As part of st larger effort to understand how binary and single stars form
from the collapse of magnetized molecular cloud cores, we perform a global
stability analysis of isopedically magnetized, singular isothermal disks (S
IDs). The work described here has precedents in earlier studies of disturba
nces in power-law disks by Zang in 1976, Toomre in 1977, Lynden-Bell & Lemo
s in 1993, Syer & Tremaine in 1996, and Goodman & Evans in 1999. We find th
e analytic criteria for the bifurcation of axisymmetric disks into nonaxisy
mmetric forms with azimuthal periodicities m = I (eccentric displacements),
2 (oval distortions), 3 (triangular distortions), etc. These bifurcations,
which occur at zero frequency, are the compressible and differentially rot
ating analogs of how the classical sequence of incompressible and uniformly
rotating Maclaurin spheroids bifurcate (secularly, under dissipative force
s) to become Dedekind ellipsoids with figure axes that remain fixed in spac
e. Like Syer & Tremaine and Lynden-Bell & Lemos, Ne also find that zero-fre
quency logarithmic spirals are possible scale-free disturbances, but our in
terpretation of the existence of such steadily propagating wavetrains is di
fferent. We give a dynamical instability interpretation based on the onset
of swing amplification by overreflection at the corotation circle of progra
de spiral density waves the pattern speeds of which have nonzero and positi
ve values. Our analysis yields identical instability criteria as the global
normal-modes treatment of Goodman & Evans, and we tentatively also identif
y dynamical barred-spiral instabilities as the "breathing mode" limit of tw
o-armed ordinary-spiral instabilities. We prove a general "reciprocity theo
rem," which states that the overreflection factors are identical for spiral
density waves launched from cavities interior or exterior to Q-barriers th
at straddle the corotation circle. This globally valid result supports a un
ifying interpretation, advocated for many years by C. C. Lin and his collea
gues (see, e.g., work by Bertin gr Lin): the coexistence of spiral structur
e in galaxies arising from the instability of internal normal modes in the
combined star/gas disk or from driving by external tidal influences associa
ted with the chance passages of companion bodies.