TY - JOUR
T1 - Stability of radial perturbations for non-uniformly rotating self-gravitating, finite, gaseous disks
AU - Yahalom, Asher
PY - 2009/3/16
Y1 - 2009/3/16
N2 - Radial stability conditions of self-gravitating, finite disks in non-uniform rotations are obtained by minimizing their energy keeping, mass and circulations constant. These global stability conditions are necessary and sufficient since no gyroscopic terms appear in the perturbed equations. This energy principle is applied to a class of finite differentially rotating disks with adiabatic index γ > 2 and with derivatives of densities that go smoothly to zero at the boundary. The global stability limits fit remarkably well Toomre's necessary conditions for local stability. I also find that for disks with adiabatic index γ = 2, Toomre's necessary local criterion is indeed a sufficient global condition for stability.
AB - Radial stability conditions of self-gravitating, finite disks in non-uniform rotations are obtained by minimizing their energy keeping, mass and circulations constant. These global stability conditions are necessary and sufficient since no gyroscopic terms appear in the perturbed equations. This energy principle is applied to a class of finite differentially rotating disks with adiabatic index γ > 2 and with derivatives of densities that go smoothly to zero at the boundary. The global stability limits fit remarkably well Toomre's necessary conditions for local stability. I also find that for disks with adiabatic index γ = 2, Toomre's necessary local criterion is indeed a sufficient global condition for stability.
KW - Energy variational principle
KW - Self-gravitating systems
KW - Stability of fluids
UR - http://www.scopus.com/inward/record.url?scp=60649088227&partnerID=8YFLogxK
U2 - 10.1016/j.physleta.2009.01.060
DO - 10.1016/j.physleta.2009.01.060
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:60649088227
SN - 0375-9601
VL - 373
SP - 1170
EP - 1176
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 12-13
ER -