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 B _ { \theta } ( 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 \lambda of Alfvén speed to sound speed in the magnetized gaseous SID , ratio \beta for the square of the stellar velocity dispersion to the gas sound speed and ratio \delta of the surface mass densities of the two SIDs .
For both aligned and unaligned spiral cases with azimuthal periodicities |m| \geq 2 , one of the three solution branches is always physical , while the other two branches might become invalid when \beta 
exceeds certain critical values .
For the onset criteria from an axisymmetric equilibrium to aligned secular bar-like instabilities , the corresponding \mathcal { T } / | \mathcal { W } - \mathcal { M } | ratio , which varies with \lambda , \beta and \delta , may be considerably lower than the oft-quoted value of \mathcal { T } / | \mathcal { W } | \sim 0.14 , where \cal { T } is the total kinetic energy , \cal { W } is the total gravitational potential energy and \cal { 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 .