Interstellar Dust models towards some IUE stars
aa r X i v : . [ a s t r o - ph . S R ] O c t Accepted to PASP
Preprint typeset using L A TEX style emulateapj v. 04/17/13
INTERSTELLAR DUST MODELS TOWARDS SOME IUE STARS
N. Katyal , , R Gupta , D B Vaidya Inter University centre for Astronomy and Astrophysics, Pune, India School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India ICCSIR, Ahmedabad, 380006, India (Received August 16, 2003; Revised September 17, 2003; Accepted September 30, 2003)
Accepted to PASP
ABSTRACTWe study the extinction properties of the composite dust grains, consisting of host silicate spheroidsand graphite as inclusions, using discrete dipole approximation (DDA). We calculate the extinctioncross sections of the composite grains in the ultraviolet spectral region, 1200˚A -3200˚A and study thevariation in extinction as a function of the volume fraction of the inclusions. We compare the modelextinction curves with the observed interstellar extinction curves obtained from the data given by theInternational Ultraviolet Explorer (IUE) satellite. Our results for the composite grains show a distinctvariation in the extinction efficiencies with the variation in the volume fraction of the inclusions. Inparticular, it is found that the wavelength of peak absorption at ‘2175˚A’ shifts towards the longerwavelength with the variation in the volume fraction of inclusions. We find that the composite grainmodels with the axial ratios viz. 1.33 and 2.0 fit the observed extinction reasonably well with a grainsize distribution, a = 0.005-0.250 µm . Moreover, our results of the composite grains clearly indicatethat the inhomogeneity in the grain structure, composition and the surrounding media modifies theextinction properties of the grains. Subject headings:
Interstellar Dust, Extinction, Ultraviolet spectra INTRODUCTIONIn 1968, the first satellite, OAO2, capable of UV obser-vations was launched. Till then, due to atmospheric ex-tinction, the astronomical studies in the ultraviolet spec-tral region were not possible. Later on other satelliteslike TD-1, Astronomical Netherland satellite (ANS) andInternational Ultraviolet Explorer (IUE) were launched.IUE has provided a wealth of data on interstellar ex-tinction in the UV region. We study the wavelengthdependence of the interstellar extinction in the UV re-gion, 1200-3200˚A , observed by the IUE satellite towardsseveral stars in the various interstellar environments; viz.diffuse interstellar medium, HII region, OB type associ-ation, reflection nebulae, dense medium and HI sources.Recent studies of interplanetary, cometary and inter-stellar dust indicate that the cosmic dust grains are in-homogeneous viz. porous, fluffy and composite. The col-lected interplanetary particles are also porous and com-posite (Brownlee 1987). Mathis (1996), Dwek (1997),Li & Greenberg (1998) and Zubko et al. (2004a) haveproposed composite grain models consisting of silicatesand amorphous carbon to explain the observed wave-length dependence of interstellar extinction, polariza-tion, albedo, IR emission and the observed elemen-tal depletion. They have used the effective mediumtheory (EMT). Iat`ı et al. (2004) have studied opticalproperties of the composite grains using the transi-tion matrix approach. Voshchinnikov et al. (2006) andVoshchinnikov & Henning (2008) have used the layeredsphere method to study the extinction properties of theporous grains. Very recently, Siebenmorgen et al. (2013)have used a dust model, consisting of a mixture of largespheroidal amorphous carbon (AMC) and silicate grains.Small grains of graphite, silicates and polycyclic aromatichydrocarbons (PAHs) are also included to explain the ex- tinction, emission, linear and circular polarization in thediffuse interstellar medium. Clayton et al. (2003b) haveused Maximum Entropy Method (MEM) and EMT for 2-component (silicates and graphite) and 3-component (sil-icates, graphite and amorphous carbon) spherical grainmodels to study the extinction properties in the MilkyWay galaxy and the Magellanic clouds. In EMT, the in-homogeneous particle is replaced by a homogeneous onewith some ‘average effective dielectric function’. The ef-fects related to the fluctuations of the dielectric functionwithin the inhomogeneous structure can not be treatedby this approach of the EMT.We have used Discrete Dipole Approximation (DDA)which allows consideration for irregular shape effects,surface roughness and internal structure within the grain(Wolff et al. 1994, 1998). Since there is no exact theoryto study these porous and composite particles, there isa need to formulate models of electromagnetic scatteringby approximate methods like EMT and DDA. We haveused DDA to calculate the extinction cross sections ofthe composite grains in the spectral UV region, 1200˚A -3200˚A , and compared the model extinction curves withthe extinction curves, derived from the IUE satellite ob-servations. For a discussion and comparison of EMTand DDA see for e.g. Ossenkopf (1991) and Wolff et al.(1998). Earlier Vaidya et al. (2001, 2007) have used com-posite grain models to interpret the average observedinterstellar extinction. Moreover, the recent results ofKatyal et al. (2011) show that the composite grain modelis more efficient as compared to the bare silicate/graphitegrain models in producing the extinction and also reduc-ing the cosmic abundance constraints. Composite dustgrain models are also being employed to analyze IR emis-sion. Recently, Vaidya & Gupta (2011) have used thecomposite grain model to interpret the observed IR emis-sion from circumstellar dust. Massa et al. (1983) havedone spectrophotometric measurements for a sample ofstars judged by Meyer & Savage (1981) to study highlyanomalous peculiar UV extinction as inferred from thebroad-band Astronomical Netherlands Satellite (ANS)data. These observations showed a discrete bump fea-ture at 2175˚A (Stecher 1965, 1969). This feature hasbeen ascribed to small graphite grains (Stecher & Donn1965; Draine & Malhotra 1993).Other possible candidate for the spectral bumpat 2175˚A could be polycyclic aromatic hydrocar-bons (PAHs) as discussed by Li & Draine (2001) andMalloci et al. (2008). Siebenmorgen et al. (2013) havealso discussed about the strong electronic transitions ofboth graphites and PAHs at 2175˚A to be responsiblefor the bump feature. Greenberg & Chlewicki (1983)have found strong correlation between the strength ofthe ‘2175˚A ’ feature and the visible extinction. They ob-tained a poor correlation between far ultraviolet (FUV)extinction, strength of the feature and visible extinctionconcluding that a wide spectrum of size distribution isneeded to explain the average observed interstellar ex-tinction curve. Xiang et al. (2011) have shown that thecarriers responsible for the 2175˚A feature and the ex-tinction in the UV might not be the same.Wavelength dependent studies of the interstellar ex-tinction curves are the best tool for understanding envi-ronment around these stars. The most commonly usedtechnique for deriving the wavelength dependence of in-terstellar extinction is the “pair method” (Massa et al.1983). Basically, the ratio of the fluxes of the reddenedand comparison star gives a direct measurement of thedust extinction towards the reddened star. The resul-tant ratio, after normalization is referred to as the ‘ex-tinction curve’. Errors resulting from poorly matchedpairs can dominate the uncertainties of individual ex-tinction curves. Fitzpatrick & Massa (1986, 1988, 1990)analyzed several IUE extinction curves and found thatall these curves could be fitted extremely well by a singleanalytical expression with six parameters.With the availability of much more observational data,revisions of earlier dust models was done as extinc-tion of light is highly subject to the interstellar en-vironments from where it passes through. Therefore,Clayton & Mathis (1988); Cardelli et al. (1989) (here-after called CCM method) found that in general, theproperties of UV extinction curves are correlated withthe extinction in the optical/IR region and that fromthe UV through the IR. They characterized this depen-dence by a single parameter, R − v , which is the ratio ofvisual extinction to total extinction of V, and is definedas R v =A(V)/E(B-V). However, the CCM method has itslimitations, both from the standpoint of understandingdust grain properties and dereddening energy distribu-tions. While the UV curve shapes indeed correlate ingeneral with R v , the R − v dependence adopted by CCMis insufficient to describe the behavior over the entirerange of observed R v values, and breaks down at small R v . Further, the CCM formula does not provide par-ticularly good fits to individual extinction curves. Evi-dently, factors other than R v , e.g. chemical composition,processing history, ambient radiant field play importantroles in determining the extinction properties. Hence, based on different interstellar environments of the stars,Aiello et al. (1988) have presented a collection of 115 ex-tinction curves derived from low dispersion IUE spectra.The atlas includes extinction originating in the diffusemedium and several major nebulae and dense clouds.The data can be easily accessed and used for variousextinction studies.The shape of extinction curves are substantially differ-ent for different R ′ v s , and hence changes in the size distri-butions is also expected. As Cardelli & Clayton (1991)have pointed out, lines of sight with large R v are idealfor examining processes that modify the grain proper-ties in dense clouds. A good correlation between thestrength of the ‘2175˚A’ UV bump feature and the vi-sual extinction was also noted by Greenberg & Chlewicki(1983). Weingartner & Draine (2001a) have constructedsize distributions for spherical carbonaceous and silicategrain populations in different regions of the Milky way,LMC and SMC to account for the observed near IR andmicrowave emission from diffuse interstellar environmentusing a fairly simple functional form, characterized byvarious parameters. They have shown that these varia-tions can be well parameterized by R v . Another studyby Kim et al. (1994) found out that denser environmentswith high R v (=5.3) have the presence of larger mean sizeof grains, though all denser regions may not necessarilyhave high R v .In the present study, we have used the ‘Pair method’which is described in the section 2.1. The main pur-pose of the present study is to infer the size distribution,shape and composition of the interstellar dust grains, invarious interstellar environments (for different values of R v ), which are consistent with the observed extinction.We use composite grain models to compare extinctiontoward these stars as observed by the IUE satellite. Wetabulate a list of the selected stars and describe the pairmethod to generate the extinction curves in the UV spec-tral regime for these stars in section 2. DDA techniqueand the generation of composite grain models using it areillustrated in Section 3. In section 4, we give the resultsof the computed model curves and compare these modelextinction curves with the observed extinction curves. Insection 4, we analyze these results in detail and compareour results in terms of size and composition with thoseobtained by others. Our conclusions from this study aresummarized in section 5. PRELIMINARY DATA REDUCTION2.1.
PAIR METHOD
The standard Pair method technique is used for a setof IUE stars to generate the extinction curves. The tech-nique involves selecting a highly reddened star and com-paring it with a star (flux standard) which has negligi-ble reddening and whose spectral features closely matchwith those of the reddened star. An extinction curve isthen constructed by the standard relation (Massa et al.(1983)): E ( λ − V ) E ( B − V ) = m ( λ − V ) − m ( λ − V ) o ( B − V ) − ( B − V ) o (1)where subscript ‘ o ’ refers to the unreddened star andother is for the reddened star. Here E(B-V) is the differ-ence in extinction between the specified wavelengths andcorresponds to the color excess. The resultant extinctioncurve E ( λ − V ) /E ( B − V ) is then plotted versus 1 /λ forselected IUE stars.2.2. Object Selection Criteria
We have selected 26 “program stars” (listed in Table 1)from Fitzpatrick & Massa (1988), Fitzpatrick & Massa(2009) and IUE spectral atlas by Wu et al. (1983). The R v values of the sample reddened stars are taken fromValencic et al. (2004). The spectral types for these 26stars lies in the range O7-B5. We have selected reddenedand dereddened stars on the basis of their visible spectraltype and the luminosity class. Spectral type mismatcherror larger than one luminosity subclass is avoided (seeTable 1) in order to account for spectral type uncertain-ties between reddened and the dereddened stars. Latetype stars are excluded because their ultraviolet energydistributions are very strong functions of their spectraltype - thus amplifying the magnitudes of error associatedwith the spectral mismatching between the reddened andunreddened stars. Massa et al. (1983) and Massa et al.(1984) give the identification of the features useful inmatching B stars near the main sequence. Most of thesample stars are selected along different line of sightsand are previously known to produce extinction curvesthat vary considerably from the average Milky way curve( R v =3.1). The lowest value of color excess E(B-V) forunreddened stars sample is 0.01 and the highest valueof E(B-V) for reddened stars sample is 0.95. The starsselected represent a range of environments; viz. diffuseinterstellar medium (DIF); HII region (HII); OB type as-sociation (OB); reflection nebulae (RN); dense medium(DEN) and radio or HI source (H/RADIO) which arementioned in second column of Table 1. Environmenttype for the stars is taken from Fitzpatrick & Massa(1988); Jenniskens & Greenberg (1993) and SIMBAD as-tronomical database. It is to be noted that the sample ofstars selected span the value of R v i.e the ratio of totalto selective extinction, from ∼ R v .Table 2 gives the observational data for the flux stan-dards which are the comparison stars.2.3. MERGING OF SPECTRAL BANDS for PairMethod
Each spectra of program star consisted of two sep-arate images, one for the shorter wavelength and an-other for the longer wavelength. Data was takenfrom following cameras: Short Wavelength Prime(SWP,1150˚A < λ < < λ < < λ < m ( λ ), with λ covering the wavelength range 1150˚A -3348˚A . Themagnitudes were further interpolated in the range 1153-3201˚A with a binning of 1˚A . Further, extinction curvesare generated using standard Pair method as discussedin Section 2.2. DISCRETE DIPOLE APPROXIMATION (DDA)An approximate technique called discretedipole approximation (DDA) was proposed byPurcell & Pennypacker (1973). It is a powerful nu-merical technique for calculating the optical propertiessuch as absorption and scattering of the target. DDAis basically designed for targets having arbitrary andirregular shape. As an approximation, the continuumtarget is replaced by an array of N dipoles. To eachdipole, a polarizibility can be assigned for a particulartarget composition. The polarizibility depends ingeneral on the dielectric properties such as complexrefractive index m = n + ik of the material inside thetarget. The polarizibility and the refractive index of thematerial can be related to each other by the well knownClausius-Mossotti condition. Each dipole interacts withthe neighboring dipoles on the application of electricfield. After evaluating the polarization P by all the N dipoles inside the target, we can solve for the absorptionand extinction cross sections of the target. The twocriteria for the validity of DDA:1) The value of | m | kd should be <
1, where m isthe complex refractive index of the material, k=2 π/λ isthe wave number in vacuum and d is the dipole spacingbetween the dipoles.2) The dipole spacing d should be small enough sothat the number of dipoles N should be large enough todescribe the target shape satisfactorily.For more detailed calculations, see Draine (1988).We have used discrete dipole scattering version 6.1(DDSCAT6.1 ) for the present study. The work byDraine & Flatau (2008) may be looked upon for a moredetailed analysis on the code.3.1. Composite grain models using DDA
For this study, we have used the DDSCAT6.1 code(Draine & Flatau 2003) which has been modified anddeveloped by Dobbie (1999) to generate the compositegrain models. The code, first carves out an outer sphere(or spheroid) from a lattice of dipole sites. Sites outsidethe sphere are vacuum and sites inside are assigned to thehost material. Once the host grain is formed, the codelocates centers for internal spheres to form inclusions.The inclusions are of a single radius and their centers arechosen randomly. The code then outputs a three dimen-sional matrix specifying the material type at each dipolesite which is then received by the DDSCAT program. Inthe present study the axial ratios (hereafter called AR) ofthe composite spheroidal grains is taken to be AR=1.33, http://code.google.com/p/ddscat TABLE 1Extinction curve details for the program stars.
HD a Flux Std (Sp Type) V B B-V E(B-V) R v a DIFF, Diffuse interstellar medium; DEN, Dense interstellar medium;HII, HII region; OB, OB association; RN, Reflection nebulaOr N, Orion Nebula; HI/Radio source.ENV type are taken from Fitzpatrick & Massa (1988); Jenniskens & Greenberg (1993) and SIMBAD astronomicaldatabase.
TABLE 2Observational data for flux standard stars
HD f ’ of graphite grain inclusion viz. f =0.1, 0.2 and 0.3.Table 3 shows the number of dipoles for each grain model along with the axial ratio and number of dipolesper inclusion with the number of inclusions for each frac-tion. The calculations of extinction cross sections of thetarget depend in general upon the orientation of the tar-get. Hence, we average over 27 orientations of the targetfor all the calculations done by DDA. For more detailson the composite grain models and the modified code seeVaidya et al. (2007).Fig. 1 illustrates a composite grain model withN=9640 dipoles composed of silicates as host (in green) TABLE 3Number of dipoles for each inclusion of the grain modelalong with axes lengths for spheroid in x,y,z directionfor host (H) and inclusion (I). Also, number of inclusionsis mentioned in brackets in column 3,4 & 5 for each of thevolume fraction f of inclusions. N (AR)
Nx/N y /N z No. of dipoles per inclusion(No. of inclusions)f=0.1 f=0.2 f=0.39640(1.33) H:32/24/24 152(6) 152(11) 152(16)I: 8/6/625896(1.50) H:48/32/32 432(7) 432(13) 432(19)I:12/8/814440(2.00) H:48/24/24 224(6) 224(11) 224(16)I:12/6/6 and graphite as inclusion (in red). The inclusions can beseen clearly in Fig. 2. There are eleven such inclusionsconsisting of 152 dipoles per inclusion. This model rep-resents a composite dust grain with volume fraction ofgraphite f = 0 . Fig. 1.—
A non-spherical composite dust grain consisting of host(in green) and inclusion (in red) with a total of N=9640 dipoleswhere the inclusions embedded in the host spheroid are shown suchthat only the ones placed at the outer periphery are seen. RESULTS AND DISCUSSIONSThe following are the principal results of this work:4.1.
Extinction efficiencies of the composite grain
Though the exact composition of the interstellar dustis still uncertain, graphites and silicates are the mostoften used for cosmic dust models (see for exampleMathis et al. (1977); Draine & Lee (1984)). We havechecked the extinction of graphite and amorphous car-bon (AMC) as possible candidates for explaining theUV feature at 2175˚A . Figure 3 shows the extinctioncurve for very small AMC and graphite grain of radius a =0.01 µm . It is seen that the AMC does not show any Fig. 2.—
This figure shows the inclusions of the composite grain.The volume fraction f of graphite inclusions is 0.2. The number ofinclusions are 11 with 152 dipoles per inclusions. peak at 2175˚A , whereas graphite prominently showsthis feature. Amorphous carbon is also highly absorb-ing at very long wavelengths and would provide most ofthe extinction longword of 0.3 µm (3.3 µm − ) as seen byDraine (1989) and Weingartner & Draine (2001b). Grainmodels with AMC are also not favored by Zubko et al.(2004b). Instead, large polycyclic aromatic hydrocar-bons (PAHs) molecules are likely candidates as car-riers of the 2175˚A feature – a natural extension ofthe graphite hypothesis (Joblin et al. 1992; Li & Draine2001). Clayton et al. (2003a) have also considered PAHsas one of the constituents in the dust model to explainthe interstellar extinction in the UV. Fig. 3.—
Extinction efficiencies for amorphous carbon (AMC)and graphite grains for very small grain size of 0.01 µm is shownin this figure. The peak in graphite curve at spectral wavelength2175˚A explains why it is being used as inclusion in our compositegrain model whereas no such peak is seen in AMC curve at 2175˚A . We calculate the extinction efficiencies Q ext for a com-posite grain model consisting of a host silicate spheroidalong with graphite inclusions with the number of dipolesbeing N = 9640, 14440 and 25896. The extinctionefficiencies are calculated for target which are prolatespheroid in our case. The volume fractions, f of thegraphite inclusions in the composite grain is varied asf=0.1, 0.2 and 0.3. The extinction efficiencies for thecomposite grain model having number of dipoles N =9640 (AR= 1.33) with the variation in the volume frac-tion of graphite inclusion are shown in Fig. 4. The vari-ation of extinction efficiencies for the composite grainmodel of the number of dipoles N = 14440 (AR = 2.0)and N = 25896 (AR = 1.50) with the variation in the vol-ume fraction of graphitic inclusions can be seen in Fig. 5and 6 respectively. It is clearly noted that the extinctionefficiencies and the shape of the extinction curves varyconsiderably as the grain size increases. The 2175˚A fea-ture is clearly seen for small grains, viz. a=0.01 µm and 0.05 µm , whereas for the larger sizes (a=0.1 µm and0.2 µm ), the feature disappears. For both the models,we see a shift in the peak wavelength at 2175˚A as thevolume fraction of the inclusion increases. Further, theextinction efficiency is seen to vary with the variation inthe volume fraction of graphite inclusion. Fig. 4.—
The figure shows extinction efficiencies for a compositegrain model with number of dipoles, N = 9640 for volume frac-tions of graphite inclusions, f=0.1, 0.2, 0.3 and 0.4. These extinc-tion curves clearly show a shift in the peak wavelength ‘2175˚A ’(4.57 µm − ) and variation in extinction efficiency as the volumefraction of graphite varies. It is also to be noted that the ‘2175˚A ’feature vanishes for large grains with a=0.2 µm Interstellar extinction curve
The interstellar extinction curve (i.e. the variation ofthe extinction with wavelength) is usually expressed bythe ratio: E ( λ − V ) /E ( B − V ) vs 1 /λ . A power law for thegrain size distribution, n(a) ∼ a − . (Mathis et al. 1977);where a min < a < a max is used for evaluating the inter-stellar extinction curve for a given grain size distribution.We calculate the extinction efficiencies of the grain mod-els using the above power law. It must be noted that Fig. 5.—
The figure shows extinction efficiencies for a compositegrain model with number of dipoles N = 14440. The shift inthe peak wavelength and variation in extinction efficiency with thevolume fraction variation of graphite is seen. Fig. 6.—
In this figure, the extinction efficiencies for a compositegrain model with number of dipoles N = 25896 and volume fractionof graphite f = 0 .
1, 0.2 and 0.3 is shown. A shift in the peakwavelength and variation in extinction efficiency as the volumefraction of graphite varies is seen. we have used two types of size distribution (i) a=0.001-0.100 µm (denoted as a
100 henceforth) and (ii) a=0.005-0.250 µm (denoted as a
250 henceforth). Earlier, we haveused the porous (Vaidya & Gupta 1997, 1999) and thecomposite spheroidal grain models (Vaidya et al. 2007)to interpret the average observed extinction curve in thewavelength range 0.1 µm -3.4 µm (Vaidya et al. 2007). Inthis paper, we use the composite spheroidal grain modelsto interpret the observed extinction in the UV, in severaldirections towards individual stars, selected from var-ious galactic environments (Fitzpatrick & Massa 1990;Valencic et al. 2004). Subsequently, in case of compositegrain models, each interstellar extinction curve of the ob-served IUE star is compared with the model curve formedfrom a χ minimized and best fit linear combination ofthe composite grains (contributory fraction p) and solidgraphite grains (contributory fraction q). By varying p and q each from 0.1 to 1.0 in steps of 0.1, a set of20 model curves are generated and on comparing thesemodel curves with the observed extinction curve of thestars, a set of reduced χ are obtained. A minimum χ from this set is chosen depending on the linear combina-tion of p and q . Hence, we obtain a net model interstellarextinction curve as a result of the linear combination of p and q which gives a minimum χ value. We use the fol-lowing formula to obtain the set of reduced χ (Bevington1969): χ j = P ni =1 ( S ji − T ki ) pp where pp is the number of degrees of freedom, S ji ( λ i ) isthe j th model curve for the corresponding p and q linearcombination of the composite grains and bare graphitegrains and T ki ( λ i ) is for the observed curve, λ i are thewavelength points with i=1,n for n=12 wavelength pointsof the extinction curves.Tables 4 shows the best fit parameters along with theminimized χ values for the composite grain model usingDDA for 26 IUE stars.Fig. 7 and 8 shows the comparison of the observedinterstellar extinction curve with the best fit model forcomposite grains generated using DDA technique. FromTable 1 & 4 it is seen that the grain models with the sizedistribution a=0.001-0.100 µm fit the observed extinc-tion curves towards stars with low R v ( 2-3), whereas,stars with high R v ( 4-6) fit the grains with the sizesdistribution, a= 0.005-0.250 µm .Our results on the composite spheroidal grain modelsi.e Table 4, Fig 7 and 8 show the best fit parameters; sizedistributions 0.001-0.1 µm ( a µm ( a f = 0 .
1, 0.2and 0.3; for the grains in the interstellar medium towardsthe 26 selected stars as observed by the IUE satellite.4.3.
Environmental effects
In order to examine how the extinction properties areinfluenced by the various dust environments, we have an-alyzed the extinction curves for stars in seven differentgalactic environments; as shown in Table 1. The vari-ation in the strength and width of the 2175˚A featureis seen for various environments i.e. from dense regionsand reflection nebulae to diffuse clouds ( Fig. 7 and 8).It can be clearly seen that the dust in the dense quies-cent environments and reflection nebulae produces broadbumps of larger widths whereas those stars lying in thediffuse environment produces narrower bumps of aver-age widths. Stars around HII regions and/or which are apart of OB association produces bump of average widthswith weak bumps. This results are in accordance withFitzpatrick & Massa (1986). They have shown that theobserved width of the bump is strongly subject to en-vironmental influences by calculating the widths of thebump and the area under the bump through the analyt-ical parameterization scheme.In Fig. 7 and 8, we show the fitting of the extinctioncurves for stars in the HII region (HII), reflection nebula (cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:1)(cid:7)(cid:8)(cid:6)(cid:1)(cid:9)(cid:10)(cid:11)(cid:12)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:2)(cid:3)(cid:11)(cid:11)(cid:6)(cid:1)(cid:7)(cid:8)(cid:6)(cid:1)(cid:9)(cid:10)(cid:11)(cid:12)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:5)(cid:3)(cid:10)(cid:13)(cid:6)(cid:1)(cid:14)(cid:15)(cid:1)(cid:8)(cid:6)(cid:1)(cid:9)(cid:10)(cid:11)(cid:12)(cid:2)(cid:3)(cid:2)(cid:16)(cid:6)(cid:1)(cid:7)(cid:8)(cid:6)(cid:1)(cid:9)(cid:10)(cid:11)(cid:12)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:2)(cid:3)(cid:11)(cid:17)(cid:6)(cid:1)(cid:18)(cid:19)(cid:8)(cid:6)(cid:1)(cid:9)(cid:10)(cid:11)(cid:12) (cid:5)(cid:3)(cid:16)(cid:17)(cid:6)(cid:1)(cid:14)(cid:20)(cid:6)(cid:1)(cid:9)(cid:10)(cid:11)(cid:12)(cid:2)(cid:3)(cid:5)(cid:10)(cid:6)(cid:1)(cid:18)(cid:19)(cid:8)(cid:6)(cid:1)(cid:9)(cid:10)(cid:11)(cid:12)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:2)(cid:3)(cid:13)(cid:11)(cid:6)(cid:1)(cid:18)(cid:19)(cid:8)(cid:6)(cid:1)(cid:9)(cid:10)(cid:11)(cid:12)(cid:2)(cid:3)(cid:11)(cid:11)(cid:6)(cid:1)(cid:18)(cid:21)(cid:22)(cid:22)(cid:6)(cid:1)(cid:9)(cid:10)(cid:11)(cid:12) (cid:5)(cid:3)(cid:4)(cid:4)(cid:6)(cid:1)(cid:7)(cid:8)(cid:6)(cid:1)(cid:9)(cid:10)(cid:11)(cid:12)
Fig. 7.—
Comparison of the observed interstellar extinctioncurves with the best fit composite grain model extinction curves(generated using DDA) in the wavelength range 3.17-7.87 µm − (3200-1200˚A ). The observed R v , environment type and the bestfit grain size distribution for the sample is mentioned inside thefigure. (RN) and dense medium (DEN + DC) with our models.The ratio, R v also varies from 2.37 for HD239693 to 4.76for HD93222. These curves further highlight star to starvariation in the extinction, demonstrating the sensitivityto local conditions. In particular, a large variation in thestrength and width of the 2175˚A feature is seen in theextinction curves for the stars lying in the dense region i.eHD37903 ( R v =4.11), HD37061 ( R v =4.29) and HD93222( R v =4.76). The shape of the extinction curves for thestars in the HII region (Fig. 7 and 8) shows variationin the spectral region, shortward of 1500˚A . In partic-ular, see the steep rise in the extinction for HD24432( R v =2.77). This star lying in the diffuse clouds is fittedby the composite dust grain model of N=9640 with a R v varies from ∼ µm )to ∼ µm ). These resultsalso show consistency for the denser medium where R v has a small value (presence of small grains) and for thediffuse regions where R v has high value (presence of TABLE 4Best fit χ values and other parameters for different composite grain models generated using DDA technique. HD χ p q N f Gr a( µm )239693 0.1552 0.2 0.4 14440 0.1 0.001-0.100185418 0.2032 0.1 0.6 14440 0.2 0.001-0.100123335 0.3719 0.2 0.4 14440 0.1 0.005-0.25018352 0.0535 0.2 0.5 14440 0.1 0.005-0.25054439 0.4001 0.1 0.4 9640 0.1 0.001-0.100179406 0.2239 0.3 0.3 14440 0.1 0.001-0.10024432 0.3149 0.4 0.4 9640 0.1 0.001-0.100217086 0.1722 0.2 0.4 14440 0.1 0.001-0.10046660 0.1488 0.1 0.5 14440 0.1 0.001-0.100281159 0.1477 0.2 0.4 14440 0.1 0.001-0.10021483 0.1714 0.3 0.3 9640 0.1 0.001-0.10053974 0.0963 0.2 0.3 9640 0.1 0.005-0.25038131 0.2747 0.5 0.3 14440 0.1 0.005-0.250217061 0.0552 0.2 0.4 14440 0.1 0.005-0.250205794 0.1625 0.1 0.4 9640 0.1 0.005-0.25046202 0.2304 0.4 0.4 14440 0.1 0.005-0.250216658 0.2200 0.4 0.4 14440 0.1 0.005-0.250149452 0.0778 0.4 0.4 14440 0.1 0.005-0.25034078 0.0920 0.3 0.4 14440 0.1 0.005-0.25037367 0.1760 0.1 0.5 14440 0.1 0.005-0.250252325 0.2172 0.2 0.4 14440 0.3 0.005-0.250147701 0.0926 0.3 0.2 9640 0.1 0.005-0.250147889 0.0652 0.2 0.4 14440 0.3 0.005-0.25037903 0.0852 0.3 0.3 14440 0.1 0.005-0.25037061 0.1372 0.2 0.2 14440 0.3 0.005-0.25093222 0.0969 0.3 0.2 14440 0.3 0.005-0.250 larger grains). These results are also consistent with thestrength of the 2175˚Afeature viz., for the larger grains(a=0.2 µm ), the feature is suppressed. See for example,Fig. 7 in Vaidya et al. (2007).We would like to discuss here a distinct contribution ofthe type of media to the spectral band feature viz., thebump at 2175˚A . We have seen that contribution to thisbump feature is due to the presence of very small graphitegrains. The size of the grain shows a tremendous effecton the extinction cross sections. Hence, weakening of thebump feature can be attributed to the removal of verysmall grains from the dust population of the media forexample; clumpy media and those of unresolved sourceswhich are classified as extended and inhomogeneous me-dia. Using effective medium theory (Bruggeman mixingrule), Kruegel & Siebenmorgen (1994) have shown vari-ation in 2175˚A bump feature and flattening of UV ex-tinction curve for fluffy dust aggregates of silicate, carbonand ice with increasing grain sizes.Extinction measured for an region is directly related tothe optical depth along the line of sight. For few of thesample stars with clumpy and dense molecular media, aweakening of 2175˚A peak along with flattening of extinc-tion curve is seen. This effect is attributed to the influ-ence of scattering on the extinction properties, speciallythe bump feature, of the stars. Natta & Panagia (1984)have observed a suppression in the 2175˚A peak followedby a flattening of far UV curve, with increasing opticaldepth of the media. They have also shown that inhomo-geneous layer of high optical depth (high R v ) tends toproduce gray extinction. Similar studies for low optical media have been con-ducted by Kr¨ugel (2009). They have investigated theinfluence of scattering on the extinction curve of stars.They have computed effective optical depth τ eff for avariety of idealized geometrical configurations (spheres,slabs and blocks) for varying optical depth τ and ana-lyzed the dependencies of effective optical thickness τ eff on the various measurable optical properties of the dustincluding τ . They also found out that standard dust issensitive to spatial resolution and the structure of themedium (clumpiness, foreground/background). The ex-tinction cross sections calculated by them, taking intoaccount the scattering effects, for clumpy, homogeneousmedia and spatially unresolved stars show marked differ-ences to the standard reddening curve.Mathis & Whiffen (1989) have fitted certain sight lines(R v =3.02, 4.83) using effective medium approximation(Bruggeman mixing rule). They used composite grains(silicates and amorphous carbon) and obtained large sizegrains as the best fit parameter for sight lines with higherR v values. Wolff et al. (1993) have used composite grainsto model interstellar polarization towards eight lines ofsight. They have used DDA to model the compositegrains. However, their composite grain model with sili-cates and amorphous carbon/ organic refractory materialfailed to reproduce the observed polarization curve.Several other groups have presented studies on size andcomposition of dust grains in interstellar medium usingvarious techniques. For example, Zubko et al. (2004b)have presented a dust model consisting of various com-ponents: PAH’s, bare silicates & AMC as well as compos- (cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:1)(cid:7)(cid:8)(cid:9)(cid:9)(cid:6)(cid:1)(cid:10)(cid:11)(cid:12)(cid:12)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:2)(cid:3)(cid:5)(cid:4)(cid:6)(cid:1)(cid:13)(cid:8)(cid:8)(cid:6)(cid:1)(cid:10)(cid:11)(cid:12)(cid:12)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:2)(cid:3)(cid:14)(cid:2)(cid:6)(cid:1)(cid:13)(cid:8)(cid:6)(cid:1)(cid:10)(cid:11)(cid:12)(cid:12)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:4)(cid:3)(cid:12)(cid:11)(cid:6)(cid:1)(cid:15)(cid:16)(cid:6)(cid:1)(cid:10)(cid:2)(cid:17)(cid:12)(cid:2)(cid:3)(cid:5)(cid:4)(cid:6)(cid:1)(cid:13)(cid:8)(cid:8)(cid:6)(cid:1)(cid:10)(cid:11)(cid:12)(cid:12)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:2)(cid:3)(cid:14)(cid:17)(cid:6)(cid:1)(cid:7)(cid:18)(cid:16)(cid:6)(cid:1)(cid:10)(cid:11)(cid:12)(cid:12)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:4)(cid:3)(cid:12)(cid:4)(cid:6)(cid:1)(cid:15)(cid:16)(cid:6)(cid:1)(cid:10)(cid:11)(cid:12)(cid:12)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:2)(cid:3)(cid:19)(cid:12)(cid:6)(cid:1)(cid:13)(cid:8)(cid:8)(cid:6)(cid:1)(cid:10)(cid:2)(cid:17)(cid:12) (cid:2)(cid:3)(cid:5)(cid:5)(cid:6)(cid:1)(cid:13)(cid:8)(cid:8)(cid:6)(cid:1)(cid:10)(cid:11)(cid:12)(cid:12) (cid:1)(cid:2)(cid:3)(cid:14)(cid:20)(cid:6)(cid:1)(cid:15)(cid:16)(cid:6)(cid:1)(cid:10)(cid:11)(cid:12)(cid:12)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:4)(cid:3)(cid:12)(cid:20)(cid:6)(cid:1)(cid:7)(cid:8)(cid:9)(cid:9)(cid:6)(cid:1)(cid:10)(cid:2)(cid:17)(cid:12)(cid:2)(cid:3)(cid:19)(cid:19)(cid:6)(cid:1)(cid:7)(cid:8)(cid:9)(cid:9)(cid:6)(cid:1)(cid:10)(cid:2)(cid:17)(cid:12)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:2)(cid:3)(cid:14)(cid:12)(cid:6)(cid:1)(cid:21)(cid:22)(cid:6)(cid:1)(cid:10)(cid:11)(cid:12)(cid:12)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:2)(cid:3)(cid:20)(cid:23)(cid:6)(cid:1)(cid:15)(cid:16)(cid:6)(cid:1)(cid:10)(cid:2)(cid:17)(cid:12)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:4)(cid:3)(cid:11)(cid:2)(cid:6)(cid:1)(cid:15)(cid:16)(cid:6)(cid:1)(cid:10)(cid:2)(cid:17)(cid:12)(cid:2)(cid:3)(cid:17)(cid:23)(cid:6)(cid:1)(cid:7)(cid:18)(cid:16)(cid:6)(cid:10)(cid:2)(cid:17)(cid:12) Fig. 8.—
Comparison of the observed interstellar extinctioncurves with the best fit composite grain model extinction curves(generated using DDA) in the wavelength range 3.17-7.87 µm − (3200-1200 ˚A ). The observed R v , environment type and the bestfit grain size distribution for the sample is mentioned inside thefigure. ite particles containing silicate, organic refractory mate-rial, water ice and voids. They have used the methodof regularization (MR) to solve for the optimal grainsize distribution of each dust component knowing theobservational constraints and the dust constituents andproperties. Clayton et al. (2003a) have employed a mod-ified version of the MEM fitting algorithm, developedby Kim et al. (1994) to fit the observed extinction ineight preferred sightlines/directions. They have used a 3-component homogeneous spherical grain model consist-ing of silicates, graphite and AMC as well as compos-ite grain model consisting of pyroxenes, AMC and vac-uum. Clayton et al. (2003a) adopted solar abundancesand used EMT (extension of Bruggeman rule) to com-pute the optical constants of composite grains. Withthe 3-component homogeneous grain, they obtained theupper size cutoffs of 0.3 µm for graphite and AMC and1 µm for silicate grains. With the composite grain mod-els, Clayton et al. (2003a) obtained the fit to the av-erage observed galactic extinction curve with 0.80 (So-lar) Si (Pyroxene) and 0.36 (Solar) C abundance andfound the upper size cutoff size for composite grain to be1 µm . Clearly, both these grain models of Clayton et al.(2003a) show deficit of small silicate and graphite grains.On the other hand, we have found all the fits withsmaller size cutoffs of 0.100 µm and 0.250 µm as com-pared to size cutoffs of Clayton et al. (2003a). Although Clayton et al. (2003b) have used AMC as a third com-ponent, we did not use it since AMC exhibits absorp-tion at about 2500˚A . It is also highly absorbing atvery long wavelengths and thus would provide most ofthe extinction longword of 0.3 µm (Draine 1989). Re-cently, Gordon et al. (2009) have analyzed FUSE+IUEextinction curves for 75 sightlines and have comparedthese curves with three different dust grain modelsgiven by Weingartner & Draine (2001b); Clayton et al.(2003b) and Zubko et al. (2004b). Gordon et al. (2009)found that the models of Clayton et al. (2003b) andZubko et al. (2004b) provide much better fits thanWeingartner & Draine (2001b) model.It is clear that the variation in the grain size distribu-tion subject to the variation in the environment indicatesthat the small sized grains coagulate onto large grains inrelatively dense environments, as expected (Draine 1985,1990). Mathis & Whiffen (1989) have fitted certain sightlines (R v =3.02, 4.83) using effective medium approxima-tion (Bruggeman mixing rule). They used compositegrains (silicates and amorphous carbon) and obtainedlarge size grains as the best fit parameter for sight lineswith higher R v values. Weingartner & Draine (2001a)have fitted a specific case of extinction toward HD21021with small value of R v =2.1 with a small grain size dis-tribution of graphite/silicate grains using a simple func-tional fitting form.Shape of the grain is an important factor in determingthe interstellar extinction. Gupta et al. (2005) have cal-culated the extinction efficiency for various shapes of sili-cate and graphitic spheroidal grains such as oblates, pro-lates and spheres using T-matrix theory. They have verywell described the considerable variation in the extinc-tion due to the different axial ratio grains as comparedto the simple case of sphere. They also find out the bestfit for explaining the observed extinction is obtained witha grain size distribution a=0.005-0.250 µm having an ax-ial ratio of AR=1.33. However, in this work, we haveused a more realistic composite dust grain model gener-ated using DDA. We find out that most of the observeddirections are well fitted by axial ratio (AR) equal to 2.0.Hence, we conclude that shape of the grain has an impor-tant role in determing the observed extinction propertiesof stars observed by IUE satellite.The composite grain models with silicate as host ma-terial and graphite inclusions, presented in this study isfound to fit the observed extinction curves towards thestars lying in various interstellar environments. It mustalso be emphasized here that we have used more real-istic DDA method to calculate the extinction efficien-cies for the spheroidal composite grains. It must alsobe noted that Perrin & Lamy (1990); Perrin & Sivan(1990), Wolff et al. (1994, 1998), Vaidya et al. (2007)and Vaidya & Gupta (2011) have shown that DDA ismore accurate than the EMT based grain models.We plan to use the composite grain model with othercarboneous materials as inclusions such as PAHs or SiC(Weingartner & Draine 2001b; Clayton et al. 2003a) forobtaining better fits in the UV region, 1500˚A -1200˚A .Wealso plan to interpret the extinction towards some morestars observed by the IUE satellite. CONCLUSIONS0We have used more realistic DDA method to calcu-late the extinction efficiencies of the spheroidal compos-ite grains made up of the host silicate and graphite in-clusions in the wavelength region of 1200˚A 3200˚A . Wehave then, used the extinction efficiencies of the compos-ite grains for a power law size distribution (Mathis et al.1977) to evaluate the interstellar extinction curves in thewavelength range 1200˚A -3200˚A . In the present study,we have used two size distributions viz. (i) a=0.001-0.100 µm and (ii) a=0.005- 0.250 µm . These extinctioncurves for the spheroidal composite grains are comparedwith the observed extinction curves obtained from theIUE satellite data to infer the parameters such as size,shape and composition of grains. The important impli-cations of the obtained results in terms of these physicalparameters (as compared to the earlier studies) are dis-cussed in the previous section. This study made use ofa more sophisticated technique for modeling a compositedust model with various parameters that are able to char-acterize the actual physical dust parameters for a sampleof stars, lying in different interstellar environments. Themain conclusions of our study are as follows:(i) The extinction properties of the composite grainsvary considerably with the variation in the volume frac-tion of the inclusions. In particular, the extinction peakat ‘2175˚A ’ shifts and broadens with variation in thegraphite inclusions.(ii) The composite spheroidal grain models, with axialratios 1.33 and 2.0 and volume fraction of inclusions f =0 . − .
3, fit the observed extinction curves reasonablywell.(iii) The ratio R v = A(V) / E(B − V) is seen to be wellcorrelated with the ‘2175˚A ’ feature. From the sample of 26 IUE stars, those lying in the dense regions withhigh Rv ( 4-5), show a weakening of the bump featureat 2175˚A followed by a flattening of far UV extinctioncurve whereas stars in the diffuse interstellar mediumwith low R v ( 2-3) show a distinct bump at this partic-ular wavelength. This study clearly indicates, how theextinction properties of the grains vary with the opticaldepth of the media (which is related to R v ) and also thegrain size. It is to be noted that scattering off many un-resolved stellar sources also flattens the extinction curveat this wavelength.These results are consistent as suggested earlierby Natta & Panagia (1984), Kruegel & Siebenmorgen(1994) and Kr¨ugel (2009).In this study, we have presented the composite grainmodel, consisting of host silicate and graphite as inclu-sions and have used the results obtained for these com-posite grain model to infer the size distributions, shapeof the grain and volume fraction of the graphite in-clusions, of the interstellar dust towards 26 stars situ-ated in the various interstellar environments. Furtherthe composite grain models, presented in this paper, si-multaneously explain the observed interstellar extinction(Vaidya et al. 2001, 2007), infrared emission from the cir-cumstellar dust (Vaidya & Gupta 2011), scattering bythe cometary dust (Gupta et al. 2006) and cosmic abun-dances (Vaidya et al. 2007). ACKNOWLEDGMENTSThe authors acknowledge the ISRO-RESPONDproject (No. ISRO/RES/2/2007-08) for funding this re-search. ——————————————
REFERENCESAiello, S., Barsella, B., Chlewicki, G., Greenberg, J. M.,Patriarchi, P., & Perinotto, M. 1988, in ESA SpecialPublication, Vol. 281, ESA Special Publication, 223–226Bevington, P. R. 1969, Data reduction and error analysis for thephysical sciences, ed. Bevington, P. R.Brownlee, D. E. in , Astrophysics and Space Science Library, Vol.134, Interstellar Processes, ed. D. J. HollenbachH. A.Thronson, Jr., 513–530Cardelli, J. A. & Clayton, G. C. 1991, AJ, 101, 1021Cardelli, J. A., Clayton, G. C., & Mathis, J. S. 1989, ApJ, 345,245Clayton, G. C., Gordon, K. D., Salama, F., Allamandola, L. J.,Martin, P. G., Snow, T. P., Whittet, D. C. B., Witt, A. N., &Wolff, M. J. 2003a, ApJ, 592, 947Clayton, G. C. & Mathis, J. S. 1988, ApJ, 327, 911Clayton, G. C., Wolff, M. J., Sofia, U. J., Gordon, K. D., &Misselt, K. A. 2003b, ApJ, 588, 871Dobbie, J. 1999, PhD. Thesis, Dalhousie UniversityDraine, B. 1989, in IAU Symposium, Vol. 135, Interstellar Dust,ed. L. J. Allamandola & A. G. G. M. Tielens, 313–+Draine, B. T. in , Protostars and Planets II, ed. D. C. BlackM. S.Matthews, 621–640Draine, B. T. 1987, ApJS, 64, 505—. 1988, ApJ, 333, 848Draine, B. T. 1990, in Astronomical Society of the PacificConference Series, Vol. 12, The Evolution of the InterstellarMedium, ed. L. Blitz, 193–205Draine, B. T. & Anderson, N. 1985, ApJ, 292, 494Draine, B. T. & Flatau, P. J. 2003, ArXiv Astrophysics e-prints—. 2008, ArXiv e-printsDraine, B. T. & Lee, H. M. 1984, ApJ, 285, 89Draine, B. T. & Malhotra, S. 1993, ApJ, 414, 632Dwek, E. 1997, ApJ, 484, 779Fitzpatrick, E. L. & Massa, D. 1986, ApJ, 307, 286—. 1988, ApJ, 328, 734—. 1990, ApJS, 72, 163—. 2009, ApJ, 699, 1209 Gordon, K. D., Cartledge, S., & Clayton, G. C. 2009, ApJ, 705,1320Greenberg, J. M. & Chlewicki, G. 1983, ApJ, 272, 563Gupta, R., Mukai, T., Vaidya, D. B., Sen, A. K., & Okada, Y.2005, A&A, 441, 555Gupta, R., Vaidya, D. B., Bobbie, J. S., & Chylek, P. 2006,Ap&SS, 301, 21Iat`ı, M. A., Giusto, A., Saija, R., Borghese, F., Denti, P.,Cecchi-Pestellini, C., & Aiello, S. 2004, ApJ, 615, 286Jenniskens, P. & Greenberg, J. M. 1993, A&A, 274, 439Joblin, C., Leger, A., & Martin, P. 1992, ApJ, 393, L79Katyal, N., Gupta, R., & Vaidya, D. B. 2011, Earth, Planets, andSpace, 63, 1041Kim, S., Martin, P. G., & Hendry, P. D. 1994, ApJ, 422, 164Kruegel, E. & Siebenmorgen, R. 1994, A&A, 288, 929Kr¨ugel, E. 2009, A&A, 493, 385Li, A. & Draine, B. T. 2001, in Bulletin of the AmericanAstronomical Society, Vol. 33, American Astronomical SocietyMeeting Abstracts, 1451Li, A. & Greenberg, J. M. 1998, A&A, 331, 291Malloci, G., Mulas, G., Cecchi-Pestellini, C., & Joblin, C. 2008,A&A, 489, 1183Massa, D., Savage, B. D., & Cassinelli, J. P. 1984, ApJ, 287, 814Massa, D., Savage, B. D., & Fitzpatrick, E. L. 1983, ApJ, 266, 662Mathis, J. S. 1996, ApJ, 472, 643Mathis, J. S., Rumpl, W., & Nordsieck, K. H. 1977, ApJ, 217, 425Mathis, J. S. & Whiffen, G. 1989, ApJ, 341, 808Meyer, D. M. & Savage, B. D. 1981, ApJ, 248, 545Natta, A. & Panagia, N. 1984, ApJ, 287, 228Ossenkopf, V. 1991, A&A, 251, 210Perrin, J. & Lamy, P. L. 1990, ApJ, 364, 146Perrin, J. & Sivan, J. 1990, A&A, 228, 238Purcell, E. M. & Pennypacker, C. R. 1973, ApJ, 186, 705Siebenmorgen, R., Voshchinnikov, N. V., & Bagnulo, S. 2013,ArXiv e-printsStecher, T. P. 1965, ApJ, 142, 1683—. 1969, ApJ, 157, L125+Stecher, T. P. & Donn, B. 1965, ApJ, 142, 16811