize the shapes of the SED, and compare them with libraries available in the literature.

This paper is organized as follows: in Sect. 2, we describe the HRS and define a gas-rich subsample on which we will focus our analysis. The ancillary data associated with this subsample are presented in Sect. 3. We present the procedure used to perform the fitting, analyze our ability to constrain the models with the data and present the results in Sect. 4. For the gas-rich galaxy subsample, we outline the most interesting relations between the output from the fitting and galaxy parameters in Sect. 5. The derivation and discussion of the new IR library is presented in Sect. 6. In Appendix A, we present the MIR photometry of all of the HRS galaxies at 8, 12, and 22 μm, which are important constraints for the SED modeling. In Appendix B, we explain the method derived to remove the stellar contribution from our data and provide new coefficients useful for future works. For completeness, in Appendix C, we give the output parameters from the SED fitting for the galaxies that are not discussed in the main part of this work (early-type galaxies and Hi-deficient galaxies). Finally, all of the relations between the output of DL07 models and the properties of the gas-rich sample are presented and discussed in Appendix D.

2. Sample

The HRS galaxies are selected according to three criteria fully described in Boselli et al. (2010b). The HRS is a volume limited sample composed of galaxies lying at a distance between 15 and 25 Mpc. The galaxies are then selected according to their K-band magnitude, the luminosity of which is a proxy for the total stellar mass (Gavazzi et al. 1996). Based on optical extinction studies and FIR observations at wavelengths shorter than 200 μm, we expect late-type galaxies to have a larger content of dust than early-types (Sauvage & Thuan 1994). Thus, two different K_mag limits have been adopted: K_mag ≤ 12 for late-types and K_mag ≤ 8.7 for early-types (in Vega magnitudes). Finally, to limit the contamination from Galactic cirrus, galaxies are selected at high Galactic latitude (b> + 55deg) and in low Galactic extinction regions (A_B< 0.2, Schlegel et al. 1998). The final sample contains 322¹ galaxies, among which are 62 early-types and 260 late-types. The HRS covers all morphological types and contains field galaxies as well as objects in high-density regions such as the Virgo cluster. We use the morphological classification presented in Cortese et al. (2012a).

Even if we present the NIR photometry and perform the SED fitting of all of the HRS galaxies, the paper focuses on the study of a subsample of 146 gas-rich galaxies. From the whole HRS sample, we remove early-type galaxies (E-S0-S0/Sa) from the analysis as the dust properties and the dust heating sources of elliptical and lenticular galaxies are different from late-type galaxies (e.g., Boselli et al. 2010a; Smith et al. 2012b). Indeed, the relative contribution of X-ray heating, stochastic heating, heating from fast electrons in the hot gas, and the size-distribution of dust grains in these environments with low-density ISM might differ from that of late-types and thus need further investigation (Wolfire et al. 1995). Furthermore, only 32% of the elliptical galaxies and 60% of the lenticulars are detected at 250 μm (Ciesla et al. 2012), yielding an incomplete photometric coverage of the IR-submm domain. Finally, some of the physical properties used in this work (birthrate parameter, Hα surface brightness, and metallicity) are not available for all of the early-type galaxies. Furthermore, a number of late-type galaxies of the HRS lie in the very dense environment of the Virgo cluster. These galaxies have their gas content stripped by the environment (Boselli & Gavazzi 2006). Herschel observations have recently shown that the dust component of Hi-deficient² galaxies is also affected by the cluster environment (Cortese et al. 2010, 2012b). In the following, we define as “gas-rich” galaxies those with Hi−def ≤ 0.4, and “Hi-deficient” those with Hi−def > 0.4, to be consistent with Boselli et al. (2012). We decide to not consider Hi-deficient galaxies in our analysis to remove the effects of the environment as a free parameter that could bias the interpretation of the results. The study of the effect of the environment on the dust properties of galaxies will be presented in a future work.

The main part of this paper is focused on the data, the SED fitting, and the analysis of the gas-rich late-type sample. The NIR photometry of all of the HRS galaxies, and the output parameters from the SED fitting obtained for the early-type galaxies and the Hi-deficient galaxies are presented in Appendix A and Appendix C, respectively.

3. Data

In order to compute the IR SEDs of the HRS galaxies, we use data from 8 to 500 μm performing the photometry on Spitzer/IRAC and WISE images and using measurements available in the literature from Spitzer/MIPS, Herschel/PACS, Herschel/SPIRE, and IRAS. These data are publicly available through the Hedam database³.

3.1. Mid-infrared: Spitzer/IRAC and WISE

For the purpose of this work, we perform the photometry of 56 out of the 146 galaxies of our subsample for which observations at 8 μm from Spitzer/IRAC were available in the Spitzer archive. The procedure is presented in Appendix A and the flux densities and associated errors are given in Table A.2. Our procedure to estimate the errors associated with the 8 μm data, based on Boselli et al. (2003a), results in a mean error of 15% (see Table 1). We also perform the WISE photometry of the gas-rich galaxies at 12 and 22 μm. As for the IRAC 8 um data, Appendix A describes the procedure we used, and gives the resulting flux densities and their associated errors. The mean errors associated with the 12 μm and the 22 μm flux densities are 6% and 13%, respectively. Comparisons between our measurements and results from the literature, as presented in Appendix A, are in good agreement. The IRAS 12 μm flux densities are available only for 15% of our galaxies, whereas all of our subsample galaxies have a 12 μm flux density from WISE. To have a homogeneous set of data, we use the WISE 12 μm flux densities.

3.2. Far-infrared: Spitzer/MIPS, IRAS, and Herschel/PACS

The reduction and photometry of MIPS data are fully described in Bendo et al. (2012a). Flux densities of 68 gas-rich galaxies are available at 24 μm, and 47 are available at 70 μm. For most of the galaxies, aperture photometry was performed using an elliptical region with major and minor axes of 1.5 times the axis sizes of the D₂₅ isophotes given by de Vaucouleurs et al. (1991). The same aperture was used in the two bands. In the case of HRS 20-NGC 3395 and its companion NGC 3396, the flux densities provided correspond to one of the pair as it is hard to disentangle the emission from the two galaxies within a pair. Thus, we do not use these measurements. The error calculation takes into account the calibration error, 4 and 10% at 24 and 70 μm (Engelbracht et al. 2007; Gordon et al. 2007), respectively, the uncertainty based on the error map, and the background noise. The three are added in quadrature. We should note that a transcription error was made in Bendo et al. (2012b) for the flux density of HRS 142. Its flux density at 70 μm is 8200 mJy instead of 1237 mJy. Despite the incompleteness of the MIPS 24 μm data, we choose to use them, when available, instead of the WISE 22 μm. This choice is due to the poor quality of some WISE 22 μm images resulting in a mean error of 13% in this band when the mean error of MIPS 24 μm is 4% only. The IRAS 25 μm data are also available for only a small part of our subsample (15%), we thus decided to not use these measurements to keep a homogeneous set of data from one galaxy to another.

Because of the incompleteness at 70 μm, we also use, when available, the 60 μm measurements from IRAS presented in Boselli et al. (2010b). The IRAS 60 μm flux densities of 128 galaxies of the subsample, with a typical uncertainty of 15%, are provided by multiple references in the literature and collected on NED: Sanders et al. (2003); Moshir & et al. (1990); Thuan & Sauvage (1992); Soifer et al. (1989); Young et al. (1996).

All of the gas-rich galaxies are detected by PACS at 100 and 160 μm, respectively (Cortese et al. 2014). They performed aperture photometry following the method used by Ciesla et al. (2012) to build the HRS SPIRE catalog (see Sect. 3.3). The apertures used to extract the fluxes are identical to those used for the SPIRE photometry. However, a refinement of the photometric aperture has been applied to some of the objects for various reasons (some galaxies were unresolved in SPIRE bands and resolved in PACS bands, some PACS maps were too small to encompass the SPIRE aperture, or the FIR emission of the galaxy was much less extended than the SPIRE aperture). Errors were estimated following the method described in Roussel (2013). The mean errors are 16% and 12% at 100 and 160 μm, respectively. The data reduction and the integrated photometry are described in Cortese et al. (2014).

3.3. Submillimetre: Herschel/SPIRE

In the SPIRE bands, all of the galaxies of the subsample are detected at 250, 350, and 500 μm, respectively. The SPIRE photometry is fully described in Ciesla et al. (2012). In summary, aperture photometry was performed in elliptical regions for extended galaxies. All apertures have been chosen to encompass the emission and to minimize the contamination of background sources. The stochastic error takes into account the instrumental uncertainty, the confusion uncertainty (due to the presence of faint background sources), and the background uncertainty (due to large scale structure, such as cirrus), with all three added in quadrature. Flux densities of point-like sources have been measured using PSF fitting on timeline data (Bendo et al. 2013). We take the last updates into account by applying the calibration corrections (1.0253, 1.0250, and 1.0125 at 250, 350, and 500 μm, respectively) and the new beam areas⁴ of 450, 795 and 1665 arcsec² at 250, 350, and 500 μm, respectively. We do not take the variations of the beam sizes into account, depending on the shape of the SED, as they are generally within the SPIRE errors. The result of these updates lowers the flux densities presented in Ciesla et al. (2012) by ≈5%. The mean errors are 6%, 8% and 11% at 250, 350, and 500 μm, respectively.

The photometric completeness of the gas-rich sample of galaxies is presented in Table 1. Upper limits are not taken into account in our fitting procedure and will thus correspond to an absence of data in Table 1.

4. SED fitting with the Draine & Li (2007) models

4.1. Draine & Li (2007) models

DL07 modeled the dust with a mixture of astronomical amorphous silicate and carbonaceous grains with the size distribution observed in the Milky Way (Weingartner & Draine 2001). Models of the LMC and SMC grain size distribution are also available.

The bulk of the dust present in the diffuse ISM is heated by a large number of stars responsible for the diffuse radiation. However, another part of the dust is located in regions close to very luminous O and B stars, in photodissociation regions (PDR). In PDRs, the light coming from the young stars is heating the dust and is much more intense than the emission coming from the old stars responsible for the diffuse radiation. In DL07 models, the relative dust mass fraction heated by each source, the diffuse component and the PDRs, is given by the γ parameter. Thus, the fraction (1 − γ) of the total dust mass is heated by U = U_min, where U is the intensity of the interstellar radiation field (ISRF) and U_min is the intensity of the diffuse ISRF, both normalized to the intensity of the Milky Way ISRF.

Recently, Aniano et al. (2012) linked the temperature of the cold dust component to the U_min parameter by approximating the DL07 SED with a blackbody multiplied by a power-law opacity and obtained ${\mathit{T}}_{\mathrm{d}}\mathrm{\approx }\mathrm{20}{\mathit{U}}_{\min }^{\mathrm{0.15}}$ K. The fraction γ of the total dust mass is exposed to a range of stellar intensities following a power-law distribution from U_min to U_max with dM/ dU ∝ U^-2. From these three parameters, we can compute ⟨ U ⟩, the mean intensity of the ISRF, from Eq. (17) of Draine et al. (2007). A last parameter aims at characterizing the emission due to the PAH. Their abundance is quantified with the parameter q_PAH, which corresponds to the fraction of the total grain mass contributed by PAH containing less than 10³ C atoms. Each model depends on the set of parameters {dustcomposition, q_PAH, γ, U_min, and U_max}. Finally, the dust mass is also a free parameter determined from the normalization of the model to the observations. Following the recommendations of Draine et al. (2007), we use only the Milky Way dust type and fix U_max = 10⁶. Thus, the free parameters of the fit are q_PAH, γ, and U_min. The normalization of the model to the data provides us with the dust mass M_dust, and the integration of the model between 8 and 1000 μm gives us the infrared luminosity L_IR.

4.2. Fitting procedure

As DL07 model the emission of the dust from 1 μm to 1 cm, we need to remove the stellar emission that contributes to the MIR data to have only the emission from the dust. In Appendix B, we describe the method we use to remove the stellar contribution and provide morphological type dependent coefficients normalized to several NIR bands, and determined using the CIGALE⁵ code (Code Investigating GALaxy Emission, Noll et al. 2009). The code computes modeled galaxy SEDs by using stellar population models from Maraston (2005), which are convolved with a given star formation history (SFH). We use an exponentially decreasing SFH, which we present in Appendix B. The coefficients (S_ν,stellar/S_ν) applied to the MIR photometry of the sample are 0.093, 0.075, 0.016, and 0.017 at 8, 12, 22, and 24 μm, respectively (see Appendix B).

The DL07 models are integrated into the filters of the corresponding photometric bands, and these modeled flux densities are compared to the observations. The ranges allowed for each parameter are presented in Table 2. For galaxies that do not have any MIPS 24 μm observations, the fit is performed using the WISE 22 μm flux densities as explained in Sect. 3.2.

We use a χ² minimization method to fit our data with the models of DL07. For each galaxy, we compute the χ² corresponding to every model using the equation: ${\mathit{\chi }}^{\mathrm{2}}\mathrm{\left(}{\mathit{a}}_{\mathrm{1}}\mathit{,}\mathit{...}\mathit{,}{\mathit{a}}_{\mathit{i}}\mathit{,}\mathit{...}\mathit{,}{\mathit{a}}_{\mathit{N}}\mathrm{\right)}\mathrm{=}\sum _{\mathit{i}\hspace{0.17em}\mathrm{=}\hspace{0.17em}\mathrm{1}}^{\mathit{M}}{\left[\frac{{\mathit{y}}_{\mathit{i}}\mathrm{-}\mathit{\alpha y}\mathrm{\left(}{\mathit{x}}_{\mathit{i}}\mathit{,}{\mathit{a}}_{\mathrm{1}}\mathit{,}\mathit{...}\mathit{,}{\mathit{a}}_{\mathit{i}}\mathit{,}\mathit{...}\mathit{,}{\mathit{a}}_{\mathit{N}}\mathrm{\right)}}{{\mathit{\sigma }}_{\mathit{i}}}\right]}^{\mathrm{2}}\mathit{,}$(1)and the reduced χ² as: ${\mathit{\chi }}_{\mathrm{red}}^{\mathrm{2}}\mathrm{=}\frac{{\mathit{\chi }}^{\mathrm{2}}}{\mathit{M}\mathrm{-}\mathit{N}}$(2)where y is the model, a_i are the parameters values of this model, x_i correspond to the observations, and σ_i the errors attributed to these observations. The number of parameters is N and M the number of observed data. We obtain the normalization factor through the following equation: $\mathit{\alpha }\mathrm{=}\frac{{\sum }_{\mathit{i}\hspace{0.17em}\mathrm{=}\hspace{0.17em}\mathrm{1}}^{\mathit{N}}{\mathit{y}}_{\mathit{i}}\mathrm{\times }\mathit{y}\mathrm{\left(}{\mathit{x}}_{\mathit{i}}\mathit{,}{\mathit{a}}_{\mathrm{1}}\mathit{,}\mathit{...}\mathit{,}{\mathit{a}}_{\mathit{i}}\mathit{,}\mathit{...}\mathit{,}{\mathit{a}}_{\mathit{M}}\mathrm{\right)}\mathit{/}{\mathit{\sigma }}_{\mathit{i}}^{\mathrm{2}}}{{\sum }_{\mathit{i}\hspace{0.17em}\mathrm{=}\hspace{0.17em}\mathrm{1}}^{\mathit{N}}\mathit{y}\mathrm{(}{\mathit{x}}_{\mathit{i}}\mathit{,}{\mathit{a}}_{\mathrm{1}}\mathit{,}\mathit{...}\mathit{,}{\mathit{a}}_{\mathit{i}}\mathit{,}\mathit{...}\mathit{,}{\mathit{a}}_{\mathit{M}}{\mathrm{)}}^{\mathrm{2}}\mathit{/}{\mathit{\sigma }}_{\mathit{i}}^{\mathrm{2}}}\mathrm{·}$(3)As the reduced χ² (${\mathit{\chi }}_{\mathrm{red}}^{\mathrm{2}}$) is calculated for each value of a parameter, we can build the probability distribution function (PDF) of this parameter. For each value of a discrete parameter, we select the corresponding minimum ${\mathit{\chi }}_{\mathrm{red}}^{\mathrm{2}}$. Thus, we have the distribution of the minimum ${\mathit{\chi }}_{\mathrm{red}}^{\mathrm{2}}$ associated with the set of values of the parameter. From this distribution, we obtain the estimated value of the parameter, as the mean value of this distribution, and the associated error as its standard deviation, proceeding as described in Noll et al. (2009). For parameters with a large range of values, we compute bins and take the minimum ${\mathit{\chi }}_{\mathrm{red}}^{\mathrm{2}}$ corresponding to each bin. Then we build the distribution. In the following discussions, we will refer to the “best” parameter as the parameter obtained directly from the model providing the minimum ${\mathit{\chi }}_{\mathrm{red}}^{\mathrm{2}}$, and to the “estimated” parameter as the parameter derived from the distribution of ${\mathit{\chi }}_{\mathrm{red}}^{\mathrm{2}}$.

This SED fitting procedure is applied to all of the galaxies of the HRS. However, from now on, this work only focuses on the gas-rich galaxy subsample, and the results for the other galaxies (early-type, and late-type deficient galaxies) are presented in Appendix C.

4.3. Mock catalogs

The χ² fitting described in the previous section provides us with a best-fit model for each galaxy. However, we need to know if the output parameters obtained from these models are reliable, i.e., if the data we have allow us to constrain these parameters. To do so, we create mock catalogs following the procedure outlined in Giovannoli et al. (2011). We first run our χ² procedure on our sample to obtain the best-fitting model and the corresponding parameters for each galaxy. The resulting best SEDs are integrated in the filters adding an error randomly distributed according to a Gaussian curve. The σ of the Gaussian curve is chosen to be the median value of the error for each band. We now have a mock catalog in which the exact values of the parameters are known. As a final step, we run our fitting procedure on this mock catalog and compare the input “best” values of the parameters to the output “estimated” values. This test allows us to evaluate the ability to constrain a parameter with the photometric coverage available for our galaxies.

We note that some galaxies of our sample are lacking 8 μm, 22−24 or 60−70 μm measurements. To estimate the impact of the lack of data on the estimation of the parameters, we build several mock catalogs using different combinations of bands to understand the importance of every photometric band. Indeed, all of the galaxies in our sample were not observed in every band. To understand the effect of the inhomogeneity of the photometric coverage of our sample and to evaluate the impact of submm data on constraining the models, we also build a mock catalog omitting SPIRE data. We present the results from the mock catalogs for U_min, γ, q_PAH, log L_IR, and log M_dust in Fig. 1 and in Fig. 2. For each parameter, we show the case where the photometric coverage is complete (Fig. 1), where there is no 8 μm flux density, in the absence of 22−24 μm data, the case where there are no 60−70 μm data and, finally, in the absence of SPIRE data (Fig. 2). For each panel of Figs. 1 and 2, we provide the best linear fit, the Spearman correlation coefficient and the median value and standard deviation of the estimated to true value ratio in Table 3. We separate galaxies having a 24 μm measurement from Spitzer/MIPS (blue filled points) from galaxies having a 22 μm measurement from WISE (red empty points). This separation allows us to see the impact of the precision of the photometry on the determination of the parameters, especially for γ, as we will discuss.

A complete photometric coverage from 12 to 500 μm is sufficient to constrain the U_min parameter, with a mean ratio between the estimated value to the true one of 1.07 ± 0.20 (Table 3). The absence of 8 μm measurement does not affect the estimation of U_min. The lack of data at 22−24 μm yields an underestimation of the parameter U_min of ≈14%, whereas the lack of 60−70 μm yields an overestimation of 18%. The worst case is when no SPIRE data is available with an overestimation of 25%, showing the importance of submm data to properly constrain U_min. Indeed, as the U_min parameter directly probes the position of the IR peak, constraints from both parts of the peak are needed for a good estimate.

Considering the γ parameter, the median ratio between the estimated and true values of the parameters is 1.18. However, this median drops to 1.01 when values of γ are larger than 0.5%. With our photometric coverage, we tend to overestimate the low values of γ. The importance of the 22 and 24 μm measurements and the associated errors is clear. When all bands are available, the precision of the MIPS 24 photometry provides good constraints on the estimate of γ, especially for values above a few percent. With a mean error of 13% on the WISE 22 photometry, there is a good correlation for values of γ above a few percent, but the errors on the estimated parameters are very large, indicating a large PDF linked to the estimation of γ. The impact of this 22−24 μm range is confirmed in the panel where these two bands are removed, the median value of the estimated to true values ratio is 3.77 ± 6.43, and the relation is flat. When the 22−24 μm bands are removed, the estimated gamma derived from the model is rather constant in whatever galaxy we model. The absence of 60−70 μm or SPIRE data does not have a large impact on the estimation of γ, but yields to a slightly more dispersed relation.

The 8 μm band directly probes the PAH emission: in the absence of the IRAC 8 band, the Spearman correlation coefficient between the estimated q_PAH and the true q_PAH decreases from 0.92 to 0.88 and the standard deviation of the estimated to true values ratio increases from 0.11 to 0.20. Interestingly, the absence of 22−24 μm data provides a median underestimation of the parameter of 23%, showing the importance of constraining the continuum to estimate the q_PAH parameter with our photometric coverage. From Fig. 1, we conclude that the presence of the 12−22−24 μm data is sufficient to have a relatively good constraint on the fraction of PAH, q_PAH, provided by the DL07 models. For our sample of galaxies, the 8 μm measurement is thus not mandatory to study q_PAH.

The L_IR and the M_dust are well constrained in all configurations. Even without the SPIRE bands, the M_dust is well constrained despite a slightly larger scatter. This constraint on M_dust comes from the fact that β is fixed in DL07 (to ≈2.06) and, as this parameter is provided by the normalization of the models to the observed data, observations at 160 μm seem to be sufficient to constrain M_dust.

All the parameters are constrained with the combination of IR bands available for this study, except γ for which MIPS 24 μm measurement is mandatory. Therefore, the discussion of γ and ⟨ U ⟩ (as ⟨ U ⟩ depends on γ) will be restricted to the galaxies having a 24 μm flux density. However, we note that this analysis from mocks allows us only to characterize our ability to constrain the parameters of DL07 given our photometric coverage.

4.4. Results of the fits

Table 4 presents the results of the fit for the 146 galaxies: the output parameters from DL07 models, L_IR and M_dust.

4.4.1. Assessment of the quality of the fit

To have a global look at the quality of the fits, we show in Fig. 3 the ratio between the observed and the modeled flux densities for each photometric band versus the stellar mass (the calculation of M_∗ is described in Sect. 5), as the HRS was selected in K-band, which is a proxy for stellar mass. For each galaxy, the values predicted by the models are obtained by integrating the best SEDs resulting from the fits into the filters of every band. Points are color coded according to the ${\mathit{\chi }}_{\mathrm{red}}^{\mathrm{2}}$ value associated with the fit.

The analysis of Fig. 3 shows that:

• Fits of galaxies with log (M_∗/M_⊙) < 10 have a better ${\mathit{\chi }}_{\mathrm{red}}^{\mathrm{2}}$ than higher mass systems for which ${\mathit{\chi }}_{\mathrm{red}}^{\mathrm{2}}$ can reach up to 20.

• At 8 μm, the models seem to systematically overpredict the observed flux density by ≈7% from low- to high-mass systems.

• At 12 μm, there is good agreement between both observed and modeled flux densities up to log (M_∗/M_⊙) ≈ 10. For higher mass galaxies, the models underpredict the observed flux densities.

• There is a systematic overestimation of the 22−24 μm by the models of 10% at 22 μm and 5% at 24 μm. For the MIPS 24 μm, this overestimation increases with the stellar mass and can reach up to 20%. Despite this trend, with a mean ratio of 0.95 and a small dispersion 0.05, there is a good agreement between the models and the observations at this wavelength.

• The 60 μm ratio is very dispersed, and the mean value of 0.96 is not representative as there is a clear trend with the stellar mass. Models underpredict the 60 μm observations of low-mass systems and overpredict them for high-mass objects. However, the mean photometric error of 15% is one of the largest of all bands and is not a strong constraint for the fit. The 70 μm observed to modeled flux density ratios follow the same trend with the stellar mass than the 60 μm, but with a smaller dispersion (σ = 0.18).

• At 100 and 160 μm, despite a large dispersion, there is a relatively good agreement between observations and models with a slight overprediction at 100 μm and underprediction at 160 μm of ≈3%.

• The 250 and 350 μm SPIRE bands are in average well fitted by the models, even if the 250 μm is slightly overestimated for the whole sample. A small trend is seen at 350 μm, the flux densities from the models tend to be lower than the observations for low-mass galaxies.

• At 500 μm, this trend becomes stronger. The 500 μm observations seem to be underpredicted by the models, especially for low-mass systems. Indeed, for galaxies with log (M_∗/M_⊙) ≈ 10, there is a clear underprediction of the 500 μm data, up to ≈40%, that increases when the stellar mass decreases.

A submm excess, such as the one observed at 500 μm, was already noticed by previous works in low-metallicity systems (e.g., Reach et al. 1995; Galliano et al. 2003, 2005, 2011; Bot et al. 2010; Gordon et al. 2010; Boselli et al. 2010b; Galametz et al. 2011; Boselli et al. 2012). Different hypotheses have been proposed to explain this excess. A very cold dust component was proposed by Galliano et al. (2003, 2005), showing that it would need to lie in a small number of dense parsec scale clumps, but Galliano et al. (2011) showed that this hypothesis was not verified in the LMC, where they had the spatial resolution to test it. Meny et al. (2007) proposed a solid-state-based, temperature-dependent emissivity increases at long wavelength, in amorphous materials. Finally, Draine & Hensley (2012) argued that this excess could be due to ferromagnetic free-flying small grains or ferromagnetic inclusions in normal grains. Changing the FIR β slope can make the excess diminish but it is not sufficient (Galliano et al. 2011). Boselli et al. (2012) noticed that a modified blackbody with an emissivity index of β = 1.5 better represents the SPIRE data of the HRS galaxies than the DL07 models, which submm slope can be approximated by β ≈ 2. However, they outlined that β = 2 is possible for metal-rich high-mass galaxies, confirming what we observe in Fig. 3. Rémy-Ruyer et al. (2013) showed with a sample of galaxies with metallicities ranging from 0.03 to 1 Z_⊙ that β obtained from modified blackbody fit shows a large spread from 0.5 to 2.5.

These disagreements between the observations and the models are difficult to interpret as they can have different origins. On the one hand, the way that errors in the photometry are computed determine the relative weights of the different bands, and thus play an important role in constraining the models, the case of the 22 and 24 μm being one illustration. On the other hand, the trend between the stellar mass and the ${\mathit{\chi }}_{\mathrm{red}}^{\mathrm{2}}$ also suggests that the models do not reproduce the observations of high-mass galaxies very well, and the 500 μm observations of low-mass systems are not reproduced by the DL07 models.

4.4.2. Statistics of the output parameters

The statistics of the fits and of the derived parameters are presented in Table 5. The median ${\mathit{\chi }}_{\mathrm{red}}^{\mathrm{2}}$ is 2.25. The median estimated value of U_min is 1.96 ± 0.47. If we consider the relation obtained by Aniano et al. (2012), this median U_min corresponds to a median temperature of the dust of 22 K. We find a median estimated q_PAH of 4.16 ± 0.42%. We obtain a median γ of 0.75 ± 0.5% when considering only the 24 μm sample. Finally, this late-type nondeficient sample is characterized by a median log (L_IR/L_⊙) of 9.47 ± 0.03 and log (M_dust/M_⊙) of 7.02 ± 0.08. We compare the dust masses we derive with those obtained for the same galaxies by Cortese et al. (2012b), using only SPIRE bands, and find good agreement. The median ratio between the M_dust of Cortese et al. (2012b) and ours is 1.02, with a standard deviation of 0.02.

The SEDs obtained from the minimum ${\mathit{\chi }}_{\mathrm{red}}^{\mathrm{2}}$ fit for each galaxy are shown in Figs. 4 and 5. They are normalized to the observed 2MASS K-band flux densities as the galaxies of our sample were selected in this band (see Boselli et al. 2010b,for a description of the K band flux densities). In each panel, we show the best-fitted SEDs, color-coded according to the estimated values of the three output parameters from the models (U_min, q_PAH and γ), plus the L_IR and the M_dust directly derived from the fits.

We notice a color gradient with U_min, indicating a relation with the shape of the SED. By definition, U_min controls the minimum and dominant equilibrium dust temperature, therefore controlling the wavelength peak of the SED, as we can see on the top panel of Fig. 4. The middle panel of Fig. 4 shows that q_PAH parameter impacts the shape of the SED handling the intensity of the PAH bands. However, our sample is dominated by galaxies with q_PAH> 4%. This concerns 91 out of 146 galaxies, implying that there is a need for models with a larger range of PAH. Furthermore, the most massive galaxies, with log (M_∗/M_⊙) > 10, have a PAH fraction >4% and larger χ² values. This suggests that the lesser quality of the fit of the most massive galaxies is due to the small range of q_PAH values available. An increase in γ translates to a bump in the 25−60 μm range, as shown in the bottom panel of Fig. 4. The lack of observational data in this range can explain the difficulty in constraining γ, already outlined in Sect. 4.3.

The fitting procedure also provides us with the L_IR and the M_dust (Fig. 5). A trend between the L_IR and the shape of the SED is visible. Late-type galaxies are more gas-rich, and thus have a higher dust content, therefore, they form more stars. The tight link between the SFR and the L_IR yields to the trend observed in the top panel of Fig. 5. No particular relation is found between M_dust and S_ν/S_K.

4.4.3. Comparison with the literature

This sample and the SINGS/KINGFISH (Kennicutt et al. 2003, 2011) sample have four galaxies in common: M 99, M 100, NGC 4536, and NGC 4725. We compare, in Table 6, the results from the fits from our procedure with those found by Draine et al. (2007) and Dale et al. (2012) fitting DL07 models. For M 99, M 100, and NGC 4725, Draine et al. (2007) did not have any submm constraint on the SED, except for NGC 4536 for which they had a SCUBA 850 μm flux density. Dale et al. (2012) benefited from a larger set of models yielding to a larger parameter space to be explored with 0.01 <U_min< 30, 3 < log U_max< 8 and 0% <q_PAH< 12%. Despite the differences with the photometric coverage for SINGS and with the parameter ranges for KINGFISH, we find results in agreement.

5. Comparison with physical parameters

We study here the relations between the output parameters of the models and various physical variables available for our sample. In a phenomenological model independent approach, the relations between these physical properties and the FIR colors of the gas-rich late-type galaxies have been analyzed in Boselli et al. (2012) where a complete description of these variables can be found. Here we provide a very brief description. The number of galaxies of our sample for which ancillary data are available are given in Table 7.

Stellar masses (M_∗) are estimated from H-band data, and from mass–luminosity relations, as determined by the chemo-spectrophotometric galaxy evolution models of Boissier & Prantzos (2000), using the relation given in Boselli et al. (2009). The effective surface brightness in H-band, μ_e(H), provides a measurement of the intensity of the ISRF produced by the old stellar population. The Hα surface brightness is a tracer of the intensity of the ionizing UV emission and provides us with information on the present star formation activity (Boselli et al. 2009). The SFRs are calculated using the standard calibration of Kennicutt (1998) to convert Hα and FUV luminosities corrected from dust attenuation using the Balmer decrement (Boselli et al. 2009) and the corrections of Cortese et al. (2008), respectively. The final SFR corresponds to the mean value of the SFR determined from the Hα data and the FUV data (Boselli et al. 2009).

The birthrate parameter b (Scalo 1986; Kennicutt 1998), defined as the ratio between the present star formation activity and the star formation activity averaged on the galaxy entire life, is defined by Boselli et al. (2001): $\mathit{b}\mathrm{=}\frac{\mathit{SFR}}{\mathrm{⟨}\mathit{SFR}\mathrm{⟩}}\mathrm{=}\frac{\mathit{SFR}{\mathit{t}}_{\mathrm{0}}\mathrm{(}\mathrm{1}\mathrm{-}\mathit{R}\mathrm{)}}{{\mathit{M}}_{\mathrm{\ast }}}\mathit{,}$(4)with t₀ the age of the galaxy, M_∗ its stellar mass, and R (assumed to be 0.3) the fraction of re-injected gas into the ISM due to stellar winds. The SFR being linked to the UV or Hα fluxes and M_∗ to the NIR fluxes, b is thus tightly linked to the hardness of the UV radiation field. Moreover, the specific star formation rate (sSFR, Brinchmann et al. 2004) is widely used and can be linked to the birthrate parameter as: $\mathit{sSFR}\mathrm{=}\frac{\mathit{SFR}}{{\mathit{M}}_{\mathrm{\ast }}}\mathrm{=}\frac{\mathit{b}}{{\mathit{t}}_{\mathrm{0}}\mathrm{(}\mathrm{1}\mathrm{-}\mathit{R}\mathrm{)}}\mathrm{·}$(5)Hughes et al. (2013) measured the metallicity of the galaxies in our sample with integrated spectroscopy, where different calibrations are used to derive 12 +log (O/H), depending on the availability of the main emission lines. A(FUV), in magnitude, is the attenuation of the nonionizing UV radiation, defined as the ratio between the FIR and the FUV (at 1539 Å) flux densities, following the recommendations of Cortese et al. (2008).

The outputs of DL07 models are compared to these integrated properties. We decompose our sample in three groups according to the morphological types of the galaxies: Sa, Sab and Sb, Sbc Sc and Scd, and Sd, Im and BCD⁶. Galaxies with a MIPS24 measurement are represented by filled symbols whereas galaxies with WISE22 are represented by empty symbols. All the relations are presented in Fig. D.1, and discussed in Appendix D. For the total sample, we give the Spearman correlation coefficient of the relations. With a number of objects larger than 100, a correlation is expected to be real with a Spearman correlation coefficient larger than 0.40. We outline here the most interesting correlations between the properties and the DL07 output parameters.

One of the strongest trends is found between the metallicity and q_PAH (ρ = 0.73, Fig. 6), Metal-rich galaxies, with 12 +log (O/H) have a high fraction of PAH. The PAH are destroyed in low-metallicity environment by the UV radiation field, which propagates more easily due to the lower dust content. This was demonstrated in Galliano et al. (2003), Boselli et al. (2004), Madden et al. (2006), Engelbracht et al. (2008), and Gordon et al. (2008) for galaxies with lower metallicities. We should note that, in this work, we observe this relation for metal-rich galaxies with 8.3 < 12 + log (O/H) < 8.85. We also confirm, on a larger sample, the results of Engelbracht et al. (2005) who found a weakening of the PAH features at low metallicity from 8 to 24 μm flux density ratios, and Smith et al. (2007) who found that the strength of the PAH bands is directly linked to the metallicity from the Spitzer/IRS spectrum of 59 nearby galaxies. However, Galliano et al. (2008) suggested that the absence of PAH could be due to a delayed injection of carbon dust by AGB stars, and Sandstrom et al. (2012) proposed that the PAH were formed in molecular clouds, which have a lower filling factor in low-metallicity environments. A good relation is found between the stellar mass and q_PAH (ρ = 0.56). Indeed, massive galaxies are also more metal-rich (Tremonti et al. 2004).

A good correlation is found between the U_min parameter, which is the intensity of the diffuse ISRF (Draine et al. 2007; Aniano et al. 2012), and the Hα surface brightness (ρ = 0.70), and a moderate anticorrelation between U_min and the H-band surface brightness in AB mag arcsec^-2 (ρ = −0.49), as shown in Fig. 7.

A similar behavior was outlined by Boselli et al. (2012) where they found relations between FIR colors sensitive to the IR emission peak (S₆₀/S₂₅₀, S₆₀/S₁₀₀ and S₁₀₀/S₅₀₀) and ΣHα and μ_e(H). This is consistent with what we observe in this work, as the U_min parameter regulates the position of the IR emission peak (see Fig. 4). The stars of the diffuse component emit the bulk of their radiation in NIR, which can be probed by the H-band surface brightness. It is thus expected to find a relation between U_min and μ_e(H). This means that the diffuse dust is heated by the old stellar component. Furthermore, a good relation is also found with ΣHα, which is the ionizing surface brightness due to the young stars. The diffuse dust component seems to be also heated by the young stars component in star forming regions. With a Spearman coefficient of −0.44, there is not a strong correlation between μ_e(H) and ΣHα that could have originated the relations with U_min. This result from integrated galaxies seems incompatible with works based on the analysis of resolved galaxies (Bendo et al. 2010, 2012a; Boquien et al. 2011). These studies showed that at wavelengths shorter than 160 μm, most of the dust is heated by massive stars whereas at wavelengths longer than 250 μm, the dust is primarily heated by evolved stellar populations. This discrepancy can be explained by the fact that the brightest regions of the galaxies dominate the emission measured with integrated flux densities. For late-type galaxies, in IR, the brightest regions are heated by star formation and thus are linked to the Hα emission, explaining the correlation that we observe. Therefore, enhanced star formation might increase U_min, in which case the interpretation of U_min may be that it no longer traces only the diffuse ISRF from evolved stars but just the lowest energy radiation field within the galaxies for integrated studies.

6. Infrared templates

Thanks to the wealth of photometric data and physical properties available for the HRS galaxies, the gas-rich galaxy sample studied in this work is ideal for building new, well-constrained, IR templates. The majority of star-forming galaxies are known to follow an SFR–M_∗ correlation, called the main sequence (MS), and galaxies that lie above this sequence are experiencing a starburst event (Elbaz et al. 2011). Several studies have put constraints on the MS at different redshifts (e.g., Peng et al. 2010; Rodighiero et al. 2011; Heinis et al. 2014). Thanks to its design, volume-limit, and completeness in the K-band, the HRS is well suited for providing constraints on the local MS as the results are relatively free of distance-related biases that could appear in a flux-limited sample of galaxies. Figure 8 places the late-type star-forming galaxies of our sample in an SFR–M_∗ plot, along with several MS estimations. The SFRs are calculated assuming a Salpeter initial mass function (IMF) and the stellar masses are calculated assuming an IMF of Kroupa, we thus corrected the SFRs by a factor of −0.17 dex, following the results of Brinchmann et al. (2004) and Buat et al. (2014). A direct comparison can be done only with the sample of Peng et al. (2010) since it is the only one based on local galaxies. The MS local estimation of Peng et al. (2010) was built from a subsample of SDSS galaxies with 0.02 <z< 0.085. Their selection is only complete at z = 0.085 above a stellar mass of ≈10^10.4M_⊙. There is relatively good agreement with the MS local estimation of Peng et al. (2010). The observed difference in the slope may come from the different ranges of stellar masses that our sample and the sample of Peng et al. (2010) cover. The best linear fit determined from our galaxies is: $\log \mathit{SFR}\mathrm{=}\mathrm{0.65}\mathrm{\times }\log {\mathit{M}}_{\mathrm{\ast }}\mathrm{-}\mathrm{6.46.}$(6)

6.1. Construction of the templates

We computed the mean SED of the whole sample of late-type nondeficient galaxies from this work to provide the typical z = 0 SED of nearby normal galaxies (Fig. 9). To do so, we averaged all the best-fit SEDs of the gas-rich subsample studied in the previous sections. We provide the mean values of all of the physical properties that are associated with the sample from which this mean SED originates (Fig. 9).

We then binned the best-fit models of the sample by birthrate parameter, SFR, dust mass, metallicity, stellar mass, H-band effective surface brightness, Hα surface brightness, and morphological type (Fig. 10). The bins (indicated on Fig. 10) have been chosen in order to have a consistent number of objects in each bin. For each bin, the best-fit models of the galaxies are averaged to provide the template corresponding.

The new set of IR templates is constrained with submm data, and they benefit from good photometric coverage of the HRS galaxies. The HRS was designed to be complete in stellar mass, and the selection criteria applied to these galaxies make our sample representative of the late-type galaxies of the local Universe. Therefore, these templates provide constraints on the dust emission in the nearby Universe. However, as these templates were built from DL07 models, we should note that they may underestimate the dust emission at λ ≥ 500 μm for low-mass systems, as discussed in Sect. 4.4. The mean SED template and the binned SED templates are available to the community via the HEDAM website⁷.

6.2. Comparison with the literature

We compare our templates with the most popular IR SED libraries used in the literature, i.e., CE01, DH02, Rieke et al. (2009), Elbaz et al. (2011), Magdis et al. (2012), Smith et al. (2012a) and Berta et al. (2013). These libraries are based on different physical assumptions, however, this discussion is mainly focused on the shape of the SEDs and not on the physical description of the dust. We thus give a brief description of these libraries here.

The CE01 empirical SEDs have been computed as a function of the L_{8 − 1000} to reproduce the ISO, IRAS, and SCUBA data of local IR luminous galaxies. They used data between 0.44 and 850 μm, however, there is a large gap of observations between 100 and 850 μm. Dale & Helou (2002) built, using a semi-empirical method, a library of galaxy SEDs following the dust mass power-law distribution as a function of the intensity of the ISRF U, i.e. dM(U) ∝ U^{− α}dU. This set of templates reproduces the IR colors of galaxies thanks to a unique parameter α linked to the S₆₀/S₁₀₀ flux density ratio. A galaxy with α ≈ 1 is active in star formation, whereas a galaxy with α ≈ 2.5 is qualified as normal. The templates of Rieke et al. (2009) are averaged templates constructed from ISO and Spitzer observations of eleven local luminous IR galaxies (LIRG) and ultra luminous IR galaxies (ULIRG). However, CE01, DH02, and Rieke et al. (2009) are pre-Herschel libraries and did not benefit from the excellent FIR/submm coverage that we have from PACS and SPIRE. Finally, Smith et al. (2012a) used a sample of galaxies selected at 250 μm from the H-ATLAS field (Eales et al. 2010). They used the models of da Cunha et al. (2008) and performed a panchromatic SED fitting based on energy balance. As a result of these fits, they provided median templates binned by physical parameters for galaxies up to z = 0.5. However, we should note that they did not have any constraint between the K band and the 100 μm flux densities.

Recent studies using Herschel data computed libraries designed for higher redshift sources. Thanks to Herschel data, Elbaz et al. (2011) showed that the MS galaxies also verify a universal total to MIR luminosity ratio: IR8 = L_IR/L₈, with L₈, the rest-frame luminosity at 8  μm, suggesting that they have the same IR SED shape. In this relation, the starburst galaxies are outliers, with higher IR8. Thus, Elbaz et al. (2011) derived a single template for MS galaxies, with a single IR8 at all redshifts up to 2, and a single template for starburst galaxies with a significantly higher value of IR8. Magdis et al. (2012) adopted the same philosophy, but introduced a variation of the shape of the SED with the redshift. They fit Draine & Li (2007) models to individual galaxies and stacked ensembles at 0.5 <z< 2 using data from MIR to millimeter range. They derived a relation between ⟨ U ⟩ and z and used it to construct template SEDs of MS galaxies from z = 0 to z = 2.5, fixing γ = 0.02 and q_PAH = 3.19% for z< 1.5 and 2.50% for z> 1.5. They assume a flattening evolution of ⟨ U ⟩ beyond z = 2.5. For starburst galaxies, they used their best fit of GN 20, a well-studied very luminous and distant submm galaxy. Berta et al. (2013) combined UV to submm data of galaxies from large fields (GOODS-N, GOODS-S, and COSMOS) to reproduce the distribution of galaxies in ten rest-frame color spaces, using a superposition of multivariate Gaussian modes. According to this model, they classified galaxies and built the median SED of each class. Each median SED was then fitted using a modified version of the MAGPHYS code (da Cunha et al. 2008) that combines stellar light, emission from dust heated by stars, and a possible contribution from dust heated by an AGN.

We compare our templates with the one available in the literature in Fig. 11, where they have all been normalized to L_{8 − 1000}. The choice of this normalization comes from the fact that these libraries are essentially used to provide a measurement of the L_IR of the galaxies, the templates of CE01 are even calibrated to this parameter. We also divide them into two categories: in the left panel, the libraries representative of the nearby Universe, and in the right panel, the libraries developed for high-z studies.

In the left panel, we focus first on the low-z libraries, From each library, we select the templates that match the properties of our sample. For CE01, we select the templates with log (L_IR/L_⊙) < 10.9, and we note that there is no template for log (L_IR/L_⊙) lower than 8.5 that could be representative of some galaxies of our sample. For DH02, based on the S₆₀/S₁₀₀ ratios of our sample, we select templates with α> 1.5. We should note that for 30% of our galaxies having a 60 μm measurement, templates with α> 4, the largest value of α available from the DH02 library, are needed to reproduce the observed S₆₀/S₁₀₀. For the Rieke et al. (2009) templates, we select those with log (L_IR/L_⊙) < 11. For the Smith et al. (2012a) library, we show the templates corresponding to log (L_IR/L_⊙) < 11. We show all of the HRS templates presented in Fig. 10. The CE01, DH02, Rieke et al. (2009), and Smith et al. (2012a) templates contain stellar emission that explain part of the differences seen at λ< 10 μm compared to ours which are purely dust emission. All the libraries here are consistent within ≈0.2 dex around 100 μm. Indeed, pre-Herschel libraries (CE01 and DH02) benefit from IRAS 100 μm measurements, and post-Herschel libraries presented here can rely on PACS data at 100 μm. This part of the SED is thus well constrained by the observations. At longer wavelength, the low-z templates have consistent shapes. However, we remark in Fig. 3 that DL07 models have difficulty reproducing the 500 μm observations, thus despite this good agreement between the different libraries, updates in the models are needed to be able to reproduce the data. At wavelength shorter than 100 μm, CE01 and DH02 templates represent dust temperatures that are significantly higher than those of Smith et al. (2012a) and this work due to selection criteria. Indeed, the IRAS selections for the normal galaxies introduce a bias toward warmer sources. The templates of Rieke et al. (2009), benefitting from the IRS (Infrared Spectrograph) spectra of Spitzer is in good agreement with the HRS templates. There is a particularly striking disagreement between the templates in MIR-FIR, which can reach up to two orders of magnitude. The pre-Herschel libraries have IR peaks that are shifted toward shorter wavelength compared to the post-Herschel ones, resulting in higher temperatures for the warm dust. What increases the disagreement between the libraries in this 20−100 μm range is the very low luminosity of the Smith et al. (2012a) median SEDs. This is probably due to the fact that Smith et al. (2012a) did not have any MIR and FIR data up to 100 μm to constrain their templates. Even if we do not take this library into account, the disagreement of the low-z libraries between 20 and 100 μm is very important. The emission in this range is a combination of emission from warm dust populations and stochastically heated grains. This warm dust, which peaks around 100 μm  and even at shorter wavelengths, is theoretically an excellent tracer of star formation. It is unclear if the larger scatter we observe in FIR is only due to uncertainties in the way templates are built (there are few observational constraints in this range), or whether this translates to variations in the physical properties in galaxies. Indeed, based on the dust emission models of Draine & Li (2007), the relative contribution of photodissociation regions and diffuse stellar component to the heating of the dust impacts the SED in this particular range.

In the right panel, we show our mean SED as a representative SED for z = 0 galaxies along with templates based on the study of high-z galaxies done with Herschel observations. As for the low-z libraries, these templates agree relatively well around 100 μm, except for the SED of the MS galaxies from Elbaz et al. (2011). At longer wavelengths, the high-z library of Magdis et al. (2012) and of this work also have the same slope. Elbaz et al. (2011) computed their SEDs template by finding the mean of all of the SEDs of their sample galaxies, normalized to 10¹¹/L_IR, resulting in a lower β for both their MS and starburst templates. The z = 0 main sequence template of Magdis et al. (2012) (thick purple solid line) is in good agreement with the mean SED of HRS galaxies. With the increase in redshift, Magdis et al. (2012) templates shift toward shorter wavelength, and thus higher dust temperature. We select some templates out of the 32 available from the library of Berta et al. (2013) by removing templates with AGN components and those typical of high-z sources, such as Lyman break galaxy template. These templates show a large variety of SED shape, temperature of the dust and PAH bands intensity. The submm part of the Berta et al. (2013) templates is very similar to Magdis et al. (2012) and the mean SED of this work, however, the MIR-FIR domain show a large range of luminosities.

7. Conclusions

Thanks to the wealth of photometric ancillary data available for the HRS, we perform the NIR photometry of the HRS galaxies (see Appendix A) and compute their IR SED from 8 to 500 μm. We provide an updated method to remove the stellar contribution in NIR and MIR using different SFH according to the morphological type of the galaxies. The Draine & Li (2007) models are fit to the HRS galaxies. Even though this work focuses on the dust properties of a gas-rich galaxy subsample, we provide the results of the SED fitting of the other HRS galaxies (early-type and Hi-deficient galaxies) in Appendix C. We note that a strong constraint in the 20−60 μm range, at least a reliable measurement at 24 μm, is mandatory to have a reliable estimation of the relative contribution of PDR to the total IR SED. The comparison between observed and modeled flux densities shows that Draine & Li (2007) models underestimate the 500 μm observations for low-mass systems. We also note an underestimation of the 160 μm measurements, especially for high-mass systems.

The median diffuse ISRF intensity of our late-type sample is 1.96 ± 0.47 times the ISRF intensity of the Milky Way corresponding to a median dust temperature of 22 K, with a median contribution of the PDRs of 0.75% ± 0.5%, and a contribution of the PAH to the total dust mass of 4.16% ± 0.42. The median log (L_IR/L_⊙) is 9.47 ± 0.03 and the median dust mass of the sample is log (M_dust/M_⊙)7.02 ± 0.08.

We compared these parameters derived from the fitting procedure to integrated properties of the galaxies. From this comparison, in agreement with Boselli et al. (2012), we confirm a good correlation between the fraction of PAH and the metallicity, implying a weakening of the emission of the PAH in galaxies with lower metallicities. We thus confirm results obtained from MIR colors studies (Boselli et al. 2004; Engelbracht et al. 2005) and spectroscopy (Smith et al. 2007). From this relation follows a good correlation between the fraction of PAH and the stellar mass, as most massive systems have higher metallicities. Moderate to good correlations are found between the minimum intensity of the ISRF and the H-band and Hα surface brightness implying that, based on integrated galaxy analysis, the diffuse dust component seems to be heated by both the young stars in star forming regions and the diffuse evolved populations. This confirms the results of Boselli et al. (2012), which were also based on an integrated study of galaxies, but is incompatible with an analysis based on resolved studies.

We placed the HRS galaxies in an SFR–M_∗ diagram, and compared them with fits of the MS galaxies at different redshifts. There is good agreement with the MS relation at z = 0 of Peng et al. (2010), even if HRS low-mass systems tend to have higher SFR. The best linear fit to the data is log SFR = 0.65 × log M_∗ − 6.29. Thanks to the good photometric coverage of our sample, we are able to provide IR templates of nearby galaxies binned by the parameters that constrain the shape of the IR SED: birthrate parameter (or equivalently the sSFR), dust mass, metallicity, stellar mass, H-band effective surface brightness, Hα surface brightness, and morphological type. We also computed the mean SED of the subsample to provide a reference for any cosmological studies and simulations. The mean SED and the library can be found on the HEDAM website⁸. We compared this set of templates to the most popular IR pre-Herschel and post-Herschel libraries. At low-z, pre-Herschel libraries have a very warm dust component compared to post-Herschel ones, due to selection effects of IRAS galaxy samples. Compared to high-z libraries, our mean SED is in good agreement with the z = 0 MS template of Magdis et al. (2012). The IR peak of the MS template of Elbaz et al. (2011) is wider than the IR peak obtained in this work, and corresponds to a lower luminosity at 160 μm. In Appendix B, we provide new photometric data in the 8, 12, and 22 μm bands, taken by Spitzer and WISE, and used in the work. We also present in Appendix B, new coefficients to remove the stellar contribution from MIR observations.

Online material

Appendix A: MIR photometry of the HRS

For the purpose of this study, we perform MIR photometry at 8, 12, and 22 μm from Spitzer/IRAC and WISE data. We thus present here the flux densities at these wavelengths for all of the HRS galaxies.

Appendix A.1: Spitzer/IRAC 8 μm

One of the output results from Draine & Li (2007) models is the PAH fraction of the total dust mass of a galaxy. Because one of the largest PAH emission features is expected at 7.7 μm, we need the IRAC (Fazio et al. 2004) 8 μm images to constrain this part of the SED.

We retrieved 8 μm images available for 129 HRS galaxies from the Spitzer Data Archive⁹. The FWHM of the PSF of the IRAC fourth channel is 1.9′′  and the maps have a pixel size of 0.6′′. As a first step, we convert the images from MJy/sr to μJy/pixel, and then remove all of the problematic pixels (NaN) by replacing them by the median value of the surrounding pixels. We remove the stars and background sources visible at 8 μm using the IRAF/imedit task from all of the images. We then extract the flux densities using apertures adapted to each galaxies to take all of the IR emission into account, and minimize the contamination from background features. As the images have small fields of view, we do not estimate residual background emission from circular annuli (as we do for WISE and Herschel/SPIRE photometry) but from the mean value of multiple 10 × 10 pixels boxes around the galaxies. IRAC flux densities need to be corrected for aperture effects to take the diffuse scattering of incoming photons through the IRAC array¹⁰ into account. We thus apply aperture corrections on our measurements using the parameters provided in Table 4 of Dale et al. (2007).

For the error calculation, we proceed as in Boselli et al. (2003b) using the same boxes as for the background residual estimation. We thus take two terms into account, one being the pixel-to-pixel error (the mean value of the standard deviation in all of the boxes) and the other one being the sky error due to large scale structures (the standard deviation of the mean values in all of the boxes). To this stochastic error, we add quadratically a calibration error of 10% as indicated in Dale et al. (2007). Galaxies with a signal-to-noise lower than 3 are considered as undetected, and an upper limit of 3σ is given.

In Table A.2, we give the IRAC 8 μm flux densities of the HRS galaxies. A flag is associated with the measurements with the following code: 0 for undetected galaxies, 1 for detected galaxies, and 2 for galaxies for which the measurement suffers from source blending.

To check the validity of our IRAC photometry, we search for IRAC 8 μm flux densities already available for HRS galaxies on NED and make the comparison (Fig. A.1). We find eight galaxies in common with the SINGS sample (the Spitzer Infrared Nearby Galaxies Survey, Kennicutt et al. 2003; Dale et al. 2007), one galaxy in common with Panuzzo et al. (2007), and two galaxies to be compared with Willmer et al. (2009). The only point that deviates from the one-to-one relationship is the data point of Panuzzo et al. (2007). It corresponds to the flux density of NGC 4435, which is very close to NGC 4438. This proximity can be problematic as outlined by Panuzzo et al. (2007) and the difference in the measurement may come from how the emission from NGC 4438 is treated. This comparison shows that our measurements are consistent with the 8 μm data taken from the literature with a mean ratio of 0.93 ± 0.04.

Appendix A.2: WISE 12 and 22 μm

NASA’s telescope WISE (Wright et al. 2010) performed an all sky survey in four NIR and MIR bands. For the purpose of this work, we use WISE data at 12 and 22 μm, observed with a resolution of 6.5′′, and 12.0′′, respectively. WISE scanned the sky with 8.8 s exposures at 12 and 22 μm (the W3 and W4 bands), each with a 47′ field of view, providing at least eight exposures per position on the ecliptic and increasing depth toward the ecliptic poles. The individual frames were combined into coadded images with a pixel size of 1.375′′. WISE achieved 5σ point source sensitivities better than 1 and 6 mJy in unconfused regions on the ecliptic in the W3 and W4 bands. Sensitivity improves toward the ecliptic poles due to denser coverage and lower zodiacal background. We retrieve the images of all of the HRS galaxies at 12 and 22 μm from the WISE Science Archive¹¹. We perform aperture photometry using the DS9/Funtools program “Funcnts”. For each galaxy, the aperture, where the flux of the galaxy is estimated, and the background annulus, where the emission from the background is estimated, are defined “manually”. They are chosen to encompass all of the emission from the galaxy and avoid any contamination from foreground/background sources.

To convert the counts extracted into Jy, we use the factors provided by the Explanatory Supplement to the WISE Preliminary Data Release Products¹², Sect. II.3.f, 2.9045 × 10^-6 Jy/DN and 5.2269 × 10^-5 Jy/DN at 12 and 22 μm, respectively. For WISE photometry of extended sources, Jarrett et al. (2013) recommended three corrections to be applied to all measurements. The first one is an aperture correction that accounts for the WISE absolute photometric calibration method using PSF profile fitting. This correction is 0.03 mag and −0.03 mag at 12 and 22 μm, respectively. The second correction is a color correction that accounts for the spectral signature of the source convolved with WISE relative system response (RSR). Because our SED fitting method integrates the models into the filters of the bands before comparing them with the data, we do not need to apply this correction. The third correction comes from a discrepancy between the WISE photometric standard “blue” stars and “red” galaxies related to an error in the W4 RSR, as described in Wright et al. (2010) and Jarrett et al. (2011). Following Jarrett et al. (2013), we apply a correction factor of 0.92 to the 22 μm flux densities of all of the spirals and disk galaxies. This correction is thus applied to HRS galaxies with morphological type of Sa and later.

We determine the errors in the measurements following the method described for the IRAC data. However, because of a correlated noise with a typical length scale larger than 10 pixels, we use 50 × 50 boxes rather than 10 × 10 pixels. Galaxies with a signal-to-noise lower than 3 are considered as undetected, and an upper limit of 3σ is given.

In Table A.2, we give the WISE 12 and 22 μm flux densities of the HRS galaxies. As for IRAC measurements, a flag is provided with the following code: 0 for undetected galaxies, 1 for detected galaxies and 2 for galaxies for which the measurement suffer from sources blending.

To check the validity of our measurements, we compared our results to the NIR and MIR ancillary data available for the HRS galaxies in Fig. A.2. We use the Spitzer/IRAC 8 μm from this work and the Spitzer/MIPS 24 of Bendo et al. (2012b). Even if the 8 μm filter from IRAC and the 12 μm filter from WISE are not overlapping enough to make a reliable comparison, and knowing that the emission process at the two wavelengths differ, we plot the comparison to identify possible outliers and thus possible issues with the photometry. IRAS data at 12 and 25 μm are also available for some of the HRS galaxies (Sanders et al. 2003; Moshir & et al. 1990; Thuan & Sauvage 1992; Soifer et al. 1989; Young et al. 1996). Some shifts in the relation can be due to the different wavelength of the data and the different response curve of the filters. There is a good correlation between IRAS and WISE data at 12 μm, but WISE flux densities tend to be higher than IRAS ones. The mean ${\mathit{S}}_{\mathrm{IRAS}}^{\mathrm{12}}\mathit{/}{\mathit{S}}_{\mathrm{WISE}}^{\mathrm{12}}$ is 1.11 with a standard deviation of 0.79. We note that the relation becomes very dispersed for flux densities below ≈80 mJy. The relation between the IRAC 8 μm and the WISE 12 μm measured in this work is good, with a standard deviation of 0.43 for the IRAC to WISE flux density ratio, and a mean value of the ratio of 1.08. There might be an effect due to the difference of wavelength, however it is difficult to quantify it as the 8 μm lies completely in the PAH emission domain.

There is good agreement between MIPS 24 μm and WISE 22 μm measurements with a mean MIPS to WISE flux density ratio of 1.22 ± 0.44. Even if very dispersed, the relation between IRAS 25 μm and WISE 22 μm flux densities is good. However, as noticed at 12 μm, the relation becomes very dispersed for ${\mathit{S}}_{\mathrm{25}}^{\mathrm{IRAS}}\mathit{<}\mathrm{80}$ mJy.

Appendix B: Removing the stellar contribution

In global galaxies, the emission in the 2−10 μm range is due to both the old stellar population and the dust (very small grains + PAHs). The contribution of these two components varies differently with the type of the galaxies, the former being dominant in ETG, the latter in star forming systems. Given that the Draine & Li (2007) models deal only with the dust component, we have to remove the stellar contribution first. This has been historically done by considering the Rayleigh-Jeans tail of the stellar emission peaked at ≈1−2 μm determined using a blackbody with T ≈ 3000 K, using the typical SED of ETG not showing any evidence of the presence of dust, or using stellar SEDs derived, for instance, from the Starburst99 models (e.g., Boselli et al. 1998; Helou et al. 2004; Draine et al. 2007). In this work, we use the CIGALE code (Noll et al. 2009), which allows us to compute the stellar SED of a galaxy using stellar population models from (Maraston 2005) convolved with a given star formation history (SFH). We refer the reader to Noll et al. (2009) for a complete description of the code.

Depending on their morphological types, the stellar populations of galaxies have very different characteristics. The elliptical and lenticular galaxies (ETG) are dominated by an old stellar population emitting in NIR whereas stellar populations of late-type galaxies are younger, emitting in UV. To properly remove the stellar contribution from the MIR emission, we need to take these differences into account.

Here, we consider an SFH with a decreasing exponential shape and an e-folding time τ. If the e-folding time of the SFH is very small (1−2 Gyr) then all of the stars are created in a very short time and evolve to become, at the age of the Universe, a very old population. On the contrary, a large e-folding (≈10−20 Gyr) corresponds to a quasi-constant SFR and stars are still being created at the age of the Universe.

To understand the impact of the choice of τ on MIR colors, we show on Fig. B.1 the variation of MIR flux densities from the models normalized to 2 μm with τ. Strong variations are seen for the 8 to 2 μm flux density ratios and the 12 to 2 μm flux density ratios (36% and 40%, respectively), whereas a very weak variation is seen at 22 μm. These variations stress the fact that estimates of the stellar emission in MIR strongly depends on the SFH of the galaxy and thus on its morphological type. Small values of τ correspond to a high S_{8 μm}/S_{2 μm} ratio, which is consistent with an important old stellar population. Thus, choosing a τ of 2 Gyr would lead to a SFH compatible with ETGs. With τ = 10 Gyr, there is less variation in the 8 to 2 μm flux density ratio. This smaller ratio implies a smaller flux density at 8 μm, which is what we expect for late-type galaxies.

To estimate the counterpart of the MIR emission due to stars in a late-type galaxy, Helou et al. (2004) used the stellar population models of Starburst 99 (Leitherer et al. 1999). Assuming that the 3.6 μm emission was purely stellar, they obtained stellar contribution factors of 0.596, 0.399, 0.232, and 0.032 at 4.5, 5.8, 8.0 and 24.0 μm, respectively. Draine et al. (2007) proposed similar values obtained from a blackbody emission with a temperature of 5000 K (0.260, 0.0326 at 8.0, and 24.0 μm, respectively). We use blackbodies of different temperatures and stellar population models computed from CIGALE and present the resulting stellar emission normalized at 2 μm in Fig. B.2. For comparison, we show the normalized observed flux densities of all the early-type galaxies of the HRS as well as those of M 99, a typical late-type galaxy of our sample. Differences in the stellar contributions are seen depending on the model (blackbody or models from CIGALE) and on the assumption on the temperature or the e-folding time. Both methods, blackbody or more complex models, pull uncertainties due to the assumption on the parameters (temperature or e-folding time). However, using the models from CIGALE allows us to take the observed differences between the stellar populations of the ETGs and LTGs into account. We thus decide to use the stellar population models computed by CIGALE, with a population aged of 13 Gyr, and consider these differences by using different e-folding times: τ = 2 Gyr for the ETGs and τ = 10 Gyr for the LTGs. In Table B.1, we calculate the coefficients and the associated errors corresponding to the stellar contribution for several NIR and MIR bands (from J to IRAS 60 μm), normalized to different bands (from J to IRAC 1). Our coefficients are in good agreement with those of Helou et al. (2004) and Draine et al. (2007), i.e., 0.589, 0.396, 0.244, and 0.044 at 4.5, 5.8, 8.0, and 24.0 μm, respectively, for the late-type galaxies.

Appendix C: Draine & Li (2007) parameters of the HRS galaxies

Even if this work is focused on the study of the dust properties of a subsample of gas-rich galaxies from the HRS, we apply the SED fitting procedure presented in Sect. 4.4 to all of the HRS galaxies. First, we removed the MIR stellar emission using the coefficients presented in Appendix B. In order to have fiducial corrected MIR flux densities, we impose the following criterion. If a galaxy has a corrected flux density lower than 2σ at 8 or 12 μm, then this galaxy is removed from the sample. At longer wavelengths, the contribution from the stellar populations to the IR emission is considered negligible.

Of the 322 HRS galaxies, 270 fulfill this criterion. However, from these 270 galaxies, we remove five that were not detected in PACS and SPIRE bands, thus having no constraints on the FIR and submm part of the SED: HRS 90, HRS 155, HRS 240, HRS 291, and HRS 316. We run our fitting procedure on 265 galaxies: 20 early-type galaxies and 245 late-type galaxies.

We present the results from the fits of the galaxies not analyzed in this work (20 early-type galaxies and 99 Hi-deficient galaxies) in Table C.1.

Appendix D: Comparison between the properties of the gas-rich galaxies and the output of DL07 models

While we describe the main results of the comparison between the output parameters of DL07 and the properties of the gas-rich galaxy sample in Sect. 5, we describe here, for each output parameters, the relations with these properties. These relations are presented in Fig. D.1. The Spearman coefficient is provided for every relation. With a number of objects larger than 100, a correlation is expected to be real with a Spearman correlation coefficient larger than 0.40.

Appendix D.1: PAH emission

The fraction of PAH correlates with all of the parameters, except the birthrate parameter, with ρ ranging from 0.45 to 0.73. The relation between the fraction of PAH, the metallicity, and the stellar mass is described in Sect. 5.

There is a weak relation between the fraction of PAH contributing to the total IR luminosity and the SFR (ρ = 0.45). We would expect a tighter correlation as PAHs are often used as SFR indicators although many caveats on this assumption have been discussed in the literature (Boselli et al. 2004; Wu et al. 2005; Calzetti et al. 2007; Zhu et al. 2008; Kennicutt et al. 2009). Indeed, the destruction of PAH in regions where the ISRF is too intense, such as PDRs, can affect the relation between the SFR and 8 μm luminosity. This leads to a weak anticorrelation with the birthrate parameter as well, and a moderate relation with the Hα surface brightness that directly probes star formation. It seems that galaxies experiencing a star formation episode, i.e., with higher b, have lower q_PAH. Indeed, previous works found that the PAH emission is inhibited within star-forming regions relative to other star formation tracers (e.g., Helou et al. 2004; Calzetti et al. 2005; Bendo et al. 2006, 2008; Pérez-González et al. 2006; Gordon et al. 2008). Another relation is found between q_PAH and the H-band surface brightness, linked to what was previously noticed by Calzetti et al. (2007) and Bendo et al. (2008) who showed that 8 μm emission is also contributed by dust heated by the diffuse nonionizing stellar component. A correlation is also found between the fraction of PAH and the FUV attenuation (ρ = 0.58). However, the trend seen on the related panel is difficult to interpret, as the relation, if real, appears to be nonlinear.

Appendix D.2: Relative contribution of PDR and diffuse regions

Here we only consider galaxies for which MIPS 24 μm measurements are available (filled symbols on Fig. D.1) to have the strongest constraint on γ (see Sect. 4.3). There is a moderate relation between γ and the birthrate parameter (ρ = 0.44). When γ increases, the contribution of the PDR to the emission of the IR SED increases. As b is linked to the hardness of the UV radiation field, both quantities are correlated. Although weak, these relations between γ and b, and γ and the metallicity are consistent as the most metal poor objects are also the most star forming. We also notice a trend between γ and the metallicity, with a Spearman correlation coefficient of ρ = −0.39. The PDR contribution to the IR SED increases when the metallicity decreases. This confirms the tendency between γ and the stellar mass already noticed from the shape of the IR SED in Fig. 4. Furthermore, when γ increases, the IR peaks widen (Fig. 4). These two points confirm the results of Smith et al. (2012a) who performed a panchromatic analysis of the SED of a 250 μm selected sample of galaxies and found that low-mass galaxies have broader IR peaks. This relation also implies that the IR SED of the most massive galaxies is dominated by the emission of the diffuse component.

Appendix D.3: Interstellar radiation field

The ISRF is characterized by the parameters U_min, which quantifies the ISRF of the diffuse stellar component, and ⟨ U ⟩, the dust heating rate parameter, which is calculated from U_min, γ, and U_max (fixed to 10⁶). Relations between ⟨ U ⟩ and the integrated properties of the galaxies are thus linked to the relations between U_min, γ, and these properties.

The relation between the intensity of the diffuse ISRF and the Hα and H-band surface brightnesses are discussed in Sect. 5. A weak correlation is observed between the birthrate parameter b and ⟨ U ⟩, with ρ = 0.48. The dust heating parameter ⟨ U ⟩ provides a direct measurement of the mean interstellar radiation field of the galaxy. This confirms the results of Boselli et al. (2010b) and Boselli et al. (2012) who found a correlation between b and the S₆₀/S₁₀₀ flux density ratio, sensitive to the dust temperature.

Appendix D.4: Infrared luminosity

An expected trend is seen between the L_IR and M_∗ as the most massive galaxies are also the most luminous as a scale effect (Kennicutt 1990). We recover the strong relation between the L_IR and the SFR as well (Devereux & Young 1990; Devereux et al. 1995; Buat & Xu 1996; Kennicutt et al. 2009). Indeed, the L_IR is widely used as a proxy for the SFR (e.g., Scoville & Young 1983; Buat & Xu 1996; Kennicutt 1998; Kennicutt et al. 2009; Kennicutt & Evans 2012).

We observe a moderate relation between the L_IR and the metallicity (ρ = 0.58). Finally, there is also a moderate trend between the L_IR and the FUV attenuation (ρ = 0.50). The energy absorbed in UV is reemitted by the dust in IR, one would expect to find a tighter relation between these two properties. Indeed, Smith et al. (2012a) found that the FIR/optical ratio increases with the L_IR indicating that the galaxies with the higher IR luminosities are also the most obscured. However, by definition, A(FUV) is the infrared to UV luminosity ratio. These two quantities are thus not independent.

Appendix D.5: Dust mass

As expected, the dust mass and the stellar mass are tightly linked with a Spearman correlation coefficient of 0.83, as a scaling effect. There is also a strong correlation between the dust mass and the SFR. A weak global trend appears with the metallicity (ρ = 0.44). Indeed, the dust mass is larger in the most massive galaxies that are also the most metal-rich (Tremonti et al. 2004).

From Fig. D.1, we conclude that all of the integrated properties, except the FUV attenuation, correlate moderately to strongly with at least one of the output of Draine & Li (2007) models: the stellar mass to the fraction of PAH, the SFR to the fraction of PAH, the birthrate parameter moderately with γ and ⟨ U ⟩, ΣHα and μ_e(H) with U_min and q_PAH, and the metallicity with q_PAH and moderately with γ. All of these properties drive the shape of the IR SED. We confirm the results of Boselli et al. (2012) who found that the metallicity, the intensity of the ionizing and nonionizing radiation field, and the birthrate parameter are key parameters in the dust emission observed in the FIR.

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Acknowledgments

We thank the anonymous referee for his/her comments, which greatly helped improve this paper. L.C. thanks Daniel Dale for sharing KINGFISH results and discussions, and also thanks Vassilis Charmandaris for useful comments and discussions. I.D.L. is a postdoctoral researcher of the FWO-Vlaanderen (Belgium). SPIRE has been developed by a consortium of institutes led by Cardiff Univ. (UK) and including Univ. Lethbridge (Canada); NAOC (China); CEA, LAM (France); IFSI, Univ. Padua (Italy); IAC (Spain); Stockholm Observatory (Sweden); Imperial College London, RAL, UCL-MSSL, UKATC, Univ. Sussex (UK); Caltech, JPL, NHS C, Univ. Colorado (USA). This development has been supported by national funding agencies: CSA (Canada); NAOC (China); CEA, CNES, CNRS (France); ASI (Italy); MCINN (Spain); SNSB (Sweden); STFC, UKSA (UK); and NASA (USA). This research has made use of the NASA/IPAC ExtraGalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration and of the GOLDMine database (http://goldmine.mib.infn.it/). This publication makes use of data products from the Wide-field Infrared Survey Explorer, which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration.

References

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