Shadows and photon spheres with spherical accretions in the four-dimensional Gauss–Bonnet black hole

We investigate the shadows and photon spheres of the four-dimensional Gauss–Bonnet black hole with the static and infalling spherical accretions. We show that, for both cases, there always exist shadows and photon spheres. The radii of the shadows and photon spheres are independent of the profiles of accretion for a fixed Gauss–Bonnet constant, implying that the shadow is a signature of the spacetime geometry and it is hardly influenced by accretion. Because of the Doppler effect, the shadows of the infalling accretion are found to be darker than in the static case. We also investigate the effect of the Gauss–Bonnet constant on the shadow and photon spheres, and we find that the larger the Gauss–Bonnet constant is, the smaller the radii of the shadow and photon spheres will be. In particular, the observed specific intensity increases as the Gauss–Bonnet constant grows.

Gravity and limb-darkening coefficients for compact stars: DA, DB, and DBA eclipsing white dwarfs

Context. The distribution of the specific intensity over the stellar disk is an essential tool for modeling the light curves in eclipsing binaries, planetary transits, and stellar diameters through interferometric techniques, line profiles in rotating stars, gravitational microlensing, etc. However, the available theoretical calculations are mostly restricted to stars on the main sequence or the giant branch, and very few calculations are available for compact stars. Aims. The main objective of the present work is to extend these investigations by computing the gravity and limb-darkening coefficients for white dwarf atmosphere models with hydrogen, helium, or mixed compositions (types DA, DB, and DBA). Methods. We computed gravity and limb-darkening coefficients for DA, DB, and DBA white dwarfs atmosphere models, covering the transmission curves of the Sloan, UBVRI, Kepler, TESS, and Gaia photometric systems. Specific calculations for the HiPERCAM instrument were also carried out. For all calculations of the limb-darkening coefficients we used the least-squares method. Concerning the effects of tidal and rotational distortions, we also computed for the first time the gravity-darkening coefficients y(λ) for white dwarfs using the same models of stellar atmospheres as in the case of limb-darkening. A more general differential equation was introduced to derive these quantities, including the partial derivative (∂ln Io(λ)/∂ln g)Teff. Results. Six laws were adopted to describe the specific intensity distribution: linear, quadratic, square root, logarithmic, power-2, and a more general one with four coefficients. The computations are presented for the chemical compositions log[H/He] = −10.0 (DB), −2.0 (DBA) and He/H = 0 (DA), with log g varying between 5.0 and 9.5 and effective temperatures between 3750 and 100 000 K. For effective temperatures higher than 40 000 K, the models were also computed adopting nonlocal thermal equilibirum (DA). The adopted mixing-length parameters are ML2/α = 0.8 (DA case) and 1.25 (DB and DBA). The results are presented in the form of 112 tables. Additional calculations, such as for other photometric systems and/or different values of log[H/He], log g, and Teff can be performed upon request.

DETERMINATION OF TRAFFIC FLOWS PARAMETERS ON THE MANAGEMENT NETWORK

The work is devoted to the actual problem of determining the parameters of dense traffic flows on the road cities network, which can be used when introducing automated traffic control systems. The subject of the study is to determine the parameters of traffic flows in the central part of the city. The purpose of the work is to develop methods for determining the parameters of traffic flows of the street and road network on the basis of empirical and analytical modeling to reduce the number of peripheral measuring devices in the automated traffic control system. Methodology. In the given thesis there was solved the applied scientific problem of short-term operational forecasting of the traffic flow intensity on the transport network using the empirical-analytical approach, in which the measurement of traffic flow parameters at the entrances to the area of traffic flow management is carried out by transport detectors, internal local objects are determined by modeling. The proposed model is based on the determination of intensities at approaches to stop lines of internal crossroads of the management area using recurrent sequences. Experimental researches of traffic flows on the network and on the crossings were carried out using video filming during periods of maximum load. A comparative analysis of the simulation results with the experimental data showed that the relative error on a network with an area of 50-60 hectares does not exceed 3%, which indicates the adequacy of the model and the possibility of using it for management tasks. Practical implications. Implementation of the empirical-analytical method in automated traffic management systems will make it possible to reduce the number of detectors by 43-46% depending on the area of traffic management and obtain a sufficient economic effect. The regularities of the movement of dense traffic flows of high specific intensity on short hauls, typical for the central parts of cities, have been investigated. Value/originality. According to experimental results there were obtained approximating models of parameters of the logarithmic normal probabilistic law of time intervals distribution in dense traffic flows, the specific intensity of which exceeds 600 vph; the changes in basic characteristics of the vehicles group in the traffic flow when driving through the road crossing taking into account its intensity and the distance from the group forming object are determined.