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**VolumeTitle** ASPConferenceSeries,Vol.**VolumeNumber** **Author** (cid:13)c**CopyrightYear**AstronomicalSocietyofthePacific Parker Winds Revisited: AnExtension to DiskWinds 2 1 TimothyR.Waters,1 DanielProga,1,2 0 2 1DepartmentofPhysics,University ofNevada,LasVegas,NV89154 n 2Princeton UniversityObservatory, PeytonHall,Princeton, NJ08544 a J Abstract. A simple, one-dimensional dynamical model of thermally driven disk 4 winds,oneinthespiritoftheoriginalParker(1958)model,ispresented. Weconsider ] twodifferentaxi-symmetricstreamlinegeometries: geometry(i)iscommonlyusedin A kinematic models to compute synthetic spectra, while geometry (ii), which exhibits G self-similarityandmorecloselyresemblesthegeometryfoundbymanynumericalsim- ulations of disk winds, is likely unused for this purpose — although it easily can be . h withexistingkinematicmodels. Wemakethecasethatitshouldbe,i.e. thatgeometry p (ii)leadstotransonicwindsolutionswithsubstantiallydifferentproperties. - o r t s a 1. Introduction [ 1 Developing baseline disk wind models analogous to the spherically symmetric Parker v model(Parker, 1958) hasproventobeadifficult task. Amajorroadblock hasbeenthe 5 uncertainty inthestreamline geometry. Anotherobvious andrelateddifficultyisposed 6 8 by the fact that accretion disks span many more orders of magnitude in physical size 0 than do stars, and they can host radically different, spatially and temporally variable, 1. thermodynamic environments. It should come as no surprise then, that despite clear 0 observational evidence of outflows from many systems, identifying the actual driving 2 mechanisms, aswellasdetermining thewindgeometry,remainsachallenge. 1 Studies of disk winds therefore rely heavily on kinematic models in order to : v quicklyexploretheparameterspacewithoutassumingaparticular drivingmechanism. i X Apopularchoiceofgeometry,onethathasbeenusedinconjunctionwithsophisticated radiative transfer simulations to model accretion disk spectra from many systems, in- r a cluding AGN (Sim et al. 2008), is the Converging model — geometry (i) in Figure 1. Recentmulti-dimensional, time-dependent simulations ofathermally drivenwindcar- ried out by Luketic et al. (2010) suggest that the Converging model may not be well- suited for sampling the entire wind, but rather only the inner portions of it. The outer portion is better approximated by a model in which streamlines emerge at a constant inclination angleitothemidplane(hencethename,theCIAmodel—geometry(ii).) We have generalized the isothermal and polytropic Parker wind solutions so that theyapply togeometries (i)and (ii). Oursolutions amount toasimple dynamical disk windmodel(seeWaters&Proga2012). Ratherthanpositing avelocity lawasisdone forkinematicmodels,thepurposeofadynamicalmodelistoimposethephysicalcon- ditionsandsolveforthewindvelocityasafunctionofdistancealongastreamline. Here wesummarize our findings for how the streamline geometry alone can result in winds withsubstantiallydifferentflowproperties,limitingourattentiontotheisothermalcase. 1 2 Waters&Proga,ParkerWindsRevisited:AnExtensiontoDiskWinds 2. Results&Conclusions The long-dashed and solid curves in the plot in Figure 1 depict the steady-state flow properties of a Parker-like disk wind traversing geometries (i) and (ii), respectively. Specifically, we plot the equivalent nozzle function (denoted N) along a streamline, in units of the gravitational radius. Also shown are N for the spherically symmetric (bottom dotted curve) and Keplerian (a radial Parker wind with a Keplerian azimuthal velocity component; topmost dashed-dotted curve) Parker winds. Revolving N about the horizontal axis sweeps out the shape of a de Laval Nozzle that yields steady-state flow properties identical to that of the wind; this shape is exponentially dependent on the effective potential and the squared ratio of the local escape velocity to the sound speed (the HEP).Comparing the throat locations and corresponding magnitudes of N forgeometries(i)and(ii),itisclearthattheCIAmodelhasasonicpointdistanceabout twice that of the Converging model (implying a smaller acceleration) and an initial MachnumberM = V /c thatissmallerbynearlyanorderofmagnitude. SinceM o o s o is a direct gauge of the mass flux density, the total mass loss rate for a CIA wind will be smaller in general. These differences all result from the confined expansion area of theCIAmodel,duetoitslackofadjacentstreamline divergence. Bothwindsexperienceareducedcentrifugalforceati = 60◦comparedtoaKeple- rianParkerwind,explainingwhythelatterhasasignificantlyhigherinitialMachnum- ber. We can therefore arrive at the result that the mass flux densities of our disk wind models are always bounded from below by that of the spherically symmetric Parker windandabovebythatoftheKeplerianParkerwind. Insummary,thedifferentproperties oftheCIAandConverging modelsaresolely due togeometric effects. If, for agivenHEPandi, the resulting velocity profiles were approximated by a beta-law, the parameters V and β (the slope) might differ by an o order of magnitude. Kinematic models that make use of a beta-law are therefore sen- sitive tothetype of windgeometry. Theimplication isthatemploying theConverging modelmayleadtosignificant overestimates oftheflowacceleration ifthetruestream- line geometry more closely resembles the CIA model. The synthetic line profiles will beaffected, especially iftheionization balance ofthewindisassumedtodepend upon thedensityortemperature profiles,whichsignificantly differforthesegeometries. 1.000 0.500 0.100 0.050 0.010 0.005 0.0010.0 0.5 1.0 1.5 2.0 Figure1. AdjacentstreamlinesdivergefromeachotherintheConvergingmodel butnotintheCIAmodel.Theplotofequivalentnozzlefunctionswascalculatedby taking HEP = 11 and i = 60◦. We have normalized N such that N ≈ M at the o nozzlethroat;thehorizontallinesmarktheexactvaluesofM . o 3 References Luketic, S., Proga,D., Kallman, T. R., Raymond,J. C., &Miller, J. M. 2010,ApJ,719, 515. 1003.3264 Parker,E.N.1958,ApJ,128,664 Sim,S.A.,Long,K.S.,Miller,L.,&Turner,T.J.2008,MNRAS,388,611.0805.2251 Waters,T.R.&Proga,D.2012,submitted