Singular isothermal disks. I. Linear stability analysis

Citation
Fh. Shu et al., Singular isothermal disks. I. Linear stability analysis, ASTROPHYS J, 535(1), 2000, pp. 190-210
Citations number
76
Categorie Soggetti
Space Sciences
Journal title
ASTROPHYSICAL JOURNAL
ISSN journal
0004637X → ACNP
Volume
535
Issue
1
Year of publication
2000
Part
1
Pages
190 - 210
Database
ISI
SICI code
0004-637X(20000520)535:1<190:SIDILS>2.0.ZU;2-U
Abstract
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.