A&A 462, 81–91 (2007) Astronomy DOI: 10.1051/0004-6361:20053881 & c ESO 2007 Astrophysics The infrared compactness-temperature relation for quiescent and starburst galaxies P. Chanial 1,H.Flores2, B. Guiderdoni3,D.Elbaz5,F.Hammer2, and L. Vigroux4,5 1 Astrophysics Group, Blackett Laboratory, Imperial College, Prince Consort Road, London SW7 2AZ, UK e-mail: [email protected] 2 Laboratoire Galaxies, Etoiles, Physique et Instrumentation, Observatoire de Paris, 5 place Jules Janssen, 92195 Meudon, France 3 Centre de Recherche Astronomique de Lyon, Université Lyon 1, 9 avenue Charles André, 69230 Saint-Genis Laval, France; CNRS, UMR 5574; École Normale Supérieure de Lyon, Lyon, France 4 Institut d’Astrophysique de Paris, 98bis boulevard Arago, 75014 Paris, France; CNRS, UMR 7095; Université Pierre & Marie Curie, Paris, France 5 Service d’Astrophysique, DAPNIA, DSM, CEA-Saclay, Orme des Merisiers, Bât. 709, 91191 Gif-sur-Yvette, France Received 22 July 2005 / Accepted 6 October 2006 ABSTRACT Context. IRAS observations show the existence of a correlation between the infrared luminosity LIR and dust temperature Td in star-forming galaxies, in which larger LIR leads to higher dust temperature. The LIR–Td relation is commonly seen as reflecting the increase in dust temperature in galaxies with higher star formation rate (SFR). Even though the correlation shows a significant amount of dispersion, a unique relation has been commonly used to construct spectral energy distributions (SEDs) of galaxies in distant universe studies, such as source number counting or photometric redshift determination. Aims. In this work, we introduce a new parameter, namely the size of the star-forming region rIR and lay out the empirical and modelled relation between the global parameters LIR, Td and rIR of IR-bright non-AGN galaxies. Methods. IRAS 60-to-100 µm color is used as a proxy for the dust temperature and the 1.4 GHz radio contiuum (RC) emission for the infrared spatial distribution. The analysis has been carried out on two samples. The first one is made of the galaxies from the 60 µm flux-limited IRAS Revised Bright Galaxy Samples (RBGS) which have a reliable RC size estimate from the VLA follow-ups of the IRAS Bright Galaxy Samples. The second is made of the sources from the 170 µm ISOPHOT Serendipity Sky Survey (ISOSSS) which are resolved by the NRAO VLA Sky Survey (NVSS) or by the Faint Images of the Radio Sky at Twenty-cm survey (FIRST). Results. We show that the dispersion in the LIR–Td diagram can be reduced to a relation between the infrared surface brightness and the dust temperature, a relation that spans 5 orders of magnitude in surface brightness. Conclusions. We explored the physical processes giving rise to the ΣIR–Td relation, and show that it can be derived from the Schmidt law, which relates the star formation rate to the gas surface density. Key words. galaxies: fundamental parameters – galaxies: starburst – infrared: galaxies – radio continuum: galaxies 1. Introduction 12 µm IRAS flux densities to estimate the compactness of op- tically bright galaxies. He showed that the ratio between the The sky survey by the IRAS satellite (Neugebauer et al. 1984) small-beam and large-beam flux densities is correlated with the led to the discovery of strong connections between global pa- global IRAS 12-to-25 µm flux density ratio which also traces rameters of galaxies in the local universe. Among them, the 60- the dust temperature. The main limitation of this work is the use µ / to-100 m flux density ratio R(60 100) versus LIR IRAS diagram of a rough compactness estimator that can not be easily related (Soifer et al. 1987) exhibits a large dispersion. The quantities to physical parameters and thus no concluding relationship was / LIR and R(60 100) of quiescent and starburst galaxies are funda- derived. mental parameters for the study of star formation. The first one Other similar attempts showed that the optical surface bright- represents the energy absorbed and reprocessed by dust and is ness (Phillips & Disney 1988) and the infrared surface brightness related to the star formation rate. The second parameter traces derived from Hα effective area (Lehnert & Heckman 1996) of IR the dust temperature Td and also provides an estimate of the star bright galaxies increase with R(60/100). However, the quanti- ffi formation e ciency as defined by the SFR per unit of gas mass tative understanding of these correlations is not straightforward (Young et al. 1986; Chini et al. 1992). because the optical surface brightness results from stars that may The first attempts to relate the infrared surface brightness not be related to the dust emission and because in the second (which we also refer to as infrared compactness) to the dust tem- study, in addition to the small size of the sample (32 galaxies), perature were hampered by the lack of sufficient infrared spa- the authors used Hα maps to estimate the star-forming region tial resolution. Devereux (1987) used ground-based small-beam size without applying an extinction correction which turns out to observations at 10 µm and compared them to the large-beam be crucial (Chanial et al., in prep.). Wang & Helou (1992) made use of the extinction-free Tables 4 and 5 are only available in electronic form at 1.4 GHz radio continuum (RC) size estimators to show that the http://www.aanda.org infrared luminosity is not proportional to the galaxy physical Article published by EDP Sciences and available at http://www.aanda.org or http://dx.doi.org/10.1051/0004-6361:20053881 82 P. Chanial et al.: The infrared compactness-temperature relation... area. They also showed an empirical relation between the mean RC surface brightness ΣRC and luminosity LRC, but they did not consider the IR color variations within their sample which, as we will show in this article, is directly related to the scatter in the ΣRC–LRC relation. More recently, Roussel et al. (2001) studied a sample of galaxies mapped by the ISOCAM camera on board ISO (Cesarsky et al. 1996) and found a correlation between the 15- to-7 µm flux density ratio and the 15 µmeffective surface bright- ness. Their sample only consists of quiescent spirals of mod- erate infrared luminosities and the authors only considered the circumnuclear region. In this paper, we extend these approaches by (1) studying statistically larger samples, (2) applying a flux-limited selec- tion criterion at 60 µm, (3) considering fundamental parameters representative of the whole galaxy, and (4) using an extinction- independent estimator of the star-forming region size, the radio continuum angular size. Section 2 describes the global parameters used in this pa- β = . per and Sect. 3 presents the galaxy samples that are used in Fig. 1. Temperature of the modified blackbodies ( 1 3) fitted to the 60 and 100 µm IRAS flux densities (abscissæ) and to additional Sects. 4 and 5 for the analysis of the luminosity-temperature far-infrared and submillimeter observations (ordinates). The SLUGS and compactness-temperature relations. The latter is modelled 450 µm subsample and the SINGS subsample are represented with in Sect. 6 and discussed in Sect. 7. filled and open circles. The dashed line is the unity line and the average uncertainties are shown in the upper left corner. 2. Parameter definitions and estimations this model cannot be ruled out, and instead favoured the anal- 2.1. The dust temperature ysis of the two-component model which offers one additional The temperature of the dust in a given galaxy is subject to spatial free parameter. By excluding galaxies with an active galactic nu- variations (Dale et al. 1999) that show a decrease from the center cleus (AGN) from their 450 µm sample and by taking the flux outwards. So, the attempt to describe the global thermal emis- densities tabulated in their article, we found a similar value of sion of the dust with one or two modified blackbodies may be β = 1.38 with a sample standard deviation of 0.17. Since only 2 χ2 > questioned. However, submillimeter observations at 450 µmand out of 25 galaxies have a reduced r 2, the single-temperature 850 µm (Dunne et al. 2000; Dunne & Eales 2001; Vlahakis et al. model provides a reasonable fit in most cases and we adopted 2005) have shown that the global emission at these wavelengths, the fiducial value β = 1.3inthispaper. which trace cold dust, does correlate with the global R(60/100), The next step is to check that it is possible to easily associate which traces warmer dust. This finding suggests that inner and an estimator to the previously defined effective dust tempera- outer emissions may be bound together. Such a property would ture, the estimator of choice being the color R(60/100) due to likely be the manifestation of the star formation regulation oc- its matchless availability in the local universe. We have already curring on a global scale, as it appears in the Schmidt law (1959) noted that the R(60/100) parameter can characterize to some ex- or in relations which involve the galaxy rotation curve such as tent the whole infrared SED of normal and starburst galaxies, the Toomre’s stability criterion (1964) and the law by Kennicutt but its precision still has to be determined. For two sets of non- (1998). AGN galaxies described in Tables 1 and 2, we compared the The often used two-component model does not reflect the effective dust temperatures exclusively derived from the 60 and fact that a single free parameter such as R(60/100) suffices to de- 100 µm IRAS flux densities to the temperatures that are derived scribe the SEDs of galaxies whose infrared emission arises from from additional far-infrared (FIR) and submillimeter observa- star formation (Dale et al.