This letter expands the stability criterion for radially stratified , vertically unstratified accretion disks incorporating thermal relaxation .
We find a linear amplification of epicyclic oscillations in these disks that depends on the effective cooling time , i.e .
an overstability .
The growth rates of the overstability vanish for both extreme cases , e.g .
infinite cooling time and instantaneous cooling , i.e .
the adiabatic and fully isothermal cases .
However , for thermal relaxation times \tau on the order of the orbital frequency , \tau \Omega \sim 1 , modes grow at a rate proportional to the square of the Brunt-Väisälä frequency .
The overstability is based on epicyclic motions , with the thermal relaxation causing gas to heat while radially displaced inwards , and cool while radially displaced outwards .
This causes the gas to have a lower density when moving outwards compared to when it moves inwards , so it feels the outwards directed pressure force more strongly on that leg of the journey .
We suggest the term “ Convective Overstability ” for the phenomenon that has already been numerically studied in the non-linear regime in the context of amplifying vortices in disks , under the name “ Subcritical Baroclinic Instability ” .
The point of the present paper is to make clear that vortex formation in three-dimensional disks is neither subcritical , i.e .
does not need a finite perturbation , nor is it baroclinic in the sense of geophysical fluid dynamics , which requires on vertical shear .
We find that Convective Overstability is a linear instability that will operate under a wide range of physical conditions for circumstellar disks .