Far-infrared spectral energy distribution fitting for galaxies near and far

Mon. Not. R. Astron. Soc. 425, 3094–3103 (2012) doi:10.1111/j.1365-2966.2012.21455.x Far-infrared spectral energy distribution fitting for galaxies near and far Caitlin M. Casey † Institute for Astronomy, University of Hawai’i, 2680 Woodlawn Drive, Honolulu, HI 96822, USA Accepted 2012 June 7. Received 2012 May 22; in original form 2012 April 9 ABSTRACT Key words: galaxies: evolution – galaxies: high-redshift – galaxies: starburst – infrared: galaxies. 1 I N T RO D U C T I O N Modelling galaxies’ multiwavelength emission has become a sophisticated effort of extragalactic astronomy. Spectral energy distribution (SED) templates, generated by modelling galaxies’ stellar populations and radiation, are used prolifically to derive stellar masses, extinction corrections and stellar ages using broad-band photometry from the rest-frame ultraviolet (UV) to infrared (IR) wavelengths. They are also commonly used to constrain redshifts photometrically (e.g. Bolzonella, Miralles & Pelló 2000). The population synthesis-generated SEDs used to fit short-wavelength data (λ ≤ 8 μm) are complex (Bruzual & Charlot 2003; Maraston 2005).  Hubble Fellow. †E-mail: They depend on the initial mass function (IMF; Salpeter 1955; Kroupa 2001; Chabrier 2003), metallicity, stellar age and starbursting time-scale – duration, frequency and strength. Although this gives rise to many free parameters in the models, the slew of broadband filters in the optical and near-IR (NIR) make this detailed SED fitting possible, even with the effects of dust obscuration/attenuation taken into account (e.g. Calzetti, Kinney & Storchi-Bergmann 1994; Calzetti 2001). Follow-up spectral observations in the optical and NIR often confirm good fits to broad-band photometry and accurate stellar population modelling. The dawn of new IR observing facilities – from the Herschel Space Observatory, the Atacama Large Millimeter Array (ALMA), to the Submillimetre Common-User Bolometer Array 2 (SCUBA2) instrument on the James Clerk Maxwell Telescope (JCMT) – has triggered a wave of interest in extending the use of these template SED libraries to the far-IR (FIR; ∼8–1000 μm rest frame),  C 2012 The Author C 2012 RAS Monthly Notices of the Royal Astronomical Society  Spectral energy distribution (SED) fitting in the far-infrared (FIR) is greatly limited by a dearth of data and an excess of free parameters – from galaxies’ dust composition, temperature, mass, orientation, opacity, to heating from active galactic nuclei (AGN). This paper presents a simple FIR SED fitting technique joining a modified, single dust temperature greybody, representing the reprocessed starburst emission in the whole galaxy, to a mid-infrared (MIR) power law, which approximates hot-dust emission from AGN heating or clumpy, hot starbursting regions. This FIR SED can be used to measure IR luminosities, dust temperatures and dust masses for both local and high-z galaxies with three to 10+ FIR photometric measurements. While the fitting technique does not model emission from polycyclic aromatic hydrocarbons (PAHs) in the MIR, the impact of PAH features on integrated FIR properties is negligible when compared to the bulk emission at longer wavelengths. This fitting method is compared to IR template SEDs in the literature using photometric data on 65 local luminous and ultraluminous infrared galaxies, (U)LIRGs. Despite relying only on 2–4 free parameters, the coupled greybody/power-law SED fitting described here produces better fits to photometric measurements than best-fitting literature template SEDs (with residuals a factor of ∼2 lower). A mean emissivity index of β = 1.60 ± 0.38 and MIR power-law slope of α = 2.0 ± 0.5 is measured; the former agrees with the widely presumed emissivity index of β = 1.5 and the latter is indicative of an optically thin dust medium with a shallow radial density profile, ≈r−1/2 . Adopting characteristic dust temperature as the inverse wavelength where the SED peaks, dust temperatures ∼25–45 K are measured for local (U)LIRGs, ∼5–15 K colder than previous estimates using only simple greybodies. This comparative study highlights the impact of SED fitting assumptions on the measurement of physical properties such as IR luminosity (and thereby IR-based star formation rate), dust temperature and dust mass, for both local and high-redshift galaxies. Far-infrared SED fitting 2 SED FITTING TECHNIQUES 2.1 Coupled greybody/power-law fitting 2.1.1 Method Deriving the fundamental physical properties of IR-luminous galaxies can be as simple as assuming an isotropically emitting blackbody. This is represented as the Planck function, Bν (T) (e.g. in units of erg s−1 cm−2 Å−1 ), and is only dependent on dust temperature T. However, if the variation in opacity (e.g. assuming a screen of dust without scattering) and source emissivity is accounted for (the fact that very few sources are perfectly non-reflective), the flux density at rest-frame frequency ν is then represented by a modified blackbody (i.e. ‘greybody’) of the form S(ν) ∝ (1 − e−τ (ν) )Bν (T ) = (1 − e−τ (ν) )ν 3 , ehν/kT − 1  C 2012 The Author, MNRAS 425, 3094–3103 C 2012 RAS Monthly Notices of the Royal Astronomical Society  (1) where S(ν) is in units of erg s−1 cm−2 Hz−1 or Jy. Optical depth is τ (ν) and fitted as τ (ν) = (ν/ν 0 )β , where ν 0 is the frequency where optical depth equals unity (Draine 2006) and β represents emissivity, or the spectral emissivity index. See Kovács et al. (2010) for a thorough discussion of the impact on β. The value of β is largely assumed to be 1.5 (and usually ranges 1–2; Hildebrand 1983), although this could be a result of the original wavelengths for which data were gathered on local starbursting samples (Dunne & Eales 2001). Some recent work points to a wider range of β values between 1 and 2.5 (e.g. Casey et al. 2011; Chapin et al. 2011). The theoretically expected value of ν 0 is 3 THz (i.e. λ0 = 100 μm), although this value is unconstrained by data (see discussion in Conley et al. 2011). In the optically thin case, the term (1 − e−τ (ν) ) reduces to ν β , and the flux density simplifies to Sot (ν) ∝ ν β Bν (T ) = ν β+3 ehν/kT − 1 . (2) The normal range of dust temperatures expected for a galaxy’s interstellar medium (ISM) heated only by star formation ranges ∼20– 60 K. When fitted to a greybody (as in equation 1 or 2), most galaxies have a notable flux density excess at wavelengths shortward of ≈50 μm (see Fig. 1, panels A and B). This MIR excess is due to a combination of hotter dust subcomponents (where dust is more compact) or dust heated by an AGN, and an optically thin medium by which the higher frequency radiation can escape. The disconnect between the observed MIR luminosities and the predicted Wein-tail luminosities has been studied for quite some time; a quite thorough discussion of dust clouds’ opacity, radial density distributions and dust mass coefficients (κ ν ) impact on observed SED is given in Scoville (...truncated)