Alexander V. Melnikov

Observations and Theoretical Analysis of Lightcurves of Natural Satellites of Planets

We present the results of photometric observations of Saturns seventh satellite Hyperion and four other planetary satellites: Saturns moon Phoebe and three Jovian satellites Himalia, Elara, and Pasiphae. The observations have been conducted from September, 1999 to March, 2000, and during September–October, 2000. Analysis of periodic variations in Hyperions lightcurve was performed. The lightcurve was modeled using the software package developed for calculating the rotational dynamics of a satellite. Our data generally indicate that over the period of observations Hyperion was in the chaotic mode of rotation.

Chaotic Asteroidal Dynamics and Maximum Lyapunov Exponents

This paper describes the results of studies of dynamical chaos in the problem of the orbital dynamics of asteroids near the 3 : 1 mean-motion resonance with Jupiter. Maximum Lyapunov characteristic exponents (MLCEs) are used as an indicator and a measure of the chaoticity of motion. MLCE values are determined for trajectories calculated by the numerical integration of equations of motion in the planar elliptical restricted three-body problem. The dependence of the MLCE on the problem parameters and on the initial data is analyzed. The inference is made that the domain of chaos in the phase space of the problem considered consists of two components of different nature. The values of the MLCEs observed for one of the components (namely, for the component corresponding to low-eccentricity asteroidal orbits) are compared to the theoretical estimates obtained within the framework of model of the resonance as a perturbed nonlinear pendulum.

Orbital dynamics of the planetary system HD 196885

The orbital dynamics of the single known planet in the binary star system HD 196885 has been considered. The Lyapunov characteristic exponents and Lyapunov time of the planetary system have been calculated for possible values of the planetary orbit parameters. It has been shown that the dynamics of the planetary system HD 196885 is regular with the Lyapunov time of more than 5 × 104 years (the orbital period of the planet is approximately 3.7 years), if the motion occurs at a distance from the separatrix of the Lidov–Kozai resonance. The values of the planet’s orbital inclination to the plane of the sky and longitude of the ascending node lie either within ranges 30° < ip < 90° and 30° < Ωp < 90°, or 90° < ip < 180° and 180° < Ωp < 300°.

On BLR Size Estimates in Reverberation Models

Following the approach of Melnikov & Shevchenko (2008), we explore how the nonlinearity in the emission-line luminosity Ll of a broad-line region cloud, in its dependence on the ionizing continuum flux Fi incident on the cloud, affects estimates of the size of the broad-line region by means of cross-correlation methods. We show that the estimates obtained by straightforward cross-correlation of emission-line and continuum light curves can significantly underestimate the BLR size. We demonstrate examples of direct reverberation modelling of AGN emission-line light curves taking into account the nonlinearity of the “Ll –Fi ” relation. This nonlinearity allows one to explain the differences in the time lags for different lines. Cross-correlation estimates of the BLR size turn out to be small in comparison to the estimates obtained by the direct reverberation modelling. The mass of the black hole (BH) in the center of the BLR is usually calculated by the formula (see, e.g., Bentz et al. 2006) MBH ≈ fcτΔV /G ≈ fRΔV /G, where τ is the time lag for an emission line, R is the BLR radius, ΔV is the width of the emission line, c is the speed of light, and G is the gravitational constant. The factor f depends on the geometry, inclination, and dynamics of the BLR. Here the BLR radius is set to be equal to cτ , as it is commonly done; the uncertainty is included in f . Note that this formula is valid, if the virial theorem is valid: in particular, the size of the BLR should be constant. A hypothesis on possible variability of the BLR size of NGC 4151 was put forward by Kaspi et al. (1996), Peterson et al. (2002), and other researchers on the basis of cross-correlation analysis of optical spectral variability data at different time intervals of observations. Our reverberation modelling of the Hα light curve data of Kaspi et al. (1996) gives the value of the BLR radius matching the majority of the BLR size estimates of other authors. This removes necessity of any special physical interpretation of the small value of the cross-correlation time lag in Hα for these light curve data. In particular, the hypothesis by Kaspi et al. (1996) that the physical size of the BLR at the moment of their observations was an order of magnitude less than usual is not necessary. This strengthens the validity of the BH mass estimates, which are based on the validity of the virial theorem. Indeed, the dynamical timescale (determined from the width of the lines) in the BLR can be of the same order or even exceed the timescale of hypothetical variations of the BLR size (according to Kaspi et al. 1996, the latter timescale is less than 2000 days). If the size variability caused by external disturbances on such short timescales is absent, then the virial mass estimates are presumably valid.

How do the small planetary satellites rotate

We investigate the problem of the typical rotation states of the small planetary satellites from the viewpoint of the dynamical stability of their rotation. We show that the majority of the discovered satellites with unknown rotation periods cannot rotate synchronously, because no stable synchronous 1:1 spin-orbit state exists for them. They rotate either much faster than synchronously (those tidally unevolved) or, what is much less probable, chaotically (tidally evolved objects or captured slow rotators).