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**FULL TITLE** ASP Conference Series, Vol. **VOLUME**, **YEAR OF PUBLICATION** **NAMES OF EDITORS**

A Simple Mo del For Mid-Infrared Emission from Normal Galaxies
B. Nikolic
1 2 1,2

, P. Alexander2 and D. Ford

2

NRAO, 520 Edgemont Road, Charlottesvil le, Va 22903, USA Astrophysics Group, Cavendish Laboratory, Cambridge CB3 0HE, UK

Abstract. We have combined up-to-date stellar population synthesis models, a simple radiative transfer approach, and a fully comprehensive dust model with the aim of developing a simple but quantitative way of interpreting the midinfrared spectra of galaxies. We apply these models to the observed correlations of mid-infrared luminosities (at 8 and 24 µm) with the star-formation rate of normal galaxies and find that the observations are naturally reproduced by our models. We further find that the observed 24 µm correlation places a weak constraint on relative distribution of dust and stars.

1.

Intro duction

Mid-infrared (mid-IR) emission from galaxies provides information on their energetics which is complementary to the far-infrared (far-IR) and arguably more useful. The reason for this is that the very small dust grains, which pro duce this emission, can b e sto chastically heated (Purcell 1976) by energetic photons, so that their p eak temp eratures are indep endent of their time-averaged temp eratures, in which case the colour temp erature of their emission is indep endent of the intensity of the radiation which heats them (Sellgren 1984). Consequently, when dust in this regime dominates the mid-IR luminosity of a galaxy, this luminosity, even when estimated from a narrow band filter, is an intrinsically weak function of the spatial distribution of the dust. This has motivated us to develop a simple mo del for the infrared emission from galaxies, concentrating on those wavelengths where transient heating can dominate. Clearly, this requires an accurate treatment of transiently heated dust and so we use the state-of-the-art techniques presented by Draine & Li (2001), Li & Draine (2001) and Weingartner & Draine (2001). We make the connection to galaxy energetics by using starburst99 (Leitherer et al. 1999) simple stellar p opulation mo dels, and simple radiative transfer, to calculate the radiation field which is heating the dust. 2. Metho d

The mo delling pro cedure we employ consists of three distinct parts: (1) Calculating the radiation field heating the dust, taking into account geometric effects and absorption by the dust; (2) Calculating the infrared radiation emitted by the dust; and, (3) Calculating the subsequent re-absorption of this infrared radiation by any further dust it encounters. 1


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Nikolic, Alexander & Ford

As mentioned ab ove, we assume the dust to b e heated by a single p opulation of stars mo deled using starburst99 (Vґ azquez & Leitherer 2005). Being interested primarily in the transiently heated regime, we consider a simple configuration in which the dust is in a geometrically thin spherical shell of radius R, with optical depth set by its total column density of hydrogen atoms n. The radiation field which heats the dust is calculated by assuming it to emanate from a central source and b e isotropic and conserved at radii less than that of the dust shell. Absorption of radiation as it traverses the shell is taken into account although scattering is neglected. For consistency, the absorption cross section of the dust is derived from the same dust mo del used to calculate the emission from the dust. Although this mo del ­ a single heating source surrounded by a single dust shell ­ is a p o or approximation to most normal star-forming galaxies, it is entirely equivalent to a more realistic mo del. If we alternatively assume star-formation to b e distributed over N indep endent sites, each with an equal star-formation rate, and a dust shell at the same radius R, this is equivalent to putting all of the star-formation in a single region and the dust at an effective radius Reff = R N . The emission from the dust is calculated using the `thermal-continuous' mo del of Draine & Li (2001) and the dust mo del parameters derived by Li & Draine (2001) and Weingartner & Draine (2001) for the lo cal interstellar medium. The final stage of the mo del is to take account of the re-absorption of this emission by further dust. Here we make another simplification by assuming that if the total column density of the dust shell is n, then any emission from dust at a p oint with column density to heating source is n will itself b e attenuated by a further column density n - n b efore escaping the shell.

3.

Results

To investigate the applicability of these mo dels to real galaxies, we tested how well they repro duce the observed correlation b etween mid-IR luminosities and star-formation rates (as traced by extinction-corrected H luminosities) of galaxies in the Spitzer extragalactic First Lo ok Survey (FLS) field (Wu et al. 2005). We rep eated the analysis of Wu et al. (2005) to obtain K -corrected 8 µm and 24 µm dust luminosities and extinction and ap erture corrected H data for these galaxies. We exclude galaxies dominated by active galactic nuclei by using the standard emission-line diagnostics. Mo del mid-IR luminosities were obtained by convolving our synthetic dust sp ectra (for a range of star-formation rates) with the Spitzer filter resp onse curves. The H luminosities for the same range of star-formation rates were obtained by converting the ionising photon pro duction rate from starburst99 stellar p opulation mo dels. The results of this comparison are shown in Figure 1, which plots the observed data p oints on the mid-IR vs H luminosity plane, together with the b est-fitting p ower law curve published by Wu et al. (2005, dashed line) and the exp ected mo del correlation for Reff = 2 kp c (solid line). With the dust mo del parameters fixed to Galactic values, the only free parameter we consider in the mo dels is Reff , the effective radius. We chose Reff = 2 kp c for the mo dels shown in Figure 1 as it yielded the b est fit to the observed correlation. The effect that


Mid-IR Emission from Normal Galaxies
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Figure 1. The correlation observed in the Spitzer FLS field between mid-IR and H luminosities (points), together with our models (solid lines) and the best-fitting power-law model of Wu et al. (2005, dashed lines). The left plot is for the IRAC 8 µm channel; the right for the MIPS 24 µm channel.
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Figure 2. A comparison of the predicted dust luminosities (broken line styles) as a function of H luminosity and the observed best-fitting power-law correlation (solid line). The shell radii were 100 pc, 2 kpc and 5 kpc for the dashed, dotted and dash-dot-dash line styles respectively (the 2 kpc and 5 kpc traces essentially overlay each other). The left plot is for the IRAC 8 µm channel; the right for the MIPS 24 µm channel.

varying Reff has on the mo del correlations is shown in the left and right panels of Figure 2 for the 8 µm and 24 µm mid-IR luminosities resp ectively. 4. Discussion and Conclusions

It can b e seen from the mo del correlation b etween mid-IR and H luminosities, shown by the solid lines in Figure 1, that mid-IR luminosity is largely a linear tracer of the star-formation rate if all of the mo del parameters are constant, as would b e exp ected for transiently heated dust. The figure also shows that the 8 µm luminosity is in theory more linear than the 24 µm luminosity. This is the case b ecause multiple-photon heating of grains can b e a significant source of emission at 24 µm at high star-formation rates. It is, however, the comparison with real galaxies that is of most interest. In Figure 1, we also show the observed p ositions on the luminosity-luminosity plane of galaxies in the FLS as well as the b est-fitting p ower-law curve of Wu et al.


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(2005). Given the relative simplicity of the mo dels we describ e, the agreement with the data is remarkably go o d. In particular, we find that the constant of prop ortionality b etween mid-IR and H luminosities is easily repro duced by our mo dels, which may b e interpreted as evidence that transiently heated dust dominates mid-IR luminosities of galaxies and that most of the radiation pro duced by young stars is absorb ed by the dust rather than escap e the galaxy. There is, however, a significant deviation b etween the data and the mo del for the 8 µm luminosity. At low H luminosities, some of the galaxies have much smaller mid-IR luminosities than would b e exp ected from the mo del. This has b een observed by Wu et al. (2005) and interpreted as due the now well-known deficiency of mid-IR emission from dwarf galaxies (e.g., Houck et al. 2004). There is also a trend for galaxies with high H luminosities to have smaller mid-IR luminosities then predicted by the mo del. This is reflected in the b est-fitting p ower law of Wu et al. (2005) which has a slop e smaller than one. This deviation is not repro duced by our mo dels which have a slop e close to one. The reason for the relatively low 8 µm emission from the most intensely star-forming galaxies is not clear. It may due to increasingly high obscuring column densities, causing the 8 µm mid-IR emission to b ecome re-absorb ed. Alternatively, it may b e due to destruction of the smallest dust grains, e.g., those with radii around 3.5 ° to A 5 ° which dominate the emission at 8 µm. A, In contrast, the correlation b etween the 24 µm and H luminosities app ears to follow our mo del well at high H luminosities. The larger size of grains resp onsible for 24 µm emission makes it p ossible to place a constraint on the relative distribution of dust and the heating sources. Figure 2 shows that effective radii in the range 1­5 kp c give a go o d agreement with the observations. The implication is that the dust resp onsible for the bulk of 24 µm emission is not necessarily very close to regions of active star formation or very hot. The observed correlation is well repro duced by placing the dust relatively far from the heating sources. Acknowledgments. We would like to thank the Spitzer FLS group for making available the data and source catalogs at 8 µm, C. Pap ovich for making available the 24 µm source catalog (Pap ovich et al. 2005) and the group at MPA for making providing emission line measurements of SDSS galaxies in the FLS 1 .
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