# Local Stability and Structure of a Differentially Rotating Star of Non-Uniform Density

### Abstract

A method is proposed to compute the theoretical estimation of physical parametersand stability of differential rotation for polytropic starsincluding mass variation. The law of differential rotation is assumed to be in the form ω^{2} (s) = b_{1 }+ b_{2 }s^{2 + }b_{3} s^{4 }, the angular velocity of rotation (ω) is a function ofdistance (s) of the fluid element from the axis of rotation.Utilizing theconcepts of Roche-equipotential and averaging approachof (Kippenhahnand Thomas, 1970)in a manner, earlier used by (Saini, et al., 2012) to incorporate the effects of differential rotation on the equilibrium structure of polytropic stellar models. The inner structure of differentially rotating polytropic models of a star is demonstrated by calculating various physical parameters for suitable combinations of parameters.

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### References

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