We construct stationary global configurations of both aligned and unaligned logarithmic spiral perturbations in a composite disc system of stellar and isopedically magnetized gaseous singular isothermal discs ( SIDs ) coupled by gravity .
Earlier models are generalized to a more general theoretical framework .
The thin gaseous SID is threaded across by a vertical magnetic field B _ { z } with a constant ratio of the surface gas mass density to B _ { z } .
In reference to SID models of Shu & Li , Shu et al. , Lou & Shen , Lou & Zou , Shen , Liu & Lou , there exist two classes of stationary magnetohydrodynamic ( MHD ) solutions with in-phase and out-of-phase density perturbations here .
Relevant parameter regimes are explored numerically .
For both aligned and unaligned cases with azimuthal periodicities |m| \geq 2 ( m is an integer ) , there may be two , one , and no solution situations , depending on the chosen parameters .
For the transition criteria from an axisymmetric equilibrium to aligned secular bar-like instabilities , the corresponding \mathcal { T } / | \mathcal { W } | ratio can be much lower than the oft-quoted value of \mathcal { T } / | \mathcal { W } | \sim 0.14 , where \mathcal { T } is the total rotational kinetic energy and \mathcal { W } is the total gravitational potential energy plus the magnetic energy .
The \mathcal { T } / | \mathcal { W } | ratios for the two sets of solutions in different ranges are separated by m / ( 4 m + 4 ) .
For the unaligned cases , we study marginal stabilities for axisymmetric ( m = 0 ) and non-axisymmetric ( m \neq 0 ) disturbances .
By including the gravitational influence of an axisymmetric dark matter halo on the background , the case of a composite partial magnetized SID system is also examined .
The global analytical solutions and their properties are valuable for testing and benchmarking numerical MHD codes .
For astrophysical applications to large-scale galactic dynamics , our model analysis contains more realistic elements and offers useful insights into the structures and dynamics of disc galaxies consisting of stars and magnetized interstellar medium .
In particular , in the presence of star burst activities , supernovae , hypernovae , superbubbles etc. , our open magnetic field geometry in disc galaxies bears strong implications on circumnuclear and spiral galactic winds .