Hydrodynamical simulations of the jet in the symbiotic star(2)

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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Recently,Karovskaetal.(2007,hereafterKCR07)re-portedthedetectionofmultiplecomponents,includinganarc,inthearchivalChandraimages.

RAqrandCHCygaretheonlytwojetsofsymbioticstarswhicharedetectedinX-rays.Whilethesetwoob-jectsareseenathighinclinations,inMWC560thejetaxisispracticallyparalleltothelineofsight.Thisspe-cialorientationallowsonetoobservetheout owinggasaslineabsorptioninthesourcespectrum.Withsuchobservationstheradialvelocityandthecolumndensityoftheout owingjetgasclosetothesourcehasbeeninvestigatedingreatdetail.Inparticulartheacceler-ationandevolutionofindividualout owcomponentsandjetpulseshasbeenprobedwithspectroscopicmon-itoringprograms,asdescribedinSchmidetal.(2001).Usingthisopticaldata,sophisticatednumericalmod-elsofthispulsedpropagatingjethavebeendeveloped(Stute,Camenzind&Schmid2005;Stute2006,here-afterPaperIandIIinthisseries).Anumberofhydro-dynamicalsimulations(withandwithoutcooling)weremadeinwhichthejetdensityandvelocityduringthepulseswerevaried.Thebasicmodelabsorptionlinepro lesinMWC560aswellasthemeanvelocityandvelocity-widthareingoodagreementwiththeobserva-tions.Theevolutionofthetime-varyinghighvelocityabsorptionline-componentsisalsowellmodeled.Thesemodelsnotonly ttheMWC560data,butarealsoabletoexplainpropertiesofjetsinothersymbioticsystemssuchastheobservedvelocityandtemperatureoftheCHCygjet.

Sofar,MWC560hasnotbeendetectedinX-rays(M¨ursetetal.1997).We ndusingthePIMMStool1thatthenon-detectionintheROSATall-skysurveysetsan1upperlimitoftheabsorbedX-ray uxof0.07countss (M¨ursetetal.1997)and7×10 13ergs 1cm 2,respectively.

Thejetsinallthreesymbioticstarsshowevidenceofepisodicity.Suchepisodicityintheejectionprocesshasbeenseeninnumericalmodelsoftheinteractionofthestellarmagnetosphereandtheaccretiondisk(e.g.Goodsonetal.1997;Mattetal.2002).Inthedisk-windscenario(e.g.Blandford&Payne1982;Andersonetal.2003)thetime-dependentemissioniscreatedbytimevariationsintheaccretionrateoftheunderlyingdisk.Unfortunately,sofarnohydrodynamicalmodelsexistforexplainingtheX-rayemissionfromsymbioticstars.Asa rststepwehavethereforeusedourexistingsim-ulations,which tMWC560,forunderstandingtheob-servedX-rayemissionpropertiesofMWC560,CHCygandRAqr.

In§2,webrie ydescribethenumericalmodelswehaveused.ThetotalX-rayluminosityanditstimedepen-denceisexaminedin§3.Aftertheresultingspectraarecalculatedin§4,weshowemissionmapsin§5andap-plyourmainresultstoX-rayobservationsofCHCyg,MWC560andRAqrin§6.Finallyourconclusionsaregivenin§7.

2.THENUMERICALMODELS2.1.Thehydrodynamicalsimulations

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http://heasarc.gsfc.nasa.gov/Tools/w3pimms.html

Wesolvedtheequationsofidealhydrodynamicswithanadditionalcoolingtermintheenergyequation

ρ

t

+ (ρv v)= p ρ Φ e

CPwhichwaswrittenby

Ziegler&Yorke(1997)andmodi edbyThiele(2000)tocalculateradiativelossesduetonon-equilibriumcool-ingbylineemission.ρisthegasdensity,pthepressure,etheinternalenergydensity,Φthegravitationalpoten-tial,vthevelocityandγtheratioofthespeci cheatsatconstantpressureandvolumewhichissettoγ=5/3.ThegeneralcapabilitiesofthecodehavebeendescribedindetailinPaperI,forourapproximationsandassump-tionsrelatedtothecoolingtreatmentwereferthereadertoPaperII.Webrie ydescribethegeometrywhichwehaveadoptedinoursimulationsbelow.

Weuseacylindricalcoordinatesystemwherethejetaxiscorrespondstothezaxisandbothcomponentsofthebinarysystemarelocatedintheplaneperpendiculartothisaxis.Thehotcomponentislocatedattheoriginofthecoordinateframe;withabinaryseparationof4AU,aredgiantisimplemented.Theredgiantissurroundedbyastellarwindwithconstantvelocityof10kms 1andamasslossrateof10 6M⊙yr 1.

Thejetisproducedwithinathinjetnozzlewitharadiusof1AU.Theinitialvelocityofthesteadyjetischosento1000kms 1anditsdensityissetto8.4×10 18gcm 33(equaltoahydrogennumberdensityof5×106cm ). These8parametersleadtoi)amasslossrateof≈10M⊙yr 1inthesteadyjet,andii)adensitycontrastbetweenthesteadyjetandtheambientmediumηof5×10 3andaMachnumberof≈60inthejetnozzleattheoriginofthecoordinatesystem.Repeatedlyeachseventhday,thevelocityanddensityvaluesinthenozzlearechangedtosimulatethejetpulseswhichareseenintheobservationsofMWC560.Thedurationofeachpulseisoneday.

Twomodels(iv’andi’)outofourexistingsetofeightmodelswerechosenforcomputingX-rayemissionprop-erties.Thesemodelsrepresentmaximum(modeliv’)andminimum(modeli’)valuesofthejetdensityinthepulses.Inmodeliv’(modeli’),thejetdensityinthepulsesishigher(lower)thanthejetdensityinthesteadyjet.Althoughmodeliv’providedthebest tfortheop-ticaldataforMWC560,ourworkinthispapershowsthatmodeli’resultsinX-raypropertieswhicharemoreappropriateforCHCyg.Forbothmodelsweusedanapproximatetreatmentofradiativecooling.ThemodelpropertiesincludingthevelocitiesanddensitiesofthejetpulsesaregiveninTable1.

Mapsoflogarithmofdensityandtemperatureformodeli’onday162andformodeliv’onday115aregiveninFig.1.Botharethelasttime-stepscalculated.

2.2.CalculatingtheX-rayproperties

WedeterminedtheexpectedX-ray uxusingtheden-sityandtemperaturemapsfromthehydrodynamical