Hydrodynamical simulations of the jet in the symbiotic star(8)

In papers I and II in this series, we presented hydrodynamical simulations of jet models with parameters representative of the symbiotic system MWC 560. These were simulations of a pulsed, initially underdense jet in a high density ambient medium. Since th

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suchemissionresultsfrominternalshocksgeneratedbycollidingjetejecta.

Consideringthesmallerdistanceof268pctoCHCyg,themodelX-ray33luminosityof2.2×1032ergs 1formodeli’and1.5×10ergs 1formodel 11iv’inthe0.2–2keVrangeimplies uxesof22.6×10ergs 1cm 2and1.74×10 10ergs 1cm ,respectively.TheinterstellarextinctionforCHCygisAv=0.006orNH=1×1020cm 2,thustheabsorbed uxis2×10 11ergs 1cm 2formodeli’and1.3×10 10ergs 1cm 2formodeliv’,respectively.Themeasured uxesofthesoftcompo-nentsassociatedwiththejet,however,lieintherange(0.4 3.8)×10 12ergs 1cm 2(Ezukaetal.1998;Galloway&Sokoloski2004;Mukaietal.2006).Sincethesemeasured uxesaresmallerthanthosepredictedbymodeli’andbyfarsmallerthanthosefrommodeliv’whichhasahigherjetpulsedensitythanmodeli’,weinferthatthejetpulsedensitiesinCHCygaresmallerthanthoseinMWC560andourmodels.If,asstatedin§3,theratiooftheX-rayluminositytothekineticen-ergypumpedintothejetisproportionaltothejetpulsedensity,wecanestimatethatthejetpulsedensityhastobereducedtoabout105cm 3tomodeltheX-ray uxobservedinCHCyg.Inordertoresolvethedi erencebetweenmeasuredandmodel uxeswithuncertaintiesinthedistancetoCHCyg,thelatterwouldhavetobeabout700pc,however,thislargevalueisveryunlikely,sincethedistancewasmeasuredwithHIPPARCOSwithanerrorof23%.

KCR07giveanobservationalestimateofthedensityinthejet,50cm 3,basedonthetotalX-rayluminosity,assuminganemittingspherewitharadiusof400AUandameanemissivityof2×10 23ergcm3s 1.How-ever,astrophysicaljets,typically,arecollimatedstruc-tureswhichhavesigni cantlysmallervolumesthanasphere.Sincewesimulatedthepropagationofthemodeljetsonlyuptoalengthof65AU,not400AU,wescaleupitsvolumeasfollows.Ifweassumethatthecross-sectionalareastaysconstantasthejetpropagatesandevolveswithtime,thejetvolumeisabout(π×62×400)AU3(Fig.9)whichissmallerbyaboutafactorof6000thanthatofaspherewitharadiusof400AU.Alter-natelyifweassumethatthelateralexpansionofthejetisproportionaltoitsaxialexpansion3,thevolumeisstilloverestimatedbyafactorofabout160.Furthermore,withinthevolumeofthejet,theX-raysareemittedbyclumpsandnotbythewholejet,i.e.the llingfactorfortheX-rayemissionis,ftemperatureof1.21<1.Inaddition,KCR07assumea×107K(1keV)toestimatetheemissivity,however,ourjetmodelsshowthatsuchhightemperaturesareonlyarchievedintheinnermostregionofthejet;atlargerdistancesfromthejetsourcealongtheaxis,theX-rayemittingknotsaresigni cantlycooler(Fig.1).ThusthevalueoftheemissitivityshouldbelowerandthedensityshouldbehigherthanestimatedbyKCR07byanothercorrectionfactorf2>1.HenceweconcludethatanaccurateestimateoftheX-rayemit-tingvolumeandthetemperaturewouldleadtoahigherdensitybyafactorof(160–6000)fgivenbyKCR07,oftheorder2/f1comparedtothevalueof104–106cm 3.ThisrangecompareswellwiththedensitiesofmaterialemittingsoftX-raysinourmodelswhichareoftheorder

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whichisseeninourmodelsafterday70(PaperII)

of105–106cm 3(Fig.1).

OtherpossibilitiestoreducetheX-ray uxesinourmodels,bringingthemclosertotheobservedonesinCHCyg,arei)alongertimescalebetweenthepulsesandii)asmallervelocitydi erencebetweenthesteadyjetandthejetpulses.Inthe rstcase,lessenergyispumpedintothejetandeachjetknotandthejetheadcancoolfurtherbeforebeinghitbythenextpulse.Inthesecondcase,thesmallervelocitydi erencereducesthetemperaturetowhichtheshockedmaterialisheated.However,thedensitycontrastthenalsohastobeadjustedinordertoreproducetheobservedpropermotionofthejetknots.Whichoftheabovescenariosisthemostlikelyonecanonlybedeterminedfromfuturesimulationswhichhavebeen ne-tunedto tthepropertiesoftheX-rayemittingmaterialinthejetofCHCyg.

In1994and2006,the uxfromthejetinCHCygwasalmost 1atthesamelevel,intherange(2.7 3.8)×10 12ergscm 2(Ezukaetal.1998;Mukaietal.2006).In2001,however,itwaslowerbyafactoroften(Galloway&Sokoloski2004).Inthecontextofourmod-els,suchadropin uxmayresultfromalargedecreaseinthedensityofthepulseswhichmaybecausedbyadropintheaccretionrateontothewhitedwarf.

6.3.RAqr

SincethejetvelocityinRAqrissmallerbyafactorof2thanthoseinourmodels,wecanonlymakeamorelimitedcomparisonofthemodelresultswiththeob-servations.Kelloggetal.(2006)andalsoKorrecketal.(2006)reportatangentialmotionofanX-rayemittingknot4of600kms 1.Korrecketal.(2006)estimatedadensityof100cm 3,however,itmaybepossiblethat,asinthecaseofCHCyg,theX-rayemittingvolumeisoverestimatedandthusthedensityisunderestimated.Kelloggetal.(2001)foundinRAqrthattheNEjetismoreluminousbyafactorof3thantheSWjet.ThespectrumtheNEjetwas ttedwithasingle-temperaturethermalplasmawithatemperatureof1.66keV,thespec-trumoftheSWjetwithaplasmatemperatureof0.2keV.Thesimplestexplanationofthisdi erenceisthattheambientmediaonbothsideshavedi erentdensitieswhichwouldleadtodi erentcompressionfactorsandthustodi erentshockheatingtemperatures.However,propermotionmeasurementsshownosigni cantdi er-encesinthevelocitiesoftheknotsinbothsidesofthejet(Paresce&Hack1994;M¨akinenetal.2004),whichwewouldexpectifdi erentambientdensitieswouldde-celeratethejetdi erentlyonbothsides.

Ourmodelingcanprovideaplausibleexplanationfortheobserveddi erencesbetweenthetwosidesofthejet,ifweassumethattheejectionofthejetpulsesonbothsidesareoutofphasewitheachother.Hollisetal.(1991)derivedakinematicageofbothjetsofabout90yrs;overtheextentofthejetwecanobserve3–6knotsintheob-servationsofe.g.Paresce&Hack(1994)whichsuggestsseveralejectioneventsinthisperiodoftime.Aperiodofabout17yearsfortheseejectioneventshasbeenin-ferredfromradioobservations(Kafatosetal.1989),thustheyaresigni cantlylargerthaninMWC560andinour

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1Korrecketal.(2006)giveanevensmallervelocityof380kmsfrominthetheirvalueTablegiven1,inhowever,thetext.

withoutexplainingthedi erence