A Distribution of DL07 model parameters

# Molecular Gas, Dust and Star Formation in Galaxies

I. Dust properties and scalings in 1600 nearby galaxies
###### Key Words.:
galaxies: ISM - galaxies: photometry - galaxies: star formation - infrared: galaxies - infrared: ISM - submillimeter: galaxies
1

## Abstract

Context:Dust and its emission is being increasingly used to constrain the evolutionary stage of galaxies. A comprehensive characterization of dust, best achieved in nearby bright galaxies, is thus a highly useful resource.

Aims:We aim to characterize the relationship between dust properties (mass, luminosity and temperature) and their relationships with galaxy-wide properties (stellar, atomic and molecular gas mass, and star formation mode). We also aim to provide equations to estimate accurate dust properties from limited observational datasets.

Methods:We assemble a sample of 1,630 nearby (z 0.1) galaxies - over a large range of stellar masses (M), star formation rates (SFR) and specific star formation rates (sSFR=SFR/M) - for which comprehensive and uniform multi-wavelength observations are available from WISE, IRAS, Planck and/or SCUBA. the characterization of dust emission comes from spectral energy distribution (SED) fitting using Draine & Li dust models, which we parametrize using two components (warm at 45 - 70 K and cold at 18 - 31 K). The subsample of these galaxies with global measurements of CO and/or H are used to explore the molecular and/or atomic gas content of the galaxies.

Results:The total infrared luminosity (L), dust mass (M) and dust temperature of the cold component (T) form a plane that we refer to as the dust plane. A galaxy’s sSFR drives its position on the dust plane: starburst (high sSFR) galaxies show higher L, M and T compared to Main Sequence (typical sSFR) and passive galaxies (low sSFR). Starburst galaxies also show higher specific dust masses (M/M) and specific gas masses (/M). We confirm earlier findings of an anti-correlation between the dust to stellar mass ratio and M. We also find different anti-correlations depending on sSFR; the anti-correlation becomes stronger as the sSFR increases, with the spread due to different cold dust temperatures. The dust mass is more closely correlated with the total gas mass (atomic plus molecular) than with the individual atomic and molecular gas masses. Our comprehensive multi wavelength data allows us to define several equations to accurately estimate L, M and T from one or two monochromatic luminosities in the infrared and/or sub-millimeter.

Conclusions: It is possible to estimate the dust mass and infrared luminosity from a single monochromatic luminosity within the Rayleigh-Jeans tail of the dust emission, with errors of 0.12 and 0.20 dex, respectively. These errors are reduced to 0.05 and 0.10 dex, respectively, if the dust temperature of the cold component is used. The dust mass is better correlated with the total ISM mass (  M). For galaxies with stellar masses 8.5 log(M/) 11.9, the conversion factor between the single monochromatic luminosity at and the total ISM mass () shows a large scatter (rms = 0.29 dex) and a weak correlation with the L. The star formation mode of a galaxy shows a correlation with both the gas mass and dust mass: the dustiest (high M/M) galaxies are gas-rich and show the highest SFRs.

## 1 Introduction

Star formation occurs within dense (), massive (), and cold ( K) giant ( pc) molecular clouds (GMC) (Kennicutt & Evans, 2012), where atomic gas, mainly atomic Hydrogen (), is transformed into molecular gas (mainly ) on dust grain surfaces (e.g., Scoville 2012). Dust grains are formed within the cool, extended atmospheres of low mass () asymptotic giant branch (AGB) stars and are dispersed into the ISM via the strong AGB star winds (Gehrz 1989). In other words, the dust content is related to the star formation history of the galaxy. Since much of our current knowledge of galaxy properties and evolution comes from studies of high temperature (T K) regions, a global understanding of star formation requires a better knowledge of the role of cold gas and dust in the star formation process.

Dust grains emit mainly in the far infrared (FIR; ) and sub-millimeter (sub-mm; ). Early studies of dust content and emission have been done both from space (IRAS, see Neugebauer et al. 1984 and ISO, see Kessler et al. 1996) and from the ground (SCUBA, see Holland et al. 1999, at the James Clerk Maxwell Telescope and MAMBO at the IRAM 30 meter telescope). More recent missions - in the mid-infrared (e.g., WISE; Spitzer), far-infrared (e.g., AKARI; Herschel), and sub-mm (e.g., Planck) - have revolutionized the field (e.g., Lutz 2014).

The IR to sub-mm emission of dust has been characterized in many samples (e.g., SLUGs by Dunne et al. 2000; HRS by Boselli et al. 2010; KINGFISH/SINGS by Kennicutt et al. 2003; Dale et al. 2005; SDSS-IRAS by da Cunha et al. 2010 ;ATLAS 3D by Cappellari et al. 2011; ERCSC by Negrello et al. 2013) and at high-z (e.g., GOODS-Herschel by Magnelli et al. 2010; H-ATLAS by Eales et al. 2010). Early studies modeled the dust grain emission using grey-body emission from one or two dust temperature components (e.g., Dunne et al., 2000; Dunne & Eales, 2001). More complex and sophisticated dust emission models available today include the MAGPHYS (da Cunha et al., 2010) code - which contains empirically-derived spectral energy density (SED) libraries from the ultraviolet (UV) to infrared (IR) - and the model developed by Draine & Li (2007, DL07 hereafter) which provides a more extensive SED library covering the IR to sub-mm. The DL07 model has been successfully applied to the Spitzer Nearby Galaxy Survey (SINGS) galaxies (Draine et al., 2007), and these authors note that the presence of sub-mm photometry is crucial to constrain the mass of the cold dust component.

The results on dust properties coming from many of the studies mentioned above are limited by poor statistics as a consequence of small samples and/or the limited sampling of the SED (especially at sub-mm wavelengths) which decreases the reliability of the SED modeling. Since dust properties are increasingly used at all redshifts to determine the evolutionary state of a galaxy, and in general for galaxy evolution studies, it is crucial to fully characterize these properties and their relationships and degeneracies in large samples of galaxies. Of specific interest is the degeneracy between dust temperatures and dust emissivity index, the inter-relationships between dust mass, temperature, and luminosity, and the relationships between these dust properties and other properties of the galaxy (e.g., stellar and gas masses, SFR, specific star formation rate; sSFR=SFR/M[yr]).

The recent availability of Planck sub-mm (350 m to 850 m) fluxes for thousands of nearby galaxies which are well studied in the optical to IR, allows, for the first time, comprehensive and accurate dust model fits to these. With a comprehensively modeled large sample of nearby galaxies in hand, one can test and refine the many scaling relations and estimators now being used at all redshifts, e.g., estimating gas mass from a single flux measurement at 850 (Scoville, 2012), or estimating dust masses (Dunne et al., 2000; Dunne & Eales, 2001) and/or luminosities (e.g., Sanders & Mirabel 1996, Elbaz et al. 2010) from a few IR flux measurements.

The ‘starburstiness’ of a galaxy is normally obtained from the ratio of the SFR and the stellar mass (M). The SFR -M plane shows that while most ’normal’ star-forming galaxies follow a ‘main sequence’ (MS) of secular star formation (Elbaz et al., 2007), a small fraction of galaxies show excessive SFR for a given M: these galaxies are referred to as starburst (SB). The MS of galaxies is observed over the redshift range z (e.g., Elbaz et al. 2007, Magdis et al. 2010, Rodighiero et al. 2011, Elbaz et al. 2011, Pannella et al. 2015, Schreiber et al. 2015) and changes smoothly with redshift (Elbaz et al., 2011). In this work we use the MS proposed by Elbaz et al. (2011), at z=0:

 SFR=M∗4.0×109[ M⊙yr] (1)

This equation defines the specific star formation rate expected for MS galaxies (MS; ). We define SB galaxies as those having , and passive (PAS) galaxies as those at . The two ‘transition’ zones between the above three classifications, i.e. dex wrt the MS locus (an intermediate SB zone) and ; dex wrt to the MS locus (an intermediate passive zone) are excluded in order to avoid contamination.

In this paper, we capitalize on the recent availability of sub-mm (Planck) fluxes (for better dust model fits) and WISE fluxes (for stellar mass determinations) to fit DL07 dust models to all nearby bright galaxies for which sufficient (for a reasonable fit to DL07 models) multi-wavelength uniform data are available from WISE, IRAS, Planck, and/or SCUBA. The resulting model fits are used to explore the relationship between dust properties (mass, luminosity, temperature) and their relationship with other galaxy-wide properties (e.g., stellar and gas masses, sSFR). The comprehensive dust modeling also allows us to refine estimations of total IR luminosity from one to a few IR to sub-mm fluxes, the dust mass from a single sub-mm flux, and sSFR from IR to sub-mm colors.

Throughout this paper we adopt a flat cosmology with and .

## 2 Sample and Data

We use two samples of nearby galaxies: (a) the sample of nearby galaxies with detections in Planck High Frequency Instruments (HFI) Second Data Release catalog and global CO J:1-0 observations (Nagar et al., submitted); and (b) all galaxies from the 2MASS Redshift Survey (2MRS; Huchra et al., 2012) which are listed as detections in the second Planck Catalog of Compact Sources at 350 m, 550 m, and 850 (PCCS2; Planck Collaboration et al., 2015).

The Nagar et al. (submitted) sample is a compilation of 600 nearby galaxies (z = 0.06) with global CO J:1-0 observations, and sub-mm fluxes from Planck catalogs at 350 m, 550 m, and 850 m or SCUBA 850 m observations. The names of the catalogs with the respective references are summarized in Table 1.

The sample spans a range of morphological types - including spiral, elliptical and interacting galaxies - and luminosities from normal to Ultra-Luminous Infrared Galaxies (ULIRGs).

The 2MRS sample consists of 44,599 nearby () 2MASS (Shectman et al., 1996) galaxies with K 11.75 mag and Galactic latitude for which spectroscopic redshifts have been obtained to 97.6% completeness (Huchra et al., 2012). We matched the 2MRS sample with the (PCCS2), using a maximum matching radius of 1 arcmin. The PCCS2 catalog contains only galaxies with high reliabilities (; signal to noise in DETFLUX). Sources with lower or unknown reliabilities, are listed in the equivalent excluded catalog (PCCS2E), which we have not used.

The Planck satellite has a beam resolution of the order of 1 arcmin (e.g. 4.22 arcmin at 350 m, Planck Collaboration et al. 2015), and the reliability catalog contains 1000 sources (e.g., 4,891 galaxies at 350 m, Planck Collaboration et al. 2015), with a density / sources/deg (e.g., 0.26 sources/deg at 350 m, Planck Collaboration et al. 2015). This means that the resolutions of WISE and 2MASS ( 1 arcsec) do not represent a problem for the match with the Planck source catalog, as we adopt a search radius of 1.0 arcmin. In order to remove any multiple match, we performed a visual inspection of all the matched objects. In some cases, we selected all the galaxies that have companions in the WISE, 2MASS and SDSS images and classified them as interacting systems. Furthermore, multiple detections in one Planck beam do not either represent a problem because the galaxies in our sample have a median diameter (parametrized as the D25 reported in HyperLeda 2) of 1.5 arcmin, with only 291 having D25 arcmin ( 18% of the final sample).

### 2.1 Flux densities and derived stellar mass

The Planck collaboration (Planck Collaboration et al., 2015) showed that, at 350 m, for sources with APERFLUX Jy, the APERFLUXes reported in the Planck catalog are in agreement with those in the Herschel Reference Survey.

Nagar et al. (submitted) compare the Planck observations at 850 m with SCUBA data (at 850 m) in nearby galaxies, revealing that the APERFLUX and the DETFLUX from Planck show the existence of some systematic difference. However, Nagar et al. (submitted) also show that simple corrections can solve this problem. They find that the observation of fluxes smaller than twice of the 90% completeness limit (304 mJy at 850 m ) needs smaller corrections if the DETFLUX is used (the correction is +70), and for greater fluxes (greater than twice of the 90% completeness limit) the fluxes are more consistent with the APERFLUX (using the correction: +139). Assuming a gray-body with a temperature of T=25 K and =1.8, Nagar et al. (submitted) obtain similar corrections for Planck observations at 350 and 550 m. For each wavelength, Nagar et al. (submitted) obtain three corrections: one with free slope and intercept, a second with intercept zero and free slope, and a third with slope one, or the expected in the case of observations at 350 and 550 m. We use the last kind of correction in our work. Additionally, to correct for the typical spectral shape of dust gray-body emission, we used correction factors of 0.976, 0.903 and 0.887 at 350 m, 550 m and 850 m, respectively Negrello et al. (2013). Following Nagar et al. (submitted), we assumed a 3% contamination from the CO emission line at Planck 850 m and negligible CO emission line contamination at Planck 350 and 550 m. After these flux density corrections are applied, the limits obtained for the Planck-derived flux densities in our sample are 500 mJy, 315 mJy, and 175 mJy, at 350 m, 550 m, and 850 m, respectively.

Mid-infrared (MIR) fluxes are obtained from the AllWISE Source Catalog ‘g’ magnitudes 3. These ‘g’ magnitudes are calculated over apertures defined using 2MASS images, with additional corrections as described in Jarrett et al. (2013). The WISE (W1-W4) filters have a limiting sensitivity of 0.08, 0.11, 1 and 6 mJy, respectively. We select only sources with signal to noise (S/N) 5, except for W4, where we consider a S/N 3. We calculate the galaxy stellar mass (M) using the WISE W1 filter (3.4 m) and the W1-W2 (4.6 m) color following the Cluver et al. (2014) calibration. The stellar mass ranges between and  for our sample. To test the consistency of our WISE-estimated stellar masses, we compare our stellar masses to those in three other catalogs based on SDSS-derived quantities (i.e. NASA-Sloan Atlas, Chang et al. 2015 and MPA-JHU catalogs, see appendix C). We obtained a good agreement with the M obtained in the NASA-Sloan Atlas (see appendix C for more details).

The infrared (IR) data comes from the Infrared Astronomical Satellite (IRAS) at 12, 25, 60 and 100 m, obtained from the Galaxies and Quasars catalog (Fullmer & Lonsdale, 1989). We consider only sources with moderate or high quality fluxes (no upper limits), with signal to noise 3.

Figure 1 shows the filter band-passes of all filters for which we compiled flux densities which were then used to constrain the DL07 dust model fits: WISE W3 (12 m) and W4 (22 m) ; IRAS 12, 25, 60 and 100 m ; Planck 350, 550 and 850 m and SCUBA 850 m. When multiple flux density measurements at the same wavelength are available, we use WISE W3 and W4 in preference to IRAS 12 and 25 m, and Planck 850 m in preference to SCUBA 850 m.

### 2.2 Gas masses and distances

For the comparison between the dust masses and the ISM content, we require HI data for our galaxies. The integrated flux of H is obtained from different surveys, detailed in table 2

The molecular gas mass () is calculated from global (non-interferometric) observations of the CO(J: 1-0) line (expressed in terms of the velocity-integrated flux or L [K km s pc] Solomon et al. 1997 ) and the conversion factor (Solomon & Vanden Bout 2005; Bolatto et al. 2013). The correlation between the galaxy metallicity and the value (Leroy et al. 2011; Sandstrom et al. 2013) shows that the takes values to times the Galactic value for sources with metallicities (12+log(O/H)) smaller than 8.2. In our sample, the stellar mass ranges between and . Over this stellar mass range, metallicities are expected to be between 8.4 and 9.1 (Tremonti et al., 2004): over this limited metallicity range, it is valid to use a constant value of (Leroy et al., 2011). In our study, we use [ (K km s pc] which includes a correction for heavy elements of 36% (Bolatto et al., 2013).

Galaxy distances are derived from the redshift listed in 2MRS or the NASA/IPAC Extragalactic Database (NED)4 except for very nearby galaxies (z 0.045; Mpc) for which we use distances from the Extragalactic Distance Database (EDD) 5.

### 2.3 AGN contamination

Since our study is focused on dust emission, it is crucial to discard galaxies in which the IR and sub-mm fluxes are highly contaminated by AGN emission. We use the Véron-Cetty & Véron (2010) catalog to identify and discard sources with AGN. This catalog contains 168,941 objects at redshifts between 0 and 6.43 (from which 5,569 are at z0.1). We discarded all (345) sources in our sample which fall within 30 of any source in the Véron-Cetty & Véron (2010) catalog. Additionally, using the AGN selection criteria showed by Cluver et al. (2014) based on WISE colors (using filters W1,W2 and W3), we rejected 43 galaxies. Finally, we excluded all (73) sources with Rayleigh-Jeans (RJ) () spectral slope significantly lower than that expected from a gray-body with and =15 K, since for these sources the emission in the RJ regime is likely contaminated by synchrotron emission. In other words, these and T values imply the exclusion of all sources with colors: , and where , and are the Planck fluxes at 350, 550 and 850 m, respectively.

### 2.4 Final sample

Since our analysis requires accurate fitting of dust model SEDs from IR to sub-mm data, we restrict the two samples above to only those galaxies for which meaningful spectral fits are found (see Sect. 4.1). The final sample - with dust SED fits - comprises 1,630 galaxies, which all have reliable M estimations. Of these galaxies, 136 are CO-detected and 1,230 have HI masses. From visual inspection of the SDSS and 2MASS images we classified 87 galaxies as interacting in the sample.

The redshift distribution of the final sample is shown in the left panel of Fig. 2. The median redshift is z=0.015 for the entire sample, with a mean of 0.012 and sigma = 0.011. For the subsample of galaxies with CO measurements, the median value is z=0.0066. with mean of 0.0032 and sigma of 0.0042. The distribution of the number of photometric data points (between 12 m and 850 m) per galaxy is shown in the right panel of Fig. 2: 21% of the sample have more than 6 photometric points, 67% have five, and only 12% have four photometric points. The subsample of galaxies with CO observations has a median of 6 photometric points per galaxy; 59% of these galaxies have 6 photometric data points and only have four photometric data points. In all cases we cover both sides of the emission peak at 100 m; for the few galaxies with only 4 photometric data points, these are distributed as 2 or 3 points at and 1 or 2 at .

## 3 Modeling Dust emission

The DL07 model describes the total galaxy spectrum by a linear combination of one stellar component, approximated by a black body with a specific color temperature T, and two dust components. One component with dust fraction = (1 - ) is located in the diffuse interstellar medium (ISM) and heated by a radiation field with constant intensity ; the other component with dust fraction = is exposed to a radiation field generated by photo-dissociation regions (PDRs) parametrized by a power-law , over a range of intensities , with .

Thus, the canonical model emission spectrum of a galaxy is:

 \emphf modelν=Ω∗Bν(T∗)+Mdust4πD2L[(1−γ)p(0)ν+γpν] (2)

where is the solid angle subtended by stellar photospheres, M is the dust mass, is the luminosity distance, and is the emitted power per unit frequency per unit dust mass from dust heated by a single starlight intensity . The dust is a mixture of carbonaceous and amorphous silicate grains characterized by the polycyclic aromatic hydrocarbon (PAH) index, , defined as the percentage of the total grain mass contributed by PAHs with less than Carbon atoms. Finally, is similar to the previous term but for dust heated by a power law distribution of starlight intensities extending from to . For a known galaxy distance, the canonical dust model is thus characterized by eight free parameters: and M.

The use of all eight free parameters in the DL07 model requires extensive observational datasets and it is computationally demanding. For the former reason, we limit the number and range of the free parameters as follows: (a) we use the Draine & Lee model library (available on the web 6). That library uses a limited parameter range for and in Eq. 2; in which takes 11 values between 0.01 and 4.58, takes 22 values between 0.10 to 25.0 and takes 5 values between to (as a reference, U = 1 corresponds to the starlight intensity estimate for the local ISM) and fixed the value ; (b) we follow Draine et al. (2007), who show that the dust emission of the galaxies of the KINGFISH sample can be well fitted using DL07 models with fixed value of ; (c) the stellar component, the first term in Eq. 2, is significant only at . Given that we use photometric data at , + we do not require to use this stellar component. To test the influence of the stellar component in fluxes at 12 and 22 m, we extrapolate the power law obtained from fluxes at 3.4 and 4.6 m(W1 and W2, respectively), deriving an influence of 4% and 1% at 12 and 22 m, respectively. This means that the stellar component does not affect our dust emission results. In summary: two parameters ( and T) are not used since we do not model the stellar component, two parameters ( and ) are fixed to a single value, two parameters ( and ) are limited in their range, and only M and are allowed to vary freely (the M is fixed after the minimization described below in Eq. (4) and runs between 0.0 and 100 in steps of 0.1). With these restrictions we generate 24,200 template SEDs, with luminosities per dust mass (/M) in and wavelengths () in . Each observed galaxy SED is fitted to each of the 24,200 SED templates solely by varying M. The best fit value of M is calculated by the minimization of , where

 χ2≡∑i(Fobsi−Mdust⟨\emphf modelν⟩i)2(σobsi)2 (3)

Here is the observed flux at the i band in Jy with an error and is the DL07 template flux per unit dust mass in units of , convolved with the response function for the i band.

The minimization of the Eq. 3 gives:

 Mdust[ M⊙]=N∑i=0Fobsi⟨\emphf modelν⟩i(σobsi)2⎛⎜ ⎜ ⎜⎝N∑i=0⟨\emphf modelν⟩2i(σobsi)2⎞⎟ ⎟ ⎟⎠−1 (4)

The accuracy of the fit is parametrized by the reduced value.

For this best fit value of M  (and for each of the 24,200 SED templates) we calculate the template spectrum from Eq. (2) and obtain the total infrared [8 to 1000 m] luminosity (L) following:

 L=∫λmaxλminLν(λ)×cλ2[ L⊙] dλ (5)

Instead of using only the final best fit template for a given galaxy, it is more robust to use a final template fit (FTF) which is the weighted mean of all templates for which . Thus, the values of M and L are calculated as the geometric mean, weighted by the individual , of all templates which satisfy our criteria.

Given that the dust in the DL07 models is distributed in two components (diffuse and PDR, each with a different radiation field intensity) a large range of dust temperatures is present. For several reasons - especially to search for systematic changes with other parameters - it is useful to characterize the dust as having a single, or at most two, temperature(s). We use two methods to characterize the effective temperature(s) of the FTF. We calculate the luminosity weighted temperature (T) of the FTF, defined as:

 Tweight[K]=N∑i=0bλi Lλ,i(N∑i=0Lλ,i)−1 (6)

where b is the Wien’s displacement constant ( 2,897 []), and is the monochromatic luminosity at wavelength . We also fit a two-temperature dust model to the FTF of the galaxy, using a cold dust component and a warm dust component , each described by a gray-body spectrum:

 Stot=A1νβB(ν,Tcold)+A2νβB(ν,Twarm) (7)

where is the frequency, and are normalization factors for each gray-body, is the dust emissivity index (assumed to be the same for both components)7, and and are the Planck functions for the cold and warm dust components, respectively. The fit was performed using the MPFIT code8, which uses a robust minimization routine to obtain the best fit. The two-temperature dust model fits were performed over the wavelength range 22 - 1000 m; wavelengths shorter than 22 m were not used to avoid the complexity of the PAH emission features.

In this work we use dust mass (M) obtained from the DL07 fits, i.e. from the FTF. However, for comparison, we also calculate the dust mass implied by the two temperature dust model fit (). The total dust mass of the two temperature dust model fit is calculated as follows: (see Dunne & Eales 2001):

 M2gbdust=S850D2Lκ850×[NcoldB(850,Tcold)+NwarmB(850,Twarm)] (8)

where , , and are the observed flux, the dust emissivity and the black body emission at 850 m, respectively, and are the dust temperatures of the cold and warm components, and and are the relative masses of the cold and warm dust components. Using the SLUGs sample, Dunne et al. (2000) obtained a dust emissivity value of . However, more recent works support lower emissivity values at 850 m: (Draine, 2003), i.e. higher dust masses for a given observed flux. In our study, we use the latter value to calculate the dust mass using the two dust components.

## 4 Results

### 4.1 Spectral fits

Using the procedure outlined in the previous Section, we were able to obtain a FTF for 1,630 galaxies. The distribution of the obtained for these fits are shown in Fig. 3: the median value is and of the spectral fits satisfy .

For our sample, the DL07 dust model fits result in the following parameter ranges. ranges between 0.0 and 0.02 with a median value equal to 0.01; 75% of the sample have in the range between 0.2 to 3.0, with a typical value equal to 1.5; shows a typical value 3.19, and 91% of the sample are best fit with templates based on Milky Way models (see Appendix A for more details).

Figure 4 shows eight example SED fits - both DL07 model fits and two temperature component fits - to galaxies in our sample. Clearly, when observed fluxes at 25 m  are absent, a large number of DL07 templates can be fitted: these templates show large differences at , but are similar at wavelengths in the Rayleigh-Jeans tail (). However, as shown by the robustness test (Section 4.2 and Appendix B) for a two-temperature component fit, the warm dust component (blue spectrum) is not affected by the absence of an observed flux at 25 m if we follow our fitting criteria (see Section 3 and Appendix B). In a similar way, the cold dust component (red spectrum) does not vary significantly between different templates, as long as the galaxy has at least one measurement in the Rayleigh-Jeans tail. The figure also illustrates that the two temperature component model (green spectrum) reproduces well both the best fit SED (yellow spectrum) and the final template fit used by us (FTF; black spectrum).

To obtain the typical SEDs of galaxies with normal (MS) and high (SB) sSFR, we use the geometric mean (weighted by ) of all MS and SB galaxies. The left panel of Figure 5 shows the composite SED of all 875 MS galaxies (red spectrum) and all 26 SB galaxies (blue spectrum), where the SB galaxies have . We also show the composite SEDs of two ‘cleaner’ sub-samples: those closest to the MS (, orange spectrum) and those with the highest SFR in our sample (, purple spectrum).

For each individual composite (MS and SB, Figure 5 middle-panel) SED, the dispersions are small in the RJ tail: they are thus easily distinguishable from each other at wavelengths longer than , as long as a good short-wavelength (25 m) point is available for relative normalization. The largest differences between the two template spectra are seen near the FIR peak: high sSFR (SB) galaxies have a more dominant warm dust component: thus their emission peak is shifted to smaller wavelengths and the width of the peak is larger.

To compare our composite SEDs to those of galaxies with well characterized SEDs, we use the spectra available in the SWIRE template library (Polletta et al., 2007)9. The SWIRE templates, which are based on the GRASIL code (Silva et al., 1998), contain SEDs for ellipticals, spirals and starburst galaxies

The composite SED of our galaxies closest to the MS is compared to templates of Sa (black line) and Sc (green line) spiral galaxies (the Sb template is not shown as it is very similar to that of Sa galaxies) in the middle panel of Fig. 5. Clearly, there is a good agreement - within the 3 dispersion - for ; at shorter wavelengths the stellar component, present in the Sa and Sc templates but not in our MS composite, is the main reason for the observed differences. The composite SED of our highest sSFR sub-sample is compared to the spectrum of Arp220 (gray), IRAS 22491-1808 (green) and IRAS 19254-7245 South (black) in the right panel of Fig. 5. The latter three spectra show a shift of the emission peak to shorter wavelengths compared to our SB composite SED, and IRAS 22491-1808 and IRAS 19254-7245 South show large absorption features at 25 m which are not seen in our composite SED or indeed in any individual DL07 template.

### 4.2 Robustness of the SED fitting

To test the robustness of our SED fitting, we examine 24 galaxies of our sample with 7 photometric observations. Then we explore how the M,L, dust temperatures (cold and warm), quantity of SEDs, and reduced vary with the amount of points and the rejection of specific points (e.g., how it is affected by the rejection of the flux at 12 and 22 m or at 350 m). The result of this test reveals that our results are very robust, with the parameters showing factors of difference smaller than 0.1 (for M, L , and dust temperatures). This means that the final results and relations obtained in our work, are robust and not affected by the amount of points or the distribution in wavelengths of them (following our SED fitting criteria, see Section 3). For more details, see Appendix B.

### 4.3 Star formation mode

The SFR is often estimated from the IR (integrated between 8 to 1000 m) and ultraviolet () luminosities (e.g., Murphy et al. 2011; Santini et al. 2014). Santini et al. (2014) suggest that both luminosities together provide the best estimate of SFR, but if only one is available, then L, rather than UV luminosity, is the more reliable. We estimate the SFR for our sample galaxies using L derived from our DL07 model fits and the relationship in Kennicutt (1998), (assumes a Salpeter initial mass function) which assumes a

 SFR [ M⊙yr]=1.78×10−10 LIR [L\sun]. (9)

The top panels of Figure 6 show the L distribution (black histogram) for our full sample. Infrared luminosities are to with a typical error of 13% and median value of . Comparing the L measured for the KINGFISH galaxies and our final sample with good SED fitting, we obtain a median ratio of 1.4. The bottom panel in Figure 6 shows the distribution of the stellar mass (M), which ranges between and with a median value of and typical error of 20%.

Figure 7 shows all our sample galaxies in the SFR-M plane. The sample covers roughly three orders of magnitude in both SFR and stellar mass, and are distributed on both sides of the locus of the Elbaz et al. (2011) MS line. Given the cutoffs in sSFR we use for SB, MS, and passive galaxies (see Sect. 1) the percentages of these sub-groups in our sample are 2.0%, 58.9% and 15.%, respectively. In on equivalent maner, the Elbaz et al. (2007) MS (dotted red line in figure 7) is used, the same sSFR displacements from the MS are used to define MS, SB and PAS galaxies, we see no great changes in the number of MS galaxies. However, the number of SBs increases (factor 1.8) and PAS galaxies decrease (factor 4.6).

### 4.4 Dust Masses, Temperatures, and emissivity index (β)

The presence of multiple dust temperatures in the DL07 models (see Sect. 3) precludes the direct application of Wien’s law to the model template (and thus our FTF) in order to obtain a dust temperature. For this reason we use two temperature component model fits to the FTF to parameterize the dust temperature (see Sect. 3). Figure 8 shows the distributions of the gray-body emissivity index (), the temperatures of the cold (T) and warm (T) dust components in the two temperature component fits, (eqn. 7), and the luminosity weighted dust temperature (, eqn. 6). In agreement with previous results (e.g Dunne & Eales 2001, Clements et al. 2010, Clemens et al. 2013) for nearby galaxies, our fitted values of are distributed over 1.3 - 1.9, with a median of 1.7 (Fig. 8). The distributions for the sSFR-classified sub-samples are significantly different: PAS galaxies show the lowest values ( median ), MS galaxies typically show values in the range =1.3 - 1.9 with , and SB galaxies typically show values of =1.7 to 1.9 with . Similar differences are seen in the distributions of, and median, temperatures of the cold dust component: the median temperature of the cold dust component is 21.4 K for PAS galaxies, 23.6 K for MS galaxies, and 27.1 K for SB galaxies.

For the full sample, the warm dust component (from the two component fit; Fig. 8) shows a median value of T=57 K. Unexpectedly, the PAS galaxies show the hottest warm components, though the relative luminosity of this warm component is neglible w.r.t. the luminosity of the cold component. MS galaxies have warm component temperatures distributed relatively tightly around T=57 K while SB galaxies show a more uniform spread in the distribution of T. In relative luminosity, however, the SBs are more dominated by the warm dust component: SB and MS galaxies show a median warm component luminosity to total luminosity (cold plus warm component) ratio of 0.01 and 0.14, respectively. If, instead, the FTF is characterized by the weighted dust temperature, the full sample shows a median weighted temperature of 24.1 K. PAS, MS and SB galaxies are clearly separated in T, with median values of 21.0, 25.2 and 31.1 K, respectively.

Figure 9 shows the distribution of the dust masses, as derived from the DL07 model fits (see Sect. 3), for the entire sample (black), and for the different sSFR sub-samples (SB in blue, MS in red and PAS in green). In the full sample, dust masses range between and , with a median value of and an estimated typical error of 20%. This median value is similar (considering our errors) to that obtained by Clemens et al. (2013) (), who used MAGPHYS modeling. Note that they corrected their model results to an emissivity value of , the same value assumed in our dust mass estimations from two dust components and in agreement with the results obtained with the DL07 templates (see below). Passive galaxies tend to have lower dust masses than MS and SB galaxies. The median dust mass for PAS, MS and SB galaxies are , , , respectively. For the two temperature component models, the cold dust component dominates the total dust mass: the median contri4bution of warm dust to the total (warm plus cold) dust mass () is 0.2%, with 97% of the sample at 1%. The highest values of (up to 4%) are seen in SB galaxies.

A comparison of the dust masses derived using DL07 models to the dust masses derived from our two component fits is shown in Figure 10. Clearly there is a systematic difference in the two values. Recall that the two component model was obtained via fits to the DL07 FTF fit rather than a fit to the individual photometric data points. The dust mass ratios show a median of 0.91, and the best fit relating the two dust masses (see Fig.10) is:

 M2gbdust[ M⊙]=10−0.34±0.06(MDL07dust[ M⊙])1.04±0.01 (10)

The symbol colors (by IR luminosity) clearly reveal that the inconsistency in the DL07 and two-component derived dust masses is correlated to the IR luminosity: sources with lower L show relatively higher DL07 model dust masses, while sources with higher L have relatively higher two gray-body-fit dust masses. Alternatively, the difference in the two masses is related to the dust temperature of the cold component, showing an increment from the bottom left corner to the right top corner for the points in the figure. The difference in masses is likely a result of the DL07 models using a more complex calculation of dust mass for a given dust luminosity, i.e., different grain types and sizes related to the parameter (see details in Draine et al. 2007), while the dust mass of the two temperature component fit is derived via a single emissivity index. In any case, the difference in dust masses is less than 0.2 dex (factor of 1.58), so these differences are relatively unimportant in the correlations presented in the following sections (which use the DL07-derived dust masses).

### 4.5 LIR, Mdust, and  Tdust Plane

The relationship between dust mass, dust temperature, and dust luminosity (L) is in general well understood (e.g., Draine & Li 2007, Scoville 2012): when dust grains absorb UV photons from young OB stars, they are heated and re-emit their energy at IR wavelengths. Clemens et al. (2013) have shown a strong correlation between the SFR/M ratio and the dust temperature of the cold dust component, especially for sources with T K. Our sample shows a similar correlation, and our larger sample size allows us to clearly demonstrate that all galaxies lie in a single plane, which we refer to as the dust plane, in the L in the L (thus SFR), M and T phase space (similar to the relation shown by Genzel et al. 2015).

Figure 11 shows a projection of this dust plane in our sample: in this case we plot L vs. M and color the symbols by the (cold component) dust temperature. The dashed black lines delineate the L-M relationships for different cold component dust temperature bins, and the purple line shows the relation between L and M obtained by da Cunha et al. (2010). Here the dust temperature used is that of the cold component of the two component fit; this is the dominant component, in mass and luminosity, for all galaxies in the sample. The best fit to this dust plane is:

 Missing or unrecognized delimiter for \left (11)

Clearly, the placement of a galaxy in the dust plane is most sensitive to the temperature of the cold component, rather than the values of M and L. For example, if the dust temperature is constant and we change M by a factor of 10, the L is required to change by a factor of 12. However, increasing T by 10 K, with constant M, requires L to increase by a factor 80. An increase in L is more easily achieved by increasing the dust temperature rather than the dust mass. The data of Clemens et al. (2013) are consistent with a plane similar to that defined by Eq. 11. However, their data suggest higher values of both L and M for a given value of T.

If the luminosity weighted dust temperature (T) is used instead of T, the sample galaxies still fall on a single dust plane, though there is a larger scatter. In this case, the dust plane is parametrized by:

 Missing or unrecognized delimiter for \left (12)

If the temperature of the warm component (from the two components fit) of the dust is used instead of the temperature of the cold component, the sample galaxies no longer fall on a single dust plane.

The correspondence between interacting galaxies and SB galaxies is one-to-one only for extreme starbursts: of all interacting galaxies in the sample, only those with high cold-dust component temperature ( K) and high SFR (, i.e. LIRGs) are classified as SBs.

While the dust plane provides a powerful tool to relate the dust mass, total IR luminosity and dust temperature of the cold component, or derive any one parameter from the other two, the comprehensive dataset available for our large local sample is difficult to obtain for other samples, especially those at high redshift. We thus provide several scaling relationships which can be used to estimate the location of a galaxy in the dust plane in the presence of limited data or, alternatively, to derive one or all parameters of the dust plane phase space.

Since the dust plane is most sensitive to changes in T, we present several relations to estimate its value using sub-mm to IR colors. Previous works, e.g., Soifer et al. (1987); Chanial et al. (2007); Hwang et al. (2010), have typically derived dust temperatures from IRAS colors: IRAS 60/IRAS 100. Here we present that based on the 100 m and 350 m color; see Appendix D for the equivalent results from other IR to sub-mm colors. The relationship between the cold component dust temperature and the 100 m to 350 m flux ratio is shown in the right panel of Figure 12. The best fit to this relationship is:

 Tcold[K]=10(1.280±0.001)(\emphf100\emphf350)(0.160±0.001) (13)

To obtain a cleaner relation, large crosses in Figure 12 show the mean value of T in bins of 0.5 mag in the color . Interestingly, the coefficients of the best fit (red dashed line) show that the values are consistent within the errors with the coefficients obtained for the complete sample.

Both the dust mass and the total IR luminosity can be estimated from a single monochromatic luminosity in the RJ tail of the dust emission. The dependence of M and L on the 350 m luminosity is shown in the left and middle panels of Fig. 12, respectively. At first glance, these relationships appear to have a large scatter. However, it is clear that this scatter can be fully explained (and removed) by the use of the temperature of the cold dust component. Thus the estimation of M and/or L can be made very accurately in the presence of an estimate of the cold dust temperature (see previous paragraph) or at least roughly in the absence of a cold dust temperature. We will address both scenarios below for the case of using the 350 m luminosity for the RJ tail luminosity (see Appendix E and F for the results of using other sub-mm frequencies).

Using the monochromatic luminosity at 350 m in the presence of a value for T, we obtain two planes to determinate L or M:

 log(LIR[ L⊙])−1.017 log(L350[WHz−1]) (14)
 −0.118 (Tcold, dust[K])+16.45=0 (15)
 log(Mdust[ M⊙])−0.940 log(L350[WHz−1]) (16)
 +0.0791 (Tcold, dust[K])+12.60=0 (17)

In the absence of a T estimation, one has to accept the full scatter seen in the left and middle panels of Fig. 12, i.e. a dispersion of 0.5 dex and 1 dex in the estimation of M and L from a single 350m luminosity. The best fit to the data points (blue lines in Figure 12, right and middle panels) is:

 LIR[ L⊙]=10−14.388±0.002(L350[WHz−1])1.046±0.005 (18)
 Mdust[ M⊙]=10−13.963±0.002(L350[WHz−1])0.920±0.005 (19)

Estimations of the dust mass and IR luminosity from other monochromatic IR or sub-mm fluxes, and estimates of the temperature of the cold dust component from other IR and sub-mm colors can be found in Appendix D, E and F.

### 4.6 Dust to Stellar Mass Ratio

The typical ratios are 0.21% and 0.25% for our entire sample and for all star-forming (non-passive) galaxies, respectively. These ratios are smaller to those obtained by Clemens et al. (2013) (median in a well defined sample of 234 nearby galaxies detected by Planck) and Clark et al. (2015) (median in the HAPLESS sample, a blind sample of 42 nearby galaxies detected by Herschel). Other three works, using the MAGPHYS code, show similar values for the dust to stellar mass ratio. da Cunha et al. (2010) shows a value between 0.23% to 0.14% depending on the stellar mass bin used in a sample of 1658 galaxies at z ¡ 0.1; Smith et al. (2012) obtain a dust to stellar mass of 0.22% from a sample of 184 galaxies at ; while Pappalardo et al. (2016) show a value of 0.18% in its main sample.

An anticorrelation between the M/M and M has been shown by Cortese et al. (2012, ; in Virgo cluster galaxies), Clemens et al. (2013) and Clark et al. (2015).

We see the same anticorrelation in our sample (Figure 13), with the points showing a large dispersion. The fits to our full sample (FS) (purple line) and to all our star-forming (SF) galaxies (non-passive galaxies; black line), are:

 MdustM∗=10−0.4±0.2(M∗[ M⊙])−0.28±0.02  FS (20)
 MdustM∗=10−1.3±0.2(M∗[ M⊙])−0.12±0.02  SF (21)

When we separate the galaxies by star-forming mode (bottom panels of figure 13), we find two interesting results: (a) SB galaxies show a much steeper anticorrelation than the other sub-samples, and (b) the source of the scatter in the anticorrelation can be traced by the temperature of the cold dust component, T (or the weighted dust temperature ). The anticorrelations obtained individually for each subsample are:

 MdustM∗=107.4±0.8(M∗[ M⊙])−0.92±0.08  SB (22)
 MdustM∗=10−2.1±0.2(M∗[ M⊙])−0.09±0.01  MS (23)
 MdustM∗=10−1.2±0.4(M∗[ M⊙])−0.17±0.04  PAS (24)

Essentially, the dust to stellar mass ratio in SB galaxies (typically 1.3%) is higher than that in MS galaxies (typically 0.24%), though the difference is smaller for galaxies at the highest stellar masses. Passive galaxies show a very low dust to stellar mass ratio, with a typical value of . Additionally, for all sSFR groups, at a given stellar mass, the galaxies with the highest T () have the smaller dust to stellar mass ratios.

### 4.7 Dust to Gas Mass Ratio

To more easily study the relation between dust and gas masses, we separate the total gas mass (hereafter referred to as interstellar medium mass or ) into two components: the molecular gas mass (), and the atomic (Hydrogen) gas mass (): . Figure 14 shows the relation between the dust mass and the atomic (left panel), molecular (middle panel) and total (right panel) gas masses.

The median gas fraction () for the full sample is %. The medians for MS, PAS, and SB galaxies are %, % and %, respectively. For all sources with HI and CO measurements, the molecular to atomic gas mass ratios () show a median value of . Even for MS and PAS galaxies is observed the same value, however SB galaxies show a huge value (). (see Table 3).

The median values of are 1.6 % and 1.3% for the galaxies with both and and for those with only measurements, respectively (see tables 3 and 4). These values are smaller than those obtained by Clements et al. (2010, 2.2%) and Clark et al. (2015, 3.9%). PAS galaxies show the highest dust to atomic mass ratios, followed by SBs and finally MS galaxies. The median dust to molecular gas mass ratio is 2.1% for all galaxies with both and , and 2.0% for all galaxies with only . Passive galaxies show the largest dust to molecular gas mass ratios followed by MS galaxies, with SB galaxies showing the lowest values. The median dust to ISM mass ratios are similar for the full sample, MS and SB galaxies (, and , respectively), while PAS galaxies show larger values ().

Figure 14 shows a clear correlation between dust mass and molecular and atomic gas mass, individually. But the correlation between dust and  shows the smallest dispersion, with the best fit:

 MISM[M\sun]=6.03(Mdust[M\sun])0.7 (25)

This correlation between ISM and dust mass has been noted previously by Leroy et al. (2011, in five Local Group galaxies) and Corbelli et al. (2012, in 35 metal-rich Virgo spirals).

The dust to gas ratio () does not systematically vary with the stellar mass for our sample galaxies (Fig. 15), despite the expected metallicity range (between 8.4 and 9.1) for this stellar mass range (M[]) (Tremonti et al., 2004). Our full sample shows a large scatter in (0.5 dex), but the scatter significantly decreases when considering SB, MS, and PAS galaxies separately. MS and PAS galaxies show a dispersion in of 0.3 dex, and SBs show a dispersion of only 0.2 dex. The median values of for MS and SB galaxies (red and blue lines in Fig. 15, respectively) are very similar to the median value of the full sample; however, PAS galaxies show a higher median (green line in Fig. 15). Additionally, the symbol colors show that the galaxies with higher gas fractions have lower values of , especially MS and PAS galaxies.

## 5 Discussion

We have modeled the dust emission using detailed DL07 dust models in an unprecedentedly large sample of 1,630 nearby (, ) galaxies with uniform photometric data from WISE (3.4 to 22 m), IRAS (12 to 100 m), Planck (350 to 850 m) and/or SCUBA (850 m). This sample covers a significant parameter space in stellar mass and SFR, and thus sSFR, going from starburst (SB; LIRGs; ) to passive (PAS; ) galaxies.

In comparison, previous studies that present detailed dust models to galaxies with sub-mm data include the KINGFISH/SINGS sample (Dale et al., 2012) of 65 nearby, normal () spiral galaxies with photometry from IRAS, Spitzer, Herschel, and SCUBA, and the ERCSC sample Negrello et al. (2013); Clemens et al. (2013) of 234 local () galaxies with photometry from IRAS, WISE, Spitzer, Herschel and Planck. The ERCSC sample was created by matching four Herschel samples, HRS, HeViCS, KINGFISH and H-ATLAS, to the Planck Early Release Compact Source Catalogue.

Note that the other large nearby sample of galaxies with dust modeling results, the sample of 1,658 galaxies in da Cunha et al. (2010), used MAGPHYS modeling applied to UV, optical, and limited IR data (2MRS, IRAS): the lack of sub-mm data is expected to lead to less reliable dust mass estimates (e.g., Draine et al., 2007).

The advantages of our sample over the ERCSC sample include: a) a sample size times larger with equivalent and consistent data observations; b) the use of the Second Planck catalog of Compact Sources, which contains only reliable detections (in this release the Planck collaboration separated the less reliable detections into a separate ’excluded’ catalog which we do not use); c) the fact that the catalogs of the Planck second release are deeper than those of the Early Release; d) the use of flux corrections to the Planck catalog fluxes (Nagar et al., submitted) to ensure consistency with the SCUBA flux scale.

We remind the reader that all galaxies fitted with dust models had between four and seven photometric points distributed between 12m and 850m. In all cases these points populated both sides of the SED peak with 2 photometric points shortward of and one photometric point at . A further indication that the available number of photometric points sufficiently constrained the fitted SED is that all templates matched to the photometry with have similar spectral shapes and parameters (such as M or L), despite the extremely large number of templates (24,200) in our work.

The differences in the dust masses obtained by us and those obtained by Draine et al. (2007, ; who used similar modeling but more extensive photometric data at ) in 17 KINGFISH/SINGS galaxies, ranges between 0.3 dex and 0.4 dex, with a median of 0.07 dex. The equivalent differences in the IR luminosities obtained by us and those obtained by Draine et al. (2007) range between 0.017 dex and 0.5 dex with a median of 0.14 dex. The largest discrepancies are seen in galaxies (e.g., NGC 6946) for which Draine et al. (2007) did not use sub-mm data. More recent results on the dust modeling of the KINGFISH/SINGS sample, which includes sub-mm fluxes for all 64 galaxies of the sample has been done in Dale et al. (2012), but the dust masses and IR luminosities obtained from the model fits were not explicitly listed. Additionally, the values of L and L calculated from the dust model fits are in overall agreement with those estimated from IRAS fluxes using the Sanders et al. (1991) equations. In fact we use our SED-derived L and L values to recalibrate the equations to estimate these values from only IRAS photometry (Appendix E).

In general, the advantage of our samples, compared to each sample which makes it up (listed in table 1), is that now we have more than one sub-mm data (usually this samples contain only one SCUBA data at 850 m, e.g. the SLUGS sample), for sources with high sub-mm emission (flux at 850 1 Jy). Even, many of these samples have sub-mm information (e.g., 2MRS, ATLAS-3D, FCRAO, Sanders et al. (1991), etc.), for first time. This means that for the first time, we have a large amount of nearby galaxies (more than ten times larger than previous works) with sub-mm information. Additionally, as a consequence of the all-sky observation by Planck, our sample reduced its selection effects only to the cutoffs of Planck (its reliable zones), without selection effects for a specific kind of galaxy, e.g., the KINGFISH/SINGS sample only select star forming galaxies.

### 5.1 Interpreting the dust temperature

We can interpret the dust temperature of the cold component (T) as the equilibrium temperature of the diffuse ISM. This interpretation is supported by the strong correlation between T and the starlight intensity parameter of the diffuse ISM () in DL07. This correlation has been demonstrated by Aniano et al. (2012, in a sample of two resolved galaxies) and used by Ciesla et al. (2014, in the HRS sample) to compare their SED fitting results with the results of other works. The problem with this interpretation is that the temperature of the diffuse ISM (thus T) is not expected to correlate with the SFR (produced in PDRs rather than the diffuse ISM). However, the dust plane shown here implies a close connection between L, M and T (see Section 4.5). Furthermore, the SFR - M relation also shows a dependence on T: T increases as one moves from sources with higher M and lower SFR to sources with lower M and higher SFR. To solve this contradiction, Clemens et al. (2013) propose that the lower dust masses in star-forming regions allow the escape of UV photons thus increasing the starlight intensity impinging on the diffuse ISM, which in turn would increase its temperature.

In agreement with the Clemens et al. (2013) results, we find that L, M and other parameters do not correlate with the warm dust component temperature (T). The parameters and (the percentage of dust mass PDRs) show only a weak correlation with T. Nevertheless, the importance of using a warm component is that when it is used the cold component temperature (T) (rather than the temperature obtained from a single component fit) shows much cleaner correlations with L, M, and the dust plane, and also better explains the systematics in, e.g., the M/M vs. M anticorrelation. Further, T, rather than, e.g., T, is more cleanly correlated with the IR to sub-mm colors.

It is useful to compare the luminosity weighted dust temperature () with the temperatures obtained from the two component fits, since is independent of our assumptions made in the two component fits. Figure 16 shows the relationship between and the T: the scatter in the data points is primarily correlated with T. The tightest correlation is found for MS and PAS galaxies with T  58 K. SBs and Intermediate SB galaxies (typically at T  58 K) show a larger scatter. A cleaner correlation is observed if we compare with a temperature obtained from a weighted addition of T and T, where the weights are the respective flux fractions (e.g. ). That is, the increase in the scatter seen in Figure 16 for T  58 K is a consequence of the increment in the fractional flux of the warm component. The use of instead of T in all the relevant relations presented in Sect. 4 produces similar results but with a larger scatter. Furthermore, IR and sub-mm colors (see appendix D) can be used to estimate T with a smaller scatter than .

We obtain a better estimation of the dust temperature of the cold component using a color. This color is based on a IR flux () and a sub-mm () flux. These estimates show a stronger relation than compared to using only two IR fluxes or only two sub-mm fluxes (e.g. the color 60 to 100 m ). The lowest end of our wavelength range (12 and 22 m) shows the least reliable estimates of T using an IR and sub-mm color. This is a consequence of the warm component influence within these fluxes. However, the shows a tight correlation with the color obtained using the flux at 22 m and one sub-mm flux, but not with the color at 12 m. This is a consequence to its proximity to the PAHs emission.

### 5.2 Dust mass as a tracer of total gas mass

Figure 17 shows the relationships between the atomic gas mass to stellar mass ratio, the L to stellar mass ratio and the dust to stellar mass ratio, with the distance of the galaxy from the MS (log (sSFR/)). These plots reveal that log (sSFR/) is weakly correlated with M and L, but tightly correlated with the dust to stellar mass ratio.

The evolution of the dust to stellar mass ratio as tracer of star formation mode (sSFR classification) was previously studied in galaxies within the redshift range by Tan et al. (2014), who use different dust to stellar mass ratios for normal star-forming galaxies and extreme SB galaxies (ULIRGs) over the redshift range 0 to 2. The largest difference was found at z0 where for normal galaxies they used the averaged value of the normal galaxies in the da Cunha et al. (2010) sample. In comparison, the normal galaxies in our sample show a large scatter ( 1.3 dex) in their dust to stellar mass ratios (see right panel of Figure 17), so that they overlap with the median dust to stellar mass ratio of extreme starbursts. This scatter is related to the gas fraction of these galaxies, where gas-rich galaxies show higher dust to stellar mass ratios. Our sample does show that SB and InSB galaxies have higher dust to stellar mass ratios than MS and PAS galaxies; in fact their dust to stellar mass ratios are higher than the data point of extreme SBs at z0 in Tan et al. (2014) even though our SBs and InSB samples are made up of LIRGs instead of ULIRGs. Thus overall, we observe median dust to stellar mass ratios higher than those used by Tan et al. (2014), and an overlap in the dust to stellar mass distributions of normal and SB galaxies.

Garn & Best (2010) have showed that galaxies with higher dust masses have higher stellar masses. However, in our work we reveal a more complex picture, in which the dust-to-stellar-mass ratio anticorrelations with the stellar mass, and the strength of the anticorrelation changes in sub-samples of galaxies separated by their star-forming mode (i.e. by sSFR; see Sect. 4.6). Thus, low stellar mass SB galaxies are dustier than massive PAS galaxies. This result is in agreement with the discussion in Clemens et al. (2013), where they conclude that despite () and M being directly proportional to metallicity (Z), galaxies with smaller M show higher /M and this effect prevails over the tendency of galaxies with smaller M to have smaller Z.

Passive galaxies of course show the lowest sSFR, dust to ISM mass ratios, and ISM to stellar mass ratios (Fig. 17). But Fig. 15 shows that even though PAS galaxies have smaller gas fractions, they have larger in comparison with MS and SB galaxies. That is, at low SFRs, decreasing SFR results in the ISM mass decreasing faster than the dust mass.

### 5.3 Estimating ISM mass from a single sub-mm measurement

The technique of using a single rest-frame monochromatic luminosity at 850 m to obtain a reasonably accurate ISM mass, developed by Scoville (2012); Scoville et al. (2014, 2016), is based on two primary assumptions: (1) a constant for galaxies with M between and , and (2) the assumption of a uniform dust temperature for all galaxies, justified because a change in factor in the dust temperature will introduce an error of only factor (0.3 dex) in the ISM mass. With these assumptions, (= /) can be used to convert a sub-mm luminosity to an ISM mass. In our sample the median value of is 12.56, with a rms of dex (Figure 18). This value is 0.44 dex (factor 2.8) lower than that obtained by Scoville et al. (2014) and 0.15 dex (factor 1.4) lower than that obtained by Hughes et al. (2017) using the VALES sample that contains 67 main sequence galaxies at 0.02 ¡ z ¡ 0.35. The scatter, and its systematics, could be explained by the two steps required to calculate . First, the conversion of L to M (e.g., Figs. 12 and 28) is relatively straightforward: the two quantities are highly proportional and almost all the scatter (factor 1.33 or 0.12 dex; take rms from the figure 12) seen in this relationship is a consequence of the variation of cold dust temperature. The conversion of dust mass to ISM mass, however, is subject to a larger (and dominant) scatter (rms=0.25 dex; Fig. 14). We note that we found no dependence of on either the IR luminosity or the galaxy stellar mass. The L values (colored bar in Figure 18) reveal that the Scoville (2012); Scoville et al. (2014, 2016) sample (large triangles) contains LIRGs galaxies, ULIRGs and galaxies with and do not show any correlation with the constant and the luminosity at 850 m. However, our galaxies (circles) show weak correlation between the