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Register a new userX-ray quasi-periodic oscillations in Lense--Thirring precession model - I. variability of relativistic continuum
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We develop a Monte-Carlo code to compute the Compton scattered X-ray flux arising from a hot inner flow which undergoes Lense-Thirring precession. The hot flow intercepts seed photons from an outer truncated thin disk. A fraction of the Comptonized photons will illuminate back the disk and the reflected/reprocessed photons will contribute to the observed spectrum. The total spectrum, including disk thermal emission, hot flow Comptonization, and disk reflection, is modelled within the framework of general relativity, taking light-bending and gravitational redshift into account. The simulations are performed in the context of the Lense-Thirring precession model for the low-frequency quasi-periodic oscillations, so the inner flow is assumed to precess, leading to periodic modulation of the emitted radiation. In this work, we concentrate on the energy-dependent X-ray variability of the model and, in particular, on the evolution of the variability during the spectral transition from hard to soft state, which is implemented by the decrease of the truncation radius of the outer disk towards Innermost Stable Circular Orbit (ISCO). In the hard state where the Comptonizing flow is geometrically thick, the Comptonization is weakly variable with the fractional variability amplitude of $leq$10%; in the soft state where the Comptonizing flow is cooled down and thus becomes geometrically thin, and the fractional variability of the Comptonization is highly variable, increasing with photon energy. The fractional variability of the reflection increases with energy, and the reflection emission for low spin is counterintuitively more variable than the one for high spin.
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The timing properties of X-ray binaries are still not understood, particularly the presence of quasi-periodic oscillations (QPOs) in their X-ray power spectra. The solid-body regime of Lense-Thirring precession is one prominent model invoked to explain the most common type of QPOs, Type C. However, solid-body precession requires a specific structure that has not been examined in light of constrained properties of accretion flows. We assume in this paper, as solid-body precession requires, a disk separated into two flows at a transition radius $r_t$: a cold outer flow and a hot inner flow (playing the role of the corona). We explore the physical structure of both flows using model-independent estimates of accretion parameters. We show that, in order to reproduce the observed X-ray spectra during luminous hard states, the hot flow must accrete at sonic to supersonic speeds, unreachable with typical viscous torques. As a result of this extreme accretion speed (or high $alpha$ parameter), no region of the disk during these states lies in the `wave-like regime required for solid-body precession. Furthermore, we expect the flow to align with the black hole spin axis via the Bardeen-Petterson effect inside a radius $r_{rm break}>r_t$. As a consequence, the hot inner flow cannot exhibit solid body precession -- as currently pictured in the literature -- during luminous hard states. Since Type C QPOs are prevalent in these states, we conclude that this mechanism is unlikely to be responsible for producing Type C QPOs around stellar mass black holes.
An elementary pedagogical derivation of the Lense-Thirring precession is given based on the use of Hamilton vector. The Hamilton vector is an extra constant of motion of the Kepler/Coulomb problem related simply to the more popular Runge-Lenz vector. When a velocity-dependent Lorentz-like gravitomagnetic force is present, the Hamilton vector, as well as the canonical orbital momentum are no longer conserved and begin to precess. It is easy to calculate their precession rates, which are related to the Lense-Thirring precession of the orbit.
The geodesics of bound spherical orbits i.e. of orbits performing Lense-Thirring precession, are obtained in the case of the $Lambda$-term within gravito-electromagnetic formalism. It is shown that the presence of the $Lambda$-term in the equations of gravity leads to both relativistic and non-relativistic corrections in the equations of motion. The contribution of the $Lambda$-term in the Lense-Thirring precession is interpreted as an additional relativistic correction and the gravito-gyromagnetic ratio is defined.
The orbital Lense-Thirring precession is considered in the context of constraints for weak-field General Relativity involving the cosmological constant $Lambda$. It is shown that according to the current accuracy of satellite measurements the obtained error limits for $Lambda$ is self-consistent with cosmological observations. The corrections of $Lambda$ term are derived for the strong field Lense-Thirring precession i.e. the frame dragging effect and for the nutation. As a result, in the context of recently proposed $Lambda$-gravity we obtain constraints for $Lambda$ in both relativistic and weak-field limits. Namely, for the latter we analyze several Keplerian systems at different scales. We find that the obtained constraints for the modified gravity corrections are several orders of magnitude tighter than those available for such effects as gravitational redshift, gravitational time delay and geodetic precession in Solar System.
Quasi-periodic oscillations (QPOs) are observed in the optical flux of some polars with typical periods of 1 to 3 s but none have been observed yet in X-rays where a significant part of the accreting energy is released. QPOs are expected and predicted from shock oscillations. Most of the polars have been observed by the XMM-Newton satellite. We made use of the homogeneous set of observations of the polars by XMM-Newton to search for the presence of QPOs in the (0.5-10 keV) energy range and to set significant upper limits for the brightest X-ray polars. We extracted high time-resolution X-ray light curves by taking advantage of the 0.07 sec resolution of the EPIC-PN camera. Among the 65 polars observed with XMM-Newton from 1998 to 2012, a sample of 24 sources was selected on the basis of their counting rate in the PN instrument to secure significant limits. We searched for QPOs using Fast Fourier Transform (FFT) methods and defined limits of detection using statistical tools. Among the sample surveyed, none shows QPOs at a significant level. Upper limits to the fractional flux in QPOs range from 7% to 71%. These negative results are compared to the detailed theoretical predictions of numerical simulations based on a 2D hydrodynamical code presented in Paper II. Cooling instabilities in the accretion column are expected to produce shock quasi-oscillations with a maximum amplitude reaching ~ 40% in the bremsstrahlung (0.5-10 keV) X-ray emission and ~ 20% in the optical cyclotron emission. The absence of X-ray QPOs imposes an upper limit of ~ (5-10) g.cm-2.s-1 on the specific accretion rate but this condition is found inconsistent with the value required to account for the amplitudes and frequencies of the observed optical QPOs. This contradiction outlines probable shortcomings with the shock instability model.
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