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Dust Masses, PAH Abundances, and Starlight Intensities in the SINGS Galaxy Sample

Dust Masses, PAH Abundances, and Starlight Intensities in the SINGS Galaxy Sample
Dust Masses, PAH Abundances, and Starlight Intensities in the SINGS Galaxy Sample

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To appear in The Astrophysical Journal

Dust Masses,PAH Abundances,and Starlight Intensities in the SINGS Galaxy Sample B.T.Draine 1,D.A.Dale 2,G.Bendo 3,K.D.Gordon 4,J.D.T.Smith 4,L.Armus 5,C.W.Engelbracht 4,G.Helou 6,R.C.Kennicutt 4,7,A.Li 8,H.Roussel 9,F.Walter 9,D.Calzetti 10,J.Moustakas 4,11,E.J.Murphy 12,G.H.Rieke 4,C.Bot 6,D.J.Hollenbach 13,K.Sheth 6,and H.I.Teplitz 5ABSTRACT Physical dust models are presented for 65galaxies in the SINGS survey that are strongly detected in the four IRAC bands and three MIPS bands.For each galaxy we estimate (1)the total dust mass,(2)the fraction of the dust mass contributed by PAHs,and (3)the intensity of the starlight heating the dust grains.We ?nd that spiral galaxies have dust properties resembling the dust in the local region of the Milky Way,with similar dust-to-gas ratio,and similar PAH abundance.The observed SEDs,including galaxies with SCUBA photometry,can be reproduced by dust models that do not require “cold”(T 10K)dust.The dust-to-gas ratio is observed to be dependent on metallicity.In the interstel-lar media of galaxies with A O ≡12+log 10(O /H)>8.1,grains contain a substantial

fraction of interstellar Mg,Si and Fe.Galaxies with A O<8.1and extended H I en-

velopes in some cases appear to have global dust-to-gas ratios that are low for their

measured oxygen abundance,but the dust-to-gas ratio in the regions where infrared

emission is detected generally appears to be consistent with a substantial fraction of

interstellar Mg,Si,and Fe being contained in dust.The PAH index q PAH–the frac-

tion of the dust mass in the form of PAHs–correlates with metallicity.The nine

galaxies in our sample with A O<8.1have a median q PAH=1.0%,whereas galaxies

with A O>8.1have a median q PAH=3.55%.The derived dust masses favor a value

X CO≈4×1020cm?2(K km s?1)?1for the CO to H2conversion factor.Except for some

starbursting systems(Mrk33,Tolo89,NGC3049),dust in the di?use ISM dominates

the IR power.

Subject headings:ISM:dust,extinction—ISM:general—galaxies:abundances—

galaxies:general—galaxies:ISM—infrared:galaxies

1.Introduction

Interstellar dust a?ects the appearance of galaxies,by attenuating short wavelength radiation from stars and ionized gas,and contributing infrared(IR),far-infrared(FIR),submm,mm,and microwave emission[for a recent review,see Draine(2003)].Dust also is an important agent in the ?uid dynamics,chemistry,heating,cooling,and even ionization balance in some interstellar regions, with a major role in the process of star formation.Despite the importance of dust,determination of the physical properties of interstellar dust grains has been a challenging task–even the overall amount of dust in other galaxies has often been very uncertain.

The SINGS galaxy sample(Kennicutt et al.2003)comprises75galaxies with a wide range of morphological types,all at distances allowing the galaxies to be resolved even at160μm.Ob-servations of this sample with all instruments on Spitzer Space Telescope(Werner et al.2004)are providing a new perspective on the dust abundances and dust properties in a diverse set of galaxies.

For67of the SINGS galaxies we have positive detections in the4bands of the Infrared Array Camera(IRAC;Fazio et al.(2004))and the three bands of the Multiband Imaging Photometer for Spitzer(MIPS;Rieke et al.(2004)),spanning wavelengths from3.6μm to160μm,the wavelength range within which dust radiates most of its power,including the PAH emission features that are prominent in many galaxies;65of these galaxies are used in the present study.For11galaxies we have global?uxes measured with the IRS16μm peak-up?lter.For17of the65galaxies,global 850μm?ux measurements are also available from the SCUBA camera on the JCMT.

The IR emission from dust depends not only on the amount of dust present,but also on the rate at which it is heated by starlight.We develop a technique for estimation of dust masses and starlight intensities in galaxies,and apply it to estimate the total dust mass M dust in each of the65

galaxies in this study.For61galaxies we are also able to estimate a“PAH index”q PAH–de?ned

here to be the mass fraction of the dust that is contributed by polycyclic aromatic hydrocarbon

(PAH)particles containing<103C atoms.In addition,we obtain information on the starlight

intensity distribution–the mean starlight intensity scale factor U ,and the fraction of the dust

heating that takes place in regions of high starlight intensities,including photodissociation regions.

The paper is organized as follows.The sample selection and observational data are summarized

in§2,the physical dust models that are used are described in§3,and the model-?tting procedure

is given in§4.In order to validate the model-?tting procedure,we?rst limit attention to the

subset of SINGS galaxies for which SCUBA data are available(we will refer to these as the SINGS-

SCUBA galaxies).In§5we demonstrate that the dust modeling procedure works well for most

of the SINGS-SCUBA galaxies,and we present dust masses,dust-to-gas mass ratios,PAH index

values,and starlight intensity parameters obtained from these model?ts.For the SINGS-SCUBA

galaxies,our models do not require any contribution from the very cold(<10K)dust that has been

reported by Krugel et al.(1998)for the spiral galaxies NGC6156and NGC6918,or the5–9K

dust that Galliano et al.(2003,2005)reported for low metallicity dwarf galaxies,or the4–6K dust

that Dumke et al.(2004)reported for the edge-on-spiral NGC4631.The global SEDs do not show

evidence for the submillimeter excess seen in the faint outer regions of NGC4631(Bendo et al.

2006b).

Submillimeter measurements are valuable to help constrain the dust models,but are unfor-

tunately not available for most galaxies.In§6we use the SINGS-SCUBA galaxies to develop a

“restricted”?tting procedure that can be applied to galaxies for which submillimeter?uxes are un-

available.For the17galaxies with global850μm?uxes from SCUBA,we show that the restricted

?tting procedure,without employing SCUBA data,recovers dust masses and starlight intensities

that are usually within a factor of two of the values obtained when the SCUBA data are used.

The restricted?tting technique is then applied to the remaining48galaxies to estimate dust

masses and starlight intensities.Dust-to-gas mass ratios for the overall sample are presented in

§7.1,where it is found that some of the SINGS galaxies have very low dust-to-gas ratios,and that the dust-to-gas ratios are correlated with both gas-phase metallicity and galaxy type.The

dust-to-gas ratios depend on the assumed value of X CO,the ratio of H2column density to CO

line intensity;in§9.4we argue that the distribution of derived dust-to-gas ratios supports X CO≈4×1020cm?2(K km s?1)?1.

Values of the PAH index q PAH are estimated for61galaxies in§7.4.Many galaxies are found

to have low values of q PAH,and q PAH is found to be strongly correlated with gas-phase metallicity.

The starlight parameters for the65galaxy sample are presented and discussed in§8.The results

are discussed in§9,and summarized in§10.

2.Data

2.1.IRAC and MIPS

Spitzer Space Telescope was used to observe all75galaxies in the SINGS sample,following the observing strategy described in Kennicutt et al.(2003).The observations in the4IRAC bands(3.6, 4.5,5.7,7.9μm)and3MIPS bands(24,71,160μm)have been reduced following the procedures described in Dale et al.(2005).The extended source aperture corrections found in Reach et al. (2005)were applied to the IRAC data.Global IRAC and MIPS photometry for these galaxies is taken from Dale et al.(2007),which included(usually modest)corrections for aperture size and nonlinearity of the71μm detectors.

Ten of the SINGS galaxies were excluded from the present study:

?NGC584(E4)may be contaminated by a background source,and also has low surface brightness in the MIPS bands compared to the foreground cirrus.

?NGC3034=M82(I0,starburst):Saturation of the bright core of this galaxy precludes global photometry.

?NGC1404(E1):An o?-center IR source contributes a signi?cant fraction of the MIPS?ux, but it is not known whether or not it is a foreground/background object.

?NGC4552(E0)has low surface brightness compared to the foreground cirrus emission,and the MIPS160μm photometry is very uncertain.

?The dwarf galaxies M81dwA and Ho IX are not detected atλ≥5.8μm.

?The dwarf galaxies DDO154and DDO165are only marginally(<3σ)detected at71and 160μm,and M81dwB is a<2σdetection at160μm.

?The dwarf starburst galaxy NGC1377shows strong silicate absorption at9.8μm and18μm (Roussel et al.2006).The objective of the present study is to model the IR spectra using a simple model that assumes the galaxy to be optically-thin atλ>3.5μm;because NGC1377 is clearly not optically thin,it has been removed from the sample.

The sample studied here therefore consists of65galaxies.MIPS71μm photometry for NGC7552 is not usable because of detector saturation,but NGC7552is retained in the sample because it is well-observed at other wavelengths and with other instruments.

Most of the dust mass in galaxies is relatively cool,radiating primarily at wavelengths in the MIPS71μm and160μm bands.Dust grains that are warmer,either because they are in regions with intense starlight,or because they are very small grains immediately following absorption of a stellar photon,may radiate strongly in the MIPS24μm band and shortward.The variety of dust

Fig. 1.—MIPS color-color plot for the65galaxies.The blue shaded area shows the region sampled by the17 galaxies for which global SCUBA?uxes are known(plotted as blue solid symbols)–these only partially cover the color-color space populated by the SINGS sample(green shaded area).Galaxies without SCUBA?uxes are shown in red.Galaxies with relatively extreme?ux ratios are labelled.

conditions found in the SINGS sample is evident from the distribution of the64galaxies in MIPS color-color space,shown in Figure1: νFν 71μm/ νFν 160μm varies by over a factor of10within our sample,and νFν 24μm/ νFν 71μm varies by a factor of8.These variations in MIPS colors presumably re?ect galaxy-to-galaxy di?erences in the intensity of the starlight heating the dust grains,although galaxy-to-galaxy di?erences in dust composition may also play a role.It is evident from the scatter in Figure1that the MIPS24/71color is not simply a function of the71/160color: the MIPS colors cannot be described by a one-parameter sequence of,e.g.,“dust temperature”. Realistic dust models will therefore need to vary at least two parameters to account for the range in observed MIPS colors.

The SINGS sample does not include any powerful AGN,and in all SINGS galaxies the global ?ux in the IRAC3.6μm band is starlight-dominated.Neglecting extinction,we can estimate the “nonstellar”?ux in longer-wavelength bands by subtracting the estimated stellar contribution, assuming a5000K blackbody.For IRAC band4,the IRS16μm Peakup band(see§2.2below)and

the MIPS24μm band,the nonstellar?uxes are:

F nsν 7.9= Fν 7.9?0.260 Fν 3.6,(1)

F nsν 16= Fν 16?0.0693 Fν 3.6,(2)

F nsν 24= Fν 24?0.0326 Fν 3.6.(3) The coe?cients0.260and0.0326in eq.(1)and(3)are close to the values0.232and0.032estimated by Helou et al.(2004).Some stars(e.g.,cool red giants,and AGB stars)have circumstellar dust that is in many cases warm enough to radiate strongly at wavelengths from8-30μm.If such stars are su?ciently numerous,the result will be a“stellar”contribution to the8,16,and24μm?uxes that will be larger than assumed in eq.(1–3).In the absence of extinction at3.6μm,equations (1–3)will therefore overestimate the?ux contributed by interstellar dust.

2.2.IRS16μm

In addition to IRAC and MIPS photometry,nine of the SINGS galaxies have been imaged using the IRS“blue peak-up”detector array,with nominal wavelengthλ=16μm.The IRS blue peak-up observations were taken as part of the IRS instrument calibration program and consist of a grid of peakup images covering the full extent of each galaxy.The reduced images,processed by IRS pipeline version S14,were mosaicked using the MOPEX program(ver.030106)to remove cosmic rays after subtraction of a custom dark image.This custom dark image was created using images taken beyond the visible extent of the galaxy.In some cases,the best dark subtraction was found to require allowing the dark image to vary with time.“Sky”(zodiacal light and Galactic cirrus)contributions were also removed by this custom dark subtraction step.The total16μm?ux was measured using the same methods used for the IRAC and MIPS?uxes(Dale et al.2005).The measured global?uxes were then scaled down by~15%,to account for a recent SSC calibration update(~10%),and the appropriate aperture correction factor(~5%).Fluxes for these11galaxies at16μm and24μm are given in Table1.The?ux density ratio Fν 16/ Fν 24varies considerably among these galaxies,from a low of0.376±0.033for NGC7552to a high of1.21±0.12for NGC3190.

Figure2a shows P16≡ νF nsν 16/( νFν 71+ νFν 160)vs.P24≡ νF nsν 24/( νFν 71+ νFν 160) for the ten galaxies for which we have16,24,71,and160μm photometry,where F nsνis the nonstellar contribution from eq.(1-3).The?ux ratio P16remains essentially constant at P16≈0.112±0.017 while P24varies by almost a factor of3,from0.06to0.18.This suggests that the16μm?ux is not emitted by the same grains as the24μm?ux.In the dust model of Draine&Li(2007, hereafter DL07),a minimum level of24μm emission is produced by single-photon heating of PAHs or ultrasmall grains(with νLν 24/L TIR≈0.03?0.06,depending on q PAH–see Fig.15of DL07), but P24increases as the starlight intensity increases.Figure2a suggests that the16μm emission may be dominated by single-photon heating of PAHs,remaining relatively constant even as P24 rises due to increased starlight heating.This is supported by Figure2b,which shows that the ratio

Fig.2.—(a)P16≡ νF nsν 16/( νFν 71+ νFν 160)versus P24≡ νF nsν 24/( νFν 71+ νFν 160)for the10galaxies imaged with the IRS16μm peak-up?lter for which we also have global MIPS?uxes(NGC7552is excluded).(b) νF nsν 7.9/ νF nsν 16vs P24,Both the ratio of nonstellar16μm emission to total IR power and the ratio of nonstellar 7.9μm emission to nonstellar16μm emission remain constant to within~15%,even as P24varies by a factor of3. of7.9μm emission to16μm emission is nearly constant for this sample,varying by only~±15% over the eight galaxies,consistent with the idea that both are primarily the result of single-photon heating of PAHs.This is consistent with the?nding by F¨o rster Schreiber et al.(2004)that,when averaged over disks of spiral galaxies,the15μm continuum intensity is proportional to the PAH intensity in the5–8μm region.

Table1.Global Fluxes(Jy)in IRS16μm Peak-Up Band

galaxy Fν 16 Fν 24 Fν 16/ Fν 24

Jy Jy

2.3.SCUBA

The dust properties in a galaxy will be best determined if submillimeter photometry is available

to constrain the quantity of cool dust present.SCUBA observations at450μm and/or850μm are

available for26of the65galaxies,1but not all of these are usable in the present study:

1.NGC4254,NGC4579,NGC5194,and NGC6946were scan-mapped,and the data processing

removes an unknown amount of extended emission.Thus global850μm(or450μm)?uxes

are not available for these galaxies.We restrict ourselves to data obtained in“jiggle map”

mode,except for the scan-map observations of NGC5195,for which background subtraction

is thought to be more reliable because of the smaller angular extent of NGC5195.

2.For some galaxies the SCUBA map did not fully cover the region where160μm emission is

detected.Dale et al.(2005)multiplied the observed SCUBA?uxes by a correction factor

based on the fraction of the160μm emission coming from the region mapped by SCUBA.

Because the850μm/160μm?ux ratio may be spatially variable,we choose here to not use

the850μm?ux estimates for galaxies where the corrrection factor exceeds1.6(NGC1097,

NGC4321,NGC4736,and NGC5033).

3.For the Sombrero galaxy,NGC4594,the850μm?ux is dominated by the AGN(Bendo et al.

2006a),and the extranuclear850μm?ux is not reliably measured,so we cannot use the

SCUBA data to constrain the dust model for this galaxy.

We thus have17galaxies where the dust models are constrained by850μm SCUBA data(with

450μm?uxes for3of the17)in addition to IRAC and MIPS data.The global?uxes F obs,b and

1-σuncertainties for each band b are taken from Dale et al.(2007).

The162galaxies for which we have global SCUBA and MIPS photometry are indicated in

Figure1.While the galaxies with SCUBA photometry span a considerable portion of the populated

region in MIPS color-color space,a number of the SINGS galaxies have MIPS colors that are outside

of the range seen among the galaxies for which SCUBA data are available.For example,NGC4725

or NGC5408,with νFν 71μm/ νFν 160μm=0.33and3.1,respectively,fall outside the range0.6–2.4observed for this ratio among the SINGS-SCUBA galaxies.The dust models discussed below

are able to reproduce the IRAC and MIPS?uxes for all of the SINGS galaxies.Galaxies such as

NGC4725or NGC2841,with the lowest values of νFν 71μm/ νFν 160μm,require cooler dust(i.e., lower starlight intensities)than any of the SINGS-SCUBA galaxies.NCG5408,with a very high value of νFν 71μm/ νFν 160μm,requires hotter dust(higher starlight intensities).Submillimeter observations would be of great value to test the predicted submm?uxes from these extreme cases.

2.4.IRAS and ISO

IRAS photometry is obtained from the latest SCANPI data for most SINGS sources,and from HiReS maps for the largest SINGS targets(optical diameters 10′),except in some bands(e.g., no IRAS12μm?ux for NGC0024).A20%calibration uncertainty estimate was applied.In the case of NGC5195(=M51b),the proximity of NCG5194(=M51a)made?ux determination more di?cult,and50%uncertainty estimates were adopted.

Ths IRAS25μm?ux densities are not used,as they are superseded by the MIPS24μm pho-tometry at essentially the same wavelength,but we employ the IRAS12μm,60μm,and100μm photometry in our model-?tting.

When available,we show ISOCAM6.75μm and15μm photometry in the?gures showing the spectral energy distributions(SEDs),but they are not used in the model-?tting.

3.Physical Dust Models

A direct estimate for the dust-to-hydrogen mass ratio M dust/M H in the local Milky Way can be obtained from the di?erence between total interstellar abundances–taken to be equal to current estimates for solar abundances–and observed gas phase abundances in di?use interstellar clouds, where the intensively studied di?use cloud on the line-of-sight toζOph is taken to be representative. Using current estimates of solar abundances,this mass inventory results in M dust/M H≈0.0073 (see Table2).

We will apply(and thereby also test)the dust models developed by Weingartner&Draine (2001a,hereafter WD01)and Li&Draine(2001,hereafter LD01),and updated by DL07.These dust models consist of speci?ed mixtures of carbonaceous grains and amorphous silicate grains,with the smallest carbonaceous grains having the physical properties of polycyclic aromatic hydrocarbon (PAH)particles;the size distributions are chosen to reproduce the observed wavelength-dependent extinction in the local Milky Way,in the Large Magellanic Cloud,and the Small Magellanic Cloud bar region(Weingartner&Draine2001a).Li&Draine(2001,2002)showed that these grain models appeared to be consistent with the observed IR emission from di?use clouds in the Milky Way and the Small Magellanic Cloud.

The DL07dust models used here adopt PAH optical properties that are slightly di?erent from those adopted by LD01.As discussed by DL07,the changes are in part to better conform to recent theoretical estimates for band strengths,and in part to improve agreement with band pro?les determined observationally by Smith et al.(2007).

The PAH emission features at3.3μm,6.2μm,7.7μm,8.6μm,11.3μm,12.0μm,12.7μm,16.4μm, and17μm are prominent in many galaxy spectra,and the dust models considered here include various abundances of PAHs;in each model the PAHs have a wide range of sizes.Because PAH

Table2.Dust Mass per H from Milky Way Abundances X(N X/N H)⊙(ppm)a(N X/N H)gas/(N X/N H)⊙a M X,dust/M H

total0.0073

Table3.Physical Dust Models

A V/N H

j M Model q PAH M dust/M a,b

H

%mag cm2/H

000.470.01005.3×10?22 2MW3.1

20 1.770.01015.3×10?22

4MW3.1

40 3.190.01025.3×10?22

6MW3.1

60 4.580.01045.3×10?22

8LMC2

05 1.510.003441.2×10?22

10LMC2

a M H≡M(H I+H2)

b M dust/M gas=[M dust/M H]/1.36

emission is mainly the result of single-photon heating,the PAH emission spectrum depends on the size(heat capacity)of the PAH.The prominent6.2μm,7.7μm,and8.6μm emission features are primarily due to PAHs with 103C atoms[see Fig.7of Draine&Li(2007)].Following DL07, we characterize the PAH abundance by a“PAH index”q PAH,de?ned to be the percentage of the total grain mass contributed by PAHs containing less than103C atoms:

q PAH≡M(PAHs with N C<103)

starlight in such regions implies that the dust grains located there radiate only a very small fraction of the total IR power.As will be seen below,an ice-free dust model appears to be satisfactory for modeling the IR emission from normal galaxies.

4.Constraining the Dust Model and Starlight Intensities

In addition to choosing a physical dust mixture(relative numbers of carbonaceous grains and silicate grains of di?erent sizes,including the fraction q PAH of the dust mass that is in PAHs), we must specify the intensity of the radiation that is heating the dust grains.Almost all of the heating of dust grains in a normal galaxy is from absorption of hν<13.6eV photons.In a normal star-forming galaxy a signi?cant(but sub-dominant)fraction of the stellar luminosity may be at hν>13.6eV,but most of these photons end up photoionizing hydrogen or helium rather than being absorbed by dust.The hν<13.6eV recombination radiation–especially Lymanα–may be largely absorbed by dust.However,the total power in ionizing photons is a minor fraction of the total stellar luminosity in a galaxy with a more-or-less steady rate of star formation.Only in galaxies that have undergone an extreme burst of star formation within the last~107yrs will the dust heating be dominated by Lymanαand Lyman continuum radiation.Only in rare cases,e.g., NGC1377(Roussel et al.2006),where the massive stars formed in a starburst are surrounded by dense,dusty H II regions,will the dust grains directly absorb a major fraction of the hν>13.6eV radiation.

The IR emission from dust is relatively insensitive to the detailed spectrum of the hν<13.6eV photons,and the DL07models simply adopt the spectrum of the local interstellar radiation?eld as a reasonable representation for the average spectrum of the interstellar radiation in a normal spiral galaxy.The speci?c energy density of starlight is therefore taken to be

,(5)

uν=U×u(MMP83)

ν

where u(MMP83)

νis the speci?c energy density estimated by Mathis et al.(1983)(hereafter MMP83) for the local Galactic interstellar radiation?eld,and U is a dimensionless scale factor.The intensity of interstellar UV radiation is often characterized by G0,the ratio of the6–13.6eV energy density relative to the value5.288×10?14ergs cm?3for the radiation?eld estimated by Habing(1968). The MMP83ISRF has u(0?13.6eV starlight)=8.65×10?13ergs cm?3,and u(6?13.6eV)= 6.01××10?14ergs cm?3.Thus U=0.88G0.

Dust at di?erent locations in the galaxy will be exposed to di?erent radiation intensities.A physically correct model would specify the locations of the stellar sources and the absorbing dust, and would solve the radiative transfer problem[e.g.,Tu?s et al.(2004)],but this would require many uncertain assumptions about the relative distributions of stars and dust,as well as massive numerical computations.

Following DL07,we suppose that a large fraction of the dust in a galaxy is located in the

di?use interstellar medium,exposed to starlight with an intensity that does not vary much within

the galaxy.This“di?use ISM”dust is idealized as being heated by a single radiation?eld,with

intensity factor U=U min.In addition,DL07suppose that a small fraction of the dust is located

in regions where the radiation?eld is more intense,with a wide range of intensities ranging from

U=U min to U=U max?U min.This would include dust in photodissociation regions,so we refer to this as the“PDR”component,and we use the power-law distribution function used by DL07.

Although this“PDR”component contains only a small fraction of the total dust mass,in some

galaxies it contributes a substantial fraction of the total power radiated by the dust.The models

do not include a component corresponding to cold dust in dark clouds;as discussed in§9.1,such

cold dust appears to account for a minor fraction of the dust mass,and a very small fraction of the

total dust luminosity.Thus,following DL07,we take the dust mass dM dust exposed to radiation

intensities in[U,U+dU]to be a combination of aδfunction and a power-law,

dM dust

U1?α

min?U1?αmax U?αfor U min≤U≤U max,α=1(6)

whereδis the Diracδfunction.This distribution function has?ve parameters:the total dust mass M dust,the fractionγof the dust mass that is associated with the power-law part of the starlight intensity distribution,and3parameters(U min,U max,α)characterizing the distribution of starlight intensities in the high intensity regions.Theδ–function term represents the fraction (1?γ)of the dust that is heated by a general di?use interstellar radiation?eld with approximately uniform intensity~U min.The power-law part of the distribution function,introduced by Dale et al. (2001)and used by Li&Draine(2002),represents the fractionγof the dust mass that is close to OB associations and is exposed to radiation with intensity U>U min;this includes the dust in“photodissociation regions”(PDRs),where radiation intensities can be orders of magnitude higher than the“average”dust grain is exposed to.Equation(6)is a very simplistic description of the distribution of dust grain environments;it neglects the possibility that the dust properties (composition,size distribution)might be variable and correlated with U,and also neglects regional variations in the spectrum of the starlight irradiating the dust.Despite its simplicity,we will see here that eq.(6)appears to capture the essential elements of the distribution of starlight intensities found in galaxies,yielding models with SEDs that approximate what is observed.

Very small particles cool almost completely between photon absorptions,and therefore the shape of the emission spectrum from these grains is almost independent of U.The larger grains, that account for more than half of the total absorption of starlight in the Milky Way,do not cool signi?cantly between photon absorptions,and their temperature depends on the intensity U. The observed FIR emission spectrum is sensitive to the temperature of these larger grains,and therefore allows us to constrain the distribution function for U.While Spitzer Space Telescope provides unprecedented sensitivity to FIR emission,the spectral coverage is somewhat sparse,with

a factor of3gap in wavelength between IRAC7.9μm and the MIPS24μm bands,and a factor of

2.9gap between the MIPS24μm and71μm bands.The IRS“Peak-Up”mode observations can be used for imaging at16μm and26μm,but these observations are not generally available.The large

gaps in wavelength coverage leave considerable uncertainty in the spectral energy distribution at wavelengths between the bands.3Furthermore,the longest wavelength band,at160μm,falls on the short wavelength side of the emission peak for dust temperatures T d (1/6)hc/(160μm)=15K.As a result,Spitzer photometry does not strongly constrain the abundance of dust with temperatures T d 15K.To determine the amount of cool dust,global submillimeter observations are required. Fortunately,such data exist for17of the65galaxies for which we have complete Spitzer photometry (or near-complete in the case of NGC7552),and this subsample will be analyzed?rst,in§5.

We select a model for the IR emission from a galaxy as follows.For each size and composition of dust,we precompute and tabulate the temperature distribution function for the dust grain illuminated by the radiation?eld of eq.(5)for selected values of U(with0.1≤U≤107),using heat capacities,absorption cross sections,and numerical methods described by Draine&Li(2001), LD01,and DL07.Neutral and ionized PAHs are assumed to have di?erent absorption cross sections. The ionized fractionφi(N C)(a function of the number N C of carbon atoms in the PAH)will depend primarily on the ratio U

T e/n e as the Milky Way).Our model-?tting procedure assumes that all galaxies have the same shape for the PAH size distribution,the same PAH ionized fraction φi(N C),and the same spectral shape of the illuminating starlight.As a result,our model?ts have ?xed ratios of PAH emission band strengths.Observations do reveal variations in PAH band ratios from one galaxy to the next–for example,L(7.7μm)/L(11.3μm)varies from~4–5to 0.7as we progress from H II-dominated nuclei to AGN-dominated nuclei(Smith et al.2007),and low values of L(7.7μm)/L(11.3μm)are also seen in some AGN-free galactic and extragalactic regions(e.g., Reach et al.2000;Hony et al.2001;Pagani et al.1999)–but most spiral galaxies have global PAH feature ratios that are near-average and characteristic of star-forming regions.

With these temperature distribution functions for the dust,and the dust absorption cross section C abs(λ),we can calculate the time-averaged IR emission for a given grain type and size for each of the discrete values of U considered;we then sum over the grain types and sizes for a dust model j M(see Table3)to?nd the power radiated per unit frequency per unit mass of dust mixture j M exposed to starlight intensity U:

p(0)ν(j M,U)=1

da j M

dT dP(k,a)

3In principle,the IRS instrument can provide6–36μm photometry,and the MIPS SED mode covers55–95μm, but observing time considerations preclude using these observing modes for large areas.

4Following LD01,we assume43%of the dust to be in the“cold neutral medium”(CNM;n e/U≈0.045cm?3, T≈100K),43%to be in the“warm neutral medium”(WNM;n e/U≈0.04cm?3,T≈6000K),and14%to be in the“warm ionized medium”(WIM;n e/U≈0.1cm?3,T≈8000K).The resultingφi(N C)is shown in Fig.7of LD01 and Fig.8of DL07.

M(j M)≡ k da dn k3ρk,(8)

where the sum runs over the di?erent grain types k(amorphous silicate,graphite,PAH0,PAH+) in the DL07dust model,withρk the density of material k,and n k(a)being the number of dust grains of type k per H nucleon,with radii≤a.

We also calculate the speci?c power per unit dust mass

(α?1)

pν(j M,U min,U max,α)≡

4πD2 (1?γ)p(0)ν(j M,U min)+γpν(j M,U min,U max,α) ,(10) where??is the solid angle subtended by the stars.For each(j M,U min,U max,α),we obtain??, M dust,andγby minimizing

χ2≡ b[F obs,b? Fν,model b]2

For the MW dust models,there are e?ectively7adjustable parameters:??,M dust,q PAH(via

j M),γ,U min,U max,andα.However,we will?x one of these parameters from the outset,by setting

α=2.This choice is based on experimentation that indicated that the quality of the?t is not

very sensitive to the precise value ofα,withα≈2providing satisfactory?ts for diverse galaxies.

Therefore we start with6parameters to be adjusted.For the galaxies with SCUBA data,we will

examine the e?ects of varying U max,but we will see in§5.4.2that setting U max=106works well;

therefore,the number of adjustable parameters is,e?ectively,5:??,M dust,q PAH,U min,andγ.

If the number of observed bands is N b,the number of degrees of freedom=(N b?5)where N b ranges from N b=9(e.g.,NGC0024,with4IRAC bands,3MIPS bands,and IRAS60,100μm)to

N b=12(e.g.,NGC3190with4IRAC bands,3MIPS bands,IRS16μm,IRAS12,60,100μm,and

SCUBA850μm).To assess the goodness of?t,we calculateχ2per degree of freedom:

χ2r≡χ2

18

Fig.3.—(a)SED for the SAap galaxy NGC3190.Rectangles show observed?uxes in the IRAC,MIPS,SCUBA bands,and the IRS16μm band;diamonds show2MASS2.2μm,and IRAS12,60,and100μm,?uxes.Vertical extent of rectangles and diamonds corresponds to±1σrange,and width corresponds to nominal width of band.Solid line shows best-?t model U max=106model,with IRAC,MIPS,IRS16μm,IRAS,and SCUBA data used to constrain the ?t;N b=12for NGC3190.Triangles show model convolved with the IRAC,MIPS,IRS16μm,IRAS,and SCUBA bands.Dot-dashed curves show separate contributions of starlight and emission from dust heated by U=U min (labelled“di?”),and dust heated by U min

The models are generally very successful in?tting the observed SEDs.The SED of NGC3190,

together with a model?t,appears in Figure3a.This is an example where the model(with U min=

2.5,U max=107,γ=1.5×10?3)provides an excellent?t to the observations,withχ2r=0.38.

The inferred dust mass is M dust=107.19M⊙,and the mean starlight intensity is estimated to be

U =2.6.Only a small fractionγ≈0.0015of the dust is in regions with starlight intensities U>U min.Also shown in Figure3a(solid line)is a?t with the upper cuto??xed at U max=106.

The model SED is nearly identical(the solid curve and dash-dot curves coincide in the plot)and

the derived dust mass is unchanged.

Figure3b shows the SED of NGC2798,a galaxy where the dust is considerably warmer than

in NGC3190.The best-?t dust model(U min=8,U max=105,γ=0.09)provides a good?t

(χ2r=0.45)to the observations,but the model with U max=106provides nearly as good a?t

(χ2r=0.46),a derived dust mass di?ering by only0.04dex,and similar q PAH(2.0%vs.2.5%).

The model?ts to NGC2798both have a noticeable“bump”near~33μm,produced by

the warm graphite grains in the DL07model.The small but nonzero conductivity for E c in

graphite5causes the absorption cross section C abs to rise to a broad local maximum near~33μm

(Draine&Lee1984,DL07).When exposed to starlight with U 104,graphite grains produce a broad emission bump peaking in the30–35μm region,depending on U.Unfortunately,the MIPS 24μm and71μm bands straddle this feature,and do not constrain it.Implications of the model 33μm feature are discussed below in§9.3.

Fig.4.—Histograms of M dust/M(H I+H2)for the12galaxies in the sample for which both H I21cm and CO1-0 have been measured,using X CO=4×1020cm?2(K km s?1)?1to estimate M(H2).

5.2.Dust-to-Gas Ratio

If the interstellar abundances of carbon and all heavier elements were proportional to the gas-phase oxygen abundance,and if the same fraction of the major condensible elements(C,O,Mg, Si,Fe)were in solid form as in the Milky Way,then all galaxies would be expected to conform to

M dust

,(13)

(O/H)MW

where(O/H)MW is the oxygen abundance in the local Milky Way,and the factor0.010is from the MW dust models in Table3.

Table4gives the estimated dust mass M dust for the17galaxies.For many of the galaxies there are measurements of21cm emission and CO emission from which the masses of H I and H2

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