Annular structures in perturbed low mass disc-shaped gaseous nebulae II : general and polytropic models

TL;DR

This paper analytically explores the formation of annular structures in low mass, perturbed gaseous discs, extending previous work to include polytropic models and small frequency perturbations, revealing exponential spacing of density maxima.

Contribution

It provides new analytical solutions for perturbed low mass gaseous discs with polytropic and general exponents, expanding understanding of disc structure formation under perturbations.

Findings

Maxima of perturbed specific mass are exponentially spaced.

Distance ratio of maxima is constant and depends on disc properties.

Annular structures can form via inward and outward gas flows.

Abstract

This is the second of two papers where we study additional analytical solutions of a bidimensional low mass gaseous disc rotating around a central mass and submitted to small radial perturbations. In a first Paper, hydrodynamics equations were solved for the equilibrium and perturbed configurations and a wave-like equation for the gas perturbed specific mass was deduced and solved analytically for several cases of exponents of the power law distributions of the unperturbed specific mass and sound speed. In this paper, two other general cases of exponents, including a polytropic case, are solved analytically for small frequencies of the perturbations. Similar conclusions to the ones of Paper I are found, namely that the maxima of the gas perturbed specific mass are exponentially spaced and that their distance ratio is a constant, function of disc characteristics and of the perturbations frequency. Gaseous annular structures would eventually be formed in the disc by inward and outward gas flows from zones of minima toward zones of maxima of perturbed specific mass.