A self-consistent model of a 22 GHz water maser in

arXiv:astro-ph/0510642v121Oct2005Astronomy&Astrophysicsmanuscriptno.agbFebruary5,2008(DOI:willbeinsertedbyhandlater)Aself-consistentmodelofa22GHzwatermaserinadustyenvironmentnearlate-typestarsNataliaBabkovskaiaandJuriPoutanenAstronomyDivision,P.O.Box3000,FIN-90014UniversityofOulu,Finlande-mail:[e-mail];[e-mail]5,2008Abstract.Westudytheconditionsforoperationofthe22GHzortho-watermaserinadustymediumnearlate-typestars.Themainphysicalprocesses,suchasexchangeofenergybetweendustandgasintheradiationfieldofastar,radiativecoolingbywatermoleculesandpumpingofwatermasersaredescribedself-consistently.Weshowthatthepresenceofdustgrainsofvarioustypes(orofonetypewithsizedistribution)stronglyaffectsthemaseraction.ThepumpingmechanismbasedonthepresenceofthedustofdifferentopticalpropertiesisabletoexplainwatermasersinthesilicatecarbonstarV778Cyg.However,themasersinthewindsfromasymptoticgiantbranchstarsrequireanadditionalsourceofheating,forinstanceduetothedustdriftthroughthegas.Keywords.circumstellarmatter–masers–radiolines:general–stars:AGBandpost-AGB–stars:late-type–stars:winds,outflows1.Introduction22GHz(616→523)ortho-watermaseremissionhasbeendetectedfrommanyastronomicalobjects,suchaslate-typestars,starformationregions,andactivegalacticnu-clei.Inrecentyears,muchprogressinstudyingmaserobjectshasbeenmadeduetoincreasingangularresolu-tionandsensitivityofradio-interferometers,whichallowonetoobtaindetailedmapsofthedistributionofmasersources.Theseobservationsprovideimportantinforma-tionaboutthestructure,physicalconditionsandkinemat-icsofthegasinthesesources.Theobservationaldatashowthatinmostofthem,maserradiationcomesfromthere-gionco-spatialwithsourcesoftheinfrareddustemission(Downesetal.1981;Yamamuraetal.2000;Danchietal.1994)and,therefore,maseramplificationmaytakeplaceinadustyenvironment.Inasymptoticgiantbranchstars(AGBs)andredsu-pergiants(RSGs),masersaremostlyobservedinstellarwinds.Watermasersobservedinsomesilicatecarbonstars,e.g.V778Cyg(Engels1994;Engels&Leinert1994),arenotassociatedwiththewinds,butmostprobablyariseinanoxygen-richdiskaroundacompanionstarinabi-narysystem(Szczerbaetal.2005).Thefirstmodelofwatermasersinlate-typestarswasproposedbyDeguchi(1977),whoconsideredanexpand-ing,sphericallysymmetriccircumstellarenvelope.Thelinephotonswereassumedtoescapefromthewindduetothehighvelocitygradients.Thegastemperaturewasnotcom-putedself-consistently,butwasassumedtobeapower-lawfunctionofdistancefromthestar.Inhismodel,thestrongestwatermasersarepredictedalongtangentialdi-rectionswherethecoherentlengthislargest.Heusedap-proximateformulaeforthecollisionalcross-sectionsandneglectedtheinfluenceofdustonthemaserstrength.Cooke&Elitzur(1985)havepresentedamoreelabo-ratemodelemployinganewsetofcollisionalcross-sectionsbyGreen(1980)andusingthewindparameterstakenfromthemodelofGoldreich&Scoville(1976).Inthismodel,theaccelerationofthewindisprovidedbytheradiationpressureonthedustparticles,thetemperaturewasassumedtobedeterminedbythestellarradiation,whilethegasisviscouslyheatedbycollisionswithfastermovingdustgrains.Cooke&Elitzur(1985)assumethesametemperatureprofileforoutflowswithverydifferentcharacteristics.Theyhaveaccountedfortheinfluenceofdustemission(usingasimplifieddustabsorptioncoeffi-cient)ontheexcitationofwatermolecule,butignoredtheeffectoflinephotonabsorptionbythedust.Thees-capeofphotonswasagainassumedtobedeterminedbythevelocitygradient.Humphreysetal.(2001)alsosimulatedmasersinthewindsinaSobolev(1960)approximation,usingmorerecentcollisionalcross-sectionsprovidedbyGreenetal.(1993).Theyobtained,however,suspiciouslyhighgastemperaturesbecauseofignoringmolecularcooling.Theinfluenceofdustabsorptiononthewatermoleculepopu-lationwasagainneglected.2Babkovskaia&Poutanen:Watermasersinlate-typestarsRecentobservationsbyMERLINandVLAhaveshownthatthewindsfromAGBsandRSGsarestronglyinho-mogeneous.Watermasersariseatdistancesof10-60AUfromAGBsandhaveatypicalsizeof2−4AUacross(Bainsetal.2003),whileinRSGsallsizesare5to10timeslarger.Moreover,thefillingfactorofthecloudsisonly∼0.01.Becauseoftherelativelysmallsizes,thevelocitygradientwithinthecloudsisnegligibleandtheSobolevapproximationbecomesquestionable.Theaforementionedmaserwindmodels(Deguchi1977;Cooke&Elitzur1985;Humphreysetal.2001)oper-ateonthedeJong(1973)mechanismofcollisionalpump-ingwherethebreakdownofthermalequilibriumoccursbecausethegasbecomestransparentfordifferenttran-sitionsatdifferentphysicaldepths.However,thepres-enceofdustcanstronglyinfluencethemaserstrength(Goldreich&Kwan1974;Kegel1975;Strelnitskij1977;Bolgovaetal.1977).Goldreich&Kwan(1974)suggestedthatthehotdustradiationcanexcitewatermoleculestothevibrationalstate,andtheheatsinkcouldbeprovidedbycollisionswithcooler(thandust)hydrogenmolecules.Thepossibilityofinversioninsuchasitua-tionwasquestionedbyDeguchi(1981).Alternatively,thecolddustcanproducethenecessaryinversion(Strelnitskij1977;Bolgovaetal.1977;Deguchi1981;Chandraetal.1984a;Collison&Watson1995;Wallin&Watson1997;Yatesetal.1997;Babkovskaia&Poutanen2004,here-afterBP04).Inanopticallythicken