Global Axisymmetric Stability Analysis for a Composite System of Two Gravitationally Coupled Scale-Free Discs

Forapositesystemofgravitationallycoupledstellarandgaseousdiscs,wehavecarriedoutalinearstabilityanalysisforaxisymmetriccoplanarperturbationsusingthetwo-fluidformalism.Thebackgroundstellarandgaseousdiscsaretakentobescale-freewithallphysicalvariablesvaryingaspowersofthecylindricalradiusrwithpatibleexponents.Theunstablemodessetinasneutralmodesorstationaryperturbationconfigurationswithangularfrequencyω=0.Theaxisymmetricstablerangeisboundedbytwomarginalstabilitycurvesderivedfromstationaryperturbationconfigurations.Becauseofthegravitationalcouplingbetweenthestellarandthegaseousdiscs,oneonlyneedstoconsidertheparameterregimeofthestellardisc.Thereexisttwounstableregimesingeneral:acollapseregimecorrespondingtolarge-scaleperturbationsandaring-fragmentationregimecorrespondingtoshort-wavelengthperturbations.Thepositesystemwillcollapseifitrotatestooslowlyandwillsuccumbtoring-fragmentationinstabilitiesifitrotatessufficientlyfast.TheoverallstablerangeagainstaxisymmetricperturbationsisdeterminedbyanecessaryD-criterioninvolvingtheeffectiveMachnumbersquaredDs2(thesquaredratioofthestellardiscrotationspeedtothestellarvelocitydispersionuptoanumericalfactor).Differentmassratioδandsoundspeedratioηofthegaseousandstellardiscponentswillaltertheoverallstability.Forspiralgalaxiesorcircumnucleardiscs,wefurtherincludethedynamicaleffectofamassivedarkmatterhalo.Astrophysicalapplicationstodiscgalaxies,proto-stellardiscsandcircumnucleardiscsaregivenasexamples.

Yu-QingLou(DepartmentofPhysics&CenterforAstrophysics,TsinghuaUniversity,Beijing,100084;NationalAstronomicalObservatories,ChineseAcademyofSciences,Beijing,100012;DepartmentofAstronomyandAstronomyandAstrophysics,TheUniversityofChicago,5640SouthEllisAvenue,Chicago,IL60637USA) 

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