Stationary perturbation configurations in a composite system of stellar and coplanarly magnetized gaseous singular isothermal discs

We construct aligned and unaligned stationary perturbation configurations in a composite system of stellar and coplanarly magnetized gaseous singular isothermal discs (SIDs) coupled by gravity. This study extends recent analyses on (magnetized) SIDs of Shu et al., Lou and Lou & Shen. By this model, we intend to provide a conceptual framework to gain insights for multi-wavelength large-scale structural observations of disc galaxies. Both SIDs are approximated to be razor-thin and are in a self-consistent axisymmetric background equilibrium with power-law surface mass densities and flat rotation curves. The gaseous SID is embedded with a coplanar azimuthal magnetic field Bθ(r) of a radial scaling r −1/2 that is not force-free. In comparison with SID problems studied earlier, there exist three possible classes of stationary solutions allowed by more dynamic freedoms. To identify physical solutions, we explore parameter space involving three dimensionless parameters: ratio λ of Alfvén speed to sound speed in the magnetized gaseous SID, ratio β for the square of the stellar velocity dispersion to the gas sound speed and ratio δ of the surface mass densities of the two SIDs. For both aligned and unaligned spiral cases with azimuthal periodicities |m| ≥ 2, one of the three solution branches is always physical, while the other two branches might become invalid when β exceeds certain critical values. For the onset criteria from an axisymmetric equilibrium to aligned secular bar-like instabilities, the corresponding T /|W −M| ratio, which varies with λ, β and δ, may be considerably lower than the oft-quoted value of T /|W| ∼ 0.14, where T is the total kinetic energy, W is the total gravitational potential energy and M is the total magnetic energy. For unaligned spiral cases, we examine marginal instabilities for axisymmetric (|m| = 0) and non-axisymmetric (|m| > 0) disturbances. The resulting marginal stability curves differ from the previous ones. The case of a composite partial MSID system is also investigated to include the gravitational effect of an axisymmetric dark matter halo on the SID equilibrium. We further examine the phase relationship among the mass densities of the two SIDs and azimuthal magnetic field perturbation. Our exact global perturbation solutions and critical points are valuable for testing numerical magnetohydrodynamic codes. For galactic applications, our model analysis contains more realistic elements and offer useful insights for structures and dynamics of disc galaxies consisting of stars and magnetized gas.