We have derived the dust emissivity in the Far-Infrared (FIR) using data
available in the literature. We use two wavelength dependences derived from
spectra of Galactic FIR emission (Reach et al. 1995). A value for the
emissivity, normalised to the extinction efficiency in the V band, has been
retrieved from maps of Galactic FIR emission, dust temperature and extinction
(Schlegel et al. 1998).
  Our results are similar to other measurements in the Galaxy but only
marginally consistent with the widely quoted values of Hildebrand (1983)
derived on one reflection nebula. The discrepancy with measurements on other
reflection nebulae (Casey 1991) is higher and suggests a different grain
composition in these environments with respect to the diffuse interstellar
medium.
  We measure dust masses for a sample of six spiral galaxies with FIR
observations and obtain gas-to-dust ratios close to the Galactic value.Comment: 5 pages, 1 ps file, A&A letter accepte

Alton, Paul B.

Bianchi, Simone

Davies, Jonathan I.

English

arXiv

We have derived the dust emissivity in the Far-Infrared (FIR) using data available in the literature. We use two wavelength dependences derived from spectra of Galactic FIR emission (Reach et al. 1995). A value for the emissivity, normalised to the extinction efficiency in the V band, has been retrieved from maps of Galactic FIR emission, dust temperature and extinction (Schlegel et al. 1998).



Our results are similar to other measurements in the Galaxy but only marginally consistent with the widely quoted values of Hildebrand (1983) derived on one reflection nebula. The discrepancy with measurements on other reflection nebulae (Casey 1991) is higher and suggests a different grain composition in these environments with respect to the diffuse interstellar medium.



We measure dust masses for a sample of six spiral galaxies with FIR observations and obtain gas-to-dust ratios close to the Galactic value

Bianchi, S.

Davies, Jonathan Ivor

Alton, P. B.

Online Research @ Cardiff

Astron. Astrophys. 344, L1–L4 (1999) ASTRONOMYANDASTROPHYSICSLetter to the EditorDust emissivity in the far-infraredSimone Bianchi, Jonathan I. Davies, and Paul B. AltonDepartment of Physics and Astronomy, University of Wales, P.O. Box 913, Cardiff CF2 3YB, UKReceived 4 December 1998 / Accepted 18 February 1999Abstract. We have derived the dust emissivity in the Far-Infrared (FIR) using data available in the literature. We usetwo wavelength dependences derived from spectra of Galac-tic FIR emission (Reach et al. 1995). A value for the emissivity,normalised to the extinction efficiency in the V band, has beenretrieved from maps of Galactic FIR emission, dust temperatureand extinction (Schlegel et al. 1998).Our results are similar to other measurements in the Galaxybut only marginally consistent with the widely quoted valuesof Hildebrand (1983) derived on one reflection nebula. The dis-crepancy with measurements on other reflection nebulae (Casey1991) is higher and suggests a different grain compositionin these environments with respect to the diffuse interstellarmedium.We measure dust masses for a sample of six spiral galaxieswith FIR observations and obtain gas-to-dust ratios close to theGalactic value.Key words: ISM: dust, extinction – infrared: ISM: continuum– infrared: galaxies1. IntroductionAssessing the quantity of dust in spiral galaxies is of primary im-portance in both understanding the intrinsic properties of galax-ies themselves and interpreting observations of the distant uni-verse: large quantities of dust can modify the optical appearanceof galactic structures like spiral arms (Trewhella 1998); if thedistribution of dust is extended, a large fraction of the radiationfrom the distant universe can be blocked (Ostriker & Heisler1984); star formation as determined from UV fluxes could beseverely underestimated thus altering our knowledge of the starformation history of the universe (Hughes et al. 1998).Dust mass can be retrieved from extinction or from emissionin the FIR. In the former case information about the star-dustrelative geometry is needed and the method can only be appliedto nearby edge-on galaxies, where the dust distribution can beinferred from extinction features (Xilouris et al. 1997, 1998). Inthe latter case there are no such limitations, and the wealth ofSend offprint requests to: Simone.Bianchi@astro.cf.ac.ukdata in the FIR and Sub-mm from instruments like the Sub-mmcamera SCUBA and from the satellites ISO and COBE, can beused to measure dust mass. Unfortunately, the determinationof dust mass is entangled with that of dust temperature andthey both rely on knowledge of the dust emissivity (Hildebrand1983), the form of which is currently highly uncertain.The emissivity (or emission efficiency, i.e. the ratio betweenthe emission cross section and the geometric cross section),Qem(λ) is usually described by a function of the formQem(λ) = Qem(λ0)(λ0λ)β(1)whereQem(λ0) is the value of the emissivity at the referencewavelengthλ0, andβ is the wavelength dependence index.While a valueβ = 1 seems to be plausible forλ < 100 µm(Hildebrand 1983; Rowan-Robinson 1992), there is observa-tional evidence for a steeper emissivity at longer wavelengths.The difference in emissivity is not unexpected, since emissionin the Mid-Infrared (25–60µm) is dominated by transientlyheated grains, while atλ > 100 grains emit at thermal equi-librium (Whittet 1992). Sub-mm observations of spiral galaxies(Bianchi et al. 1998; Alton et al. 1998b) show that it is not pos-sible to use an emissivity withβ = 1 to fit the 450 and 850µmemission. Reach et al. (1995) came to a similar conclusion. Theyused the spectrum of the Galactic plane observed by the spec-trophotometer FIRAS on board the satellite COBE, to find thatthe data are well fitted by an emissivity:Qem(λ) ∝ λ−2[1 + (λ1/λ)6]1/6 , (2)for the range 100µm to 1 cm. Eq. (2) behaves like (1) withβ = 1at smallλ (λ  λ1) andβ = 2 at largeλ (λ  λ1) (they setλ1 = 200-µm).Masi et al. (1995) measure a valueβ = 1.54 by fitting a sin-gle temperature grey-body spectrum to Galactic plane data infour bands between 0.5 and 2-mm taken by the balloon born tele-scope ARGO. Reach et al. (1995) suggest that a single tempera-ture fit may bias towards lower values ofβ (see also Wright et al.1991); over the whole FIRAS spectral range, a two temperaturegrey-body withβ = 2 at largeλ provides a significantly betterfit than a single temperature spectrum withβ ≈ 1.5. At longLETTERL2 S. Bianchi et al.: Dust emissivity in the far-infraredwavelengths theoretical calculations for crystalline substancesconstrainβ to be an even integer number (Wright 1993). Foramorphous materialsβ depends on the temperature: Agladze etal. (1996) find1.2 < β < 2 for amorphous silicate grains at atemperature of 20 K.A value for the emissivity at a specific wavelengthQem(λ0)normalised to the extinction efficiency in the optical can be de-termined by carrying out an energy balance in a reflection neb-ula, comparing the energy absorbed from the central star withthe FIR output from the surrounding dust. Alternatively, theextinction measured toward the star can be directly comparedto the optical depth in the FIR (Whitcomb et al. 1981; Hilde-brand 1983; Casey 1991). These methods are complicated bythe unknown nebular geometry and by temperature gradients inthe dust; as an example, Casey (1991) found that the extinctionmethod usually retrieves higher values than the energy balance.In this paper we use the extinction method comparing theGalactic extinction to FIR emission: in this case the same col-umn density of dust is responsible both for emission and extinc-tion and a reliable result can be obtained.2. The methodSchlegel et al. (1998; hereafter SFD) have presented a new mapof Galactic extinction. After removing emission from zodiacallight and a cosmic infrared background, they have combined the100µm map of Galactic emission taken by the DIRBE exper-iment on board the COBE satellite with the 100µm large-areaISSA map from satellite IRAS, to produce a map of Galacticemission with the quality calibration of DIRBE and the highresolution of IRAS. The dust temperature has been retrievedusing the DIRBE maps at 100µm and 240µm assumingβ=2.Knowing the temperature, the 100µm map has been convertedinto a dust column density map and subsequently calibrated toE(B-V) using colours and Mg2-index of elliptical galaxies. Wewould like to stress that the colour excess has been derived fromthe 100µm emission without any assumption about the valueof the emissivity at any wavelength. Moreover, the choice ofβdoes not affect significantly their results: whenβ=1.5 is used,the dust column density map varies only of 1%, aside from anoverall multiplicative factor that is taken account of when cali-brating with the colour excess. We have accessed the electronicdistribution of this remarkable dataset to retrieve the 9.5′/pixelmaps of the intensity at 100µm, I(100µm), the temperatureand the colour excess E(B-V) for the north and south Galactichemispheres.When the same dust grains are responsible for emission andextinction, the ratio between the extinction coefficient in the V-band and the emissivity at 100µm is equivalent to the ratio ofthe optical depthsQext(V )Qem(100µm)=τ(V )τ(100µm). (3)The above formula is correct if all of the dust grains are identical.In a mixture of grains of different sizes and materials, the ratioof emissivities in Eq. (3) can still be regarded as a mean valuecharacteristic of diffuse galactic dust, if the dust composition isassumed to be the same on any line of sight.The optical depth at 100µm, in the optically thin case, ismeasured usingτ(100µm) =I(100µm)B(100µm, Td), (4)whereB(100µm, Td) is the value of the Planck function at100 µm for a dust temperatureTd, both the intensityI(100µm)andTd coming from the maps of SFD. The optical depth in theV-band can be found from the colour excess E(B-V) maps,τ(V ) =A(V )1.086= 2.85E(B − V ), (5)where we have used a mean galactic valueA(V )/E(B−V )=3.1(Whittet 1992). Reach et al. (1995) suggest that dust emittingin the wavelength range 100–300µm traces interstellar extinc-tion. Since the FIR optical depth in Eq. (4) has been measuredusing data at 100 and 240µm, it is then justified to compare itwith extinction as in Eq. (5) to find the ratio of the extinctioncoefficient and emissivity. Knowing the optical depths from (4)and (5), we can compute a map of the ratio as in Eq. (3); weobtain a mean value ofQext(V )Qem(100µm)= 760 ± 60for both hemispheres. This value is included, together withother multiplicative factors, in the calibration coefficientp asin Eq. (22) in SFD. As pointed out by the referee, an estimatefor Qext(V )/Qem can be easily derived from that equation, ifthe DIRBE colour corrections factors, slowly depending on T,are omitted. Following this way we obtained a value of 765.5.SFD give an error of 8% forp and this is the value quoted here.Since most (≈ 90%) of the elliptical galaxies used to calibratecolour excess maps have galactic latitudeb > 20◦, one may ar-gue that the measured value is characteristic only of high latitudedust.Reach et al. (1995) find that the emissivity (Eq. 2) is bestdetermined by fitting the FIRAS spectrum on the Galactic plane.They say that high latitude data have a smaller signal-to-noiseratio and can be fitted satisfactory withβ = 2 (Eq. 1) althoughthe same emissivity as on the plane cannot be excluded. Underthe hypothesis that the same kind of dust is responsible forthe diffuse emission in the whole Galaxy, we have correctedSFD temperatures using Reach et al. emissivity (Eq. 2). Thenew temperatures are a few degrees higher than those measuredwith β = 2 (as an example we pass from a mean value of18 K in a 20◦ diameter regions around the north pole to a newestimate of 21 K). It is interesting to note that the differencebetween the two estimates of temperature is of the same orderas the difference between the temperatures of warm dust at highand low Galactic latitude in Reach et al. (1995) and this mayonly be a result of the different emissivity used to retrieve thetemperature.When the correction is appliedQext(V )Qem(100µm)= 2390 ± 190.LETTERS. Bianchi et al.: Dust emissivity in the far-infrared L3The new ratio is about three times higher, and this is a re-flection of the change of temperature in the black body emis-sion in (4): for a higher temperature, a lower emissivity in theFIR is required to produce the same emission. Uncertaintiesin Qext(V )/Qem(λ0) are thus greatly affected by assumptionsabout the emissivity spectral behaviour.3. Comparison with other measurementsWe now compare our emissivity forβ = 2 with literature resultsderived under the same hypothesis. Since no emissivity has beenderived to our knowledge assuming Eq. (2), we do not attemptany comparison with that result. All the data are scaled toλ0 =100 µm.Studying the correlation between gas and dust emissionfrom FIRAS and DIRBE, Boulanger et al. (1996) derived anemissivityτ/NH = 1.0 · 10−25 cm2 at 250µm for dust at highgalactic latitude; assuming the canonicalNH = 5.8·1021E(B−V ) cm−2 mag−1 andA(V )/E(B−V )=3.1 (Whittet 1992), thisis equivalent toQext(V )/Qem(100µm)=790. Quite similar val-ues are found in the Draine & Lee (1984) dust model, which has aβ = 2 spectral dependence in this wavelength range. At 125µmthe optical depth isτ/NH = 4.6·10−25 cm2 which correspondsto Qext(V )/Qem(100µm)=680. Sodroski et al. (1997) finds avalue for the ratio at 240µm, using literature data identifying acorrelation between B-band extinction and 100µm IRAS sur-face brightness in high latitude clouds, assuming a dust tem-perature of 18 K. Converted to our notation, using a standardextinction law, the ratio isQext(V )/Qem(100µm)=990.The measurement by Whitcomb et al. (1981) on the reflec-tion nebula NGC 7023 is the most commonly quoted valuefor the emissivity (Hildebrand 1983). Their value derived at125µm for β = 2 is only marginally consistent with ourresult. Following our notation, their result is equivalent toQext(V )/Qem(100µm) = 220 and 8001, using the energy bal-ance and the extinction method, respectively. The values ob-tained by Casey (1991) on a sample of five nebulae using theenergy balance method are a factor of 3 smaller than ours (cor-responding toQext(V )/Qem(100µm) = 80–400).In Fig. 1 we show the literature data (plotted at the wave-length they have been derived in the original papers) togetherwith our derived emissivity laws. We have added the value forDraine & Lee (1984) model at 250µm.4. Gas-to-dust ratio of external spiral galaxiesWe now exploit the FIR emissivity derived in this work by deter-mining dust masses for nearby spiral galaxies. Following Hilde-brand (1983) dust masses can be measured from FIR emissionusingMdust =F (λ)D2B(λ, Td)· 4aρ3Qem(λ), (6)1 Whitcomb et al. (1981) and Casey (1991) originally pre-sented values forQext(UV )/Qem(FIR): we have corrected toQext(V )/Qem(FIR) using the providedτ(UV ) = 2τ(V ).Fig. 1. FIR emissivity derived in this work: assumingβ=2 (solid line)and the Reach et al. (1995) spectral dependence (dotted line). Errorb rs at 125µm give the range of values of Whitcomb et al. (1981).The error bar at 250µm gives the range of values of Casey (1991).Data points are from Draine & Lee (1984) model (stars), Sodroski etal. (1997) (square) and Boulanger et al. (1996) (circle).Table 1. Sample of galaxies from Alton et al. (1998a). Gas masseshave been derived from Devereux & Young (1990) (Van Driel etal. (1995) for NGC 660) and corrected to the distances quoted by Al-ton et al. (1998a). Dust temperature and gas-to-dust ratio are derivedusing Eq. (1) withβ=2 (Qext(V )/Qem(100µm)=760), and Eq. (2)(Qext(V )/Qem(100µm)=2390). Values within brackets are derivedunder the hypothesis that ISO fluxes are overestimated by 30%.Galaxy Gas Mass emissivity (1) emissivity (2)1010 M T(K) G/D ratio T(K) G/D ratioNGC 628 1.1 16 (17) 90 (190) 18 (20) 100 (200)NGC 660 0.91 19 (21) 110 (230) 23 (26) 120 (250)NGC 5194 0.75 18 (20) 90 (180) 21 (24) 90 (190)NGC 5236 3.5 19 (21) 240 (500) 22 (25) 255 (540)NGC 6946 3.0 17 (19) 75 (150) 20 (22) 80 (160)NGC 7331 1.0 17 (19) 70 (145) 20 (22) 70 (155)whereF (λ) is the total flux at the wavelengthλ, D the distanceof the object,B(λ, Td) the Planck function,a the grain radius(0.1µm) andρ the grain mass density (3 g cm−3). The emissivityQem(λ) is derived from the ratioQext(V )/Qem(λ) assumingQext(V )=1.5 (Casey 1991; Whittet 1992).Alton et al. (1998a) provide total fluxes at 100µm and200µm from IRAS and ISO for a sample of spiral galax-ies. We have derived dust temperatures and masses usingQext(V )/Qem(100µm)=760 and 2390, forβ=2 and Reach etal. (1995) emissivities, respectively. Using literature values forgas masses, we have computed the gas-to-dust ratios. Values ofgas masses, temperatures and gas-to-dust ratios are presentedin Table 1.LETTERL4 S. Bianchi et al.: Dust emissivity in the far-infraredThe mean value of the gas-to dust ratio for the sample is 100using Eq. (1), 110 using Eq. (2). Mean temperatures go from18 K with the β = 2 emissivity to 21 K when the Reach etal. (1995) behaviour is assumed (as for the north galactic polein Sect. 2). Alton et al. (1998a) pointed out that ISO 200µmfluxes could be overestimated by about 30%; correcting for thiswe obtain a mean gas-to-dust ratio of 220–240 (forβ=2 andReach et al. (1995) emissivity, respectively). As shown above,dust masses obtained with the two methods are quite similar.This can be explained substituting Eqs. (3) and (4) into (6). Forλ = 100µm we can deriveMdust ∼ B(100µm, TGd )B(100µm, Td),whereTGd is the mean temperature of dust in the Galaxy. Fromthe equation it is clear that the dust mass determination is insen-sitive to the emissivity law used, as long as the dust temperaturein external galaxies and in our own are similar.Our range of values for the gas-to-dust ratio (100–230)encompasses the Galactic value of 160 (Sodroski et al. 1994).As a comparison, the mid-value of Whitcomb et al. (1981)would have given dust-to-gas ratios larger by a factor 1.5.5. ConclusionWe have derived the dust emissivityQem in the FIR using thewavelength dependence derived from the FIR Galactic spec-trum (Reach et al. 1995). The emissivity has been normalised tothe extinction efficiency in the V band using dust column den-sity maps calibrated to Galactic extinction (SFD).Qem dependsstrongly on the assumed wavelength dependence. For aβ = 2emissivity index we obtainedQem(λ) =Qext(V )760(100µmλ)2.This result is consistent with other values derived from FIRGalactic emission (Boulanger et al. 1996; Sodroski et al. 1997)and with the Draine & Lee (1984) dust model. The widelyquoted emissivities of Whitcomb et al. (1981; Hildebrand1983) derived from the reflection nebula NGC 7023 are onlymarginally consistent with our values, while the emissivity mea-sured by Casey (1991) on a sample of five nebulae are smaller bya factor of 3. This may suggest a different grain composition fordust in the diffuse inter-stellar medium compared to reflectionnebulae.When the wavelength dependence derived by Reach etal. (1995) on the Galactic plane is used, we obtainQem(λ) =Qext(V )2390(100µmλ)2 2.005[1 + (200µm/λ)6]1/6 .We have used the derived emissivities to measure dust massesfrom 100µm and 200µm fluxes of a sample of six spiral galax-ies (Alton et al. 1998a). We have retrieved similar dust masseswith both the spectral dependences. The gas-to dust ratios ofour sample (100–230) are close to the Galactic value of 160(Sodroski et al. 1994).Acknowledgements.We thank M. Edmunds and S. Eales for stimulat-ing discussions, and an anonymous referee for useful comments thathave improved the paper.ReferencesAgladze N. I., Sievers A. J., Jones S. A., Burlitch J. M., BeckwithS. V. W., 1996, ApJ 462, 1026Alton P. B. et al., 1998a, A&A 335, 807Alton P. B., Bianchi S., Rand R. J., Xilouris E. M., Davies J. I.,Trewhella M., 1998b, ApJ 507, L125Bianchi S., Alton P. B., Davies J. I., Trewhella M., 1998, MNRAS 298,L49Boulanger F., Abergel A., Bernard J.-P., Burton W., Desert F.-X., Hart-mann D., Lagache G., Puget J.-L., 1996, A&A 312, 256Casey S. C., 1991, ApJ 371, 183Devereux N. A., Young J. S., 1990, ApJ 359, 42Draine B. T., Lee H. M., 1984, ApJ 285, 89Hildebrand R. H., 1983, QJRAS 24, 267Hughes D. H. et al., 1998. In: The Birth of Galaxies (in press) astro-ph/9810273Masi S. et al., 1995, ApJ 452, 253Ostriker J. 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Dust Emissivity in the Far-Infrared

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