Hydrodynamic modelling of ejecta shrapnel in the Vela supernova remnant

0.85 MB·English

by  M. Miceli

Mon.Not.R.Astron.Soc.000,??–??(2002) PrintedJanuary15,2013 (MNLATEXstylefilev2.2)
Hydrodynamic modelling of ejecta shrapnel in the Vela supernova
remnant
3
M. Miceli1,2⋆, S. Orlando2, F. Reale1,2, F. Bocchino2, G. Peres1,2
1
0 1DipartimentodiFisica,Universita`diPalermo,PiazzadelParlamento1,90134Palermo,Italy
2 2INAF-OsservatorioAstronomicodiPalermo,PiazzadelParlamento1,90134Palermo,Italy

n
a
J Accepted.Received;inoriginalform

4
1
ABSTRACT

] Many supernova remnants (SNRs) are characterized by a knotty ejecta structure. The Vela
E
SNR is an excellent example of remnant in which detached clumps of ejecta are visible as
H X-ray emitting bullets that have been observed and studied in great detail. We aim at mod-
. ellingthe evolutionofejecta shrapnelin theVela SNR, investigatingtherole oftheirinitial
h
parameters(positionanddensity)andaddressingtheeffectsofthermalconductionandradia-
p
tivelosses.Weperformedasetof2-Dhydrodynamicsimulationsdescribingtheevolutionof
-
o adensityinhomogeneityintheejectaprofile.We exploreddifferentinitialsetups.We found
r thatthefinalpositionoftheshrapnelisverysensitivetoitsinitialpositionwithintheejecta,
t
s while the dependence on the initial density contrast is weaker. Our model also shows that
a moderatelyoverdenseknotscan reproducethedetachedfeaturesobservedin theVela SNR.
[
Efficientthermal conductionproducesdetectable effects by determiningan efficient mixing

1 oftheejectaknotwiththesurroundingmediumandshapingacharacteristicelongatedmor-
v phologyintheclump.
5
8 Keywords: Hydrodynamics– Shockwaves– Methods:numerical– ISM:supernovarem-
0 nants–ISM:kinematicsanddynamics–ISM:individualobject:VelaSNR
3
.
1
0
3 1 INTRODUCTION abundance pattern hasbeen observed with Suzaku in Shrapnel B
1
(Yamaguchi&Katsuda2009),butinthiscasetheoverabundances
: The ejecta in supernova remnants (SNRs) drive the exchange of
v ofthelighterelementsarelessprominent,suggestingmore effec-
mass and the chemical evolution of the galactic medium. The
i tivemixingwiththeinterstellarmedium(ISM).AChandraobser-
X structureofSNRejectahasbeenprovedtobeknotty,andseveral
vationofShrapnelA,whoseprojecteddistancefromthecenterof
r clumpshavebeenobservedatdifferentwavelegthsinremnantsof theremnant islargerby ∼ 20% than Shrapnel D, reveals instead
a core-collapse supernovae, as G292.0+1.8 (Parketal. 2004), Pup-
oversolarSi:Oratios(Miyataetal.2001).SignificantSioverabun-
pis A (Katsudaetal. 2008), and Cas A, where knots have been
dance(Si∼ 3)hasbeenconfirmedbyKatsuda&Tsunemi(2006),
observed also beyond the main shock front (Fesenetal. 2006,
whoanalyzed anXMM-Newtonobservation, findingsolarorsub-
Hammell&Fesen2008,DeLaneyetal.2010).
solarvaluesfortheO,Ne,Mg,andFeabundances. Theseresults
TheVelaSNR,beingthenearestSNR,representsaprivileged
show differences in the chemical composition between Shrapnel
target for this kind of studies, since it is possible to observe fine
A and Shrapnel B and D. In the northern rim of the Vela shell,
structures down to small physical scales. Despite the bulk of the
Micelietal.(2008)discoverednewX-rayemittingclumpsofejecta
X-rayemissionoftheVelaSNRisassociatedwiththepost-shock
whoseprojectedpositionisbehindthemainshockfront.The rel-
interstellarmedium,X-rayemittingejectahavealsobeenobserved.
ativeabundances(O:Ne:Mg:Fe)ofthesenewshrapnelareingood
Inparticular,sixprotrudingfeatures,withcharacteristicboomerang
agreementwiththoseobservedinShrapnelD.Similarabundance
morphology, (labelled Shrapnel A-F) have been identified in the
pattern have been observed also by LaMassaetal. (2008), who
VelaSNRbyAschenbachetal.(1995),whoarguedanejectaori-
foundejecta-richplasmainthedirectionoftheVelaXpulsarwind-
ginforthesestructureswhichappeartobedetachedfromtherem-
nebula.
nant.Theassociationwithejectafragmentshasbeensupportedby
morerecentobservationsperformedwithChandra,XMM-Newton, The present day morphology of SNRs and the structure of
and Suzaku. The analysis of the XMM-Newton observation of ejectaarebelievedtoreflectthephysicalcharacteristics oftheSN
ShrapnelD,hasrevealedthatO,Ne,andMgabundancesaresig- explosion (e. g., intrinsic asymmetries of the explosion, interac-
nificantly larger than solar (Katsuda&Tsunemi 2005). A similar tionoftheearlyblastwiththeinhomogeneitiesofthecircumstellar
medium,physicalprocessesintheaftermathoftheexplosion,etc.)
andtheirdetailedstudypromisestocontributetoourunderstanding
⋆ E-mail:[email protected]) oftheSNexplosionphysics.Inthelightoftheseconsiderations,it
2 M. Miceliet al.
istheninterestingtomodeltheevolutionoftheejectaknotstoun- 2 HYDRODYNAMICMODELING
derstand how the current position and chemical properties of the
2.1 Initialconditionsandmodelequations
shrapnelintheVelaSNRdependonthephysicalconditionsatthe
supernovaexplosionandonthedynamicsoftheexplosionitself. Wemodel the evolution of a shrapnel in a SNR by performing a
set of 2-D simulations in a cylindrical coordinate system (r, z),
Theevolutionofdense,supersonicclumpsofSNejectarun-
assuming axial symmetry. The system setup consists of a spher-
ning in a uniform medium has been studied by Andersonetal.
ically symmetric distribution of ejecta with initial kinetic energy
(1994)andJonesetal.(1994),whoidentifiedthreemainstagesof
K=1051erg(theinitialthermalenergyisonlythe0.2%ofK)and
evolution:abow-shockphase,aninstabilityphaseandadispersal
massM =12M⊙(representingtheinitialblastwave),wherewe
phase. However, these models do not describe in detail the inter- ej
placeadense,spherical,knot(theshrapnel)inpressureequilibrium
action of the clump with the remnant (post-shock medium, main
withthesurroundingejectaandwithcentralcoordinates(0, R ).
shock,reverseshock)anddonotincludeimportantphysicaleffects s
Theradialdensityprofileoftheejectaconsistsoftwopower-
(asthermalconductionandradiativecooling).Cid-Fernandesetal. lawsegments(ρ ∝ r−m ontheinsideandρ ∝ r−b ontheoutside),
(1996) includedradiativelossesintheir2-D models, buttheyfo-
inagreement withthedensitystructureinacore-collapseSNde-
cussed on the interaction of a knot with a very small supernova
scribed by Chevalier (2005). For our simulations, we use m = 1
remnant (∼ 1017 cm, i. e. more than 100 times smaller than the
andb=11.2,andthepositionofthetransitionbetweentheflatand
Vela SNR) evolving in an extremely dense medium (107 cm−3).
steepregimesisderivedbyfollowingChevalier(2005).Theinitial
Ahydrodynamicmodel(withoutthermalconductionandradiative
velocityoftheejectaincreaseslinearly(upto6×108 cm/s)with
cooling) specifically tuned for the Vela SNR has been developed
their distance from the center. The maximum velocity is reached
byWang&Chevalier(2002)(hereafterWC02)whofollowedthe attheinitialradiusoftheejecta,i.e.,R0 = 4.5×1018 cm.These
evolutionofashrapnelbyusing2-Dsimulationsinsphericalcoor- ej
valuescorrespondto∼ 240yraftertheexplosion,appropriatefor
dinates(becauseofthegeometryoftheirsimulations,theshrapnel
therelativelylatestages of theSNRevolution thatweaddress in
aremodeledastoroidalstructureswithverylargemasses). WC02
thisstudy.Infact,thestartingtimeofoursimulationscorresponds
didnotmodeltheearlyevolutionoftheejectaknot,butstartedtheir
to only ∼ 2% of the Vela SNR age and the shrapnel reaches the
simulations at the time t , corresponding to the first interaction
rev reverseshock∼2500−3000yraftertheexplosioninalloursimu-
oftheshrapnelwiththereverseshockfront.Theyexploreddiffer-
lations(i.e.,thesystemhasenoughtimetoevolve,beforetheinter-
entvaluesoft andofthedensitycontrastbetweentheshrapnel
rev actionoftheshrapnelwiththeSNRreverseshockoccurs).Wethen
andthesurroundingejecta,χ,andfoundthat,inordertoproduce
concludethatoursimulationscanprovidearealisticdescriptionof
anobservableprotrusionontheshockfront(likethatobservedin
theactualconditionsintheVelaSNR.
Shrapnel A-F), a very high density contrast (χ ∼ 1000) is nec-
Theinitialmassof theshrapnel is0.05 M (1.19×1033 g),
essary. With lower density contrasts (χ < 100), the shrapnel are ej
itsdensity isχtimeslargerthan that of thesurrounding ejectaat
rapidlydeceleratedandfragmentedbyhydrodynamic instabilities
distanceR fromthecenter1,anditsvelocityisthesameasthatof
andtheobservedfeaturescannotbereproduced(fortheeffectsof s
theejectaatdistance R fromthecenter. Weaimatshowing that
hydrodynamicinstabilitiesonshockedcloudsseealsoKleinetal. s
thedetachedshrapnelobservedintheVelaSNRcanbetheresult
1994 and Orlandoetal. 2005). Large density inhomogeneities in
ofmoderatelyoverdenseclumpsofejectaoriginatinginrelatively
theclumpsaredifficulttoexplaininacore-collapseSNexplosion.
internallayers.WeexploreddifferentvaluesofχandofR ,namely
WC02 argued that a model that includes the effects of radiative s
χ = 10, 20, 50, and R = 1/6 R0, 1/3 R0. Figure1 shows the
coolingmayshowthatlowervaluesofχareneededtomatchthe s ej ej
initialdensityandtemperatureconditionsforthecasewithχ=20
observed protrusions. Also, WC02 do not include in their model
andR =1/3R0.Thesimulationsetupsdiscussedinthispaperare
theeffectsofthermalconduction that,asshownbyOrlandoetal. s ej
summarizedinTable1.
(2005),canefficientlysuppressthehydrodynamicinstabilities,thus
VelaSNR isthe result of a core-collapse SNand weexpect
allowingtheshrapneltoovercomethemainshock-frontwithoutbe-
the ambient medium to be “perturbed” by the wind residuals of
ingdisrupted.Recently,theevolutionofknottyejectainaTypeIa
themassiveprogenitor star.However, weassumeforsimplicitya
SNRhasbeenmodelledbyOrlandoetal.(2012)(hereafterO12),
uniform ambient medium as in WC02, since here we are not in-
whofoundthatsmallclumpswithinitialχ<5canreachtheSNR
terestedinmodelingthedetailsoftheremnantevolution.Thefinal
shock front after ∼ 1000 yr. Nevertheless, these ejecta knots are
(i.e. after11000 yr, theageof the VelaSNR,Tayloretal. 1993)
then rapidlyeroded and do not produce significant protrusions in
radiusoftheremnantstronglydependsonthechoiceoftheambi-
theSNRshock front,thusbeingunable toreproduce thefeatures entdensityvalue,n .Wesetn =0.5cm−3,becausewiththis
observedintheVelaSNR. ISM ISM
value(andwiththechosenvaluesof K, M ,n ,b,andm),the
ej ISM
radiusoftheshellafter11000yrisR ∼5.4×1019cm,ingood
Here we present a set of 2-D hydrodynamic simulations of shell
agreement withthe observed radius of theVelaSNR,that ranges
theevolutionofan(initiallyspherical)ejectashrapnelintheVela
between5×1019cmand5.5×1019cm(byassumingadistanceof
SNR. We include in our model both thermal conduction and ra-
diativecoolingandexploredifferentvaluesofχandoftheinitial 250pc,inagreementwithBocchinoetal.1999,Chaetal.1999).
Ourmodelsolvesthetime-dependentcompressiblefluidequa-
positionoftheshrapnelintheejectaprofile.Weaimataddressing
tionsofmass,momentum,andenergyconservation.Inthreecases
theroleofthermalconductionandradiativecoolingandatunder-
weranthesame simulation with/without thermal conduction and
standinghowtheinitialpropertiesoftheshrapnelinfluenceitsevo-
radiative cooling inside our system, as shown in Table 1. As for
lution. Wealso aimat evaluating whether values of χlower than
100(χ=10−50)canreproducetheobservedfeatures. thermal conduction, weconsidered both theSpitzerand thesatu-
rated regimes, while radiative losses (that can play an important
The paper is organized as follows: the hydrodynamic model
isdescribedinSect.2,theresultsofthesimulationsareshownin
Sect.3,andourconclusionsarediscussedinSect.4. 1 Thesizeoftheclumpvariesaccordingly.
Modelingof theVela shrapnel 3
Table1.Physicalparametersofthemodelsetups(seeSect.2).TC-RLin-
dicates thatthesimulations wereperfomedbyincluding thermalconduc-
tionandradiativelosses.Inallthesetupstheinitialradiusoftheejectais
R0 =4.5×1018cm.
ej
Modelsetup χ Rs(cm) TC-RL
R1/3−CHI10 10 1.5×1018 No
R1/3−CHI10−TR 10 1.5×1018 Yes
R1/3−CHI20 20 1.5×1018 No
R1/3−CHI20−TR 20 1.5×1018 Yes
R1/3−CHI50 50 1.5×1018 No
R1/6−CHI50 50 0.75×1018 No
R1/6−CHI50−TR 50 0.75×1018 Yes
Figure 1. Density (left panel) and temperature (right panel) 2-D cross-
sectionsthroughthe(r, z)planeshowinganexampleoftheinitialcondi-
tionsofoursimulations(namely,R1/3−CHI20,seeTable1).Thesystem
consistsofanexpandingsphericallysymmetricdistributionofejectawhere
weplaceadense,isobaric,andsphericalknot.Inthiscasetheknotis20
timesdenserthanthesurroundingejecta.
roleintheVelaSNR,asshownbyMicelietal.2006)werecom-
putedforanopticallythinthermalplasma.Themodelequationsare
describedinMicelietal.(2006)(equations 1-5therein)andwere
solvedbyusingtheFLASHcode(Fryxelletal.2000).
Thecomputationaldomainextendsover8×1019 cminther
andzdirections.Weuseaxisymmetricboundaryconditionsatr=0,
reflectionboundaryconditionsatz=0,andzero-gradient(outflow)
boundaryconditions(forv,ρ,and p)elsewhere.Wetracethemo-
tionoftheejectamaterialandoftheshrapnelwithpassivetracers2.
Considering the large range in spatial scales of our simulations,
we exploited the adaptive mesh capabilities of the FLASH code
byadoptingupto10nestedlevelsofresolution(theresolutionin-
creasesbyafactorof2ateachlevel).Therefinement/derefinement
criterion(Lohner1987)followsthegradientsofdensity,tempera-
ture,andtracers.Thefinestspatialresolutionis1.95×1016 cmat
thebeginningofthesimulation,thereforethereare230computa- Figure 2. Left panel: density (left) and temperature (right) 2-D cross-
tionalcellsperinitialradiusoftheejecta,and∼10cellsperinitial sections through the (r, z) plane showing simulation R1/3−CHI20 at
radiusoftheshrapnel(thatvariesintherange1.8−2.9×1017cm). t=5000yr.Theblack/bluecontoursenclosethecomputationalcellscon-
Becauseoftheexpansionofthesystem,theresolutionisreduced sistingoftheoriginalejecta/shrapnelmaterialbymorethan90%.Thecolor
byafactorof2after2500yr.Weverifiedthatbychangingtheres- barindicatesthelogaritmicdensityscaleandthelineartemperaturescale.
olutionofoursimulationsbyafactorof2,theresultsdonotchange Rightpanel:sameasleftpanel,fort=11000yr.
significantly(seeAppendixAforfurtherdetails).
Rayleigh-Taylor and Richtmyer-Meshkov instabilities are visible
asfinger-likestructuresbothinthedensityandtemperaturemaps.
Atthisstage,theknotispartiallyerodedbythehydrodynamicin-
3 RESULTS
stabilitiesandevolvestowardacore-plumestructure.The coreof
3.1 Evolutionofthesystem the knot, however, is still significantly overdense with respect to
the surrounding shocked ejecta. The right panel of Fig. 2 shows
WefirstfocusonsimulationR1/3−CHI20.Figure2showsthe2-D
theshrapnelatt=11000yr,withitscharacteristicsupersonicbow
cross-sectionsthroughthe(r, z)planeoftemperatureanddensityat
shockprotrudingbeyondtheSNRmainshock.
differentevolutionarystagesoftheR1/3−CHI20simulation.The WC02foundthatejectaknotswithdensitycontrastχ 6 100
leftpanelshowsthesystem5000yrafterthebeginningofthesim-
arerapidlyfragmentedanddeceleratedintheintershockregionand
ulation3, when the shrapnel interacts with the inter-shock region.
donot even reachthemainshock front(theseeffectsbeing more
dramaticforsmallclumps).Nevertheless,wenoticethatthevalue
of χ in WC02 refers to the onset of the interaction between the
2 Bothtracershavezeromassanddonotmodifythedynamicsofthesys-
knot and the reverse shock and that χ is not constant during the
tem.
3 Inthefollowing,alltheageswillbereckonedfromthebeginningofour evolution of the system. In the “free” expansion phase, the den-
simulations.Weremindthereaderthatourinitialconditioncorrespondsto sityof theshrapnel doesnot drop downuniformly(asthatof the
∼240yraftertheSNexplosion. other ejecta does) and the shrapnel undergoes both diffusion and
4 M. Miceliet al.
ter.Figure4showstheevolutionofχasafunctionoftimeforthe
R1/3−CHI20 simulation. The figure shows that the ejecta knot
reachesχ > 100asitapproachesthereverseshock,henceourre-
sultsareinagreementwiththoseofWC02.Ourmodelshowsthat
aknot that was only 20 timesdenser than the surrounding ejecta
(atthebeginnigofthesimulations)canreachtheSNRmainshock
withoutbeingfragmentedintheintershockregionandcanproduce
protrusionsthataresimilartothoseactuallyobserved intheVela
SNR.
3.2 Effectsofthermalconductionandradiativecooling
Figure5showsthe2-D cross-sectionsthroughthe(r, z)planeof
temperatureand densityat t = 5000 yrand t = 11000 yrforthe
R1/3−CHI20−TRsimulation(sameparametersasR1/3−CHI20,
butincludingradiativecoolingandthermalconduction).Thediffu-
sivethermal conduction completelysuppresses theformationand
the development of hydrodynamic instabilities and smoothes the
temperatureanddensityprofiles.Thisresultisinagreement with
Figure 3. Density 2-D cross-sections through the (r, z)plane formodel
R1/3−CHI20att = 2500yr.Thecolorscaleincreaseslinearlybetween expectations,asshownbelow.Thecharacteristicamplitudegrowth
10−22g/cm3and2×10−22g/cm3.Thecontoursenclosethecomputational rate, da/dt of a single-mode perturbation of Richtmyer-Meshkov
cellsconsistingoftheoriginalshrapnelmaterialbymorethan99%(bold instabilitiescanbecalculatedas(seeRichtmyer1960)
line)and50%(narrowline).
da
=k∆vaA (1)
dt
wherekistheperturbationwavenumber,∆visthevelocityjumpat
theinstabilityandA = (ρ −ρ )/(ρ +ρ )istheAtwoodnumber.
1 2 1 2
Thecharacteristictime-scale, τ = a/(da/dt), forthegrowthof
inst
theperturbationistherefore
l
τ ≈ [s] (2)
inst
2π∆vA
where l is the structure size. As for the thermal conduction (see
Spitzer1962),
dE 2 T
=∇·[κ(T)∇T]∼ κ(T) (3)
dt ! 7 l2
cond
whereκ(T) = 5.6×10−7T5/2 ergs−1 K−1 cm−1 istheSpitzer’sco-
efficientandlisthecharacteristiclengthoftemperaturevariation.
therefore,thethermalconductiontime-scaleis:
7nk l2 nl2
Figure 4. Temporal evolution of the shrapnel/ejecta density contrast for τ = ∼2.6×10−9 [s] (4)
cond 2(γ−1)κ(T) T5/2
modelR1/3−CHI20.Thebluehorizonthallinemarksthebeginningofthe
interactionbetweentheshrapnelandtheSNRreverseshock Foracharacteristicstructurewithsizel∼4×1018 cm,parti-
cledensityn=0.8cm−3,AtwoodnumberA∼0.44,∆v∼2×107
cm/s, T ∼ 1.3×107 K (similarto that shown in Fig. 2),τ ∼
expansion.Figure3presentsaclose-upviewoftheshrapnel den- inst
1.4τ ∼ 2000 yr. Therefore, the thermal conduction diffusive
sity structure at t = 2500 yr, showing that, while the outer parts cond
processes develop faster than the hydrodynamic instabilities and
of the knot diffuse and mix withthe expanding ejecta, itscentral
densityandtemperatureinhomogenietiesaresmoothedoutbefore
core remains much denser. The density of the core of the clump
theycangrow.
dropsdownmuchmoreslowlythanthatofthesphericallyexpand-
Theevolutionofthepositionoftheshrapnelheadandthepro-
ing ejecta. Therefore, the inhomogeneous rarefaction of the knot
trusionitproducestotheremnantshockfrontaresimilarto those
makesthedensitycontrastbetweenthecoreoftheshrapnelandthe
obtainedwithoutincludingthermalconductionandradiativecool-
expandingejectahigher,andχrapidlyincreasesuntiltheshrapnel
ing. Nevertheless, the shrapnel evolution is remarkably different
reaches the reverse shock. We computed χ during the expansion
from that obtained in the pure HD simulations. In particular, as
phases, by calculating the shrapnel density, ρ , as the average of
s shownbythebluecontoursinFig.5,theejectaknotiselongated
thedensityinallthecomputational cellswheretheshrapnel con-
alongitsdirectionofmotionandrapidlyassumesacometaryshape,
tentis>90%4.Wethendividedρ bytheejectadensity(alongthe
s characterizedbyaprominenttailwhichisrichinshrapnelmaterial.
r axis) at the same distance from the origin as the shrapnel cen-
Aftert = 11000 yr,shrapnel materialispresent at ∼ 10pcaway
from the shrapnel head. Moreover, the shrapnel material is effi-
4 Thesecellsareclosertothecenteroftheknot,andarelessaffectedby cientlyheatedbythermalconductionwiththesurroundingshocked
thediffusion. ejecta.Let MXshra bethemassoftheplasmainthecomputational
Modelingof theVela shrapnel 5
R1/3-CHI20-TR R1/3-CHI20
Figure6.Temporalevolutionof MXshra (massoftheplasmainthecom-
putational cells consistingoftheoriginal shrapnel materialbymorethan
90% and having a temperature higher than 106 K) for the simulations
R1/3−CHI20−TR(bluecurves)andR1/3−CHI20(blackcurves).The
dashed lines indicate the part of MXshra that protrudes beyond the SNR
shockfront.
Figure5.SameasFig.2formodelR1/3−CHI20−TR. ulationsincludingthermalconductioninanunmagnetizedplasma
andpureHDsimulationsarelimitingcasesthatencompassthere-
sults obtained with different configurations of the magnetic field
cellsconsistingoftheoriginalshrapnelmaterialbymorethan90%
(Orlandoetal. 2008). We can then conclude that our simulations
and having atemperature higher than 106 K (and therefore emit-
providethetwoextremecasesthatbracketallthepossibleinterme-
ting thermal X-rays). Figure 6 shows the evolution of MX as
shra diatescenarios.
a function of time for the simulations R1/3−CHI20−TR and
R1/3−CHI20. When thermal conduction is at work, ∼ 90% of
theoriginalshrapnelmassisheateduptoX-rayemittingtemper- 3.3 Effectsoftheinitialconditions
ature at t = 11000 yr (i. e., at the age of the Vela SNR), while
Westudytheeffectsoftheinitialconditionsontheshrapnelevolu-
ifthermal conduction ininhibited,only50%of theoriginal mass
tionwithdifferentsimulations,asshowninTable1.Inparticular,
hastemperaturehigherthan106K.Figure6alsoshowstheamount
we explored two different initial positions of the shrapnel in the
ofX-raymassbeyondtheshockfront.InthepureHDsimulation
ejectaprofile (R = 1/6 R0, 1/3 R0) and three different density
thehotshrapnelmaterialisallbeyondtheSNRshockfront.Inthe s ej ej
R1/3−CHI20−TR simulation, only part of the X-ray emitting contrasts(χ=10, 20, 50).
Inagreement withWC02,wefound that shrapnel formedin
shrapnel isbeyond theshock frontand thereisasignificantfrac-
theinnerejectalayers(i.e.,thosethatreachthereverseshocklater)
tionoftheejectaknotmaterial(theshrapneltail)thatisinsidethe
producesmallerprotrusions.Inparticular,anejectaknot originat-
SNRshellandthatisexpectedtoemitthermalX-rays(seeSect.4).
ing at R = 1/6 R0, does not even reach the SNR shock in the
s ej
time spanned by our simulations. Therefore, our model indicates
Wepoint outthatinSNRstheefficiencyofthermal conduc-
thatshrapnelA-F(allprotrudingwellbeyondtheVelamainshock)
tioncanbesignificantlyreduced bythepresence ofthemagnetic
originatedinmoreexternal layers.LeftpanelofFig.7showsthe
field (which is not taken into account in our model). If we as-
2-Dcross-sectionsthroughthe(r, z)planeoftemperatureandden-
sume an organized ambient magnetic field, the thermal conduc-
sityattheageoftheVelaSNRfortheR1/6−CHI50simulation.In
tionisanisotropic,becausetheconductivecoefficientinthedirec-
thiscase,theknotiswellwithintheintershockregion,eventhough
tionperpendiculartothefieldlinesisseveralordersofmagnitude
its initial density contrast (χ = 50), was higher than that of the
lowerthanthatparalleltothefieldlines,whichcoincideswiththe
R1/3−CHI20 run. However, our models of knots originating at
Spitzer’scoefficientκ(T).Theeffectsofthemagnetic-field-oriented
R = 1/3 R0 clearly show that denser shrapnel produce deeper
thermal conduction in the interaction between shocks and dense s ej
protrusionsandaremorestableagainstthefragmentationandthe
clump have been investigated in detail in Orlandoetal. (2008).
decelerationinducedbythehydrodynamicinstabilitiesintheinter-
Because of the high beta of the plasma, the magnetic field lines
shock region (as in WC02)5. Fig. 7, right panel, shows the 2-D
areexpectedtoenvelopethehydrodynamicfingersthushampering
cross-sectionsthroughthe(r, z)planeoftemperatureanddensity
thethermalconductionwiththesurroundingmaterial.Atthesame
attheageoftheVelaSNRfortheR1/3−CHI50simulation.Asex-
time,themagneticfieldisexpectedtobetrappedatthetopofthe
pected,theshrapnelheadismuchfurtherawayfromtheSNRshell
ejectaclumps,andthisyieldstoanincreaseofthemagneticpres-
sureandfieldtensionwhichlimitsthegrowthofhydrodynamicin-
stabilities(seeO12andSanoetal.2012).Thebasicphysicsofthe 5 Inourruns,highervaluesofχcorrespondtosmallervaluesoftheshrap-
interactionbetween theejectaknots andtheSNRshocksissimi- nelcross-section(giventhattheshrapnelmassisfixedto1.19×1033gin
lartothat fortheinteractionof planarshocks withaninterstellar alloursimulations),andthisconcursinmakingtheknotamorepenetrating
cloud(e.g.WC02)andithasbeenshownthat,inthiscase, sim- bullet.
6 M. Miceliet al.
Figure9.Positionoftheshrapnelhead(inunitsoftheshellradiusRshell)as
afunctionoftimeforallthesimulationslistedinTable1.Blackcurvesindi-
catepurehydrodynamicmodels,whilebluecurvesindicatesimulationsin-
cludingthermalconductionandradiativecooling.Dashed/solid/thicklines
indicateχ=10/30/50,respectively.Thereddiamondsshowtheprojected
positionsofShrapnelA-D(Aschenbachetal.1995)andoftheejectaknots
FilEandRegNE(Micelietal.2008).
(Micelietal.2008)withrespecttothepositionoftheshockfrontin
Figure 7. Left panel: density (left) and temperature (right) 2-D cross- theVelaSNR.Thesevalueswerecalculatedbyapproximatingthe
sections through the (r, z) plane showing simulation R1/6−CHI50 at Vela SNR as a circular shell with angular radius 211′ and center
t=11000yr.Theblack/bluecontoursenclosethecomputationalcellscon- withcoordinatesα =8h36m19.8s, δ =−45◦24′45′′.Mod-
sistingoftheoriginalejecta/shrapnelmaterialbymorethan90%.Thecolor J2000 J2000
elsincludingtheeffectsofradiativecoolingandthermalconduction
barindicatesthelogaritmicdensityscaleandthelineartemperaturescale.
Rightpanel:sameasleftpanel,forsimulationR1/3−CHI50. (bluecurvesinFig.9)donot providesignificant differenceswith
respecttopureHDmodels(blackcurves)intermsoftheshrapnel
position.
ByconsideringallthesimulationswithR =1/3R0,wefind
s ej
thatthepositionoftheheadoftheknot,R ,after∼11000yrranges
h
between ∼ 1.1 R (for χ = 10) and ∼ 1.4 R (for χ = 50).
shell shell
ThesevaluesaresimilartothoseobservedforShrapnelB,C, and
D.
ShrapnelA,E,andF(ShrapnelE,FarenotshowninFig.9)
instead,haveR =1.57R ,R =1.88R ,andR =1.91R ,
h shell h shell h shell
respectively. Thesevalues aremuchlargerthanthoseobtained in
our simulations. Our results clearly suggest that these large dis-
tancesfromtheshellcanbeproducedbyejectaknotsoriginating
inouterejectalayers.Analternativepossibilityisthattheoriginal
densitycontrastfortheseshrapnelwas > 50.Nevertheless,Fig.9
showsthatthefinalpositionofanejectaclumpismoresensitiveto
itsinitialpositionanddependsonlyweaklyonχ.Infact,byvary-
ingtheinitialpositionoftheknotbyafactoroftwo,wefoundthat
itsfinalpositionvariesapproximatelybythesamefactor,whilea
Figure8.SameasFig.4formodelR1/3−CHI50. variationoftheinitialdensitycontrastbyafactoroffive,onlyde-
terminesa30%variationinthefinalposition.Thereforeitismore
likelythatShrapnelA,E,andFwereproducedatR >1/3R0.
s ej
thanintheR1/3−CHI20case(shownintherightpanelofFig.2). ThetwosimulationswithR = 1/6R0 show that theejecta
s ej
WecomputedthetimeevoulutionofχfortheR1/3−CHI50run knotsoriginatingintheinnerejectalayersdonotreachtheforward
byfollowingtheproceduredescribedinSect.3.1.Wefoundthat, shock,evenforthehighestdensitycontrast(χ=50).Theposition
inthiscase,theejectaknotreachesthereverseshockwitha very of the head of the knot predicted by our simulations is in agree-
highdensitycontrast(χ>1000,seeFig.8),thusproducingavery mentwiththatobservedforFilE(Micelietal.2008).X-rayemit-
prominentprotrusionintheSNR. tingejectaknotshavebeenobserved,inprojection,insidetheVela
Figure 9 shows the position of the shrapnel head (in units SNRshell(e.g.,RegNEandFilE,Micelietal.2008).However,we
of the shell radius) as a function of time for all our simula- pointoutthattheactualpositionofthese“internal”shrapnelcanbe
tions.Figure9alsoshowstheprojectedpositionsofShrapnelA-D welloutsidetheSNRshell,andthereforethevaluesreportedinFig.
(Aschenbachetal.1995)andoftheejectaknotsFilEandRegNE 9mightbeconsideredaslowerlimits.
Modelingof theVela shrapnel 7
4 DISCUSSIONSANDCONCLUSIONS
The structure of the ejecta in a SNR contains the imprint of the
metal-richlayersinsidetheprogenitorstar,andmayhelptounder-
standtheprocessesoccurringinthelateststageofstellarevolution.
Weperformedasetofhydrodynamicsimulationstostudytheevo-
lutionoftheejectaknotsintheVelaSNR.
We found that moderately overdense clumps (initial density
contrast χ ∼ 10) can produce protrusions inthe SNR shell simi-
lartothoseobservedfortheVelashrapnel.WC02foundthatonly
clumpsthatreachthereverseshockwithdensitycontrast χ>100
canreachthemainshockfrontandproducesignificantprotrusions.
This criterium is fulfilled in all our simulations. In fact, the (ini-
tially) moderately overdense clump experiences diffusion in the
“free” expansion phase, and, while its outer parts mix with the
surroundingejecta,itscentralcoreremainsmuchdenser.Thisin-
homogeneous rarefaction makes the density contrast between the
coreoftheshrapnelandtheexpandingejectahigherastheremnant
evolves,andχreachesvalues∼100−1000attheinteractionwith
thereverseshock.
Inparticular,aknotwithinitialχ=20andR =1/3R0 (sim-
s ej
ulationsR1/3−CHI20andR1/3−CHI20−TR)canexplainthe
observedfeaturesassociatedwiththeVelaShrapnelD.Figure10
shows the the ROSAT All-Sky Survey image of the Vela Shrap-
nelDinthe0.1−2.4keVenergyband,comparedwithasynthesis
oftheX-rayemissioninthe0.1−2.4keVbandderivedfromthe
R1/3−CHI20−TRsimulationat11000yr.ThesynthesizedX-ray
maphasbeenobtainedasinMicelietal.(2006):weproducedthe
3Dmapoftheemissionmeasureandtemperatureinthecartesian
space(x′, y′, z′),wherethey′axiscorrespondstothedirectionof
the line of sight and is perpendicular to the (r, z) plane. We de-
rived the distribution EM(x′, z′) vs. T(x′, z′) by considering all
thecontrbutionsalongthelineofsight,foreach(x′, z′).Wethen
synthesizedthemapoftheX-rayemissionusingtheMEKALspec-
tralcode(Meweetal.1985,Meweetal.1986,Liedahletal.1995),
assumingadistanceof250pc,andaninterstellarcolumndensity
N =2×1020cm−2.Finally,wedegradedthespatialresolutionof
H
thesynthesizedX-raymaptomatchtheresolutionoftheROSAT
imageandrandomizedthemapbyassumingPoissonstatisticsfor
thecountsineachimagebin.
Figure10showsthatthebrightX-rayspotattheapexofthe
shrapnelbow-shockandtheenhancedX-rayluminosityatthebase
oftheprotrusioncanbeexplainedbyourmodelaslocalenhance-
ments of the plasma emission measure. The overall shape of the
observedfeaturesisalsoreproductedbyourmodel.Moreover,the
massoftheX-rayemittingshrapnel predicted byourmodel is in
agreementwiththatmeasuredforShrapnelD.Infact,ithasbeen
estimatedthattheX-rayemittingmass(consideringonlythebulge
abovetheVelaSNRbowshock)is∼ 0.1M⊙ (Katsuda&Tsunemi
2005) i. e., the same order of magnitude as that obtained in our
simulation(seedashedcurvesinFig.6).VelaShrapnelDisthere-
fore consistent with being originated by an ejecta knot 20 times
denserthanthesurroundingejectaandinitiallylocatedat1/3R0.
ej
As shown in Fig. 9, we found a degeneracy in the space of the
initialparameters, andsimilarresultscanbeobtainedalsobyen- Figure10.Upperpanel:RosatAll-SkySurveyimageofVelaShrapnelDin
the0.1−2.4keVenergyband.Thebin-sizeis1.5′andtheimagehasbeen
hancing/decreasing thedensitycontrastanddecreasing/increasing
smoothedthroughaconvolutionwithaGaussianwithσ=3pixels.North
theinitialdistanceoftheknottotheexplosioncenter.However,as
isupandEastistotheleft.Lowerpanel:SynthesizedX-rayemissioninthe
explainedinSection3.3,thefinalpositionoftheshrapnelismuch
0.1−2.4keVbandforthesimulationR1/3−CHI20−TRatt=11000yr
moresentitivetoitsinitialpositionintheejectaprofile.Inconclu-
(seeSect.4).
sion, according toour model, theoriginal position ofShrapnel D
shouldnotdiffermuchfrom1/3R0.
ej
AsshowninSect.3.3,ourmodelsuggeststhatShrapnelB,C,
8 M. Miceliet al.
andDwerealloriginatedat∼1/3R0.Thisconclusionisinagree- portant role and explains the efficient mixing of the ejecta knots
ej
mentwiththeresultsofX-raydataanalysisthatshowthatShrap- observedinX-rays.
nelBandDhavesimilarabundancepatterns(Katsuda&Tsunemi
2005, Yamaguchi&Katsuda 2009).Thefragment RegNE,which
appearsinsidetheVelashell,hassimilarabundancesasShrapnelD
(Micelietal.2008)anditspositioniscompatiblewithanoriginin ACKNOWLEDGMENTS
thesamelayerwhereShrapnelB,C,andDweregenerated6.
Wethanktheanonymousrefereefortheirconstructivesuggestions
In Sect. 3.3, we also pointed out that it is highly unlikely
toimprovethepaper. Thesoftwareused inthiswork wasinpart
that Shrapnel A originated in the same ejecta layer as Shrap-
developed by the DOE-supported ASC / Alliance Center for As-
nel D. Indeed, the abundance patterns observed in Shrapnel A
trophysical Thermonuclear Flashes at the University of Chicago.
areremarkably different fromthat observed inShrapnel B and D
The simulations discussed in this paper have been performed on
(Katsuda&Tsunemi2006),thussuggestingadifferentlocationof
theHPCfacilityatCINECA,Italy,andontheGRIDinfrastructure
thisknotintheejectaprofile.Nevertheless,theSi:Oratioismuch
oftheCOMETAConsortium,Italy.
higher in Shrapnel A than in Shrapnel D and this indicates that
ShrapnelAcomesfromaregionoftheprogenitorstarbelowthat
of the Shrapnel D (e. g. Tsunemi&Katsuda 2006), at odds with
ourpredictions.Asexplainedabove,anunrealisticallyhighinitial
References
χisrequiredforaninnershrapneltoovercomeouterknots,if we
assume that the initial velocity profileof the ejectaincreases lin- AndersonM.C.,JonesT.W.,RudnickL.,TregillisI.L.,KangH.,
early with their distance from the center. A possible solution for 1994,ApJ,421,L31
this puzzling result is that the Si burning layer (or part of it) has AschenbachB.,EggerR.,TrumperJ.,1995,Nature,373,587
beenejectedwithahigherinitialvelocity,e.g.,asacollimatedjet. BocchinoF.,MaggioA.,SciortinoS.,1999,A&A,342,839
Itisnoteworthytoremarkthatinothercore-collapseSNRstheSi- ChaA.N.,SembachK.R.,DanksA.C.,1999,ApJ,515,L25
richejectamayshow averypeculiarjet-counterjet structure.The ChevalierR.A.,2005,ApJ,619,839
wellknowncaseofCasAhasbeenstudiedindetailthankstoavery Cid-Fernandes R., Plewa T., Ro´zyczka M., Franco J., Terlevich
longChandraobservation(Hwangetal.2004)showingajet(with R.,Tenorio-TagleG.,MillerW.,1996,MNRAS,283,419
aweakercounterjetstructure)composedmainlyofSi-richplasma. DeLaney T., Rudnick L., Stage M. D., Smith J. D., Isensee K.,
Lamingetal.(2006)haveperformedX-rayspectralanalysisofsev- RhoJ.,AllenG.E.,GomezH.,KozasaT.,ReachW.T.,Davis
eralknotsinthejetandconcludedthattheoriginofthisinteresting J.E.,HouckJ.C.,2010,ApJ,725,2038
morphologyisduetoanexplosivejetanditisnotarisingbecause Fesen R. A., Hammell M. C., Morse J., Chevalier R. A.,
ofaninteractionwithacavityorotherISM/CSMpeculiarstructure. BorkowskiK.J.,DopitaM.A.,GerardyC.L.,LawrenceS.S.,
ThereforeajetoriginfortheSi-richknotsissound. RaymondJ.C.,vandenBerghS.,2006,ApJ,645,283
Finally, we investigated the effects of thermal conduction, FryxellB.,OlsonK.,RickerP.,TimmesF.X.,ZingaleM.,Lamb
finding that it determines an efficient “evaporation” of the ejecta D. Q., MacNeice P., Rosner R., Truran J. W., Tufo H., 2000,
knotandaccelerateitsmixingwiththesurroundingmedium.More- ApJS,131,273
over,itaffectstheshrapnelmorphology,producingtheformationof HammellM.C.,FesenR.A.,2008,ApJS,179,195
along,metal-richtail.Enhancedmetallicitieshavebeenobserved Hwang U., Laming J. M., Badenes C., Berendse F., Blondin J.,
inthetailsofShrapnelA,B,andDandtheabundanceanalysisper- CioffiD.,DeLaneyT.,DeweyD.,2004,ApJ,615,L117
formedontheX-rayspectraclearlysuggestsanefficientmixingof JonesT.W.,KangH.,TregillisI.L.,1994,ApJ,432,194
theejectaknotswiththesurroundingmedium(Katsuda&Tsunemi Katsuda S., Mori K., Tsunemi H., ParkS., Hwang U., Burrows
2005,2006,andYamaguchi&Katsuda2009).Theseresultsarein D.N.,HughesJ.P.,SlaneP.O.,2008,ApJ,678,297
qualitative agreement with our findings. A quantitative compari- KatsudaS.,TsunemiH.,2005,PASJ,57,621
son between models and observations requires a forward model- KatsudaS.,TsunemiH.,2006,ApJ,642,917
ingapproach,consistinginthesynthesisoftheX-rayspectrafrom KleinR.I.,McKeeC.F.,ColellaP.,1994,ApJ,420,213
thesimulationsandadetailedcomparisonbetweenthesynthesized LaMassaS.M.,SlaneP.O.,deJagerO.C.,2008,ApJ,689,L121
observables and the corresponding observations (e. g., through a LamingJ.M.,HwangU.,RadicsB.,LekliG.,Taka´csE.,2006,
spatiallyresolvedspectralanalysis,asinMicelietal.2006,e.g.). ApJ,644,260
Moreover it will also be important for future models to include LiedahlD.A.,OsterheldA.L.,GoldsteinW.H.,1995,ApJ,438,
someseedmagneticfieldsinthesimulationstostudyhowtangled L115
the field becomes and what this implies for thermal conduction. LohnerR.,1987, ComputerMethods inAppliedMechanicsand
Thesefurtherstudiesarebeyondthescopeofthispaper. Engineering,61,323
In conclusion, our hydrodynamic modelling of ejecta knots MeweR.,GronenschildE.H.B.M.,vandenOordG.H.J.,1985,
intheVelaSNRallowedus tofind that:i) theobserved shrapnel A&AS,62,197
canbetheresultsofmoderatedensityinhomogeneitiesintheearly MeweR.,LemenJ.R.,vandenOordG.H.J.,1986,A&AS,65,
ejectaprofile;ii)theevolutionofashrapnelintheSNRisverysen- 511
sitivetoitsinitialpositionanddependsmuchless(butdoesdepend) MiceliM.,BocchinoF.,RealeF.,2008,ApJ,676,1064
ontheinitialdensitycontrast;iii)thermalconductionplaysanim- Miceli M.,RealeF.,Orlando S.,Bocchino F.,2006, A&A,458,
213
MiyataE.,TsunemiH.,AschenbachB.,MoriK.,2001,ApJ,559,
L45
6 Inthiscase,itsprojecteddistancefromthecenteroftheSNRmustbe OrlandoS.,BocchinoF.,MiceliM.,PetrukO.,PumoM.L.,2012,
muchsmallerthanitsactualdistance. ApJ,749,156
Modelingof theVela shrapnel 9
2E-23 4E-23 6E-23 8E-23
FigureA1.Density2-Dcross-sectionsthroughthe(r, z)planeforsimula-
tionR1/3−CHI20(leftpanel)andR1/3−CHI20−hiRES (rightpanel)at
t=5000yr.Thecolorbarindicatesthelogaritmicdensityscaleandranges
between10−25gcm−3and10−22gcm−3.
OrlandoS.,BocchinoF.,RealeF.,PeresG.,PaganoP.,2008,ApJ,
678,274
OrlandoS.,PeresG.,RealeF.,BocchinoF.,RosnerR.,PlewaT.,
SiegelA.,2005,A&A,444,505
Park S., Hughes J. P., Slane P. O., Burrows D. N., Roming
P.W.A.,NousekJ.A.,GarmireG.P.,2004,ApJ,602,L33
RichtmyerR.D.,1960,Comm.PureAppl.Math.,13,297
Sano T., Nishihara K., Matsuoka C., Inoue T., 2012, ArXiv e-
prints
SpitzerL.,1962,PhysicsofFullyIonizedGases.PhysicsofFully
IonizedGases,NewYork:Interscience(2ndedition),1962
TaylorJ.H.,ManchesterR.N.,LyneA.G.,1993,ApJS,88,529
TsunemiH.,KatsudaS.,2006,NewAR,50,521
WangC.-Y.,ChevalierR.A.,2002,ApJ,574,155
YamaguchiH.,KatsudaS.,2009,ApJ,696,1548
APPENDIXA: TESTONSPATIALRESOLUTION
AsexplainedinSect.2.1,thespatialresolutionofoursimulations
isreducedbyafactorof2att>2500yr.Tocheckwhetherthisres-
olutionissufficienttocapturethebasicevolutionofthesystem,we
repeatedsimulationR1/3−CHI20bymantainingthefinestlevel
ofresolutionatitsinitialvalue(1.95×1016 cm,hereaftersimula-
tionR1/3−CHI20−hiRES)forthewholerun.Weverifiedthat
simulationsR1/3−CHI20andR1/3−CHI20−hiRES yieldvery
similarresultsand all thequantities discussed inthepaper (posi-
tionoftheshrapnelasafunctionoftime,X-rayemittingmassof
the shrapnel, etc.) do not change significantly. Figure A1 shows
the2-D cross-sections of thedensity through the(r, z) plane ob-
tainedforsimulationsR1/3−CHI20andR1/3−CHI20−hiRES
at t = 5000 yr. Thisevolutionary stage isthemost critical,since
thesystemisstillrelativelysmallandtheejectaknotsinteractwith
thehydrodynamicinstabilitiesintheintershockregion.FigureA1
clearlyprovethatsimulationR1/3−CHI20alreadyprovidesavery
accuratedescriptionofthesystemandrunR1/3−CHI20−hiRES
doesnotintroduceanymajordifferences.