Type Ia supernovae and stellar winds in AGN driven relativistic bubbles

0.24 MB·

by  N. N. Chugai

Mon.Not.R.Astron.Soc.000,000–000(0000) Printed28January2011 (MNLATEXstylefilev2.2)
Type Ia supernovae and stellar winds in AGN driven relativistic
bubbles
1
N. N. Chugai1,2⋆, E. M. Churazov1,3, R. A. Sunyaev1,3
1
0 1Max-Planck-Institutfu¨rAstrophysik,Karl-Schwarzschild-Str.1,D-85741Garching,Germany
2 2InstituteofAstronomyofRussianAcademyofSciences,PyatnitskayaSt.48,109017Moscow,Russia
3SpaceResearchInstitute,Profsoyuznaya84/32,Moscow117810,Russia
n
a
J

7
28January2011
2

]
E ABSTRACT
H We analyse behaviorof stellar windsof evolvedstars and the outcomeof SN Ia explosions
intheAGNdrivenrelativisticbubble.Wefindthattheexpansionofwindshellsisefficiently
.
h deceleratedbytherelativisticpressure;theirbulkmotionhoweverispreservedsotheycross
p
thebubbletogetherwiththeparentstar.Thewindmaterialoccupiesasmallfractionofbubble
-
o volumeanddoesnotaffectsubstantiallytheexpansionofSNremnants.Theestimatedmaxi-
r malradiusofaSNremnantinthebubbleis30-40pc,iftheenvelopekeepsitsintegrityand
t
s remainsspherical.AfragmentationofSNshellduetoRayleigh-Taylorinstabilitycanallevi-
a atethepropagationoftheSNmaterialsotheejectafragmentsareabletocrosstherelativistic
[ bubble.Outside thebubblewindshellsandsupernovafragmentsaredeceleratedin the intr-

1 aclustermediumatclose rangeoff thebubbleboundary.The depositedSNe Ia materialcan
v enrichtheintraclustergaswithmetalsinathinlayerattheboundaryoftherelativisticbubble.
1 This process may lead to a rim of enhanced line emission. In the opposite limit, when the
9 fragmentationof supernovaremnantis moderateor absent,the SN Ia matteris advectedby
2 therelativisticplasmaandmayleavethecentralregionofthebrightclustergalaxytogether
5 withbuoyantlymovingbubbles.
.
1
Keywords: galaxies:clusters.
0
1
1
:
v
i 1 INTRODUCTION thegrowthrateofthebubbleisdefinedbythepoweroftheAGN
X
(e.g.,Gull&Northover1973;Churazovetal.2000).Pairsofbub-
Radio and X-ray observations show that in majority of regular
r blesarelocatedonbothsidesofthecentralsupermassiveblackhole
a galaxy clusters, possessing a cool core, the activity of a cen-
andoftenseveralgenerationof bubblesdifferingintheirsizeand
tral supermassive black hole mediated by AGN jets creates bub-
thedistancefromthecenterareobserved.
bles of relativistic plasma in the intra-cluster medium (ICM)
(Bo¨hringeretal. 1993; Huang&Sarazin 1998; Churazovetal. Bubbles with sizes of order 1-10 kpc are often found in the
2000; McNamaraetal. 2000; Birzanetal. 2004). X-ray data are inner regions of galaxy clusters, sharing the space with brightest
consistentwiththeassumptionthatbubblesarecompletelydevoid clustergalaxy(BCG).Forexample,inNGC1275(BCGofPerseus
ofthermalgas(Sanders&Fabian2007)althoughthelimitsonthe cluster)withintheeffectiveradiusofthegalaxy(Re ∼15kpc)we
amount of thermal gas in the bubbles are not very tight. The ab- see two bubbles on either side of the nucleus with the radius of
senceofstrongshocksintheICMsurroundingthebubblesimplies each bubble 6.3 kpc (e.g., Bo¨hringeretal. 1993; Fabianetal.
∼
thattherelativisticplasmaisinapproximatepressureequilibrium 2003).InM87(Virgocluster)thebubbleradiusis 1.4kpc(e.g.,
∼
withtheICM.Thesebubbles,inflatedbyanAGN,arebelievedto Formanetal. 2005, 2007), while the galaxy effective radius is of
beresponsibleformechanicalcouplingoftheAGNenergyrelease order7.7kpc.Weexpectthatinbothcasesbubblesshouldcontain
andthethermalstateoftheICMingalaxyclusters,groupsandin- significant fraction of the galaxy stars. These old low mass stars
dividualellipticalgalaxies.Forthisreasoneveryaspectofbubble evolveasusual,losetheirmassviathewind,andsomeofthemgive
physicsreceivesmuchattention. birthtotypeIasupernovae(SNeIa).Eveniftherelativisticbubble
Giventheubiquityofbubblesinclusters,theseobjectsshould sweeps up all the thermal gas in the process of inflation a lot of
be almost always present in the cluster core. The lifetime of the materialintheformofthestellarwindthuscanbesuppliedbythe
bubbleinthestratifiedatmosphereissetby“buoyancy”time,while starsinsidethe bubbleduring thebubble life.Thiswindmaterial
couldaffecttheexpansiondynamicsofsupernovaeexplodedinthe
bubble.
⋆ E-mail:[email protected] The question we address here is what happens to the stellar
2 N. N. Chugaiet al.
windsandSNIaejectaembeddedintherelativisticbubble.Almost M˙ =(m m )dNdm2 , (3)
weightless relativistic plasma provides highly unusual conditions 2− wd dm dt
for the dynamic evolution of wind shells and SNe. Two extreme where dm /dt is the rate at which upper limit m decreases with
2 2
scenarios are conceivable. In one limit all the wind material and time.Thisrateisdetermined bytherelationbetweenthelifetime
SNejectaaredeceleratedandmixedwithrelativisticplasma.Dur- and initial star mass t = t (m /m)β, where β = 3.2 in the range
2 2
ingsubsequent evolution thebuoyantly risingbubblesadvect this of1 2 M (Schalleretal.1992).Forthesevaluesand M = 9
material with them. In another limit the matter ejected by evolv- 1010R− M⊙ theequation (3)yields M˙ = 0.416 M R yrs1.Th×e
b,5 b,5 −
ingstarspropagates freelythrough therelativisticplasma, attains correspondi⊙ngstellardeathrateisN˙ =0.83R yr⊙1 whichisalso
b,5 −
theboundariesofthebubbleandenrichestheICMjustoutsidethe therateofwindshellformationN˙ .OneexpectthustofindN =
w w
bubblewithheavyelements.Weinvestigatedifferentscenariosof t N˙ 2.7 107R newlycreatedwindenvelopesinthebubble
b w ≈ × b,5
dynamicalevolutionofwindshellsandSNejectaandexploreob- volumewiththetotalamount ofthewindmatterinthebubbleof
servationaloutcomesofthesescenarios. 0.5N 1.4 107R M , factor 104 larger than the mass in
The structure of the paper is as follows. We first study the the fworm≈ of re×lativistbi,c5 pa⊙rticles of∼the bubble, 3pV/c2 2.4
∼ ×
expansionandbulkmotionofthewindenvelopesincludingmass 103 M .Itshouldbenoted,however,thattheN estimateignores
w
striping effects. This provides us with the estimate of the filling sofara⊙possibleescapeofwindenvelopesfromthebubble,which
factor of the wind shells ensemble. We then address the issue of isaddressedbelow.
theSNenvelopeexpansiondynamicsandbulkmotion,Rayleigh-
TaylorfragmentationoftheSNshellandpropagationofejectafrag-
2.2 Windshelldynamics
mentsintherelativisticplasma.Finally,wediscusstheimplications
ofresultsfortherelativisticbubblemattercontentsandintracluster Thedynamicaleffectofthewindmatterinthebubbleonacertain
thermalenvironment. windshellorSNejectadependsonthefillingandcoveringfactors
of wind shells. To assess the situation one needs first to find the
averagevolumeandsizeofawindenvelopeatthefinalstageofits
2 WINDMATERIALINRELATIVISTICBUBBLE expansion.Hereweassumethatthebubbleisstaticandadoptthata
starmoveswiththemeanvelocityv .Despiteasingularisothermal
s
2.1 Starsandmassinjectionrate sphereisassumedforthestellarpopulation,itisreasonabletoesti-
matev usingMaxwellvelocitydistributiontruncatedattheescape
Weconsider,asafiducialmodel,asphericalbubbleofradiusR = s
b
velocityv .ThetruncatedMaxwelldistributionistakenintheform
5kpcwiththebubblecenteratthedistanceR fromthecenterofthe e
b proposedby(King1966): f(v) [exp( v2/2σ2) exp( v2/2σ2)]
1B0C7Gy.r,Twhheecrehawraecatedroipsttitchaegbeubobfltehirsisbeuvbebloleciitsytvb ∼=23R0b0/vkbm∼s31.3(c×f. forv < ve and f = 0otherwise∝.Adopt−ingσv v=−350km−se−1,i.ve.,
b − v = 2σ = 700kms 1 wecometotheaveragevelocityv = 400
Churazovetal.2001).Attheradiir<15kpcthestellarcomponent e − s
kms 1.
inmassiveellipticalgalaxiesdominates(e.g.’Johnsonetal.2009) −
Thegeometry of thewindshell that forms asaresult of the
and its density distribution can be approximated by the singular
interactionofthewindwiththerelativisticmediumdependsonthe
isothermalspherewiththevelocitydispersionσ
v
valueofthedragforceexertedonthewindboundary. Ifthedrag
ρ= σ2v =ρ r0 2 , (1) forceisstrongthestrippedwindmaterialcreatesatrailingplume.
2πGr2 0(cid:18)r(cid:19) Ontheotherhand,ifdragforceisveryweak,thenthewindshell
whereG isgravitationalconstant andr isaradialscale1.Adopt- moveswiththestarvelocityretainingspherically-symmetricshape
0
ing r = 10 kpc and velocity dispersion σ = 350 km s 1 andeventuallymayescapetherelativisticbubble.Toexplorethis
0 v −
(Wu&Tremaine2006)onegetsthestellarmass M(<r )= M = issue we consider major stages of the mass loss at the AGB and
0 0
5.6 1011 M . This value is consistent with estimates of the to- post-AGBstage:(Steffenetal.1998;Louetal.2010):(1)theslow
tbaulbmb×laessofofrasdt⊙eiullsarRcom=pon5enktpcofthBeCGsteollfar∼m1a0s1s2 iMn⊙t.hIisnscidaesethies AwGinBd(suta=ge,10i.ek.,m10s−61y,rM,˙(2∼)s1l0o−w7sMup⊙eyrwr−i1n)do(nM˙theti1m0−e5sca1le0−o4fMthe
M 9 1010R Mb ,whereR =R /(5kpc). yr−1)duringthelast 104yroftheAGBstage,a∼nd(3)f−astwinda⊙t
s ≈The×starsarbe,5pre⊙sumablyobld,5withbanageoft 1010yr,which thepost-AGBstagew∼hichcorrespondstotheplanetarynebula(PN)
∼ stage( 104yr).Thelaststagepracticallydoesnotcontributetothe
suggeststhatthecurrentupperlimitofthestellarmassattheAGB
∼
mass loss, but turns out essential for the acceleration of the slow
stageis 1M (Schalleretal.1992).AssumingtheSalpeterinitial
massfun≈ction⊙dN/dm =Cm αwithintherangem <m<m one wind.Weadopt that 60%of thehydrogen shell islostatthefirst
− 1 2
stageand40%atthesuperwindstage(Steffenetal.1998),which
getsthenormalizingfactor
impliesthemass-lossratesM˙ 3 10 7 M yr 1attheslowwind
− −
C=(α−2)Ms[m−1(α−2)−m−2(α−2)]−1 =0.28Ms, (2) stageand M˙ ∼ 2×10−5 M⊙ y∼r−1×atthesup⊙erwindstage. Forthe
fastwindstageweadoptparametersderivedfromthemodellingof
whereα=2.35,m =0.1M ,andm =1M areused.
0.5MThe(Ssatlaarriosfaml.12=0019)M,w⊙hl⊙eilaeve∆smbe=2himndamw⊙hi=te0d.w5aMrfoifsmlowsdti=n tkhmeXs−-1ra(Lyoeumeistsailo.n20o1f0th).eTPhNe:fMa˙st∼w2in×d1p0a−ra8mMe⊙teyrsr−s1uagngdesutt=ha1t5t0h0e
thefor⊙mofslow(u ≈ 10−30kms−1)w−indwdduringthe⊙thermally 4to.5tal1k0in45eteircge.nWerhgeynrtrealenassfeerdeddutorinthgetshlioswstwagined(s∼he1ll0w4 iythr)thiseEm3as≈s
pulsingAGBstage(Vassiliadis&Wood1993).Thepresentdayin- ×
of0.5M thisenergyacceleratestheshelluptou 30kms 1,in
tegratedrateofthewindmatterinjectionintotherelativisticbubble ⊙ ≈ −
accord with the expansion velocities of evolved PN (Richeretal.
is
2008).
The mass striping rate of the wind shell scales as the shell
1 This approximation breaks at large radii to ensure convergence of the radiussquared,soatthestageofslowwindthemaximalstripping
totalstellarmass. isattainedattheendofthisstage.Theradiusofthewindshellat
TypeIa supernovaeandstellarwindsin relativisticbubbles 3
thisagecanbeestimatedfromtheenergyarguments.Thekinetic magnetic field (Narayan&Medvedev 2001). For the spectral in-
energyofthewindshellisspentonthe pV workagainstexternal dex of relativistic protons > 2 the energy of cosmic rays resides
pressure pandontheinternalenergywhichresultsinthestopping in low energy protons, which permits us to use the characteristic
radiusofthewindshell energyofrelativisticprotons 1GeV.WithB= 10 5 Gonegets
−
∼
r1 ="83π γ−γ1! M1pu21#1/3 =0.19p1−01/3 pc, (4) rg ∼3r2×1011cm.Thediffusiontimeisthen
td ∼ rwc =3×106B−51rw2,18 yr, (8)
where p = p/(10 10 ergcm 3), γ = 5/3, u = 10 km s 1, and g
10 − − 1 −
M1 =0.3M⊙areused. whererw,18 = rw/(1018cm).Fortheslowwindstagewiththefinal
Thewindshellmovesasawholetogetherwiththewhitedwarf radiusofr 0.2pcthediffusiontimeiscomparabletothedura-
unlessthebulkofthematerialisstrippedintothetrailingplume. tionofthis1s∼tage( 106 yr),whilethelifetimeofsuperwindand
ThewindshellstrippingcanbeestimatedfollowingNulsen(1982) fastwindstagesis∼significantlysmallerthanthediffusiontime.
considerationofthegasstippingforagalaxymovingintheICM. Theestimatedtimescaleofthecosmicraydiffusionsuggests
The turbulent stripping is determined by the combined effect of thatthepenetrationofcosmicraysinthewindcanaffectthewind
theKelvin-Helmholtzinstability(KHI)andtherampressuredrag. expansion dynamics at the slow wind stage making the pressure
Indeed,KHIbroadenstheboundarylayerwhichresultsinthesu- gradient smoother and thedeceleration lesspronounced. Asare-
pressionoftheKHI.Thenetstrippingrate,therefore,iscontrolled sult,thefinalradiusofthewindshellattheslowwindstageinfact
bytherampressure couldbesomewhatlarger,r >0.2pc.Ontheotherhand,theeffect
1
M˙ =πr12ρavs =1.6×10−12p110/3 M⊙yr−1, (5) cthaennroolteboefstihgenicfiocsamnitcbreacyaudsiffeuthsieondirffauptiidolnytdimroepsinfcorrelaasregser∝rard12,iusso.
whereweuseρa =3p/c2 forthedensityofambientmedium.The We conclude therefore that the stopping radius of the wind shell
1av.2erag1e07reysri,dseontcheetaimboeveofmaaswsilnodsssrhaetelliminptlhieesbthuabtbtlheeiswiRnbd/vshse∼ll A(rGwB∼m0.a5spscl)o,swshanicdhoinmciltusdtehsetchoescmoimcbrainyeddiffeffuesicotno,fiAsaGrBeaasnodnapbolset
×
loses 2 10−5 M whilemovinginthebubble,negligiblysmall estimate.
amoun∼tco×mparedto⊙themassofthewindshell,0.3M .
Alternatively, the stripping could be caused by⊙the Alfven
wavedrag.Inthisregardwenotethattheinfiniteconductivityap- 2.3 Windshellescape
proximation for the wind shell is fully applicable. A conducting
Outside the relativistic bubble the wind shell turns out in the in-
body moving with velocity v across the magnetic field B experi-
tracluster thermal gas. For the mass stripping rate M˙ = πr2ρ v
ences the drag force due to Alfven wave generation (Drelletal. w a s
adoptingthewindshellradiusr =1.5 1018cm,numberdensity
1965) w ×
ofinterstellargasn=0.02cm 3,andv =400kms 1oneobtains
− s −
Fd =(B2/4π)(v/vA)S, (6) M˙ 1.7 10−7 M yr−1.Ittakes3 106yrtocompletelystripthe
whereS istheareaoflateralsurfaceperpendiculartoB~,vA isthe c0a.5n∼Mbe⊙owb×tianidnesdheflrlo⊙omvetrhetheeqduiasttiaonnceo×fodfe∼ce1lekrpatci.oTnhoefsthameweiensdtimshaetlel
Alfvenvelocity, v B/ 4πρ withρ = 3p/c2.Strictlyspeak-
A ≈ a a asawholebydragforceπr2ρ v2.Thewindshellescapingbubble
ing, the Alfven velocity ipn the relativisic plasma (Gedalin 1993) w a s
isdeceleratedthusinaclosevicinityofthebubbleboundary.
is smaller compared to this expression by a factor of 0.7-0.9 de-
The average residence time of the wind shell in the bubble
pendingontheratioofmagnetictototalpressure;weneglectthis
R /v 1.2 107yrissomewhatsmallerthantheageofthefiducial
difference.ForasphereoftheradiusrthelateralareaisS 2πr2 b s ∼ ×
≈ bubble3 107 yr.Thetotalamountofthewindshellsresidingin
andthemassstrippingratecausedbytheAlfvenwavedragis thebubbl×eis,therefore, N˙R /v 107,whilethefillingfactor of
M˙ = B22vrAw2 ≈4.1×10−10p710/6B5 M⊙yr−1, (7) tfhe=eNnse(mRb/leRo)f3win1d0s5hpell1s.bintshe∼bubbleis (9)
whereB = B/(10 5G).ThestrippingrateduetotheAlfvendrag w w b ∼ − −10
5 −
thusturnsouttwoordersofmagnitudelargerthantherateaccord- Theprobabilityofacollisionwiththewindshellisdeterminedby
ingtoequation(5).YetevenfortheAlfvendragthemasslostdur- theratioofthebubbleradiusandthemeanfreepath.Thelatteris
(ing3th%e)reosfidtehnecweitnimdeshiseloln.lWye∼t0h.u0s1cMon⊙cwluhdiechthiastathsmeawllinfrdacsthieolnl λ=(πrw2nw)−1=64p210/3 kpc (10)
lo∼st at the slow wind stage remains almost intact while traveling wherenw = (3/4π)Nw/R3b = 2×10−5 pc−3 isthenumber density
acrossthebubble. A similarresult canbe obtained forthesuper- of windshells. Theprobabilityof shell collisionsislow, because
windstage.Theoutcomeofacombinedeffectofallthreestagesof theaveragenumberofwindshellsalongthebubbleradiusisonly
themasslossisaspherical windshell of0.5 M expanding with τ = Rb/λ = 0.08. Theaverage probability of the collision isap-
the velocityof 30 km s 1. Usingequation (4) on⊙e findsthe wind proximately [1 exp( τ)] τ = 0.08.Moreaccurateestimate
− ≈ − − ≈
shellstoppingradiusisrw=0.5p1−01/3pc. canbedoneusingexpressionfortheescapeprobabilityofthepho-
Theabove treatment of thewinddynamics suggests that the tonfromahomogeneoussphere(Osterbrock1989)
cosmic rays diffusion into the shell can be neglected. To check
3 1 1 1
whetherthisassumptionisvalidweassumeBohmdiffusioncoef- p = 1 + + exp( 2τ) , (11)
esc 4τ" − 2τ2 τ 2τ2! − #
ficientr c/3,wherer istheprotongiroradius.Thisassumptionis
g g
standardfortheanalysisofcosmicraypropagationandsupported For τ = 0.08 the equation (11) gives p = 0.94. Most of wind
esc
byobservationaldataonthecosmicrayaccelerationinsupernova shellsthereforeescapethebubblefreelyandonly6%ofwindshells
remnants(Stageetal.2006),althoughtheconceptofatangledfield collidewithanothershell.
might seriously modify a picture of the cosmic ray diffusion in Thefate of thecollided windshells depends onwhether the
4 N. N. Chugaiet al.
tic fluid. Indeed, for SN expanding with the characteristic veloc-
ity v (2E/M)1/2 = 109 cm s 1 one readily sees that the ram
−
≈
pressure is small compared to the pressure of relativistic fluid:
ρv2 = 3p(v/c)2 p. The crucial role of theexternal relativistic
≪
pressure in the SN deceleration is a distinguishing feature com-
pared tothestandard case of SNshell inthe ordinary interstellar
medium.
InouranalysisoftheSNexpansionweassumetheisotropic
pressure of the relativistic medium. This is the case, if the mean
freepathforrelativisticprotons alongthemagneticfieldismuch
lessthantheSNradius.SincetheSNexpandssubsonicallyrelative
totheexternalmedium,inwhichthesoundspeedis c/√3,the
≈
strongforwardshockdoesnotform.Thereverseshockobviously
forms,becauseouterlayersofejectaaredeceleratedbytheexternal
pressureandthevelocityjumpbetweentheundisturbedejectaand
swept-up shell exceeds the sound speed in the unshocked ejecta
( 10kms 1).TheSNisfullydeceleratedwhenthereverseshock
−
∼
Figure1. Thinshellmodelofsupernovaevolutioninrelativistic bubble. crossesthebulkoftheejectamass.
Shownaretheshellradius(a),evolutionofvelocitiesoftheshell(S),pre- ToestimatethestoppingradiusofSNonecanusetheenergy
shockvelocityofsupernovaejecta(SN),andreverseshockspeed(RS)(b),
considerations likewise wedid for the windshell expansion. The
evolutionofthereverseshocktemperature(c),X-rayluminosity(d).
initial kinetic energy E of SN should be spent on the PV work
againsttheexternalpressureandontheinternalenergy pV/(γ 1)
−
collision is adiabatic or radiative. With the average relative ve- whichgivesthestoppingradius
locity of collision u 560 km s 1 and the wind shell density
∼ − γ 1 3E 1/3
o∼ut20to0bcem−33thee1s0t1im0 sa,tecdomcopoalrianbgletimweithofththeehsyhdorcokdeydnagmasictusrcnaeles rsn =" −γ !4πp# =36p1−01/3 pc. (12)
∼ ×
rcwo/lluisi∼on3re×gi1m0e10s sa.reTphliasumsiebalen.sItnhattheboatdhiaabdaitaibcactiacseanwdinrdadsiahteilvles Wr i/thvac3hara1c0te3riysrtitcoerjeeaccthavrel,orcaittyhevrs≈ho1r0t9timkmecso−1miptatraekdestotsth∼e
approximatelyretaintheirsizesandabsolutevelocities,sotheadia- bsunbble∼life×time. sn
baticcollisiondoesnotaffecttheirescape.Inradiativecasecollided Thedynamicsoftheswept-upshellandtheX-rayemissionof
shellsmergeandformthindensepancakeofathicknessb≪rwand thereverseshockcanbeillustratedusingamodelbasedonathin
densityρc∼(rw/b)ρw,whereρwisthedensityofthewindshellbe- shellapproximation.Thissuggeststhattheshellformedbyejecta
forecollision,Thispancakeisliabletofragmentationintoclumps materialflowingintothereverseshockisconsideredasathinshell
of size a & b and average velocity ∼ vs/√2. It is easy to verify whichdynamicsisgovernedbythedynamicalpressureoftheSN
thatforfragmentswithsizesa & banddensityρc ∼ (rw/b)ρw the ejectaandexternalpressure p = 10−10 ergcm−3.Theequationof
stripping(ordeceleration)timeisgreaterthanthestrippingtimeof motionforthethinshellis
windshells.Wethusconclude thatthemostof thewindmaterial
dv r 2
escapesintothehotICM. M =4πr2 ρ v p , (13)
Inouranalysisofthewindshelldynamicsweignoredapossi- dt " (cid:18)t − (cid:19) − #
blefragmentationofthewindshellduetotheRayleigh-Taylor(RT) wheretheshellmassisdeterminedbythemassconservation
instabilityonthedecelerationoraccelerationstages.Thisomission
dM r
facilitatestheconsideration;yetitdoesnotaffectthemajorconclu- =4πr2ρ v . (14)
sionthatthewindshellmaterialescapetherelativisticbubble.As dt (cid:18)t − (cid:19)
wewill see below, the RTfragmentation favoursthe shell matter Theseequationsaresolvednumericallyassumingafreelyexpand-
escape. ingSNwiththemassof1.4M ,energyof1.5 1051erg,thedensity
distributionρ exp( v/v ),b⊙oundaryveloci×tyof4 104 kms 1,
∝ − 0 × −
andinitialouterradiusof1018cm.
3 TYPEIASUPERNOVAEINRELATIVISTICBUBBLE ResultsaredisplayedinFig.1whichshowstheevolutionof
the shell radius, velocity of the shell, boundary velocity of SN
WithSNIaproduction efficiencyψ = 0.008 per one whitedwarf ejectaandvelocityofthereverseshock,reverseshocktemperature
formedinthestellarpopulationofE-galaxies(Pritchetetal.2008) assuming full equilibration, and X-ray luminosity of the reverse
andthestellardeathrateinthebubbleoffiducialmodelN˙ =0.83 shock.Themaximalradiusofthethinshellmodelis39pc,slightly
yr−1oneexpectsψN˙tb ∼2×105 SNIaexplosionsduringtherela- larger than analytical estimate rsn = 36 pc. Remarkably, the thin
tivisticbubblelifetimetb = 3×107 yr.Wenowconsiderindetail shellshowscontractionphase(Fig.1a)whichisadirectoutcome
SNexpansionintherelativisticbubbleandanalyseanoutcomeof ofthedynamicalroleoftheexternalpressure.However,sincewe
theRayleigh-TaylorfragmentationofdeceleratingSNshell. neglecttheinternalpressureoftheshockedenvelope,theamplitude
ofthecontractionphaseinourmodelisexaggerated,sowestopthe
computationsatthisphase.TocalculatetheX-rayemissionweas-
3.1 SNexpansion
sumethatthehotplasmaintheshellisdistributedhomogeneously
Givenasmallnumberofwindshellsalongthebubbleradius(Sec- intheshellwiththethickness∆R/R =0.1.Itisratheracrudeap-
tion 2.3) the deceleration of the SN expansion in the relativis- proximationbecausethedensitydistributioninthereverseshockis
ticbubble isprobably dominated by thepressure of the relativis- expectedtobeessentiallyinhomogeneouswithapeakatthecon-
TypeIa supernovaeandstellarwindsin relativisticbubbles 5
Figure3.Radiusofthecontactdiscontinuity,separatingSNejectaandthe
Figure2. DensitydistributionforSNIaenvelopeexpandingintheICMat ICMasafunctionoftime.Fourcurvesshowncorrespondtoexplosionsin
theages 60,400,3000,2104 and105 yearsfortheICMtemperatureof theICMwiththesamepressure,butdifferenttemperatures, 0.01,1,100,
0.01keV∼(bottom)andof100keV(top).Positionofasharpwiggleinthe 104keV,frombottomtotop.Clearlythefinalsizeoftheejectaislargestin
densitydistributioncorrespondstothecontactdiscontinuityseparatingSN theICMwithhighesttemperature.
ejectaandtheICM.
tactsurface.YetitisreasonableenoughtogetanideaaboutX-ray tothevaluegivenbythethinshellmodel (Fig.1).TheX-raylu-
luminosity within a factor of two. The luminosity is maximal at minosityofthereverseshockinthemodelwith104 keVmedium
thecontractionphaseandreaches 4 1033 ergs−1 attheshock isshown inFig. 4together withtheevolutionof theradiiof the
∼ ×
temperatureof 200keV.Theequilibrationofelectronsandions, reverseshockandcontactsurface.Theluminosityevolutioniscon-
∼
however, isan oversimplification, so the shock electron tempera- sistent with the prediction of the thin shell model (Fig. 1) at the
tureandtheluminosityshouldbeconsideredapproximate. ages. 6 103 yr.However,atthefinalstageoftheejectadecel-
×
AnotherinterestingviewontheSNexpansiondynamicsinthe eration (t & 104 yr) the luminosity behavior differs from that of
relativisticbubblegivesusone-dimensionalhydrodynamicsimula- thethinshellmodel.Indeedatthisphasetheshockedgascannotbe
tionsinwhichweassumeahotrarefiednon-relativisticplasmato treatedasthinshell.Afterabout104yrthereverseshockattainsthe
beaproxy fortherelativisticfluid.Thethermalpressureistaken center.Thisisaccompaniedbytheoverallcontraction;asaresult
thesamep=10−10ergcm−3.TheICMtemperaturevariesindiffer- theemissionmeasureincreasesandtheluminosityattainsmaximal
entrunsfrom10−2 upto104 keV2.ForT =104 keVthesituation value 3 1033ergs−1.Thisisfollowedbytheexpansionwhichre-
∼ ×
isclosetothecaseoftherelativisticmediumbecausethethermal sultsintheluminositydrop.Atthemostluminousphase,L &1033
x
pressure exceeds the dynamical pressure in the upstream flow of ergs 1,theSNIaremnantlives 4 103 yr.Thetemperatureof
−
∼ ×
theforwardshock.Weassumehomologousexpansionoftheenve- theshockedejectaatthisphaseisintherangeof108 109 K,so
−
lopev randmodeltheinitialdensitydistribution10yearsafter onlyasmallfractionofthetotalluminosity(10 30%)fallsinto
theexp∝losionasρ∝e−r/r0,wherer0 =310−5 pc.Theejectamass thestandardChandraband(0.2-10keV). −
is1.4M andkineticenergyis1.5 1051erg,whilethemaximum Generally,theSNexpansiondynamicscanbeaffectedbythe
expansio⊙nvelocityissetto2104km×s−1. diffusionofrelativisticprotonsintotheejecta.Thisprocessmight
The dependence of theexpansion dynamics onthe tempera- modifydynamicsbysmoothingoutthepressurejumpatthebound-
tureoftheICM(atthesamepressure)isapparentfromFig.2.In arybetweenejectaandrelativisticfluid.Thetimeittakestofillthe
thelowtemperaturecase(bottompanel inFig. 2)mostofejecta SNbycosmicrayswiththeenergyEperparticlecanbeestimated
energyisspentonaforwardshock,whichisbarelyresolvedinour asthetimefortheprotontoescapefromtherelativisticbubblelayer
simplesimulations.Bycontrast,forthehightemperatureICMal- adjacenttoSN.ThevolumecomparablewithSNofradiusRisa
most alltheinitialkineticenergyiseventuallyconverted intothe sphericallayerofathicknessof 0.3R.AssumingBohmdiffusion
∼
enthalpyoftheejectaandonlytinyamountofenergyisdeposited coefficientD=cr /3onegetsthediffusiontime
g
intheforwardshock.Accordinglythefinalsizeoftheenvelopeat
theboundaryseparatingejectaandICMismuchlargerforthehigh (0.3R)2 R 2
t =1.5 109B yr, (15)
temperature run. Thisis further illustratedin Fig. 3, showing the d ∼ 4D × 5 30pc!
timedependenceoftheenveloperadius.Thesimulationsshowthat
ThetimeittakestofilltheSNbycosmicraysattheessentialde-
in the limit of very hot ICM the final envelope radius converges
celeration epoch turns out tremendous compared to the SN age
( 3 103 yr). We conclude, therefore, that the diffusion pene-
∼ ×
2 Weusenonrelativisticequationofstateintheseillustrativerunsevenfor trationofrelativisticprotonsintotheSNenvelopeunlikelyaffects
Te=104keV,althoughthisnotvalidforelectrons. theSNexpansiondynamics.
6 N. N. Chugaiet al.
intheslowbulkmotionatthedistancetentimeslargerthaninthe
maximumradiusattainedinthehighspeedenvelopeexpansion.
3.3 Rayleigh-Taylorinstabilityandspikedeceleration
The swept-up SN shell decelerating in the light relativistic fluid
is liable to the Rayleigh-Taylor instability (RTI) which generally
shouldresultinthefragmentationofSNshell,closetothestageof
thesignificandeceleration,i.e.,ataboutthestoppingradiusr .The
sn
situationissimilar,albeitinvertedwithrespecttoCrabnebular.The
Crabshellacceleratedbytheshockedrelativisticwindshowslong
thinRTspikesdirectedbackwardthecenter(Hesteretal.1996).In
caseof decelerated SN dense RTspikes protruded forward could
travellargedistancesbeforetheystop.Yetitshouldbeemphasised
thedifferencewiththeCrab.InthelattercasetheSNmaterialpres-
surizedbytherelativisticplasmaiscoolwiththethermalvelocity
u 10kms 1.TheSNIamaterialintheadiabaticreverseshock
crab ∼ −
ishotwiththethermalvelocityu 104kms 1.Thedensitycon-
sn ∼ −
trastintheCrabisthereforebyfactor(u /u )2 106larger.
sn crab ∼
Figure4.X-rayluminosityofthereverseshockinthemodelwiththeICM The behavior of RT spike may be affected by the KHI. For
temperatureof104keV(top)andtheradiiofthecontactdiscontinuityand acylinder spikeof theradiusamoving withthevelocityvalong
reverseshock(bottom).Theluminositydecreasesafter 104yrbecauseof itsownaxistheperturbationgrowthtimeforthemostdestructive
∼
thesignificantexpansionofthepostshocklayerbetweenthereverseshock wavenumber k 1/a ist (a/v)χ1/2, where χisthedensity
(bottom,lowercurve)andthecontactsurface(uppercurve). ∼ KH ∼
ratio of SN and bubble material. At the SN radius R = 20 pc
the contrast χ 105. The distance at which the most dangerous
∼
3.2 SNbulkmotion modegrowsisthen ∼ vtKH ∼ a√χ ∼ 300a. Wedonot awareof
anymulti-dimensionalhydrodynamicsimulationsofadensecloud
AftertheexpansionbrakingtheSNshellstillretainsthebulkmo- movinginararefiedrelativisticfluid.Acloseanalogueisthetwo-
tionwiththetypicalvelocityv = 400kms 1.Ifthedeceleration dimensional hydrodynamic simulations of a dense cloud moving
s −
ofthebulkmotionwerenegligible,theSNshellwouldescapethe inthepost-shockintercloudrarefiedgas(Kleinetal.1994).These
relativisticbubbleaftertheaverageresidencetimeR /v 107 yr. simulationsshowthatthecloudlifetimewithrespecttothefrag-
Wenowcheck,whethertherampressureandtheAlfvbensw∼avedrag mentationandfragmentdecelerationisorder 4(a/v)χ1/2,roughly
∼
cansubstantiallydeceleratethebulkmotioninsidetherelativistic four times larger than the Kelvin-Helmholtz time. Adopting this
bubble. characteristictimeonefindsthatthedistanceatwhichthespikewill
TherampressuredragforceexertedontheSNshellisF = bedestroyedanddeceleratedis 4vt 4aχ1/2 103a.Assum-
d ∼ KH ∼ ∼
πr2snρav2,wheretheambientdensityisρa =3p/c2,assumingparti- inga/R∼10−2,comparablewiththefingersincaseofCrabnebula
clesdominateinthepressure.Usingtheequationofmotion (Hesteretal.1996),onefindsthatRTspikecantravel 10R.0.3
∼
kpc,rathersmalldistancecomparedtothebubbleradius.
dv
M = πr2ρ v2, (16) Ontheotherhand,Nulsen(1982)arguesthattheincreaseof
dt − sn a
thewidthoftheboundarylayerduetotheKHIquenchesthevery
thecharacteristicdecelerationlengthcanbeestimatedas instability.Asaresultthemasslossissuppressed and eventually
Mc2 isdefinedbythemomentumtransfer[cf.equations(5)and(7)].In
ld ≈ 3πr2 p ≈69p1−01/3 kpc. (17) thiscasetheproblem of massstrippingdue toKHI isreduced to
sn theproblemofadecelerationofRTspikeswhichisanalysedinthe
ThisshowsthatthedecelerationofthebulkmotionofSNbythe nextsection.
rampressurecanbeneglected. The longitudinal magnetic field also can suppress the KHI.
The Alfven wave drag exerted on the spherical SN shell Let ρ and ρ be thedensity of rarefied and dense fluid. Accord-
1 2
is defined similarly to the case of the wind shell, i.e., Fd = ing to the criterion of the KHI in the presence of magnetic field
(1/2)B2(v/vA)r2sn. The chracteristic deceleration time is td ≈ Chandrasekhar (1961) the condition that the magnetic field turns
vsM/Fd,whilethedecelerationlength,ld ≈vstd,is offtheKHIis
ld ≈ Br2sMn v1sc2πp ≈0.3vs,400B−51p110/6 kpc, (18) B>(2πρ1)1/2v=(6πp)1/2(cid:18)vc(cid:19)≈1.4×10−6 G, (19)
p
wherevs,400 = vs/(400kms−1).Thisshowsthat theAlfvenwave where p=10−10ergcm−3,cisthelightspeed,andv=109cms−1
drageesentiallybrakesthebulkmotionoftheSNshellatthedis- areused.Therequiredmagneticfield B > 1.4 10 6 Giswithin
−
×
tancemuchsmallerthantheradiusoftherelativisticbubbleeven therangeoffieldstrengthintherelativisticbubble,whichcanbe
forweakfieldB 3 10 6G.Wethusconcludethattheejectaof aslargeasseveral10 5G.ThemagneticstabilizationofRTspikes
− −
∼ ×
SNIaexplodedintherelativisticbubblecannotescapethebubble againstKHIthusseemsquiteplausible. Hereafterweaddressthe
duetothebulkmotion.Amazingly,theSNmaterialisdecelerated decelerationofRTspikeassumingitsstability.
TypeIa supernovaeandstellarwindsin relativisticbubbles 7
3.3.1 Dragincollisionlesscase fieldso,onlyasmallfractionofRTspikesexperiencesthistypeof
adeceleration.
A typical RTspike isassumed tobe a cylinder with themass m,
radiusa,andlengthb,whichareassumedtoremainconstant.The
RTspikepesumablymovesalongtheaxisintherelativisticplasma
dominated by the relativistic particles. With the giroradius rg ∼ 3.3.2 Dragincollisionalcase
3 1011 cmandtheRTspikeradiusa 10 2r 1018 cmonly
× ∼ − sn ∼ Ifthemeanfreepathforcosmicrayprotonsissmallλ a,one
amotionalongtheregularmagneticfieldcanbecollisionless.The ≪
expectsthatthedragforceshouldbeproportionaltov2.Thegen-
meanfreepathforrelativisticprotonspropagating alongthefield
eralconditionforthatisthelargeReynoldsnumber Re> 102.To
canbeconstrainedbyscatteringontheperpendicularcomponentof
estimateReweadoptthespikeradiusa 10 2r 1018 cm,the
arandomfield.TheresultingmeanfreepathalongthemeanfieldB ∼ − sn ∼
isλ r (B/δB)2(Strongetal.2007),whereδBistheamplitudeof spikevelocityv=109cm,andλ=rgasthemeanfreepathforrel-
araknd∼omg fieldwithresonancewavenumberkresrg ∼ 1.Following gateitvsisRtiec=p3roatvo/ncsr.Ass3um1in0g5.BTh=ec1o0n−5diGtio,ni.eR.,er>g1∼023t×hu1s0i1s1fcumlfilolnede
Strongetal.(2007)weassumethepowerlawspectrumofrandom g ∼ ×
fieldenergydensityW(k) k−s with s = 1.67,betweenmaximal forλ<3×104rg ∼1015cm,whichisrathersoftrequirement.
∝ In the collisional approximation the drag force is F =
lengthscalek 1/R andandminimalscalek 1/r .The d
min ∼ b max ∼ g 3πa2p(v/c)2.Followingtherecipeoftheprevioussectiononeob-
integratedenergydensityisnormalizedaccordingtosuggestionby
Strongetal. (2007): W = B2/(8π). With these prerequisites one tainsthespikedecelerationdistance
ucgmnetc,seir(.teδa.Bi,n/λtBike)&s2or∼fg.t(hTkehmreine/slkeitvrueasa)ntsti−o1pna∼rtahmu1s0e−ties7rasabndodouλtnkcoot∼lplirs1ei0col7nurldgees∼sc,oa3lllti×hsio1ou0ng1ah8l ld ≈ 59ηrsn(cid:18)cv(cid:19)2 . (23)
regimeaswell.Oneneedsthereforetoconsiderbothcollisionless Forv=109cms−1andrsn =36pconeobtainsld ∼17ηkpc,rather
andcollisionalcases. largevaluethatexceedsbubbleradius(5kpc)evenformodestvalue
Forb athemomentexchangeoccursprimarilyviathecos- ofη 1.TherampressuredragthusalmostdoesnotdecelerateRT
mic ray co≫llisions with the lateral surface of the spike. The mo- spike∼sinsidetherelativisticbubble.
mentumtransferredtothecollidingparticlewiththeenergyE as-
suming diffusive reflection, is (E/c2)v. For theparticleflux on
∼
theunitofsurfacearea(1/4)nc,wherenisthecosmicrayconcen-
3.3.3 Alfvenwavedrag
tration,themoment transferredpersecond toallthestrikingpro-
tons(dragforce)isF = (1/2)πabǫ(v/c),whereǫ = 3pistheen- TheAlfven wavedrag can operate for thelarge conducting body
d
ergydensityofrelativisticparticles.Notethatthedragforcecould a > (v/c)r 1010 cm,whichiseasilymetforRTspikes. Using
g ∼
be derived also using average energy gain of a relativistic parti- theexpressionforthepowerradiatedintheformofAlfvenwaves
clepercollisionwiththecloud E(v/c)2 (Fermi1949).Indeed,for Drelletal.(1965))one canwritetheAlfvendrag forceacting on
a spherical cloud the total energy loss per second in that case is theplasmaspikewiththeradiusaandlengthbas
πa2ncE(v/c)2 = πa2ǫv2/c.Thisimplies thedrag force πa2ǫ(v/c),
B2 v
mwhetircihcaclofiancctiodre.swiththeaboveexpressionfor Fd withinthegeo- Fd = 2πvAab, (24)
Theequationofmotionofthespikeinthecollisionlesscase
wherev = B/ 4πρ isthe Alfvenvelocity. Note, it isonly the
withtheabovevalueofF thenreads A a
d lateralsurfacearpea( 2ab),thatmatters.Followingargumentsof
≈
dv v theprevioussectionsonegetsthespikedecelerationdistance
m = 1.5πabp . (20)
dt − c
π 3/2 √pac a
Weneglectherethehead-oncollisionswhichwouldcontributethe ld ≈5ηrsn(cid:18)3(cid:19) B bv =6ηbB−51p11/06 kpc. (25)
term of the order a/b 1 in the right hand side. Note, the
transitionfromspik∼etothe≪spherical blobcorresponds tob = 2a For fiducial model p = 10−10 erg cm−3, B = 10−5 G, v = 109
in the drag force expression. The characteristic time of the spike cm s−1 one obtains ld ≈ 6η(a/b) kpc. This result shows that in
decelerationisthus case a = b the blob can travel the distance exceeding the radius
oftherelativisticbubbleevenformoderatevaluesofη > 2.Fora
2 mc
t . (21) longspike(b a)decelerationisbyfactorb/astronger andthe
d ∼ 3πabp ≫
decelerationdistanceisaccordinglyshorter.Forb/a 10andη
∼ ∼
The ratio m/πa2 can be expressed via the surface density of the 10theRTspikecantravel 6kpc,adistancecomparablewiththe
∼
SNshell atthestopping radiusasm/πa2 = ηM/4πr2sn,wherethe adoptedbubbleradiusRb =5kpc.IttakesroughlyRb/v∼5×105
parameterη 1becausethespikeisformedbyashellpatchwith yrforthespiketoreachthethebubbleboundaryassumingthespike
theradius ≫a.Thedecelerationdistanceforthespikeisthen averagevelocityof104kms−1.
≫
TheeffectoftheAlfvenwavedragisdeterminedbythemag-
10 ca a
ld =vtd ∼ 9 ηrsnvb =1.2ηb kpc, (22) neticfield.Ifthefieldisweak, B = 3×10−6 G,thedeceleration
distance is 18 kpc, substantially larger than the bubble radius.
∼
where we make use of equation (12) and adopt v = 109 cm s 1 On the other hand, for B > 10 5 G the deceleration distance is
− −
and r = 36 pc. For η 10 and a/b 0.1the spike can travel smallerthan thebubbleradius andsignifican amount of RTfrag-
sn ∼ ∼
1kpcbeforeitgetscompletelydecelerated.Incollisionlesscase mentswillremainintherelativisticbubble.Theescapeprobability
∼
theRTfragmentsaredecelerated efficientlyinside therelativistic forRTspikeincaseofB=10 5Gcanbeestimatedadoptingmean
−
bubble.Itshouldbestressed,however,thatthecollisionlessregime freepathλ=vt =6kpc,i.e.,τ=R /λ=5/6.Equation(11)gives
d b
canberealizedonlyinthecaseofthemotionalongthemagnetic inthiscasetheescapeprobability p 0.6.
esc≈
8 N. N. Chugaiet al.
[t] shouldbecomparedwiththemassoftheICMgas,whichisalready
there.ForR =5kpcandhydrogennumberdensityn=0.02cm 3
Table1.Parametersoffiducialmodel b −
themassoftheICMintheboundarylayerwiththethicknessl =1
w
kpcis7 107 M ,i.e.,factor 5largerthanthemassdeposited
Parameter Description Value × ⊙ ∼
bythewindshells.Thedepositedwindmassscaleswiththebub-
bleradiusas R4,whereastheICMmassinthelayeris R2.We
Rb Bubbleradius 5kpc thusconclude∝thabtforthefiducialmodelthewindmaterial∝escabping
tpb PArgeessure 1031×0e1r0g7cymr 3 therelativisticbubbledoesnotchangesignificantlythedensityof
B Magneticfield −10 5G − thesurroundingICM;moreovertheeffectevensmallerincaseof
−
n NumberdensityofICM 0.02cm−3 M87inwhichbubbleradiusRb∼1.4kpc.Theeffectoftheenergy
Ms Stellarmassinthebubble 9 1010M deposition by the escaping wind shellsis alsonegligible because
N˙ Stellardeathrate 0×.83yr 1⊙ thebulkvelocitiesofthewindshellsissubsonicandthedeposited
−
N˙sn SNIarate 0.0066yr−1 massislow.ThechemicalcompositionofICMisnotaffectedby
rw Windstoppingradius 0.5pc theescapingwindshellseither.
rsn SNstoppingradius 36pc Unlike the windshells, fragments of SN ejectaescaping the
relativisticbubblemayhaveaprofoundeffectontheenrichmentof
ICMbyironpeakelements.Theresultingabundanceisdetermined
3.3.4 Spikedecelerationbywindmaterial by the width of the mixing layer. Generally, one should consider
time-dependentmodeloftheformationofmixinglayer.However,
Theaveragenumber of windshellsalong theaverage distanceto
weassumethatthemixinglayerinthefiducialmodelisformedby
thebubbleboundaryforthefiducialmodelis 0.08(Section2.2)
∼ thecumulativeeffectofallSNe.Emploingthemomentumconser-
whichmeansthatforSNfragmentstheprobabilitytocollidewitha
vationargumentsadecelerationdistancefortheRTspikeentering
windshellislow, 0.06.Aquestionarises,whathappens,anyway,
ifthecollisiontak∼esplace. theICMwiththevelocityvi anddecelerateddowntovf turnsout
tobe
Thedecelerationisdeterminedbytheratioofcolumndensi-
ties(µ)oftheprojectile(RTspike)andtarget(windshell).Forthe M
l ηln(v/v ) 0.5η pc, (27)
windshell sn ∼ i f 4πr2snρ ≈
m
µw= πrww2 =1.4×10−4 gcm−2, (26) 3w6hperce.Fwoeruηs=ed1v0i/ovnfe=ge2ts0,thne=de0c.e0le2ractmio−n3,leMng=th1ls.n4∼M5⊙,pacn.dAtrsfinrs=t
wherer =1.5 1018 cmandm =0.5M areused.Thecolumn glance the mixing layer could be identified with the deceleration
dTehnissictyomwofpathriesosnp×iksheoµwss=thηatMt/h(e4wπspri2skn)e∼wi2ll⊙×be10fu−l8lηygdeccmel−e2ra≪tedµiwn. mlayasesr.pTrohdisulcaeyderbycoSnNtaIinasduMriicnmg∼th7el×ife10ti5mMe⊙ofotfhtehbeuIbCbMlegisasM.sTnh∼e
asinglecollisionwithawindshell.Weconcludethereforethatfor 3 105 M .IfmostoftheSNmassescapesthebubble,theamount
thefiducialmodelthereisnon-negligibleprobability, 0.06,that of×escapin⊙gironinthemixinglayerturnsouttobe 105 M which
the spike will be decelerated in the bubble via collisi∼on with the correspondstotheironabundance 80 (solar). ∼ ⊙
∼ ×
windshell. Ontheotherhand,themixinglayercouldbebroaderbecause
thetotalvolumeofshockedSNfragmentsinpressureequilibrium
substantiallyexceedsthevolumeofthedecelerationlayer.Simple
estimatebaseduponthepressureequilibriumsuggeststhetotalvol-
4 DISCUSSION umeoccupiedbyshockedSNejectatobeV = N E/pwhichim-
t sn
Theaimofthispaperhasbeentogetanideaonwhathappensto pliesthelayerwidth 300pc.Ifthisisidentifiedwiththewidthof
∼
thematterejectedbythestellarpopulationofBCGembeddedinto themixinglayerthantheironabundancewillbefactortwolarger
abubbleofrelativisticplasma.Wehavefoundthattheexpansionof comparedtosolarabundanceofpre-existingICM.Theincreaseof
awindenvelopelostbyastarisstoppedbythepressureoftherela- theironabundance byfactor twochanges the0.6-2keV emissiv-
tivisticfluidwhentheradiusattains 0.5pc.Becauseofthesmall ity3byfactorsof1.8,1.5and1.3forthegastemperatures1,2and
sizeofthewindshellitsbulkmotion∼isnotdeceleratedneitherby 3keVrespectively.
therampressure,norbytheAlfvenwavedrag,sotheshellescapes Thelatterestimatessuggestcompletemixingofinjectediron
thebubbletogetherwiththeparentstar.TheSNIaexplodinginthe withtheICM,whichmaynotbethecase.Thepointisthatthede-
relativisticfluidexpandsuptomuchlargerradius 30 40pcand celerationofSNfragmentsintheICMresultsinthestrongheating
itsbulkmotioncanbeefficientlydeceleratedby∼theA−lfvenwave oftheejectamaterialuptotemperaturecorrespondingtoitskinetic
drag.UnlessaRTinstabilityoperates,theSNmaterialwouldnot energy.Mostoftheironthereforeendsupinthehighentropy/low
escape therelativisticbubble, butwillinsteadbeadvected bythe densitygaswiththeverylittleX-rayemission.Theobservational
buoyantlyrisingrelativisticfluid. outcomethuscriticallydependsonthemixingdegreebetweenhot
The RT instability can strongly modify the behavior of the SNgasandtherelativelycoolICM.
ejecta.Intheframeworkofourfiducialmodelwefindthatsignifi- Theabovepictureofmixinglayerisverycrudeandonecan-
cantfractionofSNfragmentsescapestherelativisticbubble.Inour notruleoutapossibilitythattheexpandingrelativisticbubblecon-
analysisofthisscenariowerelyonthefiducialmodelparameters tinuouslycatchesupwiththemixinglayerouterboundarysothat
outlinedinTable1.Agaslumpcrossingthebubbleboundaryand mostofthedeceleratedSNmaterialinjectedintheICMeventually
enteringtheICMisdeceleratedaftersweepingtheICMmasscom-
parablewithitsownmass.Theescapingwindshellgetsdecelerated
inthethermalplasmaofICMatthelengthoflw ∼ 1kpc(Section 3 0.6-2keVistheenergyrangewherepresentdaygrazingincidenceX-ray
2.2). The winddeposits 1.4 107 M inthislayer. Thisvalue telescopesaremostsensitive
∼ × ⊙
TypeIa supernovaeandstellarwindsin relativisticbubbles 9
turns out engulfed by the relativistic fluid. Qualitatively this sce- Forman,W.,Nulsen,P.,Heinz,S.,Owen,F.,Eilek,J.,Vikhlinin,
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isdeceleratedwellinsidethebubble.InthiscasenostrongX-ray 635,894
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verylowgasdensity). Thefateoftheirongenerated bySNIain Vikhlinin,A.,Begelman,M.,Bo¨hringer,H.,Eilek,J.,Heinz,S.,
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by observations of e.g. M87 (Churazovetal. 2001; Formanetal. Gull,S.F.,Northover,K.J.E.1973,Nature,244,80
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5 CONCLUSIONS
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6 ACKNOWLEDGEMENTS
57,285
We are grateful to Nail Inogamov and Sergey Sazonov for use- Vassiliadis,E.,Wood,P.R.1993,ApJ,413,641
ful discussions, and to Ewald Mu¨ller for sharing hydrocode. NC Wu,X.,Tremaine,S.2006,ApJ,643,210
thanksWolfgangHillebrandtfortheinvitationtoMPA.Thework
was partly supported by the Division of Physical Sciences of the
RAS (the program “Extended objects in the Universe”, OFN-16)
andtheprojectNSH-5069.2010.2.
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