PACS photometry of the Herschel Reference Survey – Far-infrared/sub-millimeter
colours as tracers of dust properties in nearby galaxies
We present Herschel/PACS 100 and 160 m integrated photometry for the 323 galaxies in the Herschel Reference Survey (HRS), a K-band-, volume-limited sample of galaxies in the local Universe. Once combined with the Herschel/SPIRE observations already available, these data make the HRS the largest representative sample of nearby galaxies with homogeneous coverage across the 100-500 m wavelength range. In this paper, we take advantage of this unique dataset to investigate the properties and shape of the far-infrared/sub-millimeter spectral energy distribution in nearby galaxies. We show that, in the stellar mass range covered by the HRS (812), the far-infrared/sub-millimeter colours are inconsistent with a single modified black-body having the same dust emissivity index for all galaxies. In particular, either decreases, or multiple temperature components are needed, when moving from metal-rich/gas-poor to metal-poor/gas-rich galaxies. We thus investigate how the dust temperature and mass obtained from a single modified black-body depend on the assumptions made on . We show that, while the correlations between dust temperature, galaxy structure and star formation rate are strongly model dependent, the dust mass scaling relations are much more reliable, and variations of only change the strength of the observed trends.
keywords:galaxies: fundamental parameters – galaxies: ISM – infrared: galaxies
It is now well established that approximately half of the radiative energy produced by galaxies is absorbed by dust grains and re-emitted in the infrared regime (Hauser & Dwek, 2001; Boselli et al., 2003; Dole et al., 2006; Dale et al., 2007; Burgarella et al., 2013). Thus, observations in the 10-1000 m wavelength range provide us with a unique opportunity not only to quantify half of the bolometric luminosity of galaxies, but also to characterise the properties of cosmic dust. Moreover, since dust grains are crucial for the star formation cycle (Hollenbach & Salpeter, 1971), such information can give us important insights into the physical processes regulating galaxy evolution (e.g., Dunne et al., 2011).
Unfortunately, despite its paramount importance, we are still missing a complete and coherent picture of dust properties in galaxies across the Hubble sequence, and of the exact role played by grains in regulating star formation (McKee & Krumholz, 2010). Indeed, we know very little about the dust composition in galaxies outside our own Local Group (Draine & Li, 2007; Compiègne et al., 2011) and if/how it is regulated by the physical conditions experienced by grains in the inter-stellar medium (ISM). Hence, our estimates of dust masses in galaxies are still highly uncertain (Finkbeiner et al., 1999; Dupac et al., 2003; Gordon et al., 2010; Paradis et al., 2010; Planck Collaboration et al., 2011b).
Luckily, the last decade has seen the start of a golden age for observational far-infrared (FIR) and sub-millimeter (submm) astronomy, providing a new boost to the refinement of theoretical dust models (Meny et al., 2007; Draine & Li, 2007; Hoang et al., 2010; Compiègne et al., 2011; Steinacker et al., 2013). In particular, the Spitzer (Werner et al., 2004), and more recently Herschel (Pilbratt et al., 2010) and Planck (Planck Collaboration et al., 2011a) space telescopes are finally gathering a wealth of information on the dust emission from thousands of galaxies up to 2. Particularly important for a proper characterisation of dust in galaxies is the radiation emitted at wavelengths 100-200 m. In this regime, the integrated emission from galaxies originates predominantly from dust in thermal equilibrium, heated by the diffuse interstellar radiation field (ISRF), which represents the bulk of the dust mass in a galaxy (e.g., Sodroski et al., 1989; Sauvage & Thuan, 1992; Calzetti et al., 1995; Walterbos & Greenawalt, 1996; Bendo et al., 2010; Boquien et al., 2011; Bendo et al., 2012). Thus, by characterising the dust emission in the 100 m wavelength domain, we have a unique opportunity to provide strong constraints to theoretical models, and to refine our census of the dust budget in galaxies.
The first natural step in this direction is to quantify how the shape of the dust spectral energy distribution (SED) varies with galaxy properties across a wide range of morphological type, star formation activity, cold gas mass and metal content. This is necessary to determine if the amount of radiation emitted at each wavelength is simply regulated by the intensity of the ISRF responsible for the dust heating, or whether it retains an imprint of the chemical composition of the grains. Indeed, only after a careful characterisation of the physical parameters regulating the dust SED, will it be possible to properly convert observables into physical quantities such as dust temperatures and dust masses.
Many recent works (Gordon et al., 2010; Skibba et al., 2011; Davies et al., 2012; Planck Collaboration et al., 2011b; Galametz et al., 2012; Auld et al., 2013) have shown that, above 100 m, the dust SED is very well approximated by a simple modified black-body (but see also Bendo et al., 2012):
where is the flux density emitted at the frequency , is the dust mass absorption coefficient at the frequency , gives its variation as a function of frequency, is the galaxy distance and is the Planck function. Mounting evidence is emerging that is not the same in all galaxies (e.g., Rémy-Ruyer et al., 2013), and may also vary within galaxies (e.g., Galametz et al., 2012; Smith et al., 2012).
Modified black-bodies are simple models and cannot properly reproduce real dust properties (e.g., Draine & Li, 2007; Shetty et al., 2009; Bernard et al., 2010). Several dust components at various temperatures contribute to the total emission along the lines-of-sight. This implies the presence of temperature mixing that can cause variations of the infrared slope, and thus in the apparent emissivity index . Nevertheless, parameterization of the dust SEDs through modified black-body fitting is a powerful tool to help understand variations of dust properties with other galaxy characteristics, especially in case of sparse sampling of the FIR/sub-mm wavelength range (e.g., high-redshift galaxies Magdis et al., 2011; Symeonidis et al., 2013). Therefore, it is extremely important to determine in which cases a single modified back-body can be used, and how temperature and dust mass estimates are affected by the assumptions made on .
In order to ascertain the dust properties of galaxies in the local Universe, and to provide new constraints to theoretical models, we have carried out the Herschel Reference Survey (HRS, Boselli et al., 2010b), a Herschel guaranteed time project focused on the study of the interplay between dust, gas and star formation in a statistically significant sample of 300 galaxies spanning a wide range of morphologies, stellar masses (8log(M/M12), cold gas contents (-3log(M/M)1), metallicities (8.212+log(O/H) 8.9), and specific star formation rates (-12 log(SFR/M)-9). The combination of Herschel/SPIRE (Griffin et al., 2010) observations with the multi-wavelength dataset we have been assembling (Ciesla et al., 2012; Cortese et al., 2012a; Boselli et al., 2013; Hughes et al., 2013), has already allowed us to have a first glimpse at how the dust content and shape of the dust SED vary with internal galaxy properties (Boselli et al., 2010a, 2012; Cortese et al., 2012b). In particular, Boselli et al. (2010a, 2012) have shown that the slope of the dust SED in the 200-500 m interval decreases from 2 to 1 when moving from metal-rich to metal-poor galaxies. However, our analyses have so far been limited by the lack of data in the 100-200 m wavelength range for the entire sample.
Thus, in this paper we present integrated Herschel/PACS (Poglitsch et al., 2010) 100 and 160 m flux densities for all the HRS sample and take advantage of our multiwavelength dataset to perform a first analysis of the properties of the dust SED across our entire sample. Corresponding to the peak of the dust SED, the 100-200 m wavelength interval is crucial not only to properly quantify the shape of the SED, but also to accurately determine the average dust temperature and total dust mass in galaxies. These data make the HRS the largest representative sample of nearby galaxies with homogeneous coverage across the 100-500 m wavelength range. In addition to releasing our dataset to the community, our primary goals are 1) to investigate how the shape of the dust SED varies with internal galaxy properties, and 2) to determine whether the integrated dust SED of HRS galaxies can always be reduced to a single modified black-body with a constant value of and, if not, what are the possible biases introduced by this assumption. The results of SED fitting with the dust models of Draine et al. (2007) will be presented in a forthcoming paper (Ciesla et al., submitted.).
This paper is organized as follows. In Sect. 2 we describe the Herschel observations, data reduction, flux density estimates and comparison with the literature. In Sect. 3 we use the PACS and SPIRE colours to investigate how the shape of the dust SED varies with internal galaxy properties. In Sec. 4, we show how the dust temperature and mass obtained from fitting a single modified black-body to the Herschel data depend on the assumptions made on . Finally, the summary and implications of our results are presented in Sec. 5.
2 The data
2.1 The Herschel Reference Survey
The HRS is a volume-limited sample (i.e., 1525 Mpc) including all late-type galaxies (261 Sa and later)
with 2MASS (Skrutskie
et al., 2006) K-band magnitude K 12 mag and all early-type galaxies (62 S0a and earlier)
with K 8.7 mag
2.2 PACS observations and data reduction
The Herschel/PACS 100 and 160 m observations of HRS galaxies presented in this work have been obtained as part of various open-time Herschel projects.
The vast majority of the data (228 out of 323 galaxies) comes from our own Herschel cycle 1 open time proposal (OT1_lcortese1). Each galaxy was observed in scan mode, along two perpendicular axes, at the medium scan speed of 20″/sec. Two repetitions were done in each scan direction. The size of each map was chosen to match the size of our SPIRE images (see Ciesla et al., 2012), making sure to have homogeneous coverage across the entire 100-500 m range.
Maps for additional 83 HRS galaxies have been obtained as part of the Herschel Virgo Cluster Survey (HeViCS, Davies et al., 2010). HeViCS mapped the Virgo cluster with both PACS and SPIRE simultaneously at the fast scan speed of 60″/sec. The observing strategy consists of scanning each 44 deg field in two orthogonal directions, and repeating each scan four times (Auld et al., 2013). The faster scan speed of the Herschel parallel mode with respect to the scan map mode, used for our observations, is compensated by the higher number of repetitions performed in the Virgo cluster, making the two datasets highly comparable (i.e., within 30%) in terms of their final noise.
PACS observations for the remaining 12 HRS galaxies have been retrieved from the Herschel public archive, and come from various projects (i.e., Kennicutt et al., 2011, KPGT_esturm_1, OT1_acrocker_1, OT2_emurph01_3, GT1_lspinogl_2, OT2_aalonsoh_2). All data have been obtained in scan mode at the medium scan speed of 20″/sec and they reach a noise level similar or lower than our own observations. For one galaxy (HRS3) only 160 m observations are available as the object lies at the edge of the 100 m map, making the data not suitable for accurate photometry. Thus, in summary, all 323 galaxies in the HRS have been observed at 160 m, whereas 100 m data are available for 322 objects.
All raw PACS data were processed from Level-0 to Level-1 within HIPE (v10.0.0, Ott, 2010) using the calibration file v48. This pre-processing includes, among the other tasks, pixel flagging, flux density conversion and coordinate assignment. To remove the 1/ noise which, at this point, still dominates the timelines, the Level-1 data were fed into Scanamorphos (version 21, Roussel, 2013), an IDL algorithm which performs an optimal correction by exploiting the redundancy in the observations of each sky pixel. No noise modelling is hence needed. The pixel size of the final maps was chosen to sample at the best the point-spread-function, at the respective wavelengths, typical of the data taken at medium scan speed: 1.7 and 2.85 arcsec pixel at 100 and 160 m, respectively (i.e., FWHM/4). The typical pixel-by-pixel noise in the map varies between 0.1 and 0.25 mJy pixel at 160 m and between 0.04 and 0.1 mJy pixel at 100 m.
In order to show the data quality of the new observations presented here, in Fig. 1 we compare the PACS images for three of our targets with the RGB Sloan Digital Sky Survey (Abazajian et al., 2009) optical and SPIRE 250 m (Ciesla et al., 2012) images. We show an example of an early-type galaxy with dust lanes (HRS45, top row), late-type galaxy (HRS48, middle row) and un-detected elliptical and its spiral companion (HRS244/245, bottom row).
2.3 PACS 100 and 160 m integrated photometry
Integrated 100 and 160 m photometry has been performed following very closely the technique used by Ciesla et al. (2012) for the SPIRE data of HRS galaxies. This is crucial to properly combine the two datasets, and to characterise the shape of the SED across the entire 100-500 m wavelength range. Thus, whenever possible, we determined integrated flux densities within the same apertures adopted in Ciesla et al. (2012). The aperture sizes are adapted to include the entire extent of the FIR emission from the galaxies, and they correspond to 1.4, 0.7 and 0.3 times the optical diameter for late-type, lenticular and elliptical galaxies, respectively. Only for 36 galaxies (11% of the sample) we choose different sizes than those used for SPIRE. There are three different reasons why we did so: a) For 23 galaxies (HRS6, 14, 22, 32, 67, 71, 75, 158, 209, 223, 225, 238, 243, 249, 255, 257, 261, 264, 286, 300, 315, 317, 322) the 100 and 160 m emission is significantly less extended than the size of the aperture used by Ciesla et al. (2012). Although this does not affect the estimate of the integrated flux density, it artificially boosts the error associated with our measurements to values always above 50%, and sometimes even higher than 100%. Thus, for these objects, we reduced the size of the aperture (on average by 26%) to obtain more realistic error estimates. We note that the size chosen is still larger than the extent of the FIR emission (so that aperture corrections are not necessary), and that the flux density estimated within these new apertures is consistent with the value obtained using Ciesla et al. (2012) apertures. b) 10 galaxies (HRS7, 68, 129, 138, 161, 174, 210, 231, 258, 308) were not spatially resolved in the SPIRE bands, and SPIRE photometry was carried out directly on the time-line data. For these cases, which are generally resolved by PACS, we chose new apertures which include all the emission from the target. c) For 3 galaxies (HRS4, 122, 263), the PACS maps available from the archive were slightly smaller than our SPIRE maps. While these maps are large enough to include the entire aperture used in Ciesla et al. (2012), no space is left to properly estimate the background. Thus, the aperture has been reduced in order to allow a more accurate background estimate, and still encompass all the emission from the galaxy.
Sky background was determined in fifteen to thirty regions, depending on the size of the target, around the chosen aperture. The use of various regions instead of just a circular annulus makes it easier to estimate the large scale variations in the background and to avoid background/foreground sources around the target. The mean sky value was then subtracted from each map before performing the flux density extraction. Since cirrus contamination is significantly less of an issue than in SPIRE images, we did not find necessary to perform a more complex modelling of the background. However, as discussed below, the effect of any residual large scale gradient is included in our error estimates.
Errors on integrated flux densities have been estimated following the guidelines described in Roussel (2013), which are consistent with what is done in Ciesla et al. (2012) for HRS SPIRE data. Briefly, there are three sources of errors that affect our measurements:
where is the flux calibration uncertainty (here assumed to be 5%; Balog et al., 2013), is the instrumental noise which depends on the number of scans crossing a pixel, and is obtained by summing in quadrature the values on the error map within the chosen aperture, and is the error on the sky measurement. As discussed in Roussel (2013), the sky uncertainty results from the combination of the uncorrelated error on the mean value of the sky ( i.e., the pixel-to-pixel variation across the image), and the correlated noise due to long time-scale drift residuals responsible for the large scale structures present in the image background ( i.e., the standard deviation of the mean value of the sky measured in different apertures around the galaxy; see also Boselli et al., 2003; Gil de Paz & Madore, 2005). In detail,
where is the number of pixels in the aperture used to integrate the galaxy flux density. As expected, for the vast majority of our objects the dominant source of error is the correlated uncertainty on the large-scale structure of the background. The average total uncertainties are 16% and 12% at 100 and 160 m, respectively.
Out of the 323 galaxies observed, 282 have been detected in both bands (284 at 160 m only). This matches the HRS detection fraction in the SPIRE bands (i.e., 284 galaxies detected at 250 m), allowing us to characterise the shape of the FIR/sub-mm SED across the entire 100-500 m range for almost 300 galaxies. In case of non detections, upper limits have been estimated as 3, using the same apertures as in Ciesla et al. (2012).
The results of our photometry are presented in Table 1. The columns are as follows:
Columns 7-8: the J2000 right ascension and declination.
Column 9: Morphological type, taken from Cortese et al. (2012a): -2=dE/dS0, 0=E-E/S0, 1=S0, 2=S0a-S0/Sa, 3=Sa, 4=Sab, 5=Sb, 6=Sbc, 7=Sc, 8=Scd, 9=Sd, 10=Sdm-Sd/Sm, 11=Sm, 12=Im, 13=Pec, 14=S/BCD, 15=Sm/BCD, 16=Im/BCD, 17=BCD.
Column 10: 100 m flux density measurement flag. Non detections=0, Detections=1, Confused (i.e., flux density estimate significantly contaminated by the presence of another object)=2. For confused galaxies, flux densities should be considered as an upper limit to the real value.
Column 11: Integrated 100 m flux density, or upper limit in Jy.
Column 12: Total uncertainty on the 100 m flux density measurement in Jy.
Column 13: 160 m flux density measurement flag.
Column 14: Integrated 160 m flux density, or upper limit in Jy.
Column 15: Total uncertainty on the 160 m flux density measurement in Jy.
Columns 16-18: Major, minor semi-axis (in arcseconds) and position angle (in degrees) of the aperture used for the photometry.
Column 19: Herschel Proposal ID.
This table, as well as all the reduced PACS maps, are publicly available on the Herschel Database in Marseille (HeDaM, http://hedam.oamp.fr/).
2.4 Comparison with the literature
In order to check the reliability of the PACS flux density measurements presented here, we compare our far-infrared integrated flux densities with the values presented in the literature, which are based on PACS, Spitzer/MIPS or IRAS observations. The results of these comparisons are shown in Fig. 2.
The difference between our flux density estimates and those presented in Dale et al. (2012) is +6% (standard deviation of 2-3%), with our flux densities being brighter, although the number statistics is very small (6 galaxies in total). This difference is within the quoted uncertainties, and is mainly due to the different technique used to estimate flux densities (i.e., different background apertures and the use of aperture corrections not adopted in this work).
Auld et al. (2013) recently published PACS flux density measurements for all the VCC galaxies in the HeViCS footprint. A comparison between the flux density estimates for the 65 detected galaxies in common reveals a nice correlation between the two estimates with a standard deviation of just 12% and 7% at 100 and 160 m, respectively. However, Auld et al. (2013) measurements are systematically 12% and 15% lower than ours.
After various tests, we concluded that there are two main reasons for this discrepancy. First, a different flux density estimate technique. Auld et al. (2013) used apertures on average significantly smaller than ours (e.g., see their Fig. 3), and then applied aperture corrections. Indeed, by using our own apertures on the Auld et al. (2013) dataset, we find no systematic offset with our 100 m data, whereas at 160 m there is still a difference of 12%.
Second, a different data reduction technique. Auld et al. (2013) used the naive projection task photProject in HIPE to reduce PACS images. This requires the use of a high-pass filter to correct for 1/ noise, and such procedure could remove diffuse emission associated to extended objects. By using the same apertures on the HeViCS maps reduced with both photProject and Scanamorphos, we find that photProject maps provide flux densities 10% lower than those obtained with Scanamorphos, while no difference is seen at 100 m. Thus, the remaining difference at 160 m is due to the use of photProject instead of Scanamorphos. Indeed, as mentioned above, this is likely due to the use of high-pass filtering which removes diffuse emission, much more commonly present at 160 m than at 100 m (see also Rémy-Ruyer et al., 2013).
We also compared our measurements to those presented by Davies et al. (2012) for the 49 galaxies in common. These are based on an early HeViCS data release and are measured on apertures much more similar to the ones we used. Our flux density measurements agree very well with these estimates (+222% and +214% at 100 and 160 m, respectively). The scatter is larger than in the case of Auld et al. (2013), but consistent with the typical uncertainty given in Davies et al. (2012). It is likely that, in this case, the different calibration between the two datasets compensates for the intrinsic differences between photProject and Scanamorphos, providing a set of measurements consistent with our own.
Spitzer/MIPS 160 m flux densities for 103 galaxies in the HRS have been published by Bendo et al. (2012). In order to perform a proper comparison with our data, we removed those galaxies which were flagged as problematic due to incomplete coverage, or simply being confused with other nearby galaxies of similar surface brightness in Bendo et al. (2012). For the remaining 65 objects in common our flux densities are 8% brighter than those of MIPS one, with quite a large scatter (22%). This large scatter is mainly due to two galaxies (which fall outside the residual plot in Fig. 2): HRS129, 258. A comparison between the PACS, SPIRE and MIPS data for these galaxies shows that the MIPS data suffer from background confusion effects, making it difficult to separate emission from the target and background sources. Moreover, the MIPS observations for these galaxies were performed in photometry mode, which produces compact maps where it is difficult to measure the background. Once these are removed from the sample, the difference between MIPS and PACS measurements becomes +1014%. Conversely, the comparison with the Spitzer/MIPS 160 m flux densities presented in Dale et al. (2007) for the 6 SINGS galaxies in our sample shows an average difference of -511%. All these values are within the 12% flux calibration uncertainty in MIPS data (Stansberry et al., 2007). A PACS-to-MIPS 160 m flux density ratio systematically higher than 1 has also been found by comparing pixel-by-pixel photometry of nearby galaxies (Aniano et al., 2012; Draine et al., 2013).
We can thus conclude that our 160 m PACS flux density measurements are consistent with those of Spitzer/MIPS within 20%, in agreement with the results obtained by the PACS Team (Paladini et al., 2012).
Finally, we compared our PACS 100 m flux density estimates with those presented in the IRAS Faint Source Catalogue (164 galaxies after exclusion of confused/contaminated objects), finding an average difference of +715% (see also Ali, 2011).
We remind the reader that, although the central wavelengths of MIPS and IRAS correspond to those of PACS, the bandpasses are not identical and part of the offsets shown above are certainly due to the different filter responses of the three instruments.
3 Far-infrared/sub-millimeter colours as a proxy for the shape of the dust SED
In the last few years, several studies have shown how infrared colours can be used as a proxy of dust properties (e.g., Boselli et al., 2010a, 2012; Dale et al., 2012; Bendo et al., 2010, 2012; Galametz et al., 2010; Boquien et al., 2011; Rémy-Ruyer et al., 2013). The novelty of the present work is that, for the first time, we cover the 100-500 m domain for a representative sample of galaxies spanning a large range in stellar mass, star formation activity, cold gas and metal content. For example, compared to the work presented in Boselli et al. (2012), which focused on Hi-normal spiral galaxies only, this analysis takes advantage of a more complete coverage at wavelengths shorter than 250 m, and includes the entire HRS sample detected by Herschel (282 versus 146 objects). Similarly, the number of HRS galaxies detected at all PACS and SPIRE wavelengths is significantly larger (i.e., 282 versus 195) than that of Auld et al. (2013), which focuses on Virgo cluster galaxies only.
Particularly interesting is to quantify how well the shapes of the dust SED at the short and long wavelength-ends correlate among each other. Indeed if, in the 100-500 m wavelength range, the dust SED can be well approximated by a single modified black-body with fixed (i.e., the variation of the dust emissivity with frequency described by ), all FIR/sub-mm colours should be strongly correlated.
The SPIRE flux densities are obtained from Ciesla et al. (2012), but we applied several corrections to these flux estimates. We multiplied their values by 1.0253, 1.0250 and 1.0125 at 250, 350 and 500 m to take into account the new SPIRE calibration (v.11), and then by 0.9097, 0.9136 and 0.8976 at 250, 350 and 500 m, to correct for the new beam areas (Bendo et al., 2013; Herschel Space Observatory, 2013). We did not make any attempt to include variations of the beam size as a function of the shape of the SED (Herschel Space Observatory, 2013), as these are generally within the measurement errors (10%). Moreover, such correction would mainly result in a systematic offset in the flux densities, whereas the relative variation between the SPIRE bands would be 3% for the ranges of investigated here. Thus, we are confident that this does not affect our conclusions.
In Fig. 3 we plot the 100-to-160 m flux density ratio, which usually embraces the peak of the dust SED,
as a function of various flux density ratios (i.e., from top to bottom: 100-to-250 m, 100-to-500 m, 160-to-500 m and 250-to-500 m) sensible
to the shape of the SED at increasingly longer wavelengths
It is clear that the farther away in wavelength two colours are, the weaker their correlation is,
as already noted by Boselli
et al. (2012). Indeed, the Pearson correlation coefficient () decreases from 0.8 to 0.2 when
moving from the 100-to-250 m to the 250-to-500 m flux density ratios (see first column of Fig. 3).
Intriguingly, the increase of a factor of 3 in scatter ()
Gas-rich/metal-poor galaxies seem to be responsible for the significant increase in scatter when moving from the 100-to-250 m to the 160-to-500 m colour-colour plots. If we consider gas-poor/metal-rich galaxies only, the scatter in the three bottom panels of Fig. 3 decreases by at least a factor 2. Indeed, performing a Kolmogorov-Smirnov test, we found that there is only a 4% chance that the 160-to-500 m colour distributions of metal-poor (12+log(O/H)8.65) and metal-rich (12+log(O/H)8.65) galaxies are drawn from the same population, as already demonstrated by Boselli et al. (2012). We note that some galaxies do not appear in the third and fourth column of Fig. 3. This is because for some objects Hi and metallicity information is not available.
Our findings suggest that, in the 100-500 m regime, the shape of the dust SED for galaxies with stellar mass 10M/M10 cannot be reproduced by simply varying the value of the average dust temperature. In other words, either must also vary (Boselli et al., 2012; Smith et al., 2012; Rémy-Ruyer et al., 2013) or multiple temperatures components are required (Shetty et al., 2009; Dunne & Eales, 2001; Boquien et al., 2011; Bendo et al., 2012; Clemens et al., 2013).
In order to visually illustrate this result, we plot in Fig. 3 and 4 the colours expected for these two different scenarios. In Fig. 3 we show the flux density ratios derived from single modified black-bodies with temperatures ranging from 10 and 40 K and values fixed to 2 (solid line) and 1 (dashed line). In Fig. 4, we show a combination of two modified black-bodies with =2. We vary the cold dust temperature () from 10 to 20 K, and the warm dust temperature () from 20 to 30 K. The four columns show different mass ratios increasing from 1 (left) to 10 (right).
It is clear that, while the temperature is the main driver of the trends observed in each colour-colour plot, only a variation in , or an additional temperature component, can explain the increasing scatter when moving from the 100-to-250 m to 160-to-500 m colours. Interestingly, the two temperature components scenario is able to reproduce the observed range of colours only if the warm component contributes negligibly to the total dust budget of the galaxy (i.e., 5; Vlahakis et al., 2005). This is easy to understand if we consider the fact that, at fixed dust mass, the flux density emitted by a black-body in the FIR/submm wavelength range increases with temperature. Thus, if the warm and cold components have the same dust mass, the warm dust dominates the total emission, and the shape of the SED is very close to that of a single black-body. Only if the cold dust component dominates the mass budget, the shape of the combined SED deviates significantly from a single black-body.
Unfortunately, with our current data it is impossible to discriminate between a varying and a multiple temperature component scenario. Our lack of coverage below 100 m makes it meaningless to perform a two temperatures fit, as the warm component is not constrained. Thus, in the rest of this paper we will focus on the single modified black-body case only, and investigate how different assumptions on can affect the interpretation of Herschel observations. A detailed comparison with the predictions of the Draine et al. (2007) dust models will be presented in a forthcoming paper (Ciesla et al., submitted.).
4 Fitting the dust SED with a single modified black-body
4.1 How well do colours trace the average dust temperature?
The results presented in the previous section show that FIR/sub-mm colours may not always represent a proxy for the average underlying dust temperature. In order to investigate this issue in more detail, it is interesting to quantify how the FIR/sub-mm colours correlate with the parameters obtained from a single modified black-body fitting. We assume either a constant value of =2, or keep this as a free parameter. The model functions were convolved with the PACS and SPIRE filter response functions and fitted to the relative spectral responsivity function-weighted flux density measurements. Best-fit parameters and their 1 uncertainties are determined via a minimisation using the Python version of the minimisation library MINUIT (James & Roos, 1975). We choose =2 simply because this seems to correctly reproduce the shape of the SED for massive, metal-rich spiral galaxies in the local Universe (Davies et al., 2012; Boselli et al., 2012; Draine et al., 2013). However, our results do not qualitatively change if a different (but fixed) value of is used. In the rest of the paper, we consider only those objects detected in all 5 PACS/SPIRE bands, and for which the reduced () corresponds to a probability 95%: i.e., 2.6 (203 galaxies) and 3 (242 galaxies) for a fixed and variable , respectively. The best-fit dust masses and temperatures for these galaxies, as well as their distance, are provided in Table 3. This guarantees that we are not contaminated by objects whose FIR/submm emission is dominated by synchrotron emission (Baes et al., 2010).
A comparison between the reduced obtained for the =free and =2 cases is shown in Fig. 5. Not surprisingly, leaving free provides on average better fits. Moreover, as shown in the central and right panel of Fig. 5, the difference between the two techniques increases when moving towards metal-poor/gas-rich systems. This is even more evident when Hi-deficient galaxies (i.e., 0.5, empty points in Fig. 5), for which the gas content is no longer a good indicator of enrichment history (Cortese & Hughes, 2009; Hughes et al., 2013), are excluded (0.38 and 0.54 for all galaxies and Hi-normal systems only, respectively).
In Fig. 6, we show how the FIR/sub-mm colours correlate with the best-fit parameters obtained from our SED fitting. Not surprisingly, all SPIRE and PACS colours strongly correlate with dust temperature if is kept fixed (we note that these results do not qualitatively change if we fix to a different value). It is also expected that the lowest scatter is observed for the colour spanning the largest wavelength range (i.e., the 100-to-500 m flux density ratio), as the variation in colour is larger, and less affected by measurement errors.
More interesting is the case when is treated as a free parameter. In this case, there is a clear difference in the colours behaviour when crossing a of 200 m. At shorter wavelengths, there is still a strong correlation of colour with temperature (0.7), while only a very weak trend is seen with (-0.15). Moving to longer wavelengths, the trends with temperature become weaker, and reverse for the 250-to-500 m colour (-0.3), whereas the correlation with becomes gradually stronger. The best relation is found with the 250-to-500 m flux density ratio (0.9), which appears to be mainly tracing variations of and not dust temperature, as also shown in Fig. 3. These results are likely a direct consequence of the fact that the FIR/submm SED for our sample peaks at 200 m, and while the PACS colours trace the peak of the dust SED, any variations in the emissivity of the grains will predominantly affect the SPIRE colours. The average value of for HRS galaxies is 1.80.5, a value consistent with what is found in the Milky Way and in other nearby galaxies (Planck Collaboration et al., 2013; Galametz et al., 2012; Boselli et al., 2012; Smith et al., 2012, 2013).
An important issue affecting any modified black-body fitting with and as free parameters is the known anti-correlation between them, which is clearly shown in the right column of Fig. 6. While it is still debated whether part of this anti-correlation has a physical origin (Shetty et al., 2009; Galametz et al., 2012; Smith et al., 2012; Juvela & Ysard, 2012; Juvela et al., 2013; Rémy-Ruyer et al., 2013; Tabatabaei et al., 2013), there is no doubt that it is mainly due to the fitting technique (Shetty et al., 2009). Indeed, in the 2D vs. plane, the region corresponding to the absolute minimum of depends on both quantities, giving rise to an anti-correlation between and . This is clearly visible by just looking at the 2D confidence levels for any modified black-body fit. Since in the first and third columns of Fig. 6 temperature and show opposite trends with colour, it is very likely that they are affected by this degeneracy. However, the significant difference in scatter between the various relations suggests that the 100-to-160 m colour vs. and 250-to-500 m colour vs. are less contaminated than the other correlations. As mentioned above, this is because the PACS colours mainly trace the peak of the dust SED, whereas the SPIRE ones are mostly sensitive to variations in the dust emissivity.
4.2 The relation between dust temperature, and integrated galaxy properties
In this section we investigate further how the variation of , necessary to reproduce the observed colours of HRS galaxies in a single modified black-body scenario, is mirrored by a variation in galaxy properties. For comparison, we will also show the results obtained by keeping fixed, since we consider this an instructive exercise to illustrate how the model assumptions influence the parameters we derive. In Fig. 7, we show how the best-fitting dust parameters, as well as the 100-to-160 m and 250-to-500 m flux density ratios, are related to gas-phase metallicities, Hi gas fractions, specific star formation rate (), stellar mass surface density [= where is the radius containing 50% of the total -band light] and stellar mass. Star formation rates are determined by combining WISE 22m (Ciesla et al., submitted.) and NUV photometry (Cortese et al., 2012a) using the recipes presented in Hao et al. (2011) as described in Cortese (2012).
By comparing the two bottom rows of Fig. 7, it is clear that the assumptions made on significantly influence the correlations between temperature and integrated galaxy properties. For fixed to 2, the strongest correlation is found with stellar mass surface density (0.45). A weak anti-correlation is visible with gas-fraction (-0.3), while no correlation is found with specific star formation rate, stellar mass or metallicity ( 0.2). Quite different results are obtained if is left free. In this case, the temperature anti-correlates very weakly with (-0.3), while it is strongly correlated with (see also Clemens et al., 2013), Hi gas fraction, metallicity and stellar mass (0.5). Even more importantly, some of the correlations show opposite trends. For a fixed value of , the temperature increases with metallicity and stellar mass surface densities, whereas it decreases for =free. The ‘reversal’ of these correlations is driven exclusively by metal-poor/gas-rich galaxies, and it is simply a consequence of the fact that, for these objects, the best-fitting value of is significantly lower than 2. Thus, many of the correlations shown in Fig. 7 depend on the assumptions made about the dust SED, and may not be physical (Magnelli et al., 2012; Roseboom et al., 2013).
In particular, we have shown (see Fig. 6) that the 100-to-160 m and 250-to-500 m flux density ratios are the best proxies for and , respectively. If all the trends observed in Fig. 7 are physical, we should find similar correlations when and are replaced by the flux density ratios. However, this is not always the case. The 100-to-160 m flux density ratio correlates only with (0.5), while the 250-to-500 m ratio correlates weakly with (-0.2), but varies strongly with stellar mass, stellar mass surface density, Hi gas fraction and gas-phase metallicity (0.6-0.7). Thus, the vs. Hi gas fraction and vs. trends might be spurious.
In summary, our analysis confirms that the typical dust temperature of a galaxies as measured from a single modified black-body is mainly related to specific star formation rate, while varies more with the degree of metal enrichment of the ISM. As discussed in the previous section, at this stage it is impossible to determine whether the variation of across the HRS indicates a variation in the dust properties/composition, or it simply highlights the need of multiple temperature components for gas-rich/metal-poor/low-mass galaxies.
4.3 Dust mass estimates
It is interesting to investigate how the variation of across the HRS for a single modified black-body affects the estimate of the dust mass reservoir. Thus, in the left panel of Fig. 8, we compare the dust masses obtained for =free and =2. Dust masses have been calculated from Eq. 1 assuming 856.5 GHz (i.e., 350 m) and 0.192 m kg (Draine, 2003). It is evident that dust masses are significantly less affected than dust temperatures by the assumptions made on . The average difference between the two measurements is 0.08 dex, with a standard deviation of 0.15 dex, which is consistent with the typical statistical error obtained from the SED fitting: 0.05 and 0.1 dex for =2 and =free. Not surprisingly, the largest difference is observed in gas-rich galaxies (filled circles, =0.140.14 dex), while the two techniques give consistent results for gas-poor systems (empty circles, =-0.020.11 dex).
This result implies that correlations involving dust masses are quite robust against the assumptions made on the shape of the SED. Different assumptions can certainly affect the exact slope of the dust scaling relations, but they are not able to produce the same dramatic inversion of some correlations observed for the dust temperature (see Fig. 7).
This conclusion is reinforced by the fact that the differences, already quite small, between the two cases might be overestimated, as we varied , by keeping fixed the value of dust opacity used to determine the dust mass. As recently shown by Bianchi (2013), this is not entirely correct because the value of is calibrated on a dust model with a well defined value of . Thus, if changes, should change as well. Unfortunately, varying along with is far from trivial, and it is only possible by either having a consistent dust model for each value of , or by comparing dust mass estimates obtained from SED fitting with the ones obtained from other independent methods: e.g., using the amount of cold gas and metals, as proposed by James et al. (2002).
Finally, it is interesting to compare the dust masses estimated by fitting a single modified black-body with =2, to those obtained by using the empirical recipes developed by Cortese et al. (2012b), which assume =2 but are based on SPIRE data only. In this way we can quantify the benefit provided by inclusion of the PACS data in the dust mass estimates. As shown in the right panel of Fig. 8, the two estimates show a good agreement with a mean difference of -0.07 dex and a standard deviation of 0.14 dex, lower than the typical uncertainty of 0.2 dex in the recipes by Cortese et al. (2012b). Even in this case, the largest offset (-0.120.11 dex) is found for gas-rich galaxies. This is a natural consequence of the fact that, for these objects, the shape of the dust SED is no longer perfectly consistent with =2.
Thus, while dust mass estimates based on SPIRE colours are a reliable tool for estimating dust masses within 0.2 dex, only a complete coverage of the 100-500 m wavelength range can provide us with accurate (within 0.1dex) dust mass estimates necessary to quantify in great detail the correlation between dust mass and other galaxy properties.
5 Summary & Conclusions
In this paper we presented PACS 100 and 160 m integrated photometry for the Herschel Reference Survey. We have combined these data with SPIRE observations to investigate how the shape of dust SED varies across the Hubble sequence. Being the largest representative sample of nearby galaxies with homogeneous coverage in the 100-500 m wavelength domain, the HRS is ideal to quantify if and how dust emission varies across the local galaxy population. Our main results are as follows.
The shape of the dust SED is not well described by a single modified black-body having just the dust temperature as a free parameter. Instead, there is a clear need to vary the dependence of the dust emissivity () on wavelength, or to invoke multiple temperature components in order to reproduce the colours observed in our sample. This is particularly important as the HRS does not include very metal-poor dwarf galaxies, for which we already knew that the dust SED is significantly different from the one of metal-rich, massive galaxies (Galliano et al., 2005; Galliano et al., 2011; Engelbracht et al., 2008; Galametz et al., 2009; Rémy-Ruyer et al., 2013). Our results suggest that the difference in FIR/sub-mm colours between giant and dwarf galaxies (Draine & Li, 2007) may not be the result of a dramatic transition in dust properties, but just the consequence of the gradual variation that we observe as a function of metal and gas content.
The variation in the slope of the dust SED strongly affects dust temperature estimates from single modified black-bodies fits. In particular, the correlations between galaxy properties and dust temperatures strongly depend on the assumptions made on : i.e., trends can disappear or even reverse. Conversely, dust mass estimates are more robust, and variations in do not produce the same dramatic inversion of some correlations observed for the dust temperature.
We confirm that the temperature of a single modified black-body is mainly related to specific star formation rate, while varies more with the degree of metal enrichment of the ISM.
The results presented in this paper may appear in contradiction with several recent works showing that the dust SED is very well reproduced by a simple modified black-body with 2 (Davies et al., 2012; Auld et al., 2013). However, all these works were focused on massive, metal-rich and relative gas-poor galaxies, for which we also find that a constant value of provides a good fit to our data. It is when we move to the gas-rich/metal-poor regime that the shape of the SED starts to change (Boselli et al., 2010a, 2012; Rémy-Ruyer et al., 2013).
Our findings overall reinforce the results already presented in Boselli et al. (2010a, 2012). However, it is important to note that the discovery of a clear variation in the shape of the SED across the HRS has only been possible thanks to the large wavelength coverage obtained by combining both PACS and SPIRE data. Indeed, with SPIRE or PACS data only, it would be not only much more difficult to show under which conditions a simple modified black-body approach does not work, but it would also be nearly impossible to quantify how model assumptions can affect the correlation of dust temperature with star formation, galaxy structure and chemical enrichment.
We thank an anonymous referee for his/her very useful comments and suggestions which have significantly improved this manuscript. LC thanks B. Draine for useful discussions, and B. Catinella for comments on this manuscript. We thank all the people involved in the construction and the launch of Herschel.
The research leading to these results has received funding from the European CommunityÕs Seventh Framework Programme (/FP7/2007-2013/) under grant agreement No 229517, and was supported under Australian Research Council’s Discovery Projects funding scheme (project number 130100664). IDL is a postdoctoral researcher of the FWO-Vlaanderen (Belgium).
PACS has been developed by a consortium of institutes led by MPE (Germany) and including UVIE (Austria); KU Leuven, CSL, IMEC (Belgium); CEA, LAM (France); MPIA (Germany); INAF-IFSI/OAA/OAP/OAT, LENS, SISSA (Italy); IAC (Spain). This development has been supported by the funding agencies BMVIT (Austria), ESA-PRODEX (Belgium), CEA/CNES (France), DLR (Germany), ASI/INAF (Italy), and CICYT/MCYT (Spain). SPIRE has been developed by a consortium of institutes led by Cardiff University (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); and Caltech, JPL, NHSC, 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 (UK); and NASA (USA).
Part of the HRS data was accessed through the Herschel Database in Marseille (HeDaM - http://hedam.lam.fr) operated by CeSAM and hosted by the Laboratoire d’Astrophysique de Marseille.
We acknowledge the 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.
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