Supplement to “Torsional oscillations of a magnetar with a tangled magnetic field” (2016, ApJL, 823, L1)

Journal Article · Sun May 01 04:00:00 EDT 2016 · Astrophysical Journal, Supplement Series

DOI:https://doi.org/10.3847/0067-0049/224/1/6· OSTI ID:22872502

Link, Bennett

We introduce a mean-field formalism with which to study the oscillations of a neutron star or other stellar object with a dipolar magnetic field plus a topologically distinct isotropic magnetic tangle that stabilizes the field configuration. In terms of the ratio of the energy density of the tangled field to that in the dipolar component b {sub t} {sup 2}, we obtain separable equations for the eigenfunctions and eigenfrequencies for a star of uniform density. We show that finite b {sub t} {sup 2} breaks the Alfvén continuum that is supported by the dipolar component of the field into discrete normal modes, and we quantify the splitting. Assuming the estimated dipole fields of 7×10{sup 14} G in SGR 1900+14 and 2×10{sup 15} G in SGR 1806–20, and tuning b {sub t} {sup 2} to match the lowest-frequency quasi-periodic oscillations observed to accompany flares in these objects, we infer b{sub t}{sup 2}=13.3 and 0.17, respectively. The predicted spectrum is about three times denser than that observed in SGR 1900+14, and much denser in SGR 1806–20. If the dipole field of SGR 1806–20 has been overestimated, the spectrum of normal modes will be less dense. We show that for b{sub t}{sup 2}≫1, as stability considerations suggest, the crust is nearly dynamically irrelevant. Moreover, density stratification generally shifts the eigenfrequencies up by about 20%, a change that can be mostly subsumed in a uniform density model with a slightly different choice of stellar radius or mass.

• OSTI ID: 22872502
• Journal Information: Astrophysical Journal, Supplement Series, Journal Name: Astrophysical Journal, Supplement Series Journal Issue: 1 Vol. 224; ISSN 0067-0049; ISSN APJSA2
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS
ALFVEN WAVES
EIGENFREQUENCY
EIGENFUNCTIONS
ENERGY DENSITY
MAGNETIC FIELDS
MASS
MEAN-FIELD THEORY
NEUTRON STARS
OSCILLATIONS
SPECTRA
TOPOLOGY