Dust grains from the heart of supernovae

0.75 MB·

by  M. Bocchio

Astronomy&Astrophysicsmanuscriptno.paper˙GRASHRev˙v08 ©ESO2016
March4,2016
Dust grains from the heart of supernovae
M.Bocchio1,2,S.Marassi2,R.Schneider2,S.Bianchi1,M.Limongi2,A.Chieffi3
INAF-OsservatorioAstrofisicodiArcetri,LargoEnricoFermi5,50125Firenze,Italy
INAF-OsservatorioAstronomicodiRoma,ViadiFrascati33,I-00040Monteporzio,Italy
INAF/IASF,ViaFossodelCavaliere100,00133Roma,Italy
Preprintonlineversion:March4,2016
ABSTRACT
6
1 Dust grains are classically thought to form in the winds of Asymptotic Giant Branch (AGB) stars. However, nowadays there is
0 increasing evidence for dust formation in Supernovae (SNe). In order to establish the relative importance of these two classes of
2 stellarsourcesofdustitisimportanttoknowwhatisthefractionoffreshlyformeddustinSNejectathatisabletosurvivethepassage
ofthereverseshockandbeinjectedintheinterstellarmedium.
r Withthisaim,wehavedevelopedanewcode,GRASH Rev,thatallowstofollowthedynamicsofdustgrainsintheshockedSN
a
M ejectaandtocomputethetimeevolutionofthemass,compositionandsizedistributionofthegrains.Weconsiderfourwellstudied
SNeintheMilkyWayandLargeMagellanicCloud:SN1987a,CasA,theCrabNebula,andN49.Thesesourceshavebeenobserved
withbothSpitzerandHerschelandthemultiwavelengthdataallowtobetterassessthemassofwarmandcolddustassociatedwith
3
theejecta.

ForeachSN,wefirstidentifythebestexplosionmodel,usingthemassandmetallicityoftheprogenitorstar,themassof56Ni,the
]
E explosionenergyandthecircumstellarmediumdensityinferredfromthedata.Wethenrunadustformationmodeltocomputethe
properties of freshly formed dust (Marassi et al. 2015). Starting from these input models, GRASH Rev self-consistely follow the
H
dynamicsofthegrainsconsideringtheeffectsoftheforwardandreverseshockandallowstopredictthetimeevolutionofthedust
. mass,compositionandsizedistributionintheshockedandunshockedregionsoftheejecta.
h
For all the simulated models, we find good agreement with observations. Our study suggests that SN 1987A is too young for the
p
reverseshocktohaveaffectedthedustmass.Hencetheobserveddustmassof0.7−0.9M inthissourcecanbesafelyconsideredas
- (cid:12)
o indicativeofthemassoffreshlyformeddustinSNejecta.Conversely,intheotherthreeSNe,thereverseshockhasalreadydestroyed
r between10and40%oftheinitialdustmass.However,thelargestdustmassdestructionispredictedtooccurbetween103and105 yr
t aftertheexplosions.SincetheoldestSNinthesamplehasanestimatedageof4800yr,currentobservationscanonlyprovideanupper
s
a limittothemassofSNdustthatwillenrichtheinterstellarmedium,theso-calledeffectivedustyields.Wefindthatonlybetween1
[ and8%ofthecurrentlyobservedmasswillsurvive,resultinginanaverageSNeffectivedustyieldof(1.55±1.48)×10−2M .This
(cid:12)
isingoodagreementwiththevaluesadoptedinchemicalevolutionmodelswhichconsidertheeffectoftheSNreverseshock.
2
Wediscusstheastrophysicalimplicationsofourresultsfordustenrichmentinlocalgalaxiesandathighredshift.
v
0 Keywords.Supernovae:individual:SN1987A,CassiopeiaA,CrabNebula,SNRN49-Dust,extinction-Galaxy:localinterstellar
7 matter-Galaxies:high-redshift.
7
6
0
1. Introduction ismuchshorterthantheassumeddustformationtimescalefrom
.
1 AGB stars. This leads to the conclusion that a large amount of
0 It is observationally and theoretically well established that a dust must be re-accreted from the gas phase. However, while
6 considerable amount of dust is efficiently formed in regions there seems to be viable mechanisms for re-formation of car-
1 aroundAsymptoticGiantBranch(AGB)stars(e.g.Weigeltetal.
bonaceousgrainsunderlowtemperatureandpressureconditions
: 2002;Woitke2006;Zhukovskaetal.2008;Olofssonetal.2010;
v (e.g.Dartoisetal.2005),silicategrainsarehardertoformunder
Schneideretal.2014;Dell’Aglietal.2015).Thisprocessisclas-
i ISMconditions(Jones&Nuth2011).
X sicallyconsideredastheprimarysourceofdustgrainsingalax-
AlthoughSNearebelievedtobeefficientinterstellardustde-
r ies (see however Schneider et al. 2014) and in the Milky Way
a the typical formation timescale is ∼ 3×109yr (Dwek & Scalo stroyers,nowadaysthereisincreasingobservationalevidencefor
the formation of non-negligible quantities of dust grains in the
1980;Gehrz1989;Jones&Tielens1994).
ejectaofSNe(e.g.Matsuuraetal.2009;Dunneetal.2009;Gall
Onthecontrary,supernova(SN)explosionsintheinterstel-
et al. 2011; Gomez 2014). Given the relatively short timescale
larmedium(ISM)triggershockwaveswhichareabletoquickly
betweentheexplosionoftwoSNe(estimatedtobe∼40yrinour
process dust grains and are considered the dominant mecha-
Galaxy,Lietal.2011),thiswouldleadtoaneffectivelyshorter
nism of dust destruction in the ISM (Barlow 1978a,b; Draine
timescalefordustformation.
& Salpeter 1979a,b; Dwek & Scalo 1980; Seab & Shull 1983;
McKee et al. 1987; Jones et al. 1994, 1996; Lakic´evic´ et al. Rapid dust enrichment is also required by millimeter (mm)
2015;Slavinetal.2015).Arecenttheoreticalworkoninterstel- and sub-millimeter (submm) observations of z > 6 galaxies
lardustdestructioninshockwavesledtoanestimatedlifetime (Watson et al. 2015) and quasars (see Valiante et al. 2014 and
of ∼ 6×107yr and ∼ 3×108yr for carbonaceous and silicate referencestherein),whichshowthattheirISMhasalreadybeen
grains in our Galaxy, respectively (Bocchio et al. 2014), which enrichedwith(cid:38) 108M ofdust.Theoreticalmodelsandnumer-
(cid:12)
1
M.Bocchio,S.Marassi,R.Schneider,S.Bianchi,M.Limongi,A.Chieffi:Dustgrainsfromtheheartofsupernovae
Table 1: Observed/estimated physical properties of the four SNe considered in the present study that we have compiled from the
paperslistedincolumn“Ref”.Thelastthreecolumnsindicatetheinputparametersusedinthesimulations.
SNR type E 56Ni M Z Age n M Ref. Emod 56Nimod Mmod
ex prog 0 dust ex prog
[1051erg] [M ] [M ] [Z ] [Years] [cm−3] [M ] [1051erg] [M ] [M ]
(cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12)
1987A IIa 1.1 0.075a 18-20a 0.4 27 1.5 0.7-0.9 g,h,i 1.0 0.075 20
CasA IIbb 1-3 0.058-0.16c 13-20b 1 335 1.9 0.1-1 j,k,l 1.5 0.11 20
Crab IIn-Pd 0.1 0.009-0.016d 9-12e 1 960 1 0.1-0.25 m 0.5 0.014 13
N49 II 1.8 N/A 18-20 0.4 4800 0.9 0.1-0.4 n,o 1.5 0.075 20
References:aArnettetal.(1989),bKrauseetal.(2008),cEriksenetal.(2009),dSmith(2013),eMacAlpine&Satterfield(2008),fRowlandsetal.
(2014),gMatsuuraetal.(2011),hIndebetouwetal.(2014),iLakic´evic´etal.(2011),jBarlowetal.(2010),kRhoetal.(2008),lDunneetal.(2009),
mGomezetal.(2012),nParketal.(2012),oOtsukaetal.(2010).
ical simulations show that these large dust masses require effi- (Bocchioetal.2014)withthedynamicsandstructureoftheSN
cientgraingrowthinthedensephasesoftheISM(Valianteetal. asmodelledbyBS07butextendingittoincludethefulldynam-
2014;Michałowski2015;Mancinietal.2015),withbothSNand icsofdustgrainswithintheejectaandinthesurroundingISM.
AGBstarsprovidingthefirstseedgrains(Valianteetal.2011). This paper is organised as follows: in Section 2 we first
One important source of uncertainty on the role of SNe present the SN sample that we have considered to compare the
as efficient dust polluters is whether the dust formed in the model predictions with observational data. In Section 3 we de-
ejectasurvivesthepassageofthereverseshock.Infact,theob- scribe the corresponding SN explosion models and the proper-
servedsupernovaremnants(SNR)arestillrelativelyyoung(age ties of dust formed in their ejecta. In Section 4 we present the
(cid:46) 5000yr) and the reverse shock has not reached the centre of structure of the numerical model, the grid used in the calcula-
theejectayet.Themeasuredmassofdustassociatedtotheejecta tion, how we describe gas and dust dynamics, and the physical
willthereforenotbeentirelyreleasedintotheISMbutpartlyde- processes included in dust processing. In Sections 5 and 6 we
stroyed. present the main results and we discuss their astrophysical im-
Only in four core-collapse SNe it has been possible to es- plications.Finally,inSection7wedrawourconclusions.
timate the amount of dust in the ejecta, using observation from
Spitzer and Herschel: SN 1987A, Cassiopeia A, Crab Nebula
and SNR N49. The photometer instruments on these two satel- 2. Supernovasample
lites,coveringtogetheralargerangeofwavelengthsfromMid-
We consider the four aforementioned core-collapse SNRs: SN
Infrared(MIR)throughFar-Infrared(FIR)andsubmm,areable
1987A,CassiopeiaA,CrabnebulaandSNRN49.InTable1we
tomeasuretheemissionfrombothcoldandwarmdustinSNe.
reportsomeoftheirphysicalproperties,asobtainedfromthelit-
However,inordertoestimatethedustmassresponsibleforthe
erature:thetypeofSN,theexplosionenergy(E ),themassof
detectedemission,correctassumptionsmustbemadeonthedust ex
56Ni, the progenitor mass (M ), the estimated metallicity (Z)
composition, size and temperature distribution. Depending on prog
the choice of the dust composition and on the size/temperature oftheprogenitorstar,theage,thenumberdensityofthecircum-
stellarISM(n )andthemeasureddustmassassociatedwiththe
ofthesmallestgrains,thedustmassestimatecanvarybyalmost 0
ejecta (M ). Some of these quantities are directly estimated
afactorof6(Mattssonetal.2015).Furthermore,emissionfrom dust
from the data, while others are obtained by comparing the ob-
colddustinthemolecularcloudsurroundingaSNcontaminates
the emission from freshly-formed dust in the ejecta and differ- servedpropertieswiththeoreticalmodels.Forexample,thepro-
genitormassandexplosionenergyofSN1987Aareobtainedby
ent observations (e.g. polarisation measurements) are therefore
fitting the observed light curve and spectrum with a theoretical
neededtodisentanglethetwocomponents(Dunneetal.2009).
The difficulty in determining how much emission comes from model (Nomoto et al. 1994, 2006). Similarly, the mass of 56Ni
isestimatedfromcomparisonbetweentheoreticalandobserved
dustintheremnantandhowmuchfromtheISMwasalsorecog-
light curves. The uncertainties / approximations of the models
nised in the recent analysis of a sample of SNRs in the LMC
areencodedinthefinalestimatesofthesephysicalquantities.
byLakic´evic´ etal.(2015):whiletheyputconstraintsonthein-
fluence of the remnant on the nearby ISM, the data lacked the
resolutionandsensitivitytostudytheamountofdustwithinthe 2.1. SN1987A
remnantsthemselves.
Inordertoestimatethedustmasswhichisreleasedintothe SN1987AisayoungSNlocatedintheLargeMagellanicCloud
ISMafterthepassageofthereverseshock,anumericalcodethat (LMC)andexplodedin1987.ObservationaldatainTable1are
simulates the dust dynamics and processing in SNe is needed. fromGomez(2013)andreferencestherein.Thedustmassesti-
Using numerical simulations, Nozawa et al. (2006, 2007) esti- mate has been updated following the recent work by Matsuura
mated that, depending on the energy of the explosion and on etal.(2015),leadingtoatotaldustmassof∼0.8M(cid:12).However,a
thedensityoftheISM,thefractionofdustsurvivingthereverse recentandnewanalysisoftheinfraredemissionfromSN1987A
shockcanvarybetween0and80%.Bianchi&Schneider(2007, by Dwek & Arendt (2015) points to a lower dust mass of
BS07)estimatedthatdependingonthedensityofthesurround- ∼0.45M(cid:12),mostlycomposedbysilicategrains.
ing interstellar medium, between 2 and 20 % of the initial dust
masssurvivesthepassageofthereverseshock.
2.2. CassiopeiaA
InthisworkwepresentanewcodecalledGRASH Revthat
treatsdustprocessinginasupernovaexplosion.Thiscodecou- CassiopeiaA(CasA)isaGalacticSNRresultingfromaSNex-
ples all the dust processing included in the GRASH EX code plosionoccurred335yearsago.Thekineticenergyhasbeenes-
2
M.Bocchio,S.Marassi,R.Schneider,S.Bianchi,M.Limongi,A.Chieffi:Dustgrainsfromtheheartofsupernovae
Table2:DustdistributionparametersandmassesforthefourSNeinthesample.
1987A CasA Crab N49
a σ M a σ M a σ M a σ M
0 dust 0 dust 0 dust 0 dust
(nm) (M ) (nm) (M ) (nm) (M ) (nm) (M )
(cid:12) (cid:12) (cid:12) (cid:12)
Al O 7.5 0.14 2.57×10−2 5.5 0.14 2.57×10−2 4.7 0.01 5.18×10−3 5.5 0.14 2.57×10−2
2 3
Fe O 9.3 0.13 0.11 9.5 0.13 0.15 6.1 0.01 2.85×10−2 7.0 0.13 0.11
3 4
MgSiO 84.9 0.08 6.58×10−6 61.6 0.08 2.67×10−5 3.0 0.11 2.68×10−3 61.5 0.08 2.74×10−5
3
Mg SiO 68.9 0.11 0.43 50.5 0.11 0.43 4.3 0.13 8.60×10−2 50.4 0.11 0.43
2 4
AC 90.4 0.13 7.15×10−2 105.2 0.13 0.12 26.0 0.14 0.11 103.2 0.13 0.12
SiO 55.5 0.16 0.19 38.9 0.16 0.187 4.5 0.03 1.11×10−2 39.0 0.16 0.187
2
M 0.84 0.92 0.245 0.88
TOT
timatedtobe∼(2−3)×1051erg(Laming&Hwang2003).The dum(Al O ),magnetite(Fe O ),enstatite(MgSiO ),forsterite
2 3 3 4 3
massoftheshockedandunshockedejectais∼3−4M (Hwang (Mg SiO )andquartz(SiO ).
(cid:12) 2 4 2
&Laming2012)andthemassofgassweptawayinthecircum- InTable2weshowtheresultingdustcompositionandmass
stellarmediumis∼8M (Hwang&Laming2009;Patnaude& distribution. The grains that condense and accrete in SN ejecta
(cid:12)
Fesen2009).Addingthemassofaneutronstarremnant,theto- followalog-normalsizedistributionfunctionoftheform,
talmassoftheprogenitorisestimatedtobe∼(15±3)M .The
(cid:12)  
ombassesrvoaftdiounsstaanssdo8c5ia0teµdmtoptohlearSimNeRtriyndfeartraeidsbModthustfr=om0.1H−er1scMh(cid:12)el. mi(a)=mmax,iexp−log2120(σa/2a0,i), (1)
Giventhelargeuncertaintyinthemassof56Ni,weadoptanin- i
termediatevalueasinputparameterofthesimulation. wherem representsthedistributionmaximum,a isthecen-
max,i 0,i
troid,σ isthewidthofthedistributionand
i
2.3. Crabnebula (cid:90) ∞
M = m(a)da, (2)
dust,i i
The small progenitor mass (8-10 M(cid:12)), the low explosion en- 0
ergy(1050 erg)andmassofsynthesized56Ni(0.009-0.016M ),
(cid:12)
isthetotaldustmassforthei-thgrainspecies.Table2showsa ,
which are significantly less than the energy and nickel mass 0
σandM forthesixdominantgrainspeciesineachSN.
expected for ordinary SNe, all suggest that the Crab could be dust
In this work we consider a carbon grain density ρ =
the result of an electron-capture SN event (Smith 2013). The
adopted 56Ni mass for the simulation is intermediate between 2.2g cm−3. However, presolar grain measurements indicate a
wide range of density for carbonaceous grains formed in SNe
theobservedones.
(e.g. Amari et al. 2005, 2014). We explore this scenario in
AppendixA.
2.4. SNRN49
TheestimatedphysicalpropertiesofN49havebeentakenfrom 4. TheGRASH Revcode
Park et al. (2012). Otsuka et al. (2010) reports a mass of warm
dustof∼0.1−0.4M .Emissionfromalargemassofcolddust 4.1. Gasdynamics
(cid:12)
isalsoobserved,butitisnotpossibletodisentanglethecontri-
Thedynamicsoftheexpansionofasupernovaisclassicallydi-
butioncomingfromdustintheunshockedejectafromthatinthe
videdintothreemainstages(seeFig.1):
parentcloud.
For this source, there is no estimate of the 56Ni mass avail- 1. Ejecta-dominated (ED) expansion phase: as the supernova
able. We therefore adopt the same value used to model SN explodes a shock wave is triggered and propagates into the
1987A. ISM(forwardshock,FS).Atthesametimeareverseshock
(RS)propagatesintotheejecta.Theejectaisinfreeexpan-
sion.
3. Structureoftheejectaandgraindistribution 2. Sedov-Taylor(ST)phase:themassoftheinterstellarmaterial
sweptupbytheshockwavebecomescomparabletothemass
Starting from a homogeneous set of solar metallicity presuper- of the ejecta. The ejecta is in adiabatic expansion and the
nova models with masses in the range [13-130] M(cid:12) (Chieffi radiativecoolingisnegligible(Taylor1950;Sedov1969).
& Limongi 2013) simulated by means of the FRANEC stellar 3. Pressure-driven snowplough (PDS) phase: the shock wave
evolutionary code (Limongi & Chieffi 2006), we have selected slows down to velocities (cid:46) 200km/s and radiative cooling
the most suitable model for each SN according to the physi- becomes the main cooling process. The outermost shell of
cal properties listed in Table 1. These four selected models are theejectaispushedintotheambientmediumduetothepres-
then used as input for the dust formation code (BS07), where sureofthehotgasinsideit.
classical nucleation theory in steady state conditions was ap-
plied. Here we use the latest version of dust formation model, Finally, when the velocity of the shock front becomes low
whichimplementsanupgradedmolecularnetwork,asdescribed enough(∼10km/s),theremnantmergeswiththeISM.
in detail in Marassi et al. (2015). We follow the formation of Aunifiedandself-similarsolutionfortheevolutionofaSNR
sixdifferentdustgrainspecies:amorphouscarbon(AC),corun- fromtheEDphasethroughtheSTphasewasfoundbyTruelove
3
M.Bocchio,S.Marassi,R.Schneider,S.Bianchi,M.Limongi,A.Chieffi:Dustgrainsfromtheheartofsupernovae
wheret∗ =t/t and,
PDS PDS
E2/7
R =14 51 pc (8)
PDS ζ1/7n3/7
m 0
isthepositionoftheforwardshockatthetimet .
PDS
The validity of these analytical solutions is guaranteed by
thecomparisonwithhydrodynamicalsimulationsbyCioffietal.
(1988) and Truelove & McKee (1999). As a further check, we
comparetheanalyticalapproximationswithrecenthydrodynam-
ical simulations (Slavin et al. 2015). In the inset in Fig. 1 we
show the analytical forward shock position and velocity (black
lines) and those retrieved from Fig. 2 in Slavin et al. 2015 (red
lines).Theanalyticalsolutionisagoodapproximationthrough-
outtheconsideredtimeintervalandthediscrepancyintheposi-
tionoftheforwardshockisneverlargerthan∼2%.
Fig.1:Positionoftheforwardandreverseshocks(blacklines)as
afunctionoftimefromtheEDphasethroughthePDSphase.In
theinsetwecomparetheposition(solidline)andvelocity(dot- 4.2. Simulationgriddynamics
dashedlines)oftheforwardshockcomputedusingtheanalytical
solution (black lines) with the simulation by Slavin et al. 2015 WedividetheejectaintoNssphericalshellsandweassumethat
(redlines). theyallhavethesamewidth∆R=Rej/Ns,whereRejistheejecta
radius. The velocity of each shell is initially determined by the
homologousexpansionoftheejecta:
& McKee (1999) by comparing with the results of a hydrody- (cid:115)
namicalnon-radiativesimulation.Theyconsideredthefollowing v =v Rj, v = 10Eex. (9)
characteristicscalesoflengthandtime: j ejR ej 3M
ej ej
R ≡ M1/3ρ−1/3,
ch ej 0 where v is the velocity of the j-th shell and v is the velocity
j ej
t ≡ E−1/2M5/6ρ−1/3, (3) oftheejectaradius.AdditionalN sphericalshellsaredefinedto
ch ex ej 0 s
modeltheISMaroundtheexpandingejecta.Weconsideramax-
where M is the mass of the ejecta, ρ is the ISM density and imumdistanceofR ∼200pcfromthecentreoftheejectaand
ej 0 max
E is the explosion energy. The position of the forward (R ) dividethespacebetweenR andR inN shellsofequalwidth
ex FS ej max s
andreverse(R )shockswithrespecttothecentreoftheejecta ∆R = (R −R )/N . At the beginning of the simulation,
RS ISM max ej s
foruniformejectaarewelldescribedby: theseISMshellsareatrest.
Wethenletthesystemevolve.Thesimulationtimestep,∆t,
RFS(t∗)=2.01Rcht∗(1+1.72t∗3/2)−2/3, is uniquely determined by the dynamics of the reverse shock.
R (t∗)=1.83R t∗(1+3.26t∗3/2)−2/3, (4) Itisdefinedasthetimeintervalduringwhichthereverseshock
RS ch
crossesoneshellinsidetheejecta,untilitreachesthecentreofit.
duringtheEDphase,whileduringtheSTphasethesetwoquan- Ateachgiventime,shellsthathavenotyetbeencrossedbythe
titiescanbeapproximatedby: reverse shock keep expanding homologously and adiabatically.
This implies that the external and internal boundaries of each
R (t∗)=R (1.42t∗−0.254)2/5, shell expand at their initial velocity, leading to a larger volume
FS ch
R (t∗)=R t∗(0.779−0.106t∗−0.533lnt∗), (5) andtoalowerdensity.Thegastemperatureintheshellchanges
RS ch
accordingto:
wheret∗ =t/t .
ch
Whentheforwardshockreachesvelocities(cid:46)200km/sthese  1/γ
eraqduiaattiiovnescodoolinnogtmreupsrtesbeenttaakegnoiondtoaapcpcroouxnimt.aCtiioonffiaentyaml.o(r1e9a8n8d) T(cid:48)j =TjVV(cid:48)j , (10)
j
foundthefiducialtimefortheonsetofthePDSphasetobe,
whereT andV arethetemperatureandvolumeofthe j-thshell
E3/14 j j
t =1.33×104 51 yr, (6) atagiventimet,theprimedvariablesarethesamequantitiesat
PDS ζ5/14n4/7 timet+∆tandγistheadiabaticindex(assumedtobeγ =1.41,
m 0 Chieffi&Limongi2013,forthegasintheejectaandγSN =5/3
ISM
whereE = E /1051erg,ζ =1forsolarabundancesandn is for the ISM). Similarly, shells in the ISM which have not yet
51 ex m 0
theISMnumberdensity.Theyfoundalsothattheforwardshock been crossed by the forward shock remain at rest and their gas
canbeapproximatedwiththefollowinganalyticalexpression: propertiesremainunchanged.
On the contrary, when a shell is invested by the reverse or
(cid:32)4 1(cid:33)3/10 forward shock, it experiences strong variations in density, ve-
R =R t∗ − , (7)
FS PDS 3 PDS 3 locity and temperature that are well described by the standard
4
M.Bocchio,S.Marassi,R.Schneider,S.Bianchi,M.Limongi,A.Chieffi:Dustgrainsfromtheheartofsupernovae
Rankine-Hugoniotjumpconditions: Eq.11):
|v |=|v(cid:48) −v |
rel j j
γ+1
ρ(cid:48)j = γ−1ρj, = γ+2 1vsh (12)
2
v(cid:48)j =vj− γ+1vsh, (11) withrespecttotheshockedgas.
In the model by BS07 dust grains were kept in the same
γ−1 m
T(cid:48) =2 v2 shell for the whole simulation without considering their full
j (γ+1)2kB sh dynamics. Also, once the reverse shock invested a given shell,
the grains in that shell were assumed to be at constant velocity
(givenbyEq.12)inordertotakethegrainerosionupperlimit,
where ρ(cid:48), v(cid:48) and T(cid:48) are the density, velocity and temperature
j j j withoutconsideringtheactionofdragforces.However,depend-
of the j-th shell (being it in the ejecta or in the ISM) after ingonthegasanddustproperties,dustgrainsmodifytheirve-
the passage of the shock, m is the mean particle mass, kB the locityaccordingtothefollowingequation(McKeeetal.1987):
Boltzmann’sconstantandv isthevelocityoftheshockinthe
sh
referenceframeoftheshellbeforebeinginvestedbytheshock.
dy dχy F
This velocity corresponds to v˜RS and vFS for the reverse and rel = rel − D, (13)
forward shocks, whose analytical expressions can be found in dt dt 2χ mgr
Truelove&McKee(1999).
whereχistheshockcompression,F thecouplingforceandm
D gr
The velocity of shells between the reverse and forward
thegrainmass.Thefirsttermontheright-handsideisknownas
shocks (hit by a shock at earlier times) is obtained interpolat-
betatronacceleration(Cowie1978;Shull1978).Inthepresence
ingbetweenthevelocityofthereverseandforwardshock.Asin
ofamagneticfield, B,charged(withcharge|q|)dustgrainsgy-
Bianchi & Schneider (2007), we have compared the dynamical
ratearoundmagneticfieldlineswithatrajectorydeterminedby
evolution predicted by the model with the output of numerical
theLarmorradius:
simulationsbyvanderSwaluwetal.(2001)andDelZannaetal.
(2003),findinggoodagreementuntilt∼104yr. r = mgrvrel,⊥, (14)
L |q|B
Thereverseshockvelocityinthereferenceframeoftheun-
shocked ISM reaches an inversion point at t = t and then it
rev where v is the component of the relative velocity between
rel,⊥
achievesnegativevelocities,causingtheimplosionofpartofthe
gas and dust which is perpendicular to magnetic field lines. A
ejecta. This process has been investigated in detail through nu-
rapidincreaseinthegasdensityduetoshockcompressionwill
mericalsimulationsbyCioffietal.(1988).Beforereachingthe
thenleadtoanenhancementofthemagneticfieldstrengthanda
centreoftheejecta,thetemperatureandpressureinthecoreof
consequent(betatron)accelerationandreductionoftheLarmor
the ejecta increase, effectively reflecting the reverse shock, and
radius.Onthecontrary,thecouplingtermreducesthegrainve-
leading to the so-called “echoes of thunder” described in their locity as a result of the combined effect of collisional (direct)
work. In order to qualitatively reproduce this mechanism we
couplingandofplasmadrag(Draine&Salpeter1979b):
makethefollowingapproximation:foralltheshellsoftheejecta
thatareinvestedbythereverseshockaftertrev(j< j∗with j∗the FD = FD(collisional)+FD(plasma). (15)
shellinvestedbythereverseshockatt ),wesettheshellveloc-
rev
ity to zero, therefore assuming that the bouncing of the reverse The relevant relations that define plasma drag are reported in
shockwouldeffectivelycancelouttheinwardvelocity.Theve- Eqs.3-6ofBocchioetal.(2014).
locityoftheseshellswillremainzerountiltheendofthesimula- In this model we do not describe the ionisation state of the
tionandshellsinbetweenthe j∗-thshellandtheforwardshock gas. However, for a sufficiently high gas temperature we can
have velocities obtained from interpolation. During this phase, consider the gas as fully ionised. Therefore the shocked gas is
radiativecoolingofthegasduetoatomicprocessesstartstobe assumedtobecomposedbyH+,He++ andO+,whichrepresent
importantanditistakenintoaccountusingthecoolingfunction themostabundantspecies.InFig.2weshowtheratiobetween
byRaymondetal.(1976).Theerrormadeonthepositionofthe plasma and collisional drag as a function of the gas tempera-
outermostshelloftheejectacomputedbythismodelisalways tureandfordifferentgrainsizesanddriftvelocities.Plasmadrag
smallerthanafactorof∼ 2whencomparedwiththeresultsof hasanegligibleeffectonthedynamicsofsmallgrains,whileit
numericalsimulations(Cioffietal.1988).Moreover,sinceonly exceeds collisional drag for ∼ 100 nm grains at gas tempera-
aquarteroftheejectaisinvestedbythereverseshockaftert , tures (cid:46) 5×106K. However, if the velocity is sufficiently large
rev
alltheseapproximationsaffectonly(cid:46)2%ofthedustmass. (vrel ∼ 1000km/s)plasmadragisnegligibleatallgastempera-
turesandforallgrainsizes.
Ithasbeenshownthatbetatronaccelerationefficientlyaffect
4.3. Dustcoupling the dynamics of interstellar dust grains invested by supernova-
triggered shock waves (Jones et al. 1994, 1996; Bocchio et al.
The dynamics of dust is governed by its coupling to the gas. 2014). However, this process is probably not relevant for dust
Initially,dustiscoupledtotheunshockedejectaanduniformly producedinSNe.Thereisevidenceformagneticfieldlinesdis-
distributed.Foragivenshell, j,bothgasanddusthavethesame tributed radially inside the ejecta both from polarimetry obser-
velocity,vj.Thepassageofthereverseshockinthe j-thshellof vations(e.g.Dunneetal.2009)andfromnumericalsimulations
the ejecta will affect the dynamics of both gas and dust in that (e.g.Inoueetal.2013;Schure&Bell2014).Inthecaseofsym-
shell. The gas is instantaneously modified according to Eq. 11 metric ejecta, the velocity of grains is mostly oriented radially
and takes a velocity v(cid:48), while dust grains, having more inertia, andbetatronaccelerationisthereforenegligibleinsidetheejecta.
j
decouple from the gas and move with an initial velocity (see In the ISM, shock compression is important during the PDS
5
M.Bocchio,S.Marassi,R.Schneider,S.Bianchi,M.Limongi,A.Chieffi:Dustgrainsfromtheheartofsupernovae
changeveryrapidlyandthedivisioninsub-gridtimeintervalsis
notnecessary.
4.5. Dustprocessing
Weconsiderfourmainphysicalprocesses:
1. Sputteringduetotheinteractionofdustgrainswithparticles
inthegas;
2. Sublimationduetocollisionalheatingtohightemperatures;
3. Shatteringintosmallergrainsduetograin-graincollisions;
4. Vapourisation of part of the colliding grains during grain-
graincollisions.
The sputtering process can be estimated following the for-
malism by Tielens et al. (1994) as revisited by Bocchio et al.
(2014).Thesputteringrateisexpressedas:
dN (cid:88)
Fig.2: Ratio between plasma and collisional drag as a function sp =2πa2 n <Yv>, (18)
of the gas temperature for different grain radii. Drift velocities dt i i
are indicated by the line style (V = 10,100,1000km/s for i
rel
solid,dottedanddashedlines,respectively). where dNsp is the number of sputtered atoms per unit time, a is
dt
thegrainradius,n thenumberdensityofthei-thionand
i
(cid:90)
phase,whentheshockfrontisatlowvelocities(v (cid:46)200km/s) <Yv>= Yvf (v)dv, (19)
sh i i skM
andthegascoolsduetotheemissionofradiation.However,dust
grainsejectedfromtheinterioroftheSNarealmostatrestwith where Y is the sputtering yield (assuming a semi-infinite tar-
i
thepost-shockgasduringthisphase(seeSection5)andtheyare get) of the i-th ion, v is the relative velocity between grain and
thereforenotaffectedbythebetatronacceleration.Hencewedo
gas particle (a combination of the thermal and drift velocities)
notincludebetatronaccelerationinthisversionofthecode. and f (v)istheskewedMaxwelliandistribution(Shull1978;
skM
Guillet2008;Bocchioetal.2014).Weusethesamesputtering
yields derived by Tielens et al. (1994) and used by BS07 and
4.4. Dustgrainnumbermatrix
Nozawaetal.(2006,2007).
Inordertokeeptrackofallthegrainsinthesimulationwede- Energetic ions can have a penetration depth which is com-
fineamatrix,M,where-foreachofthe2Ns shellsandforeach parableorevenlargerthanthesmallestgrainsconsideredinthis
relative velocity between grains and gas in the shell - we store work.Forexamplea∼1keVHe+ion(correspondingtotheen-
the number of grains, their size and composition. Initially, the ergyofanioninahotgaswithT ∼8×106K)hasapenetration
g
grainsoccupythematrixelementscorrespondingtotheshellsin depth R ∼ 10nm in graphite and therefore it is likely to cross
p
theejectaandzerorelativevelocity.Ateachtimestep,grainsare grainsofradiussmallerthanR withoutleadingtoanysputter-
p
displacedaccordingtothelawsdescribedaboveandthematrix ing of the target. This effect was taken into account in models
elements are updated. A particular care is required when drag byJuracetal.(1998)andSerraD´ıaz-Cano&Jones(2008)and
forcesaretoostrongandgrainvelocitieschangetooquicklydur- thenadoptedbyBocchioetal.(2014)forsputteringofinterstel-
ingonesimulationtimestep.Inthatcasethetimestepisdivided larcarbonaceousgrainsinsupernova-triggeredshocks.Usinga
into ni = 50 time intervals (each of duration δt) and the grain similarapproach,hereweextendthelatterstudytosimulatethis
velocity,vt+∆t,andposition,dt+∆t,aredeterminedbyasub-grid effectforallthetargetmaterialsconsideredinGRASH Rev.The
modelfollowing: sputteringyield,Y ,ofagrainofradiusaisthenexpressedas:
a
(cid:88)ni (cid:32)dv(cid:33) Y =Y f(x), (20)
vt+∆t =vt+ dt δt, a ∞
i=1 i where Y is the sputtering yield for a semi-infinite target, x =
∞
dt+∆t =dt+(cid:88)ni viδt, (16) a/(0.7Rp)and f(x)isafunctionthatcanbeparametrisedas:
 
where v isi=t1he intermediate velocity at each time t + iδt. f(x)=1+p1exp−(ln2x/pp22)2−p4exp(cid:104)−(p5x−p6)2(cid:105). (21)
i 3
Computingthechangeingrainradius, a,ateachofthe n time
i
intervalswouldhavebeentootime-consumingandwetherefore Thefunction f(x)dependsonthetargetmaterialandthesixpa-
accountforthegrainerosioninthisway: rameters used are reported in Table 3. In general this function
tendstounityforsufficientlylargegrains(withrespecttoR ,i.e.
at+∆t =at+ 21(cid:32)ddat(cid:12)(cid:12)(cid:12)(cid:12)v=vt + ddat(cid:12)(cid:12)(cid:12)(cid:12)v=vt+∆t(cid:33), (17) rxa→dii∞co)manpdartaebnldesttooztehreoifoonrspmeanleltgrartaiionns(di.eep.txh,→th0e).sFpourttpgerrianing
yieldisenhancedandcanreachvaluesY ∼ 4Y forgraphitic-
a ∞
where da is the grain radius derivative calculated as described type grains. For a detailed explanation of the method used to
dt
in Section 4.5 and the subscript indicates the velocity at which retrievetheparametersinvolvedinEq.21,thereaderisreferred
theprocessingiscalculated.Thegrainradiusgenerallydoesnot to Appendix B. Finally, since the mass of (sub-)nanoparticles
6
M.Bocchio,S.Marassi,R.Schneider,S.Bianchi,M.Limongi,A.Chieffi:Dustgrainsfromtheheartofsupernovae
is negligible for all the SN models considered, we do not im-
plementanymoleculedissociationprocess(e.g.Micelottaetal.
2010b,a)aswasdoneinBocchioetal.(2014).
Table 3: Parameters for the analytical modelling of the size-
dependentsputtering.
Al O Fe O MgSiO Mg SiO AC SiO
2 3 3 4 3 2 4 2
p 1.1 1.2 1.0 1.5 4.9 0.85
1
p 0.39 0.55 0.50 1.2 0.55 1.2
2
p 1.1 1.0 1.0 0.57 0.77 0.56
3
p 1.9 1.9 1.8 1.1 4.7 1.1
4
p 2.1 2.0 2.1 0.52 3.0 1.6
5
p 0.78 0.80 0.76 0.37 1.2 0.29
6
Sublimationisimplementedwiththesamemethoddescribed
by BS07, using the thermal sublimation rates by Guhathakurta
& Draine (1989) and Draine & Hao (2002). In agreement with
BS07, we find this process to provide a negligible contribution
todustdestructionforalltheSNmodels.
Grain-graincollisionsleadtotheformationofcratersinthe
twocollidinggrains.Thematterejectedfromthecraterisfrag-
mented or even vapourised and brought back to the gas phase.
Shatteringandvapourisationprocessesareimplementedfollow-
ing equations by Jones et al. (1994, 1996). However, some of
the grain materials present in this work were not in the origi-
nalpapers.Weadoptvaluesfromtheliteratureforthedifferent
grainproperties(seeTableB.1).Foradetaileddescriptionofthe
computation of the relevant quantities the reader is referred to
AppendixC.
Giventhelowdensityofdustintheejecta,grain-graincol-
lisions are rare and shattering and vapourisation lead to minor
processing with respect to sputtering. This result can be bet- Fig.3:Mg2SiO4 testparticletrajectory,sizeandvelocityinthe
terunderstoodifwecalculatethetimescalebetweengrain-grain ejecta of SNR N49. Green and red lines indicate particles ini-
collisions, ∆t . Particles with a mean number density n¯ and a tially placed at one-forth and half of the radius of the ejecta,
coll
typical radius a, in motion in a given volume will have a mean respectively.Theinitialsizeofparticlesis10,100and1000nm
freepath: fordotted,solidanddashedlines,respectively.Inthetoppanel,
black lines indicate the positions of forward and reverse shock
1
λ= , (22) andthebluelineistheboundarybetweentheejectaandtheISM.
πa2n¯
andthetimescalebetweentwocollisionsisgivenby:
λ
∆t = , (23)
coll v¯ theexplosionenergy,theprogenitormass(n0,Eemxopd,Mpmroogdlisted
inTable1)andtheinitialdustmass,compositionandsizedistri-
with v¯ the typical relative velocity between particles. As an
example we consider a SN ∼ 104yr after the explosion. The bution(Mdust,a0,σforeachgrainspecieslistedinTable2).The
numberofshellsusedforthesimulationgridisfixedandequal
volume occupied by dust is roughly a sphere of radius 10 pc.
to2N =800.However,wenotethatthisrepresentsarobustpa-
Assuming 0.5 M of silicate grains with an average radius of s
(cid:12)
50 nm, the mean grain number density is n¯ ∼ 10−11cm−3. rameter;halvingordoublingthenumberofshellsthesimulation
Then,consideringameanrelativevelocityofv¯ ∼ 500km/s,the outputremainsunchanged.
timescale between grain-grain collisions is ∆t ∼ 8×105yr, Inthefollowingsectionswepresenttheresultsofthesimu-
coll
lations.
showingthattheseeventsarerare.Furthermore,withtheexpan-
sionoftheejectaandthedispersionofgrainsintotheISM,the
frequencyofcollisionsisevenlower.
5.1. Testparticledynamicsandprocessing
Ateachtimestepinthesimulationthegrainsinallthecells
ofthematrixMareprocessedbythefourmechanismsdescribed Tobetterunderstandthebehaviourofindividualdustgrains,we
aboveandthematrixisupdated. first illustrate the dynamics of a few test particles, giving as an
inputtothecodetheirinitialposition,sizeandmaterial.
We consider the simulation of SNR N49 and we define six
5. Results
test particles made of Mg SiO with radii of 10, 100 and 1000
2 4
We run the GRASH Rev code for four SNe with the following nm initially placed at a distance of one-forth and half of the
input parameters: the number density of the surrounding ISM, initial radius of the ejecta. In Fig. 3 we show their trajectories
7
M.Bocchio,S.Marassi,R.Schneider,S.Bianchi,M.Limongi,A.Chieffi:Dustgrainsfromtheheartofsupernovae
(upperpanel),thesizeevolution(centralpanel)andrelativeve- dust erosion is efficient. For all the four SNe, we predict final
locitieswithrespecttothegas.Thepositionofforwardandre- dust masses which are ∼ 5−50% of those estimated using the
verse shocks are indicated by black lines while the position of modelbyBS07,wherethedisplacementofgrainsandtheeffect
theboundarybetweentheejectaandtheISMbytheblueline. oftheforwardshockwereneglected.
Initiallyalltheparticlesareatrestwithrespecttotheejecta.
When the reverse shock reaches the shell where the particles
reside, the gas undergoes a jump in conditions (Eq. 11) while
dustgrainsarenotinstantaneouslycoupledandassumeaveloc-
ity given by Eq. 12 with respect to the gas. Immediately after
the passage of the reverse shock, depending on the gas condi-
tions and grain size, dust grains are slowed by drag forces and
processedduetocollisionswithgasparticlesandothergrains.
Small grains (a = 10 nm, dotted lines) are quickly stopped
and destroyed within the ejecta, while larger grains (a =
100,1000 nm, solid and dashed lines, respectively) are eroded
to a lower extent. Furthermore, 100 nm grains which were ini-
tiallyplacedatone-forthoftheejecta(greenlines)haveenough
inertiatocrosstheforwardshockwhile100nmgrainsinitially
placedathalfoftheejecta(redlines)arestoppedanddestroyed
in∼105yr.
As soon as a grain crosses the forward shock, its relative
velocity with respect to the unshocked ISM gas, v(cid:48) , will be
ISM
enhancedto
v(cid:48) =v +v , (24)
ISM ISM sh
where v is the relative velocity between the grain and the
ISM
shockedISMandv istheshockvelocity.Becauseoftheeffect
sh
of drag forces, grains will again slow down in the unshocked
ISM. In this medium, if the velocity of a grain is too low (e.g.
green solid line in Fig. 3), it can be reached by the faster for-
ward shock and will cross the shock front a second time. This
time,therelativevelocitybetweengrainandgasisreducedand
thegrainisalmostatrestintheshockedgas,thereforeavoiding
furtherprocessing.
Hence, it is clear that the fate of individual grains depends
not only on its initial size but also on its initial position within
theejecta.
5.2. Dustmassevolution
Fig.4: Dust mass evolution as a function of time for the four
In Fig. 4 we show the time evolution of the dust mass follow-
SNeconsideredinthisstudy(1987A:black,CasA:green,Crab:
ingtheSNexplosion.Theevolutionstartsattheendofthedust
blue and N49: red). Solid lines represent GRASH Rev results
nucleationphase.Eachlinerepresentstheevolutionof asingle
and dashed lines the results obtained by BS07 model using the
SN (1987A: black, CasA: green, Crab: blue and N49: red) and
sameinitialconditions.Datapointsrepresenttheobserveddust
the data points illustrate the dust mass estimated from the ob-
masses and the shaded region indicate the time interval when
servations (see Section 2). As a comparison we also show the
dustprocessingfadesout.
mass evolution computed using the model by BS07, assuming
no drag forces (dashed lines). In the inset we highlight results
forthetimeintervalt=105−106yrinalogarithmicscale.
ThedustmassestimatedusingGRASH Revsimulationsare
in good agreement with the observations, except for SNR N49
for which the dust mass predicted by GRASH Rev is ∼ 15% 5.3. Dustmassdistribution
larger than the upper mass limit of the range of values inferred
fromobservations(0.4M ,seeTable1andsection5.3).Amore In Fig. 5 we show the predicted mass in different dust species
(cid:12)
detailed comparison between model predictions and observa- as a function of the grain size for Cas A, Crab and N49. The
tionsisgiveninSection5.3. initial mass distributions (obtained as described in Sect. 3) are
Attimest ∼ 103−104yrthereverseshockdestructionpre- shown with solid lines, while the dust mass distributions at the
dictedbyGRASH Revislessimportant thanthatpredictedby timecorrespondingtotheageoftheseSNe,t ,isrepresented
obs
BS07. In fact, during this time interval, because of the passage bythehistograms.Onlythemostabundantspeciesaredisplayed
of the reverse shock dust is decoupled from the gas and travels here:Fe O (green),Mg SiO andSiO (summeduptogetherin
3 4 2 4 2
inbetweenthereverseandforwardshockswherethegascondi- orange)andAC(blue).WedonotshowtheresultsforSN1987A
tionsaremilder.Fort (cid:38)104yr,mostofthegrainsreachregions becausethereverseshockhasnotyetaffectedthemassofdust
behind the forward shock where gas conditions are harsh and formedinthisSN(seeFig.4).
8
M.Bocchio,S.Marassi,R.Schneider,S.Bianchi,M.Limongi,A.Chieffi:Dustgrainsfromtheheartofsupernovae
Table4:Dustmasses(expressedinM )attheobservationtime,t ,andattheendofthesimulation,t .
(cid:12) obs end
1987A CasA Crab N49
t t t t t t t t
obs end obs end obs end obs end
M 2.57×10−2 1.24×10−6 2.14×10−2 3.00×10−6 3.66×10−3 1.51×10−6 6.19×10−3 3.93×10−6
Al2O3
M 0.11 1.46×10−5 0.13 6.78×10−6 1.58×10−2 2.00×10−6 3.02×10−2 2.27×10−5
Fe3O4
M 6.58×10−6 5.91×10−8 2.4×10−5 1.65×10−9 1.80×10−3 1.87×10−6 1.84×10−5 1.70×10−7
MgSiO3
M 0.44 2.10×10−3 0.40 1.34×10−5 6.19×10−2 1.38×10−4 0.28 1.48×10−3
Mg2SiO4
M 7.15×10−2 8.50×10−3 0.12 1.07×10−2 7.85×10−2 2.57×10−4 0.11 3.86×10−2
AC
M 0.19 1.26×10−4 0.16 6.15×10−6 6.80×10−3 2.08×10−5 9.65×10−2 3.51×10−4
SiO2
M 0.84 1.07×10−2 0.83 1.07×10−2 0.17 4.21×10−4 0.52 4.02×10−2
TOT
Thedustmassdistributionattheobservationtimeisshifted
towards small grains and reduced in mass as a result of dust
processing(comparetheentriesinTables2and 4).Thiseffect
is more evident for the oldest SN remnant, N49. Furthermore,
small grains are more affected by processing than large grains,
reflectingthebehaviouroftestparticlesseeninFig.3.
Inwhatfollows,thedustsizeandcompositionpredictedby
GRASH RevforthesethreeSNeattheirrespectiveagesiscom-
paredwiththedustpropertiesadoptedtoestimatethedustmass
fromIRandsubmmobservations.
ForCasAourmodelpredictslittledestructionandthethree
dominantspeciesarecharacterizedbyamassdistributionwhich
is similar to the initial one. About 0.77 M of dust is still un-
(cid:12)
shockedandthereforeonly0.06M ofdustislikelytobewarm
(cid:12)
andcollisionallyheatedbythehotpost-shockgas.Thesevalues
areingoodagreementwiththemassofcoldandwarmdustob-
tained from fitting observations (0.1−1M from Herschel and
(cid:12)
polarimetryobservationsand0.02−0.054M fromSpitzerdata,
(cid:12)
Rhoetal.2008;Arendtetal.2014).
TheCrabNebulahasbeenobservedwithHerschelatwave-
lenghtsbetween51and670µmbyGomezetal.(2012).Theyfit
theobservedemissionwithtwo-temperatureblackbodies,infer-
ringadustmassof0.11(0.24)M whencarbonaceous(silicate)
(cid:12)
grainopticalpropertiesareusedtofitthedata.Atthetimecor-
responding to the age of this SN, we predict a total dust mass
of 0.17 M , in good agreement with the observations, with an
(cid:12)
almost equal contribution from silicates (∼ 0.09M ) and car-
(cid:12)
bon grains (∼ 0.08M ). However, the predicted grain compo-
(cid:12)
sition is more complex than assumed to fit the data. The sim-
ulation predicts that ∼ 0.023M of dust lies between the for-
(cid:12)
wardandreverseshock,probablyemittingathightemperatures,
whilethewarmdustmassinferredfromthedataisestimatedto
be6−8×10−3M .However,inordertofitthedata,allgrains
(cid:12)
are assumed to be either at high temperature (T ∼ 55 - 63 K)
w
oratlowtemperature(T ∼28-33K).Giventhelargerangeof Fig.5: Dust mass distributions for CasA, Crab and N49 at for-
c
predictedgrainsizes,thisassumptionislikelytobeaverypoor mation(solidlines)andobservationtimes(histograms).Ineach
approximation. panelweshowthethreedominantdustspecies:Fe3O4 (green),
Mg SiO and SiO (summed up together in orange) and AC
ObservationsofwarmdustemissioninN49byOtsukaetal. 2 4 2
(blue).
(2010)indicateadustmassof0.1(0.4)M ifcarbonaceous(sil-
(cid:12)
icate) grains are assumed as the main constituent of dust. The
coldcomponentishardtodetectobservationallyasitisstrongly
contaminated by the emission of dust in the parent cloud at a
similar temperature. Only a single dust temperature has been inated by silicate grains, which is only ∼ 15% larger than the
used to fit the data (Otsuka et al. 2010) and this could lead to observed warm dust mass when silicate optical properties are
a large uncertainty in the estimated dust mass (Mattsson et al. assumed.
2015).GRASH RevsimulationpredictsthatinSNRN49there- Given the uncertainties in inferring the dust mass from the
verse shock has already processed much of the ejecta and only data,wecanconcludethatthemodelpredictionsprovidearea-
0.04M ofdustisstillintheunshockedregion,emittingascold sonable estimate of the mass of dust that has survived the pas-
(cid:12)
dust. Hence, we predict a warm dust mass of ∼ 0.48M , dom- sageofthereverseshock.Basedonoursimulation,wecancon-
(cid:12)
9
M.Bocchio,S.Marassi,R.Schneider,S.Bianchi,M.Limongi,A.Chieffi:Dustgrainsfromtheheartofsupernovae
cludethatadustmassof[0.7−0.9]M ,suchastheoneobserved tion (Lee et al. 2015; Owen & Barlow 2015). When this is
(cid:12)
inSN1987A,canbesafelyconsideredtoberepresentativeofthe taken into account, the inferred dust masses are generally
efficiencyofdustproductioninmassivestars,astheejectahave larger.Industformation/destructionmodels,aclumpyejecta
notyetbeeninvestedbythereverseshock.Thisconclusiondoes wouldalsofavouralargerdustmassas(i)theformationof
notapplytotheotherthreeSNethatwehaveconsidered,where- dustgrainswouldbemoreefficient,thereforecreatinglarger
attheestimatedtimefromtheexplosions-between10and40% grainsand(ii)thehighercontrastindensitybetweenthedif-
ofthefreshlyformeddusthasalreadybeendestroyed.However, fuseandclumpygaswouldslowthereverseshock,leading
for none of the SNe considered, the reverse shock travelled to tolessdustprocessing.
the center of the ejecta. This implies that current observations
In addition, the mass of the progenitor stars and the explo-
cannotbeusedtoestimatethemassofdustthatwillbeinjected
intheinterstellarmedium,thesocalledeffectivedustyield. sion energy for some SNe are also difficult to reconstruct from
the available data. These do not impact the estimated mass of
freshly formed dust1 but may affect the destruction efficiencies
5.4. TheeffectiveSNdustyields bythereverseshock.Asanexample,assuminganincreaseinthe
The final time of the simulation is assumed to be t = 106yr explosion energy by a factor 2 for Cas A leads to 60% smaller
where the velocity of the forward shock is v (cid:46) 1en0dkm/s and dustmassattobs thanthevaluereportedinTable4.However,as
sh itisclearfromFigure4,thismodelwouldstillbeinagreement
dust grains are either destroyed or embedded in the ISM gas.
with the observed dust mass, given the large errorbars. Hence,
Table4illustratesthepredicteddustmassattheendofthesimu-
lation.WefindthattheeffectivedustmassesinjectedintheISM the uncertainties which affect the measured dust mass encom-
passtherangeofdustmassespredictedbythemodelfordiffer-
fromtheseSNewillbesignificantlysmallerthaninferredfrom
entinitialexplosionparameters.
present observations: ∼ 1% of the currently detected mass for
Giventheseuncertainties,themodelsdescribedinthispaper
SN1987A and CasA, ∼ 8% for N49 and less than 1% for the
appeartowellreproducethedustmassesinthefourSNethatwe
Crab nebula. The resulting dust yields depend on the progeni-
haveconsidered.Theaverageeffectivedustyieldisestimatedto
tormass,explosionenergyandtheageoftheSN,andlieinthe
range[4.21×10−4−4.02×10−2]M .GrainsintheCrabnebula be(1.55±1.48)×10−2M(cid:12).Thisisingoodagreementwiththe
sufferalargestdestruction.Infact,th(cid:12)eCrabnebulahasalowex- dust yield used in chemical evolution models based on BS07
dustyieldswithmoderatedestructionbythereverseshock.For
plosionenergyandprogenitormasscomparedtotheotherSNe.
aSalpeterinitialmassfunction(IMF),theaveragedustmassin-
Thisleadstotheformationofsmallerdustgrains(e.g.ACgrains
haveanaveragesizeofa =26nmwhileintheotherthreeSNe jectedbySNeintheISMis(2.50−2.73)×10−2M(cid:12)forSNpro-
0 genitorswithmetallicities0.1Z ≤Z ≤1Z andacircumstellar
a ∼90−100nm)andtoalowerdustmass.Forthesamereason, (cid:12) (cid:12)
si0licate grains are destroyed more efficiently. As a result, more mediumdensityof1cm−3(Valianteetal.2009,2011,2014;see
alsoFig.6inSchneideretal.2014).
than 60% of the dust mass that will be injected in the ISM is
In the Milky Way, the timescale between the explosion of
in the form of carbonaceous grains. These grains, being larger
twoSNehasbeenestimatedtobe∼40yr(Lietal.2011).Using
than grains of other species, have more inertia and, depending
themeaneffectivedustyieldthatwehaveobtainedleadstoaSN
on their initial position, can cross both the reverse and forward
dustproductionrateof(3.9±3.7)×10−4M yr−1.Thisvaluecan
shock,reachingtheunshockedISMandsurvivingtheexplosion. (cid:12)
becomparedtothedustproductionratebyAGBstars.Because
ofsourceconfusionintheGalacticplane,surveyshavetargeted
6. Discussionandastrophysicalimplications the Magellanic Clouds to make a global census of dusty AGB
stars, inferring dust production rates of ∼ 2 × 10−5M /yr for
(cid:12)
Thedustmassobtainedfromfittingobservationsisdetermined the Large Magellanic Cloud (LMC, Riebel et al. 2012) and of
underseveralassumptions,whichmakethemeasurementrather ∼8×10−7M /yrfortheSmallMagellanicCloud(SMC,Boyer
(cid:12)
uncertain. et al. 2012), with variations among the results of different sur-
veys (Matsuura et al. 2013), and in good agreement with theo-
1. Often, a single dust material and size is used to reproduce
reticalpredictions(Venturaetal.2012b,a,2014).Hence,evenin
the dust emission. However, dust in SNRs is rich in com-
theLMC,thecurrentdustproductionratebyAGBstarsappears
positionandeachmaterialhasawidesizedistribution.This
to be more than one order of magnitude smaller than that esti-
is reflected in the dust temperature distribution: for exam-
matedfromoursampleoffourSNe.Yet,therelativeimportance
plesmallgrainsareheatedtohighertemperaturescompared
of AGB stars and SNe as dust producers depends on the initial
to larger grains and their emission per unit mass will be
mass function and on the star formation history of each galaxy
higher. Mattsson et al. (2015) noted that depending on the
grain size/temperature distribution the measured dust mass (Valianteetal.2009).
Yet, the importance of stellar sources of dust is limited by
can vary up to six times the original value but that most of
grain destruction in SN-driven interstellar shocks. The dust de-
thecomplicationderivesfromtheassumedgrainmaterial.
struction timescale in the Milky Way has been estimated to
2. InmanycasesandespeciallyinyoungSNe,mostofthedust
be τ ∼ 108,109yr by Bocchio et al. (2014) and Slavin
massresidesintheunshockedejectaandisthereforelikelyto des,MW
et al. (2015), respectively. Rescaling these values by the ra-
becoldwithasimilartemperaturetothatofdustinthepar-
tio between the ISM mass in the Milky Way and in the LMC
ent cloud (radiative transfer calculations in SN1987A pre-
dict temperatures T = 15 − 20K; Wesson et al. 2015). (MISM,MW/MISM,LMC ≈ 100), the dust lifetime in the LMC can
dust be estimated as ∼ 106 − 107yr, in agreement with the recent
Theemissionfromthesetwosourcescomesfromthesame
observational study by Lakic´evic´ et al. (2015), which leads to
spatialregionandarethereforeentangledandfurthermulti-
wavelength observations are therefore needed for a correct 1 As an example, changing the explosion energy adopted for CasA
dustmassevaluation. from1.5×1051ergto3×1051erginducesonlya 5%differenceinthe
3. ForCasAandtheCrabNebula,recentobservationssuggest dust mass. Asimilar difference is foundif we increase theNi56 mass
that the unshocked ejecta have a clumpy density distribu- adoptedfortheCrabfrom0.014M to0.058M .
(cid:12) (cid:12)
10