Progress report on the work done in 2003 at the UK Astrophysical Fluids Facility of Leicester University, England, and supported by the European Community "Access to Research Infrastructure action of the Improving Human Potential" Program.

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GROUP LEADER: Marek A. Abramowicz
HOME LABORATORY: Chalmers Institute of Technology, Sweden
TELEPHONE: +46-31-772-3135

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Wlodek Kluzniak and I have noticed that the QPO variability frequencies in the X-ray flux of the BH source GRO J1655-40 are in the 3:2 ratio, and that that rational ratios are a genuine, typical property of QPOs observed in BH and NS sources. Rational ratios suggest that a resonance may be at work here. Working in 2002 at UKAFF, we explored an idea that a parametric resonance affects nearly circular, nearly Keplerian, nearly equatorial plane motion of test particles around a black hole or a neutron star. We numerically constructed a simple model, which reproduces rather well the Sco X-1 observational data. In 2003, we plan to continue this work at UKAFF by considering a much more advanced fluid model of the phenomenon.

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No difficulties have been encountered. Several sub-projects have been completed, of which I will mention two most interesting.

01. Mathematical improvements of the theory: We found an exact mathematical formulation of our theory that explains kHz QPOs as a non-linear orbital resonance. Using the multiple-scale method, Paola Rebusco and Jiri Horak found general analytic solution relevant to the astrophysical situation in question. This rather difficult mathematical result has several important consequences, including the one for the "normal branch oscillations" (NBOs) in the Z sources. Until now, the NBOs were thought to be physically distinct from the kHz QPOs. We demonstrated that a low-frequency modulation of the kHz QPOs is a natural consequence of the non-linear relativistic resonance suggested previously by us to explain the properties of the high-frequency twin peaks. Our theory reproduces the 6 Hz NBOs of frequency and amplitude of the kHz QPOs reported by Yu, van der Klis and Jonker.

02. Observed variability from oscillating torus: Michal Bursa developed a supercomputer code to trace off-equatorial plane null geodesics in a general (numerically given) stationary, axially symmetric metric. We used his code to calculate observed variability that is due to strong-field effects (relativistic Doppler and lensing) of almost axially symmetric, oscillating sources. This was never calculated before. For the first time one sees that a very strong luminosity modulation may be achieved in almost axially symmetric situation.


01. Gravitating discs around black holes
Topical Review
V Karas, J-M Hure and O Semerak
Classical and Quantum Gravity, 21, R1-R51 (2004).

02. Non-linear resonance in the accretion disk of a millisecond pulsar
W.Kluzniak, M.A. Abramowicz, S.Kato, W.H. Lee, N.Stergioulas
Astrophysical Journal Letters, 603, L89-L92, 2004

03. Interpreting black hole QPOs
Invited lecture: X-Ray Timing 2003: Rossi and Beyond (Harvard, 2003)
M.A. Abramowicz, W.Kluzniak
In print: "X-Ray Timing 2003: Rossi and Beyond", ed. P. Kaaret, F. K. Lamb, & J. H. Swank (Melville, NY: American Institute of Physics).

04. The orbital resonance model for twin peak kHz QPOs
M.A. Abramowicz, W.Kluzniak, Z.Stuchlik, G.Torok
In print: Astronomy and Astrophysics

05. The importance of discovering a 3:2 twin-peak QPO in a ULX or how to solve the puzzle of intermediate mass black holes
M.A. Abramowicz, W.Kluzniak, J.E. McClintock, R.A. Remillard
In print: The Astrophysical Journal Letters

06. High-frequency QPOs as a problem in physics: non-linear resonance
Presented at: X-Ray Timing 2003: Rossi and Beyond (Harvard, 2003)
W.Kluzniak, M.A. Abramowicz, W.H. Lee
In print: "X-Ray Timing 2003: Rossi and Beyond", ed. P. Kaaret, F. K. Lamb, & J. H. Swank (Melville, NY: American Institute of Physics). astro-ph/0402013

07. Twin peaks kHz QPOs: mathematics of the 3:2 orbital resonance
P. Rebusco
In print: Publications of the Astronomical Society of Japan

08. The Hartle-Thorne circular geodesics
M.A. Abramowicz, G.J.E. Almergren, W. Kluzniak, A.V. Thampan
Submitted: Classical and Quantum Gravity

09. Of NBOs and kHz QPOs: a low-frequency modulation in resonant oscillations of relativistic accretion disks
J.Horak, M.A. Abramowicz, V.Karas, W. Kluzniak
Submitted: The Astrophysical Journal Letters

All the papers listed above acknowledge that computations reported in them were performed using the UK Astrophysical Fluids Facility. They also acknowledge the support of the European Community - Access to Research Infrastructure action of the Improving Human Potential Program.

This report was sent to James Gray at UKAFF

A questionnaire about the EU program and the UKAFF facility was taken from:
completed, and sent to Ms. Brigitte Sambain of the European Commission in Brussels