A geometrically thin accretion disc around a Maclaurin spheroid

Abstract

We investigated a semi-analytic and numerical model to study a geometrically thin and optically thick accretion disc around a Maclaurin spheroid (MS). The main interest is in the inner region of the so-called α-disc, α being the viscosity parameter. Analytical calculations are done assuming radiation pressure and gas pressure dominated for close to the Eddington mass accretion rate and M˙ ≲ 0.1 M˙Edd, respectively. We found that the change in the eccentricity of theMS causes a change at the high-frequency region in the emitted spectra. We found that disc parameters are dependent on the eccentricity of the MS. Our semi-analytic results show that qualitatively an increase in the eccentricity of the MS has the same behaviour as a decrease in the mass accretion rate. Numerical work has been carried out to see the viscous time evolution of the accretion disc around an MS. In a numerical model, we showed that if the eccentricity of an object is high, the matter will diffuse slowly during its viscous evolution. This gives a clue how spin-up or spin-down can change the time evolution of the accretion disc using a simple Newtonian approach. The change in spectra can be used to determine the eccentricity and thus the period of the MS.