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The Dust in Lyman Break Galaxies Uma P. Vijh Ritter Astrophysical Research Center, University of Toledo,Toledo, OH 43606 [email protected] 3 Adolf N. Witt 0 0 Ritter Astrophysical Research Center, University of Toledo,Toledo, OH 43606 2 [email protected] n and a J 7 Karl D. Gordon Steward Observatory, University of Arizona, Tucson, AZ 85721 1 v [email protected] 1 2 1 1 0 ABSTRACT 3 0 WepresentouranalysisofUVattenuationbyinternaldustofalargesample(N=906galaxies) h/ ofLymanBreakGalaxies(LBGs). Usingspectralenergydistributions(SEDs)fromthePE´GASE p galaxyspectralevolutionmodelwe apply dust attenuationcorrectionsto the G−R colorsusing - theWitt&Gordon(2000)modelsforradiativetransferindustygalacticenvironmentstoarriveat o r theUVattenuationfactors. WeshowthatthedustintheLBGsexhibitSMC-likecharacteristics st ratherthanMW-like,andthatthedustgeometryinthesesystemsismostlikelytoberepresented a by a clumpy shell configuration. We show that the attenuation factor exhibits a pronounced v: dependenceontheluminosityoftheLBG,a1600 ∝(L/L⊙)α,where0.5≤α≤1.5. Theexponent i α depends on the initial parameters of the stellar population chosen to model the galaxies and X the dust properties. We find that the luminosity weighted averageattenuation factor is likely to r a be in the range from 5.7−18.5, which is consistent with the upper limits to the star formation rate at 2<z <4 set by the FIR background. This implies that the current UV/optical surveys do detect the bulk of the star formation during the epoch 2 < z < 4, but require substantial correctionfor internal dust attenuation. Subject headings: dust, extinction—galaxies: high-redshift—galaxies: ISM—ISM:evolution 1. INTRODUCTION number of short-lived, high-mass stars and this gives, in principle, a measure of the actual star Inthelastfewyears,largesamplesofstarform- formation rate (SFR). ing galaxies have been observed at high redshift Attenuation due to internal dust presents one (z > 2) using the Lyman Break technique (Stei- of the biggest obstacles to interpreting these ob- del & Hamilton 1993). So far these surveys have servations. Attenuation depends not only on the been carried out mostly at optical wavelengths, amount of dust, its composition and size distri- which explores the rest-frame UV/FUV region of bution but also on its scattering properties and the spectral energydistribution (SED) of galaxies the geometry of the dust and its distribution rel- in the range 2 < z < 4. The UV luminosity in ative to the sources (Witt, Thronson, & Capuano these star-forming galaxies relates directly to the 1 1992), none of which are well known for these assumptions made are that these systems have a high-z objects. The question of dust attenuation, shell geometry and that the dust is clumpy, for therefore,becomesimportantwhenestimatingthe both of which there are strong indications (Gor- starformationratehistory(SFRH)oftheuniverse don, Calzetti & Witt 1997). We explore the de- from observation of rest-frame UV fluxes of star- pendence of dust opacity on the intrinsic UV lu- forming galaxies at high redshift. minosity of the LBGs. We further investigate the Manyattemptshavebeenmadetoestimatethe possible evolution of the dust opacity in LBGs SFRH in the recent years. One of the firstwas by with respect to redshift and also the origin and Madau et al. (1996). This study, however, under- nature of dust in the early universe. estimated the effects of dust. The fact that high Thelayoutofthepaperisasfollows. Insection redshift galaxies are intrinsically very dusty be- 2 we describe the data and their limitations. Sec- came apparent with the advent of the ISO obser- tion 3 discusses the SEDs and the initial parame- vationsinthemid- andfar-IR(Pugetetal.1996). ters used to model the intrinsic colors of the LBG DeepsurveysintheFIRgaverisetogalaxycounts, population. Insection4wedescribethedustmod- and COBE data on the FIR background resulted els and the attenuation functions used. Section 5 in upper limits for the SFR (Elbaz et al. 1999; describestheanalysisandtheresultsobtained. In Puget et al. 1999; Altieri et al. 1999;Aussel et al. section6wepresentadetaileddiscussioncompar- 1999). Even after correction for dust attenuation ingandcontrastingourresultswithpreviouswork there still remained a discrepancy in the SFRs as as well as the implications of our results. Finally, determined by UV/optical surveys and the FIR section 7 summarizes our conclusions. background. There is a debate whether all the star-formation in the universe is in fact being de- 2. DATA tected by current UV/optical surveys. Poggianti Our data consisted of R-magnitudes, colors & Wu (2000), Poggianti, Bressan, & Franceschini (U − G,G − R) and spectroscopic redshifts of (2001) and Rigopoulou et al. (2000) report inde- n ∼ 935 LBGs (Charles Steidel 2001, private com- pendent evidence on both local and high-z lumi- nousstarburstsinwhich∼70%−80%ofthebolo- munication). TheUV-dropouttechniquewasused to identify these galaxies at z ∼ 3 and spec- metricfluxfromyoungstarsiscompletlyobscured troscopic redshifts were obtained using the Low- bydustandremainshiddenintheUV/opticalsur- resolutionImagingSpectrographontheKecktele- veys (even after correction for dust). Adelberger scopes. Adetaileddescriptionofthefiltersandthe & Steidel (2000) on the other hand suggest that observations can be found in Steidel & Hamilton the observed850µm galaxy counts and the back- (1993) and Steidel, Pettini, & Hamilton (1995). ground can be explained by the LBG population Forrest-framespectraofsomeoftheseobjectssee byapplyingaproportionalitycorrectiontotheop- Pettini et al. (2001). Since the U-dropout was a tical flux, using the locally observed distribution selectioncriterionfortheLBGs,theU −Gcolor, of the mm-to-optical flux ratios. n at best, was only a 1 sigma detection. Therefore We believe these conflicts can be resolved by weonlyusedthe G−Rcolorforouranalysis. We an improved knowledge of the dust, its properties also excluded the objects spectroscopicallyidenti- and geometry in the high-z galaxies. We present fied as AGNs and QSOs,reducing the sample size our analysisfor the attenuationcorrectionforUV to 906 galaxies. emission from a large sample (N=906) of Lyman Itwasunfortunatethatwewereabletosalvage Break Galaxies (LBGs), due to internal dust, at only one color for such a large sample. Determin- redshift 2 < z < 4. This is the largest sample ing the stellar content, dust content, dust prop- of spectroscopically identified high-z galaxies to erties and the dust-star geometry, all from just date. We rely on radiative transfer calculations one color is dangerous. Therefore, as a check for to estimate the dust attenuation in each individ- ourmodelparameters,weappliedourmodelstoa ual galaxy. In this approach no assumptions are smaller LBG sample for which longer colors were madetorelatedifferentSFRindicators,nordowe also available. We used the V and H magnitudes apply relations which have only been established from Papovich,Dickinson, & Ferguson (2001) (31 in the local universe, to high-z objects. The only 2 galaxies) and Sawicki & Yee (1998) (17 galaxies). anunreddenedspectralenergydistribution(SED) TheH denotestheABmagnitudesfromtheNIC- from dust-free models of young star-forming pop- MOSF160WfilterandIRIMontheKittPeak4.0 ulations for use as a template. We used the m. V denotes the AB magnitudes from the HST PE´GASE2 galaxy spectral evolution model (Fioc F606W filter. The HST images were smoothed to & Rocca-Volmerange 1999) to model the LBG match the much poorer PSF of the ground based SEDs. The prominent feature of this model is IR observations. See Papovich, Dickinson, & Fer- that it includes stellar evolutionary tracks with guson (2001) and Sawicki & Yee (1998) for com- non-solarmetallicities and contributionfromneb- plete descriptions of the data. ular emission. Zackrisson et al. (2001) provide TheG−Rsampleissubjecttocertainselection a comparison of different galaxy spectral evolu- effects: only galaxieswith G−R<1.2werespec- tion models used in recent studies. They show troscopically studied and included in this sample, that the broad-band UV colors predicted by their shown in Figure 1. This selection effect has sig- model and the PE´GASE2 codes are not signifi- nificantconsequencesforthe reddeningestimates, cantly different for a large range of metallicities. particularly at large redshifts. No effects are in- There are differences in the V−K color, but this troduced on the blue-limit of the observed colors, color is of little consequence in star-forming re- andtheprogressivereddeningoftheentiresample gions. Afterchoosingtheinitialparameterstode- at z > 3 can be attributed to absorption by the scribe an LBG, the resulting SED was redshifted intergalactic medium. (Madau 1995). bythemeasuredredshiftandconvolvedwiththeG and R transmission curves (Charles Steidel 2001, private communication; also see Steidel & Hamil- ton (1993)) to get the G−R colors, using codes that are a part of the PE´GASE2 package. Thesyntheticspectraarecomputedatspecified ages after the onset of the star formationepisode. The properties ofthe stellar populations are computed basedonthe shape ofthe initialmass function (IMF) and its upper and lower limits. Other parameters used to compute the SED are the initial metallicity of the ISM and the star formation history. Working with only one UV color, we face the dilemma produced by the age-reddening degeneracy. For a given source, we are unable to distin- Fig. 1.—G−Rcolorplottedagainstspectroscopic guish between the cases of an older (and there- redshiftz for906LBGs. Theuppercut-offatG− fore redder), dust-free population and that of a R∼1.2isaselectionlimit. Progressivereddening younger, dust-reddened population. There are at z > 3 is because of IGM absorption (Madau various factors that can redden the colors of a 1995). galaxy; age of the stellar population, increased metallicity, higher amounts of dust or any com- bination of these factors. In principle, this de- 3. SPECTRAL ENERGY DISTRIBU- generacy cannot be broken working with one UV TIONS color alone. In our analysis we break this degeneracy arbitrarily by analyzing the sample under The G − R color of sources at z ∼ 3 pro- twosetsofassumptionsregardingthetimedepen- videsameasureoftheFUVspectralslopeintheir rest frame. The large range of G− R colors in dence of dust formation in these high-z galaxies, as discussed in the next two subsections. In each the LBGs at a given redshift suggests that the of the two cases we assume a fixed ageof the stel- sources are reddened by different amounts and lar population for all the LBGs and assume con- thatthis reddeningis mainly due to dustintrinsic ditions that leads to an upper-limit and a lower to the sources. It is therefore necessary to obtain 3 limit on the dust attenuation. We find that only dening is a consequence of rapidly forming dust. a small fraction of the color range of the LBGs We further assumed that dust formation follows canbe attributed to agealone; mostofitmust be the formation of massive stars on a nuclear time due to reddening by internal dust. As shown in scale. In order to get an absolute lower envelope Figure 2, at a given redshift (z ∼ 2), the G−R to the data at higher redshifts (z > 2.5) we had color gets redder by 0.26 as the galaxy ages from toassumelowermetallicities(andcorrespondingly 0yr to 1Gyr andby0.15asthe galaxyagesfrom younger ages). The initial metallicity of the ISM 50 Myr to 1 Gyr. The color range for the ob- was varied from 0.1 Z⊙ to 0.01 Z⊙ with z = 2 to served LBGs at the same redshift is 1.6. Analysis z =4respectively. Inordertomimicthebehavior under two different sets of assumptions based on of the data at the blue envelope we had to in- the timescale of dust formation helps in resolving crease the higher mass limit for the IMF at larger this age-reddening degeneracy as far as it exists. redshifts. WeusedaSalpeterinitialmassfunction Furthermore we verify our model parameter as- with a lower mass limit of 0.1 M⊙. Studies of the sumptions by applying them to a subset of the early metal pollution of the intergalactic medium LBGs for which longer colors (V −H) were avail- show that the IMFs are increasingly biased to- able. At z ≥ 3, the colors of a galaxy are fur- ward higher masses at large redshifts (see Abia ther reddened by IGM absorption. Both optically et al. (2001) and references therein). Also Lloyd- thin Lyman−α forest clouds and optically thick Ronning,Fryer,&Ramirez-Ruiz(2002)showthat Lyman-limit systems contribute to the reddening if massive stars are the progenitors of long lived of background sources (Madau 1995). We have gamma ray bursts, the IMFs at large redshifts corrected our assumed SEDs for this effect using need to be flatter with much higher upper mass the values provided in Madau (1995). limits. The upper mass limit for our models was varied from 120 M⊙ to 200 M⊙ with z = 2 to z = 4 respectively. We divided the sample into four redshift bins (2 ≤ z < 2.5, 2.5 ≤ z < 3, 3 ≤ z < 3.5, and 3.5 ≤ z < 4), to simulate the changingbehaviorofthe data withredshiftas well as to study the possible evolutionof the dust properties. Table 1 shows the parameters which were required to match the bluest observed colors with an unreddened SED for case I. A con- stantStarFormationRate(SFR)of100M⊙ yr−1 was used at all redshifts. The colors were exam- ined at different ages after the star formationhad started as noted in Table 1 under the column la- beled “Age”. Values for the UV-spectral slope β were calculated as prescribed by Calzetti (2001) Fig. 2.— G−R color predicted by increasingly for the spectral range 0.126 µm < λ < 0.26 µm. older SEDs as a function of redshift z. The range A scenario favoring an IMF biased toward mas- on observed colors of the LBGs cannot be ex- sive stars, low stellar metallicity, and substantial plained by age alone. dustformationona107 yrtimescaleissupported by the equivalent width distribution and number counts ofLyman−αemissiongalaxiesin the early 3.1. Case I universe by Malhotra & Rhoads (2002). The in- In this case we assumed that we are observ- trinsic colors of all the galaxies are assumed to ing the LBGs within a short time into their first correspond to this young model. episode of star formation. The dust free model In this case the model parameters were cho- was chosen to represent the very youngest, bluest sen so as to provide a blue envelope to the sam- LBG. This implies that only the very bluest of ple, representing the youngest unreddened galax- the LBGs are dust free and that increased red- ies. In doing this, we have assumed a short time- 4 scale for dust formation and assumed that only those found by Shapley et al. (2001). The initial the youngestsystemsaredustfree. Insuchyoung metallicity of the ISM was set to 0.2 Z⊙ and the star forming systems Type II supernovae(SNe II) colors were sampled at 320 Myr. This larger age arethedominantsourcesofdustproduction. (For andhighermetallicityvis-a-viscaseIresultinred- a detailed study on the observed properties of SN der colorsfor the dust-free (unreddened) galaxies, dust see Wooden (1997)). Modeling the dust con- and all the galaxies with colors bluer than this tent of a nearby low metallicity galaxy incorpo- were assumed to be dust-free. Table 1 shows the rating dust from SNe II Hirashita, Hunt, & Fer- parameters used for the analysis of this case. rara (2002) show that the dust mass reaches its For this case, we assume that the galaxies maximum in ∼ 2 × 107 yr. Edmunds & Eales 320Myr oldandyoungerarestill dust free. Dust (1998) model dust masses in galaxies and show forms in these galaxies at later times. This long that the dust content in galaxies with high star time-scale for the dust formation implies that the formation rates advances within a factor of 2 of dust formation in these galaxies was primarily a the maximum values at very young ages. For result of the evolved intermediate mass stars and m⋆/mtot = 0.2, if one considers mtot = 1011 M⊙, the dust production time-scales are linked to the andSFR=100M⊙yr−1,dustmassesgrowwithin evolution time-scales of intermediate mass stars. a factor of 2 of the maximum in 2×107 yr. This As explained earlier, we adoptan age of 320 Myr assumptionoftheshorttime scalefordustforma- to account for the fact that Shapley et al. (2001) tion results in larger dust attenuation factors for found that this was the median age of LBGs us- these galaxies. ing a multi-wavelength study, and this approach results in a lower estimate to the amount of dust 3.2. Case II in these systems. In this case we assumed longer timescales for These two cases are not just two possible sce- dust formation, consistent with the assumption narios, but from the viewpoint of dust forma- that mass loss from evolved lower-mass stars is tionscenariosareextrememodels,andtheirrange the principal contributor to dust formation. This of results will cover any reasonable intermediate process follows the slower (τ ∼ 109 yr) evolution- model. arytime scaleofthe stars;itismoresignificantin the present universe and less so in the high-z uni- 4. DUST MODELS AND ATTENUA- verse(Edmunds 2001). The modelparametersfor TION FUNCTIONS this case were chosen, so as to arrive at a conser- TorelatetheSEDsgeneratedwiththeassump- vativelowerlimittotheamountofdustpresentin tions outlined in Sec. 3 to the observed colors,we LBGs responsible for partial attenuation of their need to know the wavelength dependence of the UV flux. Shapley et al. (2001) analyzed 81 LBGs dust attenuation function in these galaxies. It is forwhichtheyalsohadK andJbandfluxes,and s important to distinguish between the terms ex- thesewerefoundtohaveagesbetween10Myrand tinction and attenuation. The term “extinction 1 Gyr with a median value of 320 Myr. We as- law ” was originally defined for stars. It quanti- sumethatgalaxieswithpopulationsyoungerthan fiesthewavelengthdependenceofdustabsorption 320 Myr are dust free and that dust appears only andscatteringoutofthelineofsighttowardpoint through subsequent evolution. The 320 Myr old sources. In distant galaxies however the situation SED is therefore used as a reference for all LBGs is quite different. There are two main reasons: (i) with colors redder than those implied by this ref- Thecomplexgeometryofthelightsourcesandthe erence. As we were not attempting to model the dustdistributionand(ii)thefluxscatteredoffthe bluest LBGs, dividing the sample into different dustgrainsisreturnedintothelineofsightincom- redshift bins would not constrain the model pa- plex ways. Thus the “attenuation” depends criti- rametersinanyway. Therefore,inthiscasewedo cally on the geometry of the dust and the sources not divide the sample into different redshift bins. A constant SFR of 100 M⊙ yr−1 and a Salpeter andthe opticaldepth andscatteringproperties of the dust. IMFwithlowerlimitof0.1M⊙andanupperlimit of 125M⊙ were chosen,which areconsistent with In recent years the wavelength dependence of 5 Table 1 Parameters assumed for SEDs under Case I and Case II Redshift Range Initial Metallicity Age Upper mass limit β Case I 2.0<z ≤2.5 0.1 Z⊙ ∼50 Myr 120 M⊙ −3.14±0.04 2.5<z ≤3.0 0.1 Z⊙ ∼50 Myr 135 M⊙ −3.5±0.02 3.0<z ≤3.5 0.01 Z⊙ ∼0 yr 150 M⊙ −3.76±0.02 3.5<z ≤4.0 0.01 Z⊙ ∼0 yr 200 M⊙ −3.82±0.02 Case II 2.0<z <4.0 0.2 Z⊙ ∼320 Myr 125 M⊙ −3.04±0.04 dustattenuationinstarforminggalaxieshasbeen uationlawbecomesflatterinthefar-UV.Thus,as estimated by the so called “Calzetti law”, which Figure 3 shows, there is not a single attenuation is an empirical determination of the observed at- law, e.g. the Calzetti “law”, but a series of attenuation function derived by averaging over a tenuation laws with a functional form dependent small sample of UV-bright local starburst galax- upon the amount of dust present. WG2000 have ies (Calzetti, Kinney & Storchi-Bergmann 1994; also shown that the Calzetti law corresponds to Calzetti et al. 1995, 2000). This empirical law theattenuationfunctionforaclumpyshellgalaxy leads to a correlation between the UV spectral withSMC dustofintermediatedustopticaldepth slope β and the FUV attenuation. The FUV flux of τ =1.5 (see Figure 3). One cannot expect all V has then been corrected for attenuation, assum- the LBGs to have the same amount of dust given ing this correlation holds for all redshifts. This their wide range of observed colors. law however has limitations; while applicable to The clumpy models of WG2000 assume a spa- the particular sample there is no evidence that tial filling factor of 0.15 for denser clumps, em- thislawappliesoverallredshiftsorthatitapplies bedded into a low density inter-clump medium, to systems with substantially more dust than is with a density contrast of 100 : 1. As shown present in the local sample of UV-bright galaxies. in an earlier study (Witt & Gordon 1996), this Bell(2002)demonstratesthatnormalstar-forming set of conditions leads to a power-law spectrum galaxies deviate substantially from the starburst of cloud masses that closely resembles that found β−AFUV correlation. Wehavethereforechosento in the galactic ISM. The dependence of radiative address the question of dust attenuation with the transferonotherchoicesofclumpinessparameters radiativetransfermodelsofWitt&Gordon(2000) was fully explored by Witt & Gordon (1996). In (henceforth WG2000). These models incorporate the absence of any other information, we assume multiple scattering radiative transfer calculations that the structural details of the ISM in LBGs for different galactic environments, filled with ei- resemble that of the MW galaxy. The geometry ther homogeneous dust or a two-phase clumpy of the WG2000 shell models assume an inner vol- dust distribution. Figure 3 shows the attenuation ume (r ≤0.3R) occupied by stars, surrounded by functionsusingtheclumpyshellmodelsforvarious a shell (0.3R < r ≤R) of dust distributed either optical depths. In these models, τV should be in- homogeneously or in a two-phase clumpy distri- terpretedasameasureofthedustmass(τV ∝dust bution. While relative sizes of star-filled volume mass)wheretheactualamountofdustwouldscale and the dusty shell are to some degree arbitrary, withthesizeofthesystem. Astheamountofdust, theyaremodeledafterheappearanceofgiantstar- measured by the visual optical depth for a corre- formingcomplexes,e.g. NGC604inM33(Hunter spondinghomogeneousmodelincreases,theatten- et al. 1996). Important aspects are that the dust 6 is situated between the sources and the observer, thusmaximizingtheattenuation,yetcloseenough to the sources so that scattered light becomes an integralpartofthefluxreceivedfromthecomplex. In this study we have used the clumpy shell models to estimate the dust attenuation for the LBGs (See sec. 5.1 for a more detailed analysis of the dust geometry). Figure 4 shows the rela- tionship between the attenuation at 1600 ˚A and the optical depth for SMC-clumpy shell and SMC - homogeneous shell models. In the homoge- neousmodelsthedusthasuniformspatialdensity. This effectively represents a screen geometry, and the attenuation rises linearly with optical depth. Whereas in the two-phase clumpy models, at low values of τ both the dust clumps and the inter- V clumpmediumareopticallythinandtheattenua- tionincreasesproportionalto the amountofdust, similar to the homogeneous case. At higher values of τ the clumps are starting to become opti- V callythick butthe inter-clumpmediumis stillop- tically thinandthe attenuationvariesless rapidly with the amount of dust. At intermediate optical depths the attenuation is influenced both by the dust clumps and the inter-clump medium. 5. ANALYSIS 5.1. The Nature and Geometry of the Fig. 3.—Attenuationfunctionsfromclumpyshell Dust in LBGs modelsatdifferentopticaldepths τ comparedto V There are significant variations in the dust theCalzettilaw. Dottedlineistheattenuationde- propertiesindifferentgalacticenvironmentsofco- scribed by E(λ−V)/E(B−V) for MW-like dust eval galaxies within the local group itself. In the at τ = 1.5. Long-dashed line is the attenuation V LMC, the UV extinction curves show a distinctly curveforSMC-likedustatτ =0.5,short-dashed V different behavior between the 30 Dor region (a forSMC-likedustatτ =1.5,anddash-dottedfor V mini-starburst)(Walborn1991)andtherestofthe SMC-like dust at τ = 4.5. Solid line represents V LMC (Clayton & Martin 1985; Fitzpatrick 1985, theCalzettilawwherethesolidsquaresarephoto- 1986;Misselt,Clayton,&Gordon1999). The2175 metricpoints. TheCalzettilawcanbereproduced ˚A bump isweakerandthe far-UVriseis stronger by SMC-Clumpy shell model with τ =1.5. V nearthe30DorregionthanintherestoftheLMC. In the bar-regionof the SMC, the averageextinc- tioncurveis characterizedbya roughlylinearrise (vs. λ−1) increasing toward shorter wavelengths without a 2175 ˚A bump (Prévot et al. 1984; Thompson et al. 1988; Gordon & Clayton 1998). Yet, there is one sight line that has an extinction curve with a significant 2175 ˚A bump (Lequeux et al. 1982; Gordon & Clayton 1998). In M31, the extinction curve is consistent with that of the average Galactic extinction within the associated 7 uncertainties,althoughthe 2175˚A bump may be the NorthandSouthHubble DeepFieldissimilar weak (Bianchi et al. 1996). Using IUE data for to SMC-like dust. Figure 6(a) shows the model- sightlinesthroughlow-densityregionsofthe MW predicted curves for SMC clumpy dust under the disk and halo Clayton, Gordon, & Wolff (2000) caseI assumptionsfor the intrinsic SED,andFig- show that many of the sight lines have extinction ure 6(b)forthe case II assumptions. We conclude curves with weak bumps and very steep far-UV thatthedustinthissampleofLBGsisbetterrep- extinction reminiscent of the Magellanic Clouds. resented by SMC-like dust, which lacks the 2175 Modeling the SEDs of 30 starburst galaxies Gor- ˚A feature. don, Calzetti & Witt (1997) found that the dust Even though multi-color information is avail- in these systems has extinction properties similar able for some LBGs, such samples are much to the SMC lacking the 2175 ˚A feature present smaller and therefore less complete, being ad- in the galactic extinction curve. However, Motta versely affected by observational limitations. We et al. (2002) report on the detection of a signif- have chosen to work with the largest sample of icant 2175 ˚A feature in the extinction curve of LBGs available to date. Unfortunately this im- a normal-type galaxy at z = 0.83. Massarotti et plies that we infer dust content, dust properties, al. (2001a) report that some galaxies in the HDF stellar content and dust-star geometry all with spectroscopic sample show the 2175 ˚A feature. a single color. As a check to our model SED The limited evidence available so far suggests assumptions, we analyzed a smaller sample of that the absence of the 2175 ˚A feature is associ- LBGs for which longer wavelength colors were atedwithhighSFR,butthisisfarfromconclusive. available. Figure 7 is the V −H color vs. red- In the presence of this ongoingdebate, the nature shiftforLBGs (datafromPapovich,Dickinson,& ofthedustintheLBGsneedstobeaddressed. We Ferguson (2001) and Sawicki & Yee (1998)). The use the fact that the presence of the 2175 ˚A fea- curves on the figure are model-predicted curves turehasadrasticallydifferenteffectonthe G−R for SMC clumpy dust, with the dust-free intrin- color in the 2 < z < 2.6 range compared to dust sic SED produced under the same assumptions without the 2175 ˚A feature to test the LBG data as our case I analysis. The colors predicted by a for the presence of the 2175 ˚A band. We red- dust-free SED under case II assumptions is also denedtheassumedSED(caseI)withtheWG2000 shown for reference. Comparison of Figure 6(a), clumpy attenuation functions with increasing op- 6(b) with Figure 7 clearly shows that the smaller tical depths of τ =0.25,0.5,1.0,5.0,7.0, & 10.0, V −H sample spans the same range in attenua- V with both MW- and SMC-like dust. These SEDs tions and that our model parameters are robust. werethenredshiftedandtheG−Rcolorwascalcu- This also implies that these two samples of LBGs lated at the different redshifts. For z ≥3 the col- are subsamples of galaxies in the same evolution- orswerecorrectedforIGMabsorptionusingvalues ary stage. in Madau (1995). Figure 5 is a plot of the G−R We need a fundamental understanding of the colorvs. the redshift, wherethe differentlines are environmentthat producesthe largerangeofred- thecolorsobtainedfortheintrinsicSEDreddened dening that is observed. The dust geometry is a with different amounts of MW-like dust. We find important factor in the amount of reddening pro- thatMW-likedustcannotexplaintherangeofob- duced. For a local sample of starburst galaxies served colors in the 2 < z < 3 range. As the Gordon, Calzetti & Witt (1997) have shown that 2175 ˚A feature passes through the G and R fil- the dust geometry is best represented by an inter set at different z, the predicted G−R color nerdust-freesphereofstarssurroundedbyastar- first gets bluer (till z < 2.45) and then gets pro- free shell of clumpy dust such as represented by gressively redder for increasing amounts of dust theWG2000shellmodels. Inoue(2002)hasfound (see Figure 5). On the other hand, the curves the dust in HII regions to be best described by modeled by SMC-like dust (Fig. 6) for increas- a shell geometry. Also Buat et al. (2002) find ing values of attenuation span the observedrange that the clumpy shell geometry as described in of colors quite well. Using color-color plots Gor- WG2000 fits very well with their analysis of the don, Smith, & Clayton (1999) also reached the UV SEDs of starburstgalaxies. Different dust ge- conclusion that the dust in starburst galaxies in ometriesareanalyzedinWG2000. Notallgeome- 8 111111111.........555555555 111111111 G-RG-RG-RG-RG-RG-RG-RG-RG-R 000000000.........555555555 AAAAAAAAA111111111666666666000000000000000000 mmmmmmmmmaaaaaaaaaggggggggg 000000000 0.5903 1.075 1.752 (a) SMC-Dust Case I 33..495249 4.605 Fig. 4.— Attenuation at 1600 ˚A , A1600 (mag) ---------000000000.........555555555 222222222 222222222.........555555555 333333333 333333333.........555555555 444444444 against dust optical depth, τ for different ge- RRRRRRRRReeeeeeeeedddddddddssssssssshhhhhhhhhiiiiiiiiifffffffffttttttttt zzzzzzzzz V 111111111.........555555555 ometries. Solid line represents SMC-like dust in a Clumpy-shell geometry and dashed line repre- sentsSMC-likedusthomogeneouslydistributedin 111111111 a shell geometry. 1.5 G-RG-RG-RG-RG-RG-RG-RG-RG-R 000000000.........555555555 AAAAAAAAA111111111666666666000000000000000000 mmmmmmmmmaaaaaaaaaggggggggg 1 000000000 0.5903 1.075 1.752 (b) SMC-Dust Case II 33..495249 G-R 0.5 ---------000000000.........555555555 222222222 222222222.........555555555 333333333 333333333.........555555555 4.605 444444444 A mag RRRRRRRRReeeeeeeeedddddddddssssssssshhhhhhhhhiiiiiiiiifffffffffttttttttt zzzzzzzzz 1600 0 0 0.335 Fig. 6.— G−R color vs. redshift with the col- 0.642 1.154 ors obtained for the SED reddened with differ- 2.801 3.597 ent amounts of SMC-like dust, (a) under Case I -0.5 2 2.5 3 3.5 4 assumptions and (b) under Case II assumptions. Redshift z The attenuation produced at 1600 ˚A is indi- cated for each of the lines. The values of τ in V Fig. 5.— G − R color vs. redshift where the the models that produce these attenuations are different lines are the colors obtained for the 0,0.25,0.5,1.0,5.0,7.0,and10.0. intrinsic SED reddened with different amounts of MW-like dust. The attenuation (in magnitudes) produced at 1600 ˚A , A1600 is indi- cated for each of the lines. The values of τ V in the model that produce these attenuations are 0,0.25,0.5,1.0,5.0,and10.0. Even large amounts of dust cannot explain the red colors in the 2 ≤ z ≤3 region. 9 tries produce the same amounts of reddening for ing each curve partially accounts for color differ- given amounts of dust; to produce equal amount ences which may be attributed to a range in the ofreddeningothergeometrieswouldrequiremuch intrinsicagesoftheSED.Theattenuationforeach larger dust masses. In their Figure 11 WG2000 galaxyintherest-framewavelengthfortheRfilter showthatonlytheshellmodelsreproduceaslarge is then noted. The attenuations andz are usedto a range of ∆β as observed. One should note that arriveat the absolute magnitudes, luminosity dis- the observed G−R color and β are not identi- tances and the intrinsic UV luminosities. We find cal. The G −R color is a rest-frame UV-color, thatthebulkoftheLBGsareextremelyluminous, whose rest-frame UV base wavelengths vary with L ∼ 1011 −1012L⊙, corresponding to the LIRG redshift(G=1610˚A atz =2to966˚A atz =4, and ULIRG population in the present universe. R=2310 ˚A at z =2 to 1386 ˚A at z =4), while Starforminggalaxies,bothinthelocaluniverse the wavelengths for β are fixed (1200 ˚A–2600 ˚A). and in the early universe have been shown to ex- It is not surprising that a large fraction of the hibit a correlation between dust attenuation and galaxies at z > 2 are best described as resem- their intrinsic luminosity. Adelberger & Steidel bling centrally concentrated “blobs”, which are (2000), in their Figure 11, relate the dust lumi- probablytheprogenitorsofourpresent-daygalac- nosity to the total luminosity of starbursts in the tic bulges and elliptical galaxies (van den Bergh local universe, at z ∼ 1 and at z ∼ 3. Calzetti 2002). The choice of a spherical star-forming et al. (1995), Sullivan et al. (2001), and Wang region, relatively free of dust surrounded by a & Heckman (1996) report similar correlations be- dust shell seems to be an appropriate geometry tween different star formation indicators to the to describe these objects. A justification for the FIR luminosity (which is directly related to the clumpy-shellgeometryofthe LBGsisduetotheir amount of dust). Hopkins et al. (2001) analyze large SFRs, up to ∼1000 M⊙yr−1 in some cases. theeffectofdust-reddeningdependentonSFRap- Such massive star formation activity will blow pliedtodifferentSFRindicatorssuchasUVlumi- awaythegasanddustintothesurroundingregion. nosity, H flux, FIR Luminosity and radio lumi- α Stars are expected to spend the very beginning nosity at 1.4 GHz. They show that discrepancies of their evolution deeply embedded in dusty envi- between these methods can be explained by such ronments,laterdispersingthe molecularclouds in an effect. All these trends imply that the more whichtheywereborn(Calzetti,Kinney&Storchi- luminous galaxies are dustier. Bergmann 1994, and references therein). In our Inthis studyalsowefindacorrelationbetween analysis too, we find that the shell geometry best the intrinsic UV luminosity and the dust atten- explains the observed colors for reasonable values uation in these systems. The LBGs have almost of dust optical depths. constantapparentmagnitude (∼24.5)but a wide range of colors. This seems to imply a correlation 5.2. TheRelationBetweentheDustOpac- between the intrinsic luminosity of these galaxies ity and the Intrinsic UV Luminosity and their reddening. Given our large sample and of LBGs systematicanalysiswecanarriveataquantitative result, but we should point out that this relation To estimate the intrinsic UV luminosity of the is not unique; it is dependent upon the dust ge- LBGs we need to adopt a cosmology: throughout this paper we use H0 =65 km s−1 Mpc−1,ΩM = ometry, dust properties and the assumedintrinsic SED. We find, 0.3,ΩΛ =0.7,unlessotherwisespecified. Thered- dened SEDs were redshifted and the colors were α calculated for different amounts of dust, result- a1600 ∝ L1600 ˚A (1) ing in a range of attenuations at 1600 ˚A (A1600), (cid:18) L⊙ (cid:19) at different redshifts. The attenuation for each where a1600 is the linear attenuation factor re- galaxy was then computed. This was done as fol- latedtotheattenuationA1600 (inmag)asa1600 = lows: The color curves corresponding to selected 100.4A1600. The value of α is slightly different for values of the attenuation at 1600 ˚A , A1600, are case I and caseII. For case I,the meanrest-frame as shown in Figure 6(a) and 6(b). Dividing the UV luminosity of all the galaxiesin each attenua- sample into finite-sized ranges of color surround- tion interval was calculated for each redshift bin. 10