Extinction curves expected in young galaxies

0.54 MB·

by  Hiroyuki Hirashita

Mon.Not.R.Astron.Soc.000,1(2005) Printed2February2008 (MNLATEXstylefilev2.2)
Extinction curves expected in young galaxies
Hiroyuki Hirashita1,2⋆†, Takaya Nozawa3, Takashi Kozasa3,
4 5
Takako T. Ishii †, and Tsutomu T. Takeuchi ‡
5
1GraduateSchoolofScience,NagoyaUniversity,Nagoya464-8602,Japan
0
2SISSA/InternationalSchoolforAdvancedStudies,ViaBeirut4,34014Trieste,Italy
0
3DivisionofEarthandPlanetarySciences,GraduateSchoolofScience,HokkaidoUniversity,Sapporo060-0810,Japan
2
4KwasanObservatory,KyotoUniversity,Yamashina-ku,Kyoto607-8471,Japan

n 5Laboratoired’AstrophysiquedeMarseille,TraverseduSiphonBP8,13376MarseilleCedex12,France
a
J

0 Accepted2004December10;Submitted2004September8
1

1
ABSTRACT
v
We investigatethe extinctioncurvesof younggalaxiesin which dustis suppliedfromType
8
II supernovae(SNe II) and/or pair instability supernovae(PISNe). We adopt Nozawa et al.
5
(2003)forcompositionsandsizedistributionofgrainsformedinSNeIIandPISNe.Wefind
1
1 thattheextinctioncurveisquitesensitivetointernalmetalmixinginsupernovae(SNe).The
0 extinctioncurvespredictedfromthemixedSNearedominatedbySiO2 andischaracterised
5 bysteeprisefrominfraredtoultraviolet(UV).ThedustfromunmixedSNeshowsshallower
0 extinctioncurve,becauseofthecontributionfromlarge-sized(∼0.1µm)Sigrains.However,
/ the progenitormass is importantin unmixed SNe II: If the progenitormass is smaller than
h
∼ 20M ,theextinctioncurveisflatinUV;otherwise,theextinctioncurverisestowardthe
p ⊙
- shortwavelength.Theextinctioncurveobservedinahigh-redshiftquasar(z = 6.2)favours
o thedustproductionbyunmixedSNeII.Wealsoprovidesomeusefulobservationalquantities,
r
sothatourmodelmightbecomparedwithfuturehigh-zextinctioncurves.
t
s
a Key words: dust, extinction — galaxies: evolution — galaxies: high-redshift— galaxies:
:
v ISM—supernovae:general—quasars:individual:SDSSJ104845.05+463718.3
i
X
r
a
1 INTRODUCTION IIorPISNemaytriggertheformationoflow-massstars(Schneider
etal.2003).
Dust grains play a crucial role in the formation and evolution
Sincedustisimportantevenintheearlystageofgalaxyevolu-
of galaxies. Dust grains absorb stellar light and reemit it in far
tion,itiscrucialtoknowhowmuchdustandwhatspeciesofdust
infrared (FIR), controlling the energy balance in the interstellar
form. Todini &Ferrara(2001), following the method by Kozasa,
medium (ISM) and protostellar gas clouds. Also, the surface of
Hasegawa,&Nomoto(1989,1991),showthatdustmassproduced
dustgrainsisasiteforanefficientformationofH molecules(e.g.
2
Cazaux&Tielens2002,2004),whichactasaneffectivecoolantin by a SN II is roughly 0.1–0.4 M⊙. They also find that SNe II
formamorphouscarbonwithsizearound300A˚ andsilicategrains
metal-poorISM.Thoseeffectsofdustturnoneveninaverymetal-
around10–20A˚.Schneider,Ferrara,&Salvaterra(2004)extendthe
poorenvironment(∼1%ofthesolarmetallicity;Hirashita&Fer-
rara2002;Morgan&Edmunds2003),anditisarguedthatthestar progenitormassrangetotheregimeofPISNe(140–260M⊙)and
formationrateisenhancedbecauseofthefirstdustenrichmentin findthat30–60M⊙ofdustformsperPISN.Thegrainradiiaredis-
tributedfrom0.001to0.3µm,dependingonthespecies.Themoti-
thehistoryofgalaxyevolution.Thefirstsourceofdustintheuni-
vationforconsideringPISNecomesfromsomeevidenceindicating
verseisTypeIIsupernovae(SNeII)orpairinstabilitysupernovae
(PISNe),sincethelifetimeoftheirprogenitorsisshort(∼106yr). that the starsformed frommetal-free gas, Population III (PopIII)
stars,areverymassivewithacharacteristicmassofafewhundred
Inthelocaluniverse,dustgrainsarealsoproducedbyevolvedlow
solarmasses(Bromm&Larson2004,andreferencestherein).Such
massstars(Gehrz1989), but thisproduction mechanism requires
massivestarsareconsideredtobeginpaircreationofelectronand
muchlonger(& 1Gyr)timescales.ThefirstdustsuppliedbySNe
positronaftertheheliumburningphase,andfinallyendtheirlives
withexplosive nuclear reaction disrupting thewhole stars(Fryer,
Woosley,&Heger2001).ThisexplosioniscalledPISN.
⋆ E-mail:[email protected]
Nozawaetal.(2003)alsocalculatethedustmassintheejecta
† PostdoctoralFellowoftheJapanSocietyforthePromotionofScience
(JSPS). of PopIII SNe II and PISNe, carefully treating the radial density
‡ PostdoctoralFellowoftheJSPSforResearchAbroad. profileandthetemperatureevolution.Sinceitisstilldebatedhow
2 H. Hirashitaet al.
mechanisminthecourseofgalaxyevolution.Thehighest-redshift
Table1.Summaryofgrainspecies.
BAL quasar in their sample, SDSS J104845.05+463718.3 (here-
Species conditiona Refb d(egnscimty−(δ3j)) raefstetfrraSmDeSSwaJ1v0el4e8n+g4th63λ7)<at1z7=006A˚.2. (sIhnowthsisapraepders,peaclltrtuhme watavthee-
lengthsareshownintherestframeofobservedgalaxies.)However,
C u 1 2.28 at λ > 1700 A˚, there is no indication of reddening. Then they
Si u 2 2.34 suggest the extinction curve tobe flat at λ & 1700 A˚ and rising
SiO2 m/u 3 2.66 at λ . 1700 A˚. Maiolino et al. (2004b) find that the extinction
Fe u 4 7.95
curve of SDSS J1048+4637 is different from that of low-z BAL
FeS u 5 4.87
quasarsandisinexcellent agreement withtheSNIIdustmodels
Fe3O4 m 6 5.25
by Todini &Ferrara(2001). It isinteresting toextend their work
Al2O3 m/u 7 4.01
MgO u 8 3.59 tovariousdustformationmodelsinNozawaetal.(2003).Theex-
MgSiO3 m/u 9 3.20 tinctioncurveshouldbedifferentfromSNeIItoPISNeandfrom
Mg2SiO4 m/u 10 3.23 mixedSNetounmixedSNe.Dustproductioninsuchvariouscon-
ditionsisextensively investigated inNozawa et al.(2003); hence
weaimatinvestigatingtheextinctioncurvebasedontheirresults.
a The classifications “m”, “u”, and “m/u” mean that the species is In addition to Maiolino et al. (2004a), evidence for dust en-
formedinmixed,unmixed,andbothsupernovae,respectively. richmenthasbeenobtainedatveryhighz(>5),wherethecosmic
b Referencesforopticalconstants:(1)Edo(1983);(2)Edward(1985); age is less than 1 Gyr, by the recent sub-mm and millimetre ob-
(3) Philipp (1985); (4) Lynch & Hunter (1991); (5) Semenov et al. servations of distant quasars (Bertoldi et al. 2003; Priddey et al.
(2003);(6)Mukai(1989)(forλ < 0.14µm,weadoptthevalues at 2003). At lowerz (. 5), direct indicationsof high-z dust comes
λ = 0.14 µm);(7) Toon,Pollack, & Khare (1976); (8) Roessler & fromthereddeningofbackgroundquasars(Fall,Pei,&McMahon
Huffman(1991);(9)Dorschneretal.(1995);(10)Ja¨geretal.(2003). 1989;Zuoetal.1997).Thedepletionofheavyelementsinquasar
absorptionlinesystemsalsosupportsthepresenceofdustindistant
efficiently the mixing of atoms within supernovae (SNe) occurs, systems (Pettini et al. 1994; Molaro, Vladilo, & Centurion 1998;
Nozawaetal.(2003)treattwoextremecasesforthemixingofel- Levshakov et al. 2000; Vladilo 2002; Ledoux, Petitjean, & Sri-
ements: one is the unmixed case in which the original onion-like anand2003).Thereareseveralobservationsofextinctioncurvesup
structureofelementsispreserved,andtheotheristhemixedcase toz ∼1bytakingadvantageofthegravitationallensing(Falcoet
inwhichtheelementsareuniformlymixedwithintheheliumcore. al.1999;andMun˜ozetal.2004).Spectropolarimetricobservations
Afterexamining thosetwocases, they show that theformed dust of two radio galaxies at z ∼ 1.4 reveal the 2200-A˚ dust feature
speciesdependlargelyonthemixingofseedelementswithinSNe, inscatteredlight(Solo´rzano-In˜arreaetal.2004).However,mostof
because the dominant reactions change depending on theratioof theobservationsofextinctioncurvesarelimitedtorelativelylowz,
availableelements(seeSection2.1formoredetaileddescription). wheredustisnotonlyproducedbySNeII,butalsobyevolvedlate-
Nozawaetal.(2003)predictlargerdustmassthanTodini&Ferrara typestars.Inthefuture,observationalsamplesofextinctioncurves
(2001)forSNeII.Howmuchandwhatkindofgrainspeciesform couldbeextendedtohigh-z primevalgalaxies,wheredustispre-
in SNeII and PISNeisstill amatter of debate, partly depending dominantlyproducedinSNeIIand/orPISNe.Thisworkcouldbe
onthedegreeof mixingwithintheHe-core, andonthemodel of appliedtosuchfutureobservationstorevealthesizeandcomposi-
SNeemployed inthecalculations; Woosley&Weaver(1995) for tionofdustoriginatingfromSNeIIorPISNe.
SNe II in Todini & Ferrara (2001), Heger & Woosley (2002) for Wefirstdescribeourtheoreticaltreatmenttocalculatetheex-
PISNeinSchneideretal.(2004),andUmeda&Nomoto(2002)for tinctioncurvesofSNIIandPISNdustinSection2.Weexamine
PopIIISNeinNozawaetal.(2003). Theformedgrainspeciesin ourresults,andprovidesomeobservationallyconvenientquantities
thecalculationofNozawaetal.(2003)arelistedinTable1. inSection3.Wediscussourresultsfromtheobservational view-
Someobservationshavedetectedinfraredradiationfromex- pointinSection4,andfinallygivetheconclusionofthispaperin
tragalactic SNe II (e.g. Dwek et al. 1983; Moseley et al. 1989; Section5.
Kozasa,Hasegawa,&Nomoto1989).Thisradiationhasbeeninter-
pretedtobeoriginatingfromdustformedinSNeII.FIRandsub-
millimetre (sub-mm) observations of Galactic SN remnants also
2 MODEL
have recently put further constraints on the dust mass formed in
SNe II (Cas A: e.g. Arendt, Dwek, & Moseley 1999; Dunne et
Ouraimistoderivethetheoretical extinctioncurvesofdust pro-
al.2003; Hinesetal.2004; Kepler: e.g.Morgan etal.2003). Al- ducedinSNeIIandPISNe.Weadopt thedust productionmodel
thoughFIRandsub-mmobservationsareusefultoknowthedust
byNozawaetal.(2003),whoinvestigatevariousprogenitormass
amount,theemissivity,whichreflectsthecomposition,andthedust
ofSNeIIandPISNewithacarefultreatmentofphysicalprocesses
amountaredegeneratedintheobservedFIRandsub-mmluminos- (internalmixing,temperatureevolution,etc.).
ity.Therefore,inordertoconstrainthemodelofdustformationin
SNeII, another independent information on the dust amount and
compositionisnecessary.
2.1 DustproductioninSNeIIandPISNe
Extinctioncurvesareoftenusedtoinvestigatethedustprop-
erties(e.g.Mathis1990).Recently,byusingasampleofbroadab- Nozawaetal.(2003)investigatetheformationofdustgrainsinthe
sorption line(BAL) quasars, Maiolino et al. (2004a) have shown ejecta of PopIII SNe (SNe II and PISNe, whose progenitors are
thattheextinctionpropertiesofthelow-redshift(z<4,wherezis initiallymetal-free).Thecalculationtreatssomedetailscompared
theredshift)sampleisdifferentfromthoseofthehigh-z(z>4.9) withTodini&Ferrara(2001):(i)theradiativetransferequationin-
sample.Thisresultissuggestiveofachangeinthedustproduction cludingtheenergydepositionofradioactiveelementsissolvedto
Extinctioncurves of younggalaxies 3
calculatethetimeevolutionofgastemperature,whichstronglyaf- InFigure1,weshowthesizedistributionadoptedinthispa-
fectsthenumberdensityandsizeofnewlyformedgrains;(ii)the per, where the size distribution function fj(a) is defined so that
radial profile of density of various metals is considered; (iii) un- fj(a)daisproportionaltothenumberofgrainsinaradiusinterval
mixedanduniformlymixedcaseswithintheheliumcorearecon- [a, a+da](jindicatesthespecies).Thefourfigurescorrespondto
sidered. thefourcasesinTable2.Thenormalisationoffj(a)isdiscussedin
In the unmixed case, Nozawa et al. (2003) assume that the Section3.4,andweonlyapplyanarbitrarynormalisationtoeach
originalonion-likestructureofelementsispreserved.Ontheother figure.
hand,inthemixedcase,theyuniformlymixalltheelementsinthe
heliumcore.TheyalsoassumethecompleteformationofCOand
2.2 CalculationofExtinctionCurves
SiO molecules, neglecting the destruction of those molecules: no
carbon-bearinggraincondensesintheregionofC/O < 1andno Inordertocalculateextinctioncurves,theopticalconstantsforthe
Si-bearinggrain,except foroxidegrains,condenses intheregion grainsarenecessary.WeadoptthereferenceslistedinTable1for
ofSi/O<1.TheformationofCOandSiOmaybeincompletebe- theopticalconstants.Byusingthoseopticalconstants,wecalculate
causeofthedestructionbyenergeticelectronimpactwithinSNe. theabsorptionandscatteringcrosssectionsofhomogeneousspher-
Todini & Ferrara (2001) treat both formation and destruction of icalgrainswithvarioussizesbasedontheMietheory(Bohren&
COandSiO,findingthatbotharemostlydestroyed.Thedecrease Huffman 1983). The efficiency factor of extinction, which is de-
ofCOleadstotheformationofcarbongrains,whichcouldfinally finedasthecrosssectiondividedbythegeometricalcrosssection,
be oxidised with available oxygen. The destruction of SiO could isdenotedasQext,j(λ,a).Thisefficiencyfactorisafunctionof
decreasetheformationofgrainscomposedofSiO2,MgSiO3,and thewavelengthλandthedustsizea(jdenotesthegrainspecies).
Mg2SiO4,andincreaseotheroxidisedgrainsandSigrains.Obser- Theopticaldepthofgrainjasafunctionofwavelength,τλ,j,
vationally,itisstilldebatedifCOandSiOareefficientlydestroyed iscalculatedbyweightingthecrosssectionsaccordingtothesize
ornot.AdetaileddiscussiononthisissuecanbefoundinAppendix distributionasshowninFigure1:
BofNozawaetal.(2003).
∞
In the unmixed ejecta, a variety of grain species (Si, Fe, τλ,j =Z πa2Qext,j(λ, a)Cfj(a)da, (1)
Mg2SiO4, MgSiO3, MgO, Al2O3, SiO2, FeS, and C) condense, 0
while in the mixed ejecta, only oxide grains (SiO2, MgSiO3, whereC isthenormalisationconstant relatedtothecolumnden-
Mg2SiO4,Al2O3,andFe3O4)form.Thespeciesaresummarised sityofdust.ThedeterminationofCisnotimportantfortheextinc-
inTable1.Thedifferenceintheformedspeciesbetweenmixedand tioncurvebecausetheextinctioncurveispresentedintheformof
unmixedcasesaremainlyderivedbytheformationofmolecules. Aλ/AV (Aλ istheextinctioninunitsofmagnitudeatwavelength
Thecarbondust isnot produced intheirmixedcase, because the λ,andtheV-bandwavelengthis0.55µm),wheretheconstantC
carbonandoxygenaremixedandcombinedtoformCOmolecules. iscanceled.ThedeterminationofCisnecessarywhenwequantify
Onthecontrary,itformsinunmixedSNe,sincethereisacarbon- thecolumndensity(equation5).Theextinctioninunitsofmagni-
rich region at a certain radius of SNe. The formation of SiO tudeisproportionaltotheopticaldepthas
moleculesalsoaffectstheformedspecies:inthemixedejectaonly
A =1.086τ , (2)
oxidesilicategrainsform,whileintheunmixedejectanon-oxide λ,j λ,j
grainscanforminoxygen-poorregions. where A is the extinction of species j in units of magnitude
λ,j
Thesizeofthegrainsonthelocationofformationsiteinthe as a function of λ, and the factor 1.086 comes from 2.5log e.
10
ejecta spans a range of 3 orders of magnitude, depending on the ThetotalextinctionA iscalculatedbysummingA forallthe
λ λ,j
grain species. The size distribution function summed up over all concerningspecies:
the grain species is approximated by a broken power law. This
size distributionis different from that of the SN II calculation of Aλ= Aλ,j. (3)
Todini & Ferrara (2001), which has a typical sizes of 300 A˚ for Xj
amorphouscarbonand10–20A˚ foroxidegrains.Thedifferenceis
mainly comes from thedifferent treatment of the ejecta: Nozawa
etal.(2003)considerthedensityandtemperaturestructureswithin 3 RESULTS
theheliumcore,whileTodini&Ferrara(2001)donot.Schneideret
3.1 ExtinctioncurvesofvariousSNe
al.(2004),basedonthemodelofTodini&Ferrara(2001),findfor
PISNealargerangeofdustsize,depending onthespecies.Their In Figure 2a, we show the extinction curves of the four cases in
resultissimilartothemixedcaseinNozawaetal.(2003). Table2:(a)mixedSNeII;(b)unmixedSNeII;(c)mixedPISNe;
Weadopt therepresentativeprogenitor massofSNeIIas20 (d)unmixedPISNe.Thecontributionofeachspeciesisalsoshown.
M⊙ andthat of PISNeas170 M⊙. Thesizedistributionof each TheextinctioncurveisnormalisedtoAV.
grainspeciesisalmostindependent oftheprogenitor mass,ifthe Theextinctioncurvesofdust produced bythemixedSNeII
SNtypeisfixed(SNIIorPISN),exceptforunmixedSNeII(Sec- and PISNe are dominated by SiO (Figures 2a and c). Actually,
2
tion3.1).Therefore,weconcentrateonlythosetwomassesinthis SiO2isthemostabundantdustcomponentinamixed20M⊙ SN
paper. However, therelativemassratioamongspecies mildlyde- II.However,ina30M⊙ SNII,theproductionofMg2SiO4isen-
pendsontheprogenitormass,andwecommentonitlatershowing hancedby2.7timesrelativelytothatofSiO ,andinthiscase,the
2
the contribution of each species to the extinction curve (Section contributionofMg SiO totheextinctioncurvebecomes2.7times
2 4
3.1).Wealsoinvestigatethemixedandunmixedcases.Therefore, larger.Asaresult,theextinctioncurveisdominatedbythesteep
wetreatfourcases:(a)mixedSNeII;(b)unmixedSNeII;(c)mixed risingcurveofMg2SiO4forλ.0.14µm.Forthemixed170M⊙
PISNe;(d)unmixedPISNe,assummarisedinTable2.Allthefor- PISN,theextinctioncurveisalsodominatedbySiO .Nozawaet
2
mulationandtheresultscanbeseeninNozawaetal.(2003).Inthis al.(2003)alsoexaminealargerprogenitormass(200M⊙),where
paper,weassumethegrainstobeuniformandspherical. SiO is the dominant species in dust mass. Therefore, we expect
2
4 H. Hirashitaet al.
Table2.Modelsofdustproductioninsupernovae.
Model Progenitormass Mixing RV hσd(V)/mdi hσd(0.3µm)/mdi
(M⊙) (104cm2g−1)
a 20 mixed 2.4 0.98 2.8
b 20 unmixed 3.3 2.2 4.4
c 170 mixed 1.4 0.75 3.0
d 170 unmixed 5.0 2.1 4.1
Galactica — — 3.1 3.4 6.3
a QuantitiesderivedfromobservationalpropertiesoftheGalacticextinctionproperties(Spitzer1978;Cardellietal.1989;Mathis1990).We
shouldnotethatitisnotnecessarytoexplaintheGalacticpropertieswithourmodels,becausetheorigin,composition,andsizeofdustare
different.
Figure1.Sizedistributionfunctionofeachgrainspeciesin(a)themixedejectawiththeprogenitorof20M⊙,(b)theunmixedejectawiththeprogenitorof
20M⊙,(c)themixedejectawiththeprogenitorof170M⊙,and(d)theunmixedejectawiththeprogenitorof170M⊙.Thecorrespondencebetweenthe
speciesandlinesisshowninthefigures.
thattheextinctioncurveofmixedPISNealwaysshowacurvesim- SNe II, because a significant amount of large (a & 0.1 µm) Si
ilartotheoneinFigure2c. grainsefficientlyabsorblong-wavelengthphotons.Inamoremas-
siveSNIIwiththeprogenitor massof30M⊙,theproduction of
TheextinctioncurveofdustproducedbytheunmixedSNeII Mg SiO is enhanced by 2.2 times compared with Si, while the
2 4
(Figure2b)isdominatedbyMg2SiO4andFeSforλ.0.5µm.At amount of FeS isalmost thesame; consequently thecontribution
thelongerwavelength,(λ&0.5µm),Sidominatesthecurve.The ofMg SiO totheextinctioncurveisenhancedbyafactorof2.2
2 4
extinctioncurvesofunmixedSNeIIareflatterthanthoseofmixed
Extinctioncurves of younggalaxies 5
Figure2.ExtinctioncurvescalculatedforthedustproductionmodelslistedinTable2:(a)themixedejectawiththeprogenitorof20M⊙;(b)theunmixed
ejectawiththeprogenitorof20M⊙;(c)themixedejectawiththeprogenitorof170M⊙;and(d)theunmixedejectawiththeprogenitorof170M⊙.The
contributionofeachspeciesisalsoshown.EachcurveisnormalisedtotheV-band(λ=0.55µm)valueofthetotalextinctioncurve.Thecorrespondence
betweenthespeciesandlinesisshowninthefigures.
relative to the Si contribution, and the extinction curve becomes (SMC) (Pei 1992). It is not necessary that our theoretical curves
steeper.Ontheotherhand,inlessmassiveunmixedSNe,thepro- explaintheGalacticandSMCcurves,sinceinthosetwoenviron-
duction of amorphous carbon isenhanced, leadingtothecarbon- ments, dust grains are also produced by late-type stars withlong
dominatedflatextinctioncurve.Therefore,theextinctioncurveof lifetimes.
unmixedSNeIIissensitivetotheprogenitormass,andtheprogen- Wedonotenterdeeplytheinfraredregime.Theinfraredprop-
itormassdependenceisshowninSection3.2. ertiesofdustgrainsareaddressedinTakeuchietal.(2004,inprepa-
The extinctioncurve of unmixed PISNeisalso flat,because ration;seealsoTakeuchietal.2003).
ofSicontribution.Thecurvemildlyrisestowardultraviolet(UV)
because of contribution fromMg SiO . If theprogenitor mass is
2 4
3.2 ProgenitormassdependenceofunmixedSNeII
200 M⊙, the production of Si is enhanced by twice relative to
Mg2SiO4,andthecontributionofSibecomescomparabletothatof As mentioned in Section 3.1, the progenitor mass dependence is
Mg2SiO4eveninUV.Thismakestheextinctioncurveflatterthan significantinthecaseofunmixedSNeII.Therefore,weexamine
thatshowninFigure2d. variousprogenitormassesexaminedbyNozawaetal.(2003);i.e.
In general, the extinction curves of mixed cases are steeper theprogenitor massesof13,20,25,and30M⊙.InFigure3,we
thanthatofunmixedcases.Thisisbecausethedustopacityofthe presentthesizedistributionforeachspecies(Figures3a,b,c,and
mixedSNeIIisdominatedbysmall(a ∼ 0.01µm)SiO2 grains. dcorrespond totheprogenitor massesof13,20,25,and30M⊙,
Onthecontrary, largeSigrainsproducedinunmixedSNehavea respectively).Basedonthosesizedistributions,wecalculatetheex-
largecrosssectionuptothenearinfrared(NIR). tinctioncurvesbythemethoddescribedinSection2.2.Theextinc-
AllthefourextinctioncurvesarecomparedinFigure5a.We tioncurveaswellasthecontributionfromeachspeciesisshownin
alsoshow theextinction curves of theGalaxy (Cardelli,Clayton, Figure4.Weseethatthe13M⊙extinctioncurveisdominatedby
&Mathis1989withRV = 3.1)andtheSmallMagellanicCloud carbongrains,whosetypicalsizeislarge(∼ 0.1µm).Suchlarge
6 H. Hirashitaet al.
Figure3.Sizedistributionfunctionofeachgrainspeciesintheunmixedejectawiththeprogenitormassesof(a)13M⊙,(b)20M⊙,(c)25M⊙,and(d)30
M⊙.Thecorrespondencebetweenthespeciesandlinesisshowninthefigures.
carbongrainsproduceaflatextinctioncurveaspresentedinFigure afactorof∼ 2.Thentheastronomicalsilicatepredictsanextinc-
4a.Astheprogenitor massbecomes larger,thecontributionfrom tioncurveswithashallowerslopeinNIR.However,thedifference
Si becomes larger. Although the Si extinction curve is flat, other does not affect our results, since the contribution of Mg SiO is
2 4
speciessuchasMg SiO ,FeS,Fe,andSiO contributetotheris- important in UV. The Mg SiO data presented in Scott & Duley
2 4 2 2 4
ingcurveatshortwavelengthsinacomplexway.Asaresult,ifthe (1996) has a similar optical constants to Draine & Lee(1984) in
dustproductionoccursintheunmixedSNeII,theextinctioncurve UVandtoouradoptedvaluesinopticalandNIR.
tendstobesteeperastheprogenitormassbecomeslarger.Thefour
extinctioncurvesarecomparedinFigure5b.
3.3 Comparisonwithstandardsilicateandgraphite
The contribution of carbon grains is small in the four cases
Itisusefultocompareourpredictionwithastandard“astronomi- presentedinFigure2.Ifweusetheopticalconstantofgraphitein
calsilicate”inDraine&Lee(1984).TheiropticalconstantsinUV Draine&Lee(1984)andthesizedistributionofcarbongrainsin
arebasedonolivine(Mg,Fe) SiO (Huffman&Stapp1973),and Nozawaetal.(2003),weseeaweakbumparound2200A˚ andthe
2 4
thenearestspeciesinourmodelisMg SiO .Ouropticalconstant overall contribution of carbon isreduced by afactor of two. The
2 4
assumedforMg SiO isalmostthesameasthatof“astronomical changeofcarbonopticalpropertiesdoesnotaffectthetotalextinc-
2 4
silicate” in UV, but the astronomical silicates have a larger cross tion.However, Nozawaetal.(2003) show thatcarbonbecomesa
section in the optical and NIR than our Mg2SiO4. We calculate principalspeciesiftheprogenitormassisaround13M⊙.Inpartic-
the extinction curve of the astronomical silicate by using the op- ular,theproductionofMg2SiO4ismuchreducedina13M⊙ SN
ticalconstant ofDraine&Lee(1984)andthesizedistributionof II.Indeed,carbongrainsdominatetheextinctioncurvein13M⊙
Mg SiO calculatedbyNozawaetal.(2003).Theextinctioncurve unmixed SNe.Regardlessof whichoptical constant weadopt for
2 4
calculated by this method is the same as our extinction curve of carbongrains, weobtainaflatUVextinctioncurve fora13M⊙
Mg SiO inUV,butattheV band,thedifferencebecomesatmost unmixedSNII(seeSection4.1).
2 4
Extinctioncurves of younggalaxies 7
Figure4.ExtinctioncurvescalculatedforthedustproductionmodelsofunmixedSNIIejectawiththeprogenitormassesof(a)13M⊙,(b)20M⊙,(c)25
M⊙,and(d)30M⊙.EachextinctioncurveisnormalisedtothevalueattheV band(λ=0.55µm)ofthetotalextinctioncurve.Thecontributionofeach
speciesisalsoshown.Thecorrespondencebetweenthespeciesandlinesisshowninthefigures.
3.4 Usefulquantities ratio,andδj isthematerialdensityofgrainspeciesj.Wecalculate
The extinction curve is often characterised by the parameter RV (δ1j9f6r8o)manthdethraedmiuassspeorfuantoitmmsoavleecrualgeedliswteidthitnheRiosboiteop&erWataioldibnauSmN
definedas
ejecta.Thematerialdensityδj foreachspeciesislistedinTable1.
RV ≡ AV , (4) Torelatethedustcrosssectiontothedustmass,wedefinethe
E(B−V) crosssectionperunitdustmass,hσ (λ)/m i,as
d d
∞
wtlienhncegtrtiehonE(0c(.uB4r4v−eµiVmn))t.h≡ReoVApBtrioc−uaglA.hTlVyh,eqavunaadlnuBteifyicnadtlhciceualiatnetecsdltihnfeaotrBioe-nabcaohnfdththweeoarveexet--- hσ (λ)/m i≡ Xj Z0 πa2Qext,j(λ, a)fj(a)da. (6)
d d ∞
icaleIxttiisncatlisoonucsuerfvueltiossrehloawtenthineTexabtilnec2ti.ontothedustamount,be- Xj Z0 34πa3δjfj(a)da
causedustmassalsoconstrainthedustproductionmodelingalax-
Then, the following expression of extinction is derived by using
ies(e.g.Hirashita&Ferrara2002).Forthisaim,weshoulddeter-
equations(1),(2),(3),(5),and(6):
minethenormalisationconstantCinequation(1).TheconstantC
isdeterminedtorealisethetotaldustcolumndensityas A =1.086µm N Dhσ (λ)/m i. (7)
λ H H d d
∞
µmHNHD=C Z 43πa3δjfj(a)da, (5) bWaendprpoevriduenittheduvsatlumesasosf)hiσndT(aVb)le/m2.dBiy(thuesincrgosthsissevcatilouneitnhethdeuVst
Xj 0
amountcanbequantifiedifweknowN fromotherobservations
H
whereµisthegasmassperhydrogennucleus(assumedtobe1.4in (for example, observations of Lyα absorption line). Then, AV is
thispaper;Spitzer1978),m isthemassofahydrogenatom,N obtainedobservationallyforprimevalgalaxies(asysteminwhich
H H
isthecolumndensityofhydrogennuclei,Disthedust-to-gasmass dustispredominantlysuppliedbySNeIIorPISNe),weobtainthe
8 H. Hirashitaet al.
Figure5.Comparisonbetweentheextinctioncurvescalculatedbyourmodels.(a)Extinctioncurvesofvarioustypesofprogenitors.Thethicksolid,dotted,
dashed,anddot-dashedlinescorrespondtoModelsa,b,c,anddinTable2,respectively.(b)ExtinctioncurvesforvariousprogenitormassesofunmixedType
IISNe.Thethicksolid,dotted,dashed,anddot-dashedlinescorrespondtotheprogenitormassesof13,20,25,and30M⊙,respectively.Wealsoshowthe
extinctioncurvesoftheGalaxy(dot-dot-dot-dashedline)andtheSmallMagellanicCloud(SMC)(thindashedline)onlyforthereference.Itisnotnecessary
thatourmodelexplainstheGalacticorSMCcurve.
dust-to-gasratio.ThecolourexcessE(B−V)maybemoreeasily at λ < 0.17 µm. The plausible range derived by Maiolino et al.
obtained, and inthis case, RV listed inTable 2 could be used to (2004b)isshownbytheshadedareasinFigure6.InFigure6a,the
derivetheextinctionAV. fourtheoreticalcurvescalculatedbyourmodelareshown.Theex-
IntheGalacticISM,NH/AV =1.9×1021cm−2mag−1and tinctioncurvescalculatedwiththemixedSNmodelsaretoosteep
D = 6×10−3 (Spitzer1978). Byusingequation (7),weobtain toexplaintheobservationaldata.
hσd(V)/mdi=3.4×104cm2g−1fortheGalacticdust.Wehave ThemodelswiththeunmixedSNeagreesquitewellwiththe
obtainedsimilarvaluesinModelsbandd(bothassumeunmixed observational data. The extinction curve of unmixed SNe II de-
SNe)andsignificantlysmalleronesinModelsaandc(bothassume pendsontheprogenitormassasshowninSection3.2.InFigure6b,
mixedSNe). weshowtheUVextinctioncurvesofunmixedSNeIIwiththepro-
The dust cross section per mass is also calculated for a UV genitormassesof13,20,25,and30M⊙(solid,dotted,dashed,and
wavelength(0.3µm).InTable2,welisthσd(0.3µm)/mdi.The dot-dashed lines, respectively). The flat behaviour of 13 M⊙ ex-
difference between the models is relatively small. Therefore, the tinctioncurvecomesfromthecarboncontribution,whichproduces
UV dust extinction is a better tracer of the dust column density aslightbumparound1/λ ∼ 4µm−1.Therisetowardtheshorter
thantheopticalextinction. wavelength is mainly caused by Mg SiO . Since the production
2 4
ofMg SiO isenhancedinthemassiveprogenitors,theextinction
2 4
curvebecomessteeperformoremassiveprogenitors.Theunmixed
SNIImodelsareroughlyconsistentwiththecurrentobservational
4 OBSERVATIONALDISCUSSION
dataathighz.Itisinterestingtonotethattheobservationalranges
4.1 Comparisonwithhigh-zdata liebetweentheflatcurvepredictedforlow-mass(13M⊙ and20
M⊙) progenitors and thesteepcurve predicted by high-mass (25
At present, there are few observational works of the extinction
M⊙ and30M⊙)progenitors. Therefore,themixtureofunmixed
curves at z > 5, where the cosmic age is shorter than 1 Gyr. SNeIIwithvariousprogenitormassmayexplaintheobservational
Withthisshorttimescale,thedustispredominantlyformedbySNe
extinctioncurve.
II and PISNe, since their progenitors have short lifetimes while
Therefore,wecalculateextinctioncurvesweightedbyIMF:
evolvedlowmassstarsrequirelongertimescalestoevolveandpro-
ducedust.Maiolinoetal.(2004b)usetheextinctioncurveofSDSS
mu
J1048+4637totestthehypothesisthatdustispredominantlysup- A (φ)≡ A (m)φ(m)dm, (8)
λ Z λ
pliedbySNeII.Theyexplaintheextinctioncurvebythedustpro- ml
duction model of Todini & Ferrara (2001). They also investigate
various initial stellar metallicities from 0 to solar after averaging wheremistheprogenitormass,m andm are,respectively,the
l u
the grain properties for different SNe II over the Salpeter stellar lowerandupper masslimitsofstarswhichcauseSNeII,A (m)
λ
initialmassfunction (IMF),and findthat their theoretical extinc- is the extinction calculated for the progenitor mass m (correctly
tioncurvesagreewiththeobservationaldataofSDSSJ1048+4637 weightedforproduced dustmass;i.e.,A (m)islargeifthepro-
λ
inthewholemetallicityrange. genitorproducesalargeamountofdust),andφ(m)istheIMF(the
We also use the restframe UV extinction curve of SDSS numberofstarswiththemassrangeof[m, m+dm]isproportional
J1048+4637showninFigure2ofMaiolinoetal.(2004b).Theex- toφ(m)dm).Thenormalisationofφ(m)isnotimportantinthis
tinctioncurveisflatatλ>0.17µm,anditincreaseswithasmaller paper,becausetheextinctioncurveisalwaysshownafterbeingnor-
ratethantheSMCextinctioncurvetowardtheshorterwavelength malisedbyAV andthenormalisingconstantofφ(m)iscancelled
Extinctioncurves of younggalaxies 9
Figure 6. Ultraviolet extinction curves normalised to the extinction at 0.3 µm. The range observationally derived by Maiolino et al. (2004b) for SDSS
J1048+4637isshownbytheshadedareaineachfigure.(a)Modelpredictionsforvarioussupernovamodels(Modelsa–dinTable2).(b)Resultsforvarious
progenitormassesunmixedSNeII.Thesolid,dotted,dashed,anddot-dashedlinescorrespondtotheprogenitormassesof13,20,25,and30M⊙,respectively.
(c)AveragedextinctioncurvesofunmixedSNeII.Theweightofeachprogenitormassisdeterminedbyinitialmassfunctions,whichareparameterisedby
thepower-lawindex(x)andthelowerandupperstellarmasses(mlandmu,respectively).Thethicksolid,dotted,anddashedlinesrepresenttheresultsfor
x= 1.35,0.35,and2.35,respectively,with(ml,mu)= (8M⊙,40M⊙)(ModelsA,B,andCinTable3,respectively).Thethinsolidanddottedlines
showtheresultsfor(ml,mu)=(13M⊙,40M⊙),and(8M⊙,30M⊙),respectively,withx=1.35(ModelsDandEinTable3,respectively).
out.Weassumethefollowingpower-lawformoftheIMF: (8 M⊙, 30 M⊙), respectively. All the examined IMFs are sum-
marisedinTable2,andarelabeledasModelsA–E.
φ(m)=Km−(x+1), (9) As expected from Figure 6b, the contribution from massive
SNe II tends to increase the slope of the extinction curve. Then,
ModelsBandDpredictsteeperextinctioncurvesthanthedataof
whereK isthenormalising constant. TheSalpeter IMFisrepro-
Maiolinoetal.(2004b).Therefore,thecontributionfromtheSNeII
duced by x = 1.35. We examine x = 1.35, 0.35, and 2.35. An
whoseprogenitormassisaround13M⊙isnecessarytoobtainthe
appropriate stellar mass range for SNe II (core collapse SNe) is
flatextinction curve consistent withtheobservational data. How-
selected as ml = 8 M⊙ and mu = 40 M⊙ (Heger & Woosley ever,inordertoreproducetherisetowardtheshorterwavelength
2002).WeusethecalculatedextinctioncurvesofunmixedSNeII
λ.0.15µm,thecontributionfrommassiveSNeIIisnecessary.In
withm = 13, 20, 25, 30 M⊙, and interpolate or extrapolate the particular,ModelCpredictsanextinctioncurveslightlyinconsis-
valuestoobtaintheextinctioncurvesofarbitraryprogenitormass. tentaround1/λ∼8µm−1.WeshouldemphasizethattheSalpeter
The slopes x = 0.35 (2.35) represents the case where massive
IMF(ModelA)reproducestheobserveddataverywell.
(lessmassive)starsareselectivelyproduced.Theextinctioncurves
weighted for the IMFs are shown in Figure 6c, where the thick
solid,dotted,anddashedlinesrepresenttheresultswithx=1.35,
4.2 Observationalstrategy
0.35,and2.35,respectively.Wealsoinvestigatetheeffectofvary-
ingm andm withx=1.35:thethinsolidanddottedlinesinFig- Alargesampleofhigh-zquasarsandgalaxieswillbeobtainedby
l u
ure6cshow theresultswith(ml, mu) = (13M⊙, 40M⊙)and futureobservations.Sincethecosmicageatz =5isabout1Gyr,
10 H. Hirashitaet al.
Wehavealsoderivedthedustcrosssectionperunitdustmass.
Table3.Initialmassfunctions.
This quantity is useful to estimate the dust column density from
Model x ml mu extinction.TheUVextinctiontracethedustcolumndensitybetter
(M⊙) (M⊙) thantheopticalextinction.Theextinctionalsoaffectstheobserv-
abilityofothermolecularoratomiclines.Theresultofthispaper
A 1.35 8 40
canbeusedtoestimatetheextinctioneffectinhigh-zgalaxies.
B 0.35 8 40
Finally, our results are compared with a high-z extinction
C 2.35 8 40
curve observationally derived for SDSS J1048+4637 at z = 6.2
D 1.35 13 40
E 1.35 8 30 byMaiolinoetal.(2004b). Thecomparison favoursSNeIIwith-
outinternalmixingassourcesofdustgrains.Thecombinationof
variousprogenitormassrangingfrom∼ 10M⊙ to∼ 30M⊙ ex-
thedustsuppliedbylate-typestarsdoesnotdominatethetotaldust plainswelltheobservedextinctioncurve.Ourtheoreticalextinction
amountatz > 5.Therefore,iffutureobservationscollectalarge curvescouldbefurtherutilisedwhenasampleofhigh-zextinction
spectroscopic sampleofquasarsatz > 5,wecandirectlyinves- curvesistakenbyfutureobservations.
tigatetheextinctioncurveofdust,whosesourceisprobably SNe
IIand/or PISNe.Althoughwehavecalculatedthedust formation
basedonthePopIIIprogenitors,wecanapplyourmodeltometal-
enriched systems aslong asthedust ispredominantly formed by
ACKNOWLEDGMENTS
SNeIIand/orPISNe,becausethedustcompositionandsizedistri-
butionismuch lesssensitive totheprogenitor metallicitythanto We thank R. Maiolino, the referee, for useful comments, and R.
theprogenitormass. Maiolino, S. Bianchi, R. Schneider, and A. Ferrara for kindly
The shape of the extinction curve of high-z galaxies can be providing us with their data on the extinction curve of SDSS
comparedwiththetheoreticalcurvesinthispapertoconstrainthe J1048+4637.HH,TTI,andTTTaresupportedbytheJapanSociety
sizeandcompositionofgrains.Themeasurementofextinctionen- forthePromotionofScience.TKissupportedbyaGrant–in–Aid
ablesustomeasurethedust-to-gasratioofhigh-z galaxies,ifwe for Scientific Research from JSPS (16340051). We fully utilized
useequation (7)and thecrosssection per dust masslistedinTa- theNASA’sAstrophysicsDataSystemAbstractService(ADS).
ble2.Therefore,thedustproductionhistoryinhigh-zuniversecan
alsobeinvestigatedbasedonthispaper.
Some theoretical works (Bromm & Larson 2004 and refer-
ences therein) suggest that first stars born from primordial gas
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