Extinction curves flattened by reverse shocks in supernovae

0.36 MB·English

by  Hiroyuki Hirashita

Mon.Not.R.Astron.Soc.000,1(2007) Printed2February2008 (MNLATEXstylefilev2.2)
Extinction curves flattened by reverse shocks in supernovae
1⋆ 2 3 2
Hiroyuki Hirashita , Takaya Nozawa , Tsutomu T. Takeuchi , and Takashi Kozasa
8 1CentreforComputationalSciences,UniversityofTsukuba,Tsukuba305-8577,Japan
0 2DepartmentofCosmosciences,GraduateSchoolofScience,HokkaidoUniversity,Sapporo060-0810,Japan
0 3InstituteforAdvancedResearch,NagoyaUniversity,Nagoya464-8601,Japan
2

n
a 2007December7
J

7
ABSTRACT
1
WeinvestigatetheextinctioncurvesofyounggalaxiesinwhichdustissuppliedfromTypeII
] supernovae(SNe II) and/orpairinstability supernovae(PISNe). Since athigh redshift(z >
h 5), low-mass stars cannot be dominant sources for dust grains, SNe II and PISNe, whose
p
progenitorsaremassivestarswithshortlifetimes,shouldgovernthedustproduction.Here,we
-
o theoreticallyinvestigatetheextinctioncurvesofdustproducedbySNeIIandPISNe,taking
r intoaccountreverseshockdestructioninducedbycollisionwithambientinterstellarmedium.
st WefindthattheextinctioncurveissensitivetotheambientgasdensityaroundaSN,sincethe
a efficiencyofreverseshockdestructionstronglydependsonit.Thedestructionisparticularly
[ efficientforsmall-sizedgrains,leadingtoaflatextinctioncurveintheopticalandultraviolet

1 wavelengths.Sucha largeambientdensityas nH & 1 cm−3 producestooflat anextinction
v curvetobeconsistentwiththeobservedextinctioncurveforSDSSJ1048+4637atz = 6.2.
9 Althoughthe extinctioncurveis highlysensitive to the ambientdensity,the hypothesisthat
4 thedustispredominantlyformedbySNeatz ∼6isstillallowedbythecurrentobservational
6 constraints.Forfurtherquantification,theambientdensityshouldbeobtainedbysomeother
2 methods. Finally we also discuss the importance of our results for observations of high-z
1. galaxies,stressingapossibilityofflatextinctioncurves.
0
Key words: dust, extinction — galaxies: evolution — galaxies: high-redshift— galaxies:
8
ISM—supernovae:general—quasars:individual:SDSSJ104845.05+463718.3
0
:
v
i
X
r 1 INTRODUCTION To quantify the above effects of dust in the early stages of
a
galaxy evolution, it is crucial to know how much dust and what
Dustgrainsplayanimportantroleintheformationandevolution
species of grains form in supernovae (SNe). It has been sug-
ofgalaxies.Dustgrainscontroltheenergybalanceintheinterstel-
gested by some observations of nearby SNe that dust is indeed
lar medium (ISM) by absorbing stellar light and reemitting it in
producedinSNe,althoughthequantityofformeddustisstillde-
farinfrared(FIR).Also,thesurfaceofdustgrainsisasiteforan
bated (e.g. Moseleyetal. 1989; Dunneetal. 2003; Morganetal.
efficientformationofH2molecules(e.g.Cazaux&Tielens2004), 2003;Hinesetal.2004;Sugermanetal.2006;Meikleetal.2007;
whichactasaneffectivecoolantinmetal-poorISM.Thoseeffects
Rhoetal.2007).BytreatingthenucleationandaccretioninSNe,
ofdustturnonevenat∼ 1%ofthesolarmetallicityaccordingto
thedust compositionandsizedistributionaretheoreticallycalcu-
thecalculation byHirashita&Ferrara(2002),who arguethat the
lated(Kozasa,Hasegawa,&Nomoto1989,1991).Recently,inor-
starformationrateisenhancedbecauseofthefirstdustenrichment
dertoexaminetheeffectsofdustinPopulationIII(PopIII)objects,
inthehistoryofgalaxyevolution. Thefirstsourcesofdustinthe
the formation of dust in SNe II and PISNe is extensively exam-
Universe are Type II (core-collapse) supernovae (SNe II) or pair
ined (Todini&Ferrara 2001; Nozawaetal. 2003, hereafter N03,
instabilitysupernovae(PISNe),sincethelifetimesoftheirprogen-
Schneider,Ferrara,&Salvaterra2004).Themotivationforconsid-
itors are short (∼ 106 yr). In the local Universe, dust grains are
ering PISNe comes from some evidence indicating that the stars
also produced by evolved low mass stars (Gehrz 1989), but this
formedfrommetal-freegas,PopulationIII(PopIII)stars,arevery
productionmechanismrequiresmuchlonger(&1Gyr)timescales.
massivewithacharacteristicmassofafewhundredsolarmasses
The first dust supplied by SNe II or PISNe may trigger the for-
(e.g.Nakamura&Umemura2001;Bromm&Larson2004).Such
mation of low-mass starsvia dust cooling (Schneideretal. 2003;
massivestarsareconsideredtobeginpaircreationofelectronand
Omukaietal.2005).
positron after the helium burning phase, and finally an explosive
nuclearreactiondisruptsthewholestars(Fryer,Woosley,&Heger
2001;Heger&Woosley2002).ThisexplosioniscalledPISN.
⋆ E-mail:[email protected]
2 H. Hirashitaet al.
Recently,thehypothesisthatthedustformationisdominated
Table1.Summaryofgrainspecies.
bySNeIIand/orPISNeathighredshift(z)isobservationallyex-
aminedforsomeobjects.Weexpectthatatz > 5,whenthecos- Species conditiona Refb density(δj)
mic age is less than 1 Gyr, the main sources of dust grains are (gcm−3)
SNeIIandPISNe(e.g.Dwek,Galliano,&Jones2007).Extinction
curves can be used to investigatethe dust properties (e.g. Mathis C u 1 2.28
1990).Byusingasampleofbroadabsorptionline(BAL)quasars, Si u 2 2.34
Maiolinoetal. (2004a) show that the extinction properties of the SiO2 m/u 3 2.66
Fe u 4 7.95
low-z (z < 4)sampleisdifferent fromthoseof thehigh-z (z >
FeS u 4 4.87
4.9)sample.Thisresultissuggestiveofachangeinthedustpro-
Fe3O4 m 5 5.25
ductionmechanisminthecourseofgalaxyevolution.Thehighest-
Al2O3 m/u 6 4.01
zBALquasarintheirsample,SDSSJ104845.05+463718.3(here- MgO u 7 3.59
after SDSS J1048+4637) at z = 6.2 shows an extinction curve MgSiO3 m/u 8 3.20
flat at wavelength λ & 1700 A˚ and rising at λ . 1700 A˚. Mg2SiO4 m/u 4 3.23
Maiolinoetal. (2004b) show that the extinction curve of SDSS
J1048+4637 isinexcellentagreementwiththeSNIIdustmodels
byTodini&Ferrara(2001).Bianchi&Schneider(2007)consider a The classifications “m”, “u”, and “m/u” mean that the species is
dust destruction byreverse shock in SNe,suggesting that 2–20% formedinmixed,unmixed,andbothsupernovae,respectively.
oftheinitialdustmasssurvives,andthattheextinctioncurveafter b References for optical constants: (1) Edo (1983); (2) Piller
the destruction is still consistent with that of SDSS J1048+4637. (1985); (3) Philipp (1985); (4) Semenovetal. (2003); (5) A.
Morerecently,Strattaetal.(2007)showthatthedustextinctionin Triaud and H. Mutschke (2006 private communication and see
thehostgalaxyofGRB050904atz=6.3canbeexplainedbythe http://www.astro.uni-jena.de/Laboratory/OCDB/oxsul.html); (6)
extinctioncurveofSDSSJ1048+4637, furthersupportingthatthe Toon,Pollack,&Khare (1976); (7) Roessler&Huffman (1991); (8)
SNeIIarethemainsourcesof dustatz > 6.Also,Willottetal. Semenovetal.(2003)(TheopticalconstantsofMg2SiO4areusedfor
λ60.3µm).
(2007) find asimilar extinction property for CFHQS J1509-1749
(z=6.12)tothatofSDSSJ1048+4637.
Thereareother seriesof theoreticalpapersontheextinction tion by N07. By using the results by N07, the extinction curves
curvesofhigh-zobjects.Hirashitaetal.(2005,hereafterH05)cal- arecalculated by thesame method as inH05. The outlineof our
culate the extinction curve based on the dust production calcula- calculationisreviewedasfollows.
tion by N03. They also reproduce the extinction curve of SDSS
J1048+4637 byusingthethedust productioninSNeII,although
2.1 DustproductionanddestructioninSNeIIandPISNe
thedustcompositionandsizedistributionaredifferentfromthose
of Todini&Ferrara (2001). Recently, Nozawaetal. (2007, here- N03 calculate the dust composition and size distribution in the
afterN07)havetreatedthedustdestructionbythereverseshockas ejectaofPopIIISNeIIandPISNebasedonthesupernovamodel
done by Bianchi&Schneider (2007), but considering the motion of Umeda&Nomoto (2002), carefully treating the radial density
ofdustrelativetogascausedbythedragforceandthedestruction profile and the temperature evolution. As mentioned in H05, the
ofdustintheradiativephaseaswellasinthenon-radiativephase resultinggraincomposition andsizedistributionarenot sensitive
ofsupernova remnants. Then,theyshow thatthesizedistribution to the metallicity of progenitor (N03). Thus, the assumption of
of grainssupplied inthe ISMisstrongly modifiedby thereverse zero-metallicity is not essential in this paper, and our results can
shock. Grains smaller than ∼ 0.02 µm are efficiently destroyed beapplicabletometal-enrichedsystems.Sinceitisstilluncertain
if theambient hydrogen number density islarger than0.1 cm−3. howefficientlythemixingofatomswithinSNeoccurs,N03treat
Thus,itisimportanttoreexaminetheconsistencybetweentheob- twoextremecasesforthemixingofelements:oneistheunmixed
servedextinctioncurveandthereverseshockdestruction. caseinwhichtheoriginalonion-likestructureofelementsispre-
Inthispaper,wecalculatetheextinctioncurvesbasedonthe served,and theother isthemixedcaseinwhichtheelementsare
dustpropertiescalculatedbyN07,whohavefocusedontheeffect uniformlymixedwithintheheliumcore.Theyshowthattheformed
ofreverseshockdestructioninSNe.Then,wecomparetheresults dustspeciesdependlargelyonthemixingofseedelementswithin
withobservedextinctioncurvesathighz.Thispaperisorganized SNe,becausethedominantreactionschangedependingontheratio
asfollows.First,wedescribeourtheoreticaltreatmenttocalculate ofavailableelements.Theformedgrainspeciesinthecalculation
theextinctioncurvesofSNIIandPISNdustinSection2.Weshow ofN03arelistedinTable1.
andexamineourresultsinSection3.Wediscussourresultsfrom In the unmixed ejecta, a variety of grain species (Si, Fe,
theobservationalviewpointinSection4,andfinallygivethecon- Mg2SiO4, MgSiO3, MgO, Al2O3, SiO2, FeS, and C) condense,
clusionofthispaperinSection5. while in the mixed ejecta, only oxide grains (SiO2, MgSiO3,
Mg2SiO4,Al2O3,andFe3O4)form.Thespeciesaresummarized
inTable1.BasedontheresultsinN03,N07treatthedustdestruc-
tionbythereverseshockinthesupernovaremnant.Theyfindthat
2 MODEL
small-sizedgrainssufferdustdestructionbythereverseshockand
Wederivethetheoreticalextinctioncurvesofdustgrainsproduced thatthefinalgrainsizedistributionisbiasedtolargergrainsthan
in SNe II and PISNe and subsequently destroyed by the reverse theoriginaldistributioncalculatedbyN03.Weadopttheirresults
shock.Thosegrainsareconsideredtobesuppliedintheinterstellar as the properties of grains supplied to the interstellar space. Fol-
spaces.ThegraincompositionandsizedistributioninSNebefore lowingH05,weadopttherepresentativeprogenitormassofSNeII
thedestructioniscalculatedbyN03,whoseresultsareadoptedas as20M⊙ andthatofPISNeas170M⊙.Wealsoinvestigatethe
theinitialconditionsforthecalculationsofreverseshockdestruc- mixedandunmixedcases.Therefore,wetreatfourcases:
Flattenedextinctioncurves 3
(a)mixedSNeII; dominatedbySiandC.However,asshowninH05,theextinction
(b)unmixedSNeII; curvewithoutreverseshockdestructionisdominatedbyMg2SiO4
(c)mixedPISNe;and andFeSforλ . 0.5µmandbySiforλ & 0.5µm.SinceSiand
(d)unmixedPISNe. Cgrainsarelargerthantheotherspecies,theysurvivethereverse
All the formulation and the results can be seen in N03 and N07. shock more than the others. For the same reason, the extinction
Thegrainsareassumedtobehomogeneousandspherical. curveofunmixedPISNeisdominatedbySi.Alsofortheunmixed
SNeIIandPISNe,theextinctioncurvesofgrainsafterthereverse
shockdestructionareflatter,sincesmall-sizedgrainsareselectively
2.2 Opticalconstantsandextinctioncurves destroyedandthemeansizeofthegrainsbecomeslarge.
In order to calculate extinction curves, the optical constants of
grainsarenecessary.WeadoptthereferenceslistedinTable1for
3.2 Dependenceontheambientmediumdensity
the optical constants. Here, we only explain the difference from
H05. The optical constants are updated for Fe3O4. For MgSiO3, AsshownbyN07,theefficiencyofthereverseshockdestructionis
we adopt the optical constants of Mg2SiO4 at λ 6 0.3 µm, sensitivetothedensityoftheambientmedium.Hereweinvestigate
wherethecurrentlyavailableexperimentaldataarerelativelypoor thevariationoftheextinctioncurveforvariousambientdensities.
(Dorschneretal.1995).ForSiandSiO2,weadopttheopticalcon- N07haveexaminedthreecasesfortheambienthydrogennumber
stants for amorphous instead of crystal since the grains rapidly density: nH = 0.1, 1, and 10 cm−3. N07 show that the grains
growinSNe.Subsequentsputteringduetothereverseshockmay are almost completely destroyed for nH = 10 cm−3. Thus, we
also tend to destroy crystal structures and to form more compli- calculate the cases for nH = 0.1 and 1 cm−3. For comparison,
catedamorphoussolids.Theinfraredbroadfeatureatλ ≃ 21µm wealsoshowtheresultswithoutthereverseshockdestruction(this
isalsobetter explained by amorphous SiO2 thanby crystal SiO2 case is called non-destruction case). For the details for the non-
(Rhoetal.2007).Wediscusstheuncertaintyintheassumedopti- destructioncase,seeN03andH05.TheresultsareshowninFigure
calconstantsinAppendixA. 2. As expected, the extinction curve becomes flatter for a larger
Byusingthoseopticalconstants,wecalculatetheabsorption ambient density because the destruction efficiency of small-sized
andscatteringcrosssectionsofhomogeneoussphericalgrainswith grainsislarger.InSection4,ourresultsarecomparedwithhigh-z
varioussizesbasedontheMietheory(Bohren&Huffman1983). dataofextinctioncurve.
Then,theopacityofgrainj(jdenotesagrainspecies)asafunction Bianchi&Schneider (2007) also state that the extinction
ofwavelength,τλ,j,iscalculatedbyweightingthecrosssections curvebecomesflatter,althoughtheystartfromadifferentdustfor-
accordingtothesizedistribution.Theextinctioncurveispresented mation model based on Todini&Ferrara (2001). The differences
intheformofAλ/Aλ0 (Aλistheextinctioninunitsofmagnitude between Bianchi&Schneider (2007) and the present work are
atwavelengthλ,andλ0isareferencewavelength).Theextinction partlyduetothedifferencesinopticalconstants:amorphouscarbon
inunitsofmagnitudeisproportionaltotheopticaldepthasAλ,j = isresponsibleformostoftheextinctionintheirwork.Furthermore,
1.086τλ,j, where Aλ,j is the extinction of species j in units of theirresultsshowmoresurvivalofsmallgrainsthanthoseofN07.
magnitudeasafunctionofλ.ThetotalextinctionAλiscalculated AsmentionedinN07,thedifferencecomesfromthetreatmentof
bysummingAλ,j foralltheconcerningspecies: grainmotion:InN07,thetrapofgrainsinahotanddensezonebe-
tweenforwardandreverseshocksisproperlytreated,andthiseffect
Aλ =XAλ,j. (1) enhances the destruction of small-sized grains. Thus, our results
j show flatter extinction curves than those of Bianchi&Schneider
Formoredetails,seeH05.Sincewenormalizetheextinctionata (2007)especiallywhentheambientgasdensityislarge.
certainwavelengthλ0,onlyrelativevaluesofτλ,j areimportant.
4 OBSERVATIONALDISCUSSION
3 RESULTS
4.1 Comparisonwithhigh-zdata
3.1 Extinctioncurvesafterthereverseshockdestruction
H05showthatthedustproductionmodeloftheunmixedSNeIIin
AsshowninN07,thefinalsizedistributionofgrainsafterthere- N03isconsistentwiththeextinctioncurveofSDSSJ1048+4637.
verse shock destruction is sensitive to the density of the ambient However,itiscrucialtocompareournewresultsincludingthere-
ISM.HerewestartfromtheresultsfornH =1cm−3,wherenHis verseshockdestructionwithSDSSJ1048+4637. Inparticular,we
thehydrogennumber densityintheambientmedium,toexamine may obtain constraints on the ambient gas density as well as the
theeffectofgraindestructionontheextinctioncurve.InFigure1, progenitors.WecompareourresultswiththerestframeUVextinc-
weshowtheresultingextinctioncurvesofthefourcasesinSection tion curve of SDSS J1048+4637. The plausible range derived by
2.1.Thecontributionofeachspeciesisalsoshown.Wenormalize Maiolinoetal.(2004b)isshownbytheshadedareasinFigure3.
theextinctiontoAV (i.e.,λ0 =0.55µm). IneachpanelofFigure3,weshowthetheoreticalextinction
Theextinctioncurvesof dustproduced bythemixedSNeII curves calculated for various ambient hydrogen number densities
andPISNearedominatedbySiO2(Figures1aandc;inthePISN (sameasFigure2butnormalizedtotheextinctionatλ=0.3µm,
case,onlythecontributionfromSiO2appearsandthetotalextinc- i.e.,λ0 =0.3µm).Wealsoshowtheresultsofthenon-destruction
tion curve is identical to the extinction curve of SiO2). The ex- case. Because of the variation caused by the destruction, various
tinction curve is flatter than that without destruction because the typesofprogenitorsmaybeallowed.Forexample,themixedSNe
reverseshockefficientlydestroyssmallgrainsandthemeangrain II are consistent with the observed extinction curve if nH ∼ 1
sizebecomeslarger. cm−3. In all cases, the ambient number density nH & 1 cm−3
The extinction curve for the unmixed SNe II (Figure 1b) is producestooflatextinctioncurvestobeconsistentwiththedata.
4 H. Hirashitaet al.
Figure1.Extinctioncurvesofgrainsproducedin(a)themixedejectawiththeprogenitorof20M⊙,(b)theunmixedejectawiththeprogenitorof20M⊙,
(c)themixedejectawiththeprogenitorof170M⊙,and(d)theunmixedejectawiththeprogenitorof170M⊙.Theambienthydrogennumberdensityis
assumedtobenH =1cm−3.Theextinctionisnormalizedtothevalueatλ=0.55µm.Thecorrespondencebetweenthespeciesandthelinesisshownin
eachpanel.NotethatsomeofthespeciesarealmostcompletelydestroyedanddonotappearonthefiguresandthatinPanel(c),onlySiO2contributestothe
totalextinctioncurve.
4.2 AmbientdensityaroundSNe occur and the final gas density is much higher. However, if we
consider 3-dimensional complex structureof interstellar medium,
In the previous subsection, we have shown that the extinction
the density around a massive star is hard to predict theoretically.
curvesaresensitivetotheambientdensityofSNe.Thus,itisimpor-
Thus,atthismoment,adirectconstraintonthegasdensityinSDSS
tanttoconstrainthedensityfirst.Unfortunately,thereisnodirect
J1048+4637byusingforexampleexcitationstatesofmolecularor
observationalconstraintonthegasdensityinSDSSJ1048+4637.
atomiclinesisdesired.
It israther interesting to point out that the extinction curves Insummary,thecurrentobservationalextinctioncurveatz ∼
fornH .0.1cm−3oftheunmixedSNeIIisquiteconsistentwith 6canbeexplainedbythehypothesisthatdustisproducedbySNe
theextinctioncurvesofSDSSJ1048+4637.ThemixedSNeIIalso
IIand/orPISNeanddestroyedsubsequentlybyreverseshocks.In
reproducetheobservationalextinctioncurvequitewelliftheambi-
addition, theresultsinthispaper newly propose that theambient
enthydrogennumberdensityis∼ 1cm−3.Theextinctioncurves densityshouldbelessthan∼1cm−3,sincethereverseshockde-
of PISNe are too flat for nH & 1 cm−3. Considering the uncer- structionflattenstheextinctioncurvetoomuchifnH &1cm−3.
taintyintheobservational data,however, theextinctioncurvesof
PISNearenotrejectedfornH ∼0.1–1cm−3.
Theoretically, it ispossible toexamine thedensity evolution
4.3 Flatextinctioncurvesathighz?
aroundtheprogenitorsofSNe.Kitayamaetal.(2004)showthatin
smallobjectswhosetypicalhalomassis∼106M⊙,theentiregas AsshowninSection3,aflatextinctioncurveisnaturallyproduced
cloudiscompletelysweptbytheionizationfront,andthedynam- byreverseshockdestructioninSNe.Atz >5,whereitisprobable
ical expansion of the ionized region reduces the ambient density thatSNeIIorPISNepredominantlysupplydustgrains,itisworth
downtonH . 1cm−3.Onthecontrary,inmoremassiveobjects, investigatingpossibilitythatextinctioncurvesareflat.
theevacuationofthegasaroundamassivestardoesnotefficiently Indeed,therearesomepiecesofsupportingevidenceforflat
Flattenedextinctioncurves 5
Figure2.Extinctioncurvesofgrainsforvariousambienthydrogennumberdensities(nH = 1and0.1cm−3forthesolidanddashedlines,respectively).
Thecasewithoutthereverseshockdestruction(non-destructioncase)isalsoshownineachpanel(thedashedline).Theprogenitormodelineachpanelisthe
sameasthatinFigure1.
extinction curves at z > 5. Among the samplein Maiolinoetal. ever,therearesomeobservationalresultsthatshownosignificant
(2004a), two BAL quasars, SDSS J1044−0125 at z = 5.8 and reddening of DLAs (Murphy&Liske 2004; Ellison,Hall,&Lira
SDSS J0756+4104 at z = 5.1, show no reddening but are de- 2005). The flat extinction curve proposed above has importance
tectedatsub-mm(Priddeyetal.2003).Thesub-mmobservations thatthelackofreddeningdoesnotnecessarilymeantheabsenceof
yield dust masses inthe range 108−9 M⊙ for those two quasars. dust.OtherthanDLAs,someobjectswhoseextinctioncurvesare
The absence of reddening and the presence of sub-mm emission derivedbygamma-raybursts(Chen,Li,&Wei2006)orbygravi-
(dust emission) may be contradictory, but they are consistent if tationallensing(e.g.Falcoetal.1999;Mun˜ozetal.2004)seemto
weassume aflat extinction curve. An extremely small reddening haveaflatextinctioncurveinUV.
of a BAL quasar SDSS 1605−0112 at z = 4.9 (Maiolinoetal.
2004a)mayalsobeattributedtoaflatextinctioncurve.Inthefu-
4.4 Possibilityofsubsequentsteepening
ture, extinction curves of high-z sub-mm samples (Bertoldietal.
2003; Priddeyetal.2003; Robsonetal.2004; Beelenetal.2006) Dust grains supplied into interstellar spaces suffer various pro-
incomparisonwiththeoreticalmodelingofsub-mmemission(e.g. cesses that modify their size distribution. One of such processes
Takeuchietal. 2003, 2005) enable us to further investigate the isthe destruction by forward shocks of supernova remnants. The
propertiesandoriginsofdustgrainsintheearlyUniverse. dustdestructionbyforwardshockshasalreadybeenexaminedby
Alsoatlowerz (. 5),itmaybeworthtoconsider possibil- Nozawa,Kozasa,&Habe (2006).Herewehaveexamined theef-
ity of flat extinction curves. Direct indications of dust at z . 5 fect of forward shock destruction and have confirmed that one
come, for example, from the reddening of background quasars passage of a supernova forward shock has negligible influence
(Falletal.1989;Zuoetal.1997).Thedepletionofheavyelements on the extinction curve. This is because after an efficient sput-
inquasar absorption linesystems, especiallydamped Lyαclouds tering in supernova remnants the opacity is already dominated
(DLAs), also supports the presence of dust in distant systems by large grains which are hard to destroy. However, shattering
(e.g. Pettinietal. 1994; Vladilo 2002; Ledouxetal. 2003). How- mayincreasethenumberofsmall-sizegrains(Borkowski&Dwek
6 H. Hirashitaet al.
Figure3.Extinctioncurvesnormalizedatλ=0.3µm.ThesametheoreticalcurvesasthoseinFigure2areplotted.Theshadedareaineachpanelshowthe
rangeobservationallyderivedbyMaiolinoetal.(2004b)forSDSSJ1048+4637atz=6.2.
1995; Jones,Tielens,&Hollenbach 1996), steepening the extinc- extinctioncurveishighlysensitivetotheambientdensity,thehy-
tioncurve.Quantitativestudyoftheeffectofshatteringontheex- pothesis that the dust ispredominantly formed by SNeat z ∼ 6
tinctioncurveisleftforfuturework. isstillallowedifnH issmallerthan1cm−3.Forfurtherquantifi-
cation, the ambient density should be constrained by some other
methods.
Itisworthnotingthataflatextinctioncurveproducedbyef-
5 CONCLUSION
fectivereverseshockdestructionmayexplaintheabsence ofred-
Wehave theoreticallyinvestigatedthe extinctioncurves of grains dening of systems in which dust is known to be present by far-
produced in SNe II and PISNe. Since at high z(> 5), low-mass infrared/sub-mmemissionorbydepletionofheavyelements.
starscannotbedominantsourcesfordustgrains,SNeIIandPISNe,
whoseprogenitorsaremassivestarswithshortlifetimes,cangov-
ernthedustproduction.Whileourpreviousworks(N03andH05)
didnotconsider thereverseshockdestructioninducedbyacolli-
ACKNOWLEDGMENTS
sionwithambient interstellarmedium, weadopt thecomposition
and size distributionof grains of N07, who take intoaccount the WethankR.Maiolinoandhiscollaboratorsforkindlyprovidingus
reverseshockdestruction. withtheirdataontheextinctioncurveof SDSSJ1048+4637. We
Wehavefoundthattheextinctioncurveissensitivetotheam- arealsogratefultoS.Bianchiforhelpfulcommentsthatimproved
bientgasdensityaroundSNe,sincetheefficiencyofreverseshock thispaperverymuch.HHhasbeensupportedbyGrants-in-Aidfor
destruction is largely dependent on it. The destruction is signifi- ScientificResearchoftheMinistryofEducation,Culture,Sports,
cantforsmall-sizedgrains,leadingtoaflatextinctioncurveinthe Science and Technology (MEXT) of Japan (Nos. 18026002 and
opticalandUV.SuchalargeambientdensityasnH &1cm−3pro- 18740097). TNalsohasbeensupportedbythesamegrants(Nos.
ducestooflatanextinctioncurvetobeconsistentwiththeobserved 18104003and19740094).TTThasbeensupportedbytheSpecial
extinctioncurveforSDSSJ1048+4637 atz = 6.2.Althoughthe CoordinationFundsforPromotionScienceandTechnology(SCF)
Flattenedextinctioncurves 7
commissionedbytheMEXT(MEXT)ofJapan.Wefullyutilized Nozawa, T., Kozasa, T., Umeda, H., Maeda, K., & Nomoto, K.
theNASA’sAstrophysicsDataSystemAbstractService(ADS). 2003,ApJ,598,785(N03)
Nozawa, T., Kozasa, T., Habe, A.,Dwek,E.,Umeda, H.,Tomi-
naga,N.,Maeda,K.,&Nomoto,K.2007,ApJ,666,955(N07)
Omukai,K.,Tsuribe,T.,Schneider,R.,&Ferrara,A.2005,ApJ,
626,627
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APPENDIXA: COMPARISONBETWEENCRYSTALAND
Mujica,R.,Juarez,&Y.2004a,A&A,420,889
AMORPHOUSGRAINS
Maiolino, R., Schneider, R., Oliva, E., Bianchi, S., Ferrara, A.,
Mannucci,F.,Pedani,M.,&RocaSogorb,M.2004b,Nat,431, As mentioned in Section 2.2, the optical constants of crystal Si
533 and SiO2 are available, while we have used those of amorphous
Mathis,J.S.1990,ARA&A,28,37 SiandSiO2.Sincethosespeciesdominatetheextinctioncurves,it
Meikle,W.P.S.,etal.2007,ApJ,665,608 isimportanttoexaminetheuncertaintycausedbyassumedmate-
Morgan,H.L.,Dunne,L.,Eales,S.A.,Ivison,R.J.,&Edmunds, rialstates. Theoptical constants of crystal Siand SiO2 aretaken
M.G.2003,ApJ,597,L33 fromEdward(1985)andPhilipp(1985),respectively.Asarepre-
Moseley, S. H., Dwek, E., Glaccum, W., Graham, J. R., & sentative,weexaminethecaseofnH =1cm−3.Inthemixedand
Loewenstein,R.F.1989,Nature,340,697 unmixedcases,thedifferencebetweencrystalandamorphousare
Mun˜oz, J.,A.,Falco,E.E.,Kochanek, C.S.,McLeod,B.A.,& examinedforthedominantspecies,SiO2andSi,respectively.
Mediavilla,E.2004,ApJ,605,614 InFiguresA1aandb,weshowtheextinctioncurveswiththe
Murphy,M.T.,&Liske,J.2004,MNRAS,354,L31 progenitor masses of 20 M⊙ and 170 M⊙, respectively, for the
Nakamura,F.,&Umemura,M.2001,ApJ,548,19 mixedsupernovae.Fromthosefigures,weobservethattheoverall
Nozawa,T.,Kozasa,T.,&Habe,A.2006,ApJ,648,435 trendissimilarbetweenthetwospeciesofSiO2.Thusweconclude
8 H. Hirashitaet al.
FigureA1.ThesameasFigure3forthemixedSNIIandPISNfornH=1 Figure A2. The same as Figure 3 for the unmixed SN II and PISN for
cm−3(solidlinesinpanelsaandb,respectively).ForSiO2,weadoptthe nH = 1 cm−3 (solid lines in panels a and b, respectively). For Si, we
opticalconstantsofamorphousandcrystalsolidsforthesolidanddotted adopt theoptical constants ofamorphous andcrystal solids forthe solid
lines.Forotherspecies,thesameopticalconstantsasthoseinFigure3are anddottedlines.Forotherspecies,thesameopticalconstantsasthosein
applied. Figure3areapplied.
thatthetwospeciesofSiO2areindistinguishableintheextinction
curvewithintheuncertaintyinthecurrentobservationaldata.
In Figure A2, we make the same kind of comparison for
unmixed SNe, but the difference between crystal and amorphous
speciesisexaminedforSi.Ascanbeseenfromthefigure,thedif-
ferenceissmallerthantheuncertaintyintheobservationaldata.