Open AccessOn the r‐mode spectrum of relativistic stars in the low‐frequency approximation
Author(s) -
Ruoff Johannes,
Kokkotas Kostas D.
Publication year - 2001
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1046/j.1365-8711.2001.04909.x
Subject(s) - physics , continuous spectrum , eigenvalues and eigenvectors , barotropic fluid , stars , perturbation (astronomy) , excited state , neutron star , classical mechanics , formalism (music) , mode (computer interface) , astrophysics , quantum electrodynamics , quantum mechanics , mechanics , computer science , operating system , art , musical , visual arts
The axial modes for non‐barotropic relativistic rotating neutron stars with uniform angular velocity are studied, using the slow‐rotation formalism together with the low‐frequency approximation, first investigated by Kojima. The time‐independent form of the equations leads to a singular eigenvalue problem, which admits a continuous spectrum. We show that for , it is nevertheless also possible to find discrete mode solutions (the r modes). However, under certain conditions related to the equation of state and the compactness of the stellar model, the eigenfrequency lies inside the continuous band and the associated velocity perturbation is divergent; hence these solutions have to be discarded as being unphysical. We corroborate our results by explicitly integrating the time‐dependent equations. For stellar models admitting a physical r‐mode solution, it can indeed be excited by arbitrary initial data. For models admitting only an unphysical mode solution, the evolutions do not show any tendency to oscillate with the respective frequency. For higher values of l it seems that in certain cases there are no mode solutions at all.