Non-Linear Resonance in Nearly Geodesic Motion in Low-Mass X-Ray Binaries. Abramowicz, M. A., Karas, V., Kluzniak, W., Lee, W. H., & Rebusco, P. Publications of the Astronomical Society of Japan, 55:467–466, April, 2003.
Non-Linear Resonance in Nearly Geodesic Motion in Low-Mass X-Ray Binaries [link]Paper  doi  abstract   bibtex   
We have explored the ideas that parametric resonance affects nearly geodesic motion around a black hole or a neutron star, and that it may be relevant to the high-frequency (twin) quasi-periodic oscillations that occur in some low-mass X-ray binaries. We have assumed the particles or fluid elements of an accretion disc to be subject to an isotropic perturbation having a hypothetical but rather general form. We find that the parametric resonance is indeed excited close to the radius where epicyclic frequencies of the radial and meridional oscillations are in a 2 : 3 ratio. The location and frequencies of the highest amplitude excitation vary with the strength of the perturbation. These results agree with actual frequency ratios of twin kHz QPOs that have been reported in some black hole candidates, and they may be consistent also with correlation of the twin peaks in Sco X-1.
@article{abramowiczNonLinearResonanceNearly2003,
	title = {Non-{Linear} {Resonance} in {Nearly} {Geodesic} {Motion} in {Low}-{Mass} {X}-{Ray} {Binaries}},
	volume = {55},
	issn = {0004-6264},
	url = {http://adsabs.harvard.edu/abs/2003PASJ...55..467A},
	doi = {10.1093/pasj/55.2.467},
	abstract = {We have explored the ideas that parametric resonance affects nearly geodesic motion around a black hole or a neutron star, and that it may be relevant to the high-frequency (twin) quasi-periodic oscillations that occur in some low-mass X-ray binaries. We have assumed the
particles or fluid elements of an accretion disc to be subject to an isotropic perturbation having a hypothetical but rather general form. We find that the parametric resonance is indeed excited close to the radius where epicyclic frequencies of the radial and meridional oscillations are in a 2 : 3 ratio. The location and frequencies of the highest amplitude excitation vary with the strength of the perturbation. These results agree with actual frequency ratios of twin kHz QPOs that have been reported in some black hole candidates, and they may be consistent also with correlation of the twin peaks in Sco X-1.},
	urldate = {2020-01-24},
	journal = {Publications of the Astronomical Society of Japan},
	author = {Abramowicz, Marek A. and Karas, Vladimir and Kluzniak, Włodzimierz and Lee, William H. and Rebusco, Paola},
	month = apr,
	year = {2003},
	keywords = {J1550-564), J1655-40, QPOs, X-rays: binaries, X-rays: individual (Scorpio X-1, accretion, general relativity},
	pages = {467--466},
}

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