Astronomičeskij žurnal

This work continues the analysis of the model for calculating the thermal structure of an axisymmetric protoplanetary disk, initiated in the paper by Pavlyuchenkov (2024). The model is based on the well-known Flux-Limited Diffusion (FLD) approximation with separate calculation of heating by direct stellar radiation (hereinafter referred to as the FLD^s method). In addition to the previously described FLD^s model with wavelength-averaged opacities, we present a multiband model mFLD^s, where the spectrum of thermal radiation is divided into several frequency bands. The model is based on an implicit finite-difference scheme for the equations of thermal radiation diffusion, which reduces to a system of linear algebraic equations written in hypermatrix form. A modified Gauss method for inverting the sparse hypermatrix of the original system of linear equations is proposed. The simulation results described in the article show that the midplane radial temperature profile obtained with the mFLD^s method has a variable slope in accordance with the reference Monte Carlo radiative transfer simulations. The mFLD^s model also qualitatively reproduces the non-isothermality of the temperature distribution along the angular coordinate near the midplane, which is not provided by the FLD^s method. However, quantitative differences remain between the reference temperature values and the results of mFLD^s. These differences are likely due to the diffusive nature of the FLD approximation. It is also shown that the characteristic times for the disk to reach thermal equilibrium within the mFLD^s model can be significantly shorter than in FLD^s. This property should be taken into account when modeling non-stationary processes in protoplanetary disks within FLD-based models.

More than half of currently known stars have nearby exoplanets with size between Earth and Neptune, called super-Earths and mini-Neptunes. The California-Kepler Survey (CKS) studied data from NASA’s Kepler mission and revealed a bimodal distribution of planets with by radius ( is the radius of the Earth). It occured that there was a lack of planets with radii . The CKS did not take into account data from other missions and exoplanets discovered by non-transit methods. All data from this mission were limited to 2022. This article examines the distribution of super-Earths and mini-Neptunes, taking into account all data on exoplanets known by 2024 from the NASA catalog. Mini-Neptunes and super-Earths with known radii were selected. There were 937 such planets, including 366 planets with known mass. Since the radius of a planet can only be determined by the transit method, the distribution by radii is built using the data of transit planets, but, unlike CKS, not only the data of the Kepler mission are taken. The data for the remaining distributions are selected regardless of the method of their detection and the telescope used. We show that the current data are best fitted by a double-peaked Gaussian distribution, which describes two populations of planets: rocky (hereinafter super-Earths) and exoplanets with gas envelopes (exoplanets surrounded by hydrogen-helium atmospheres, but consisting mainly of heavy elements — ice and rock, hereinafter mini-Neptunes). The magnitude of the gap between populations at present is analyzed. It is shown that the gap is filled evenly on both sides; in CKS, the first peak is significantly smaller than the second, that is, there were fewer super-Earths than mini-Neptunes. Perhaps more super-Earths have been discovered recently, which is why there was a shortage of them in the CKS. The composition of some exoplanets was determined using theoretical models of the dependence of mass on radius.

The results of the study of the correlation between the Doppler widths (FWHM) of emission lines in the spectra of close and some wide binary systems of the WR+OB type and the system’s orbit inclination are presented in order to search for the effects of the orientation of the WR stellar wind. The widths of the studied lines do not show a correlation with the orbital inclination, and no significant orientation effects for the WR wind were detected.

Rope flux models of solar flares associate the phenomenon of quasi-periodic pulsations of flare radiation with a parametric catastrophe that occurs when the top of a twisted magnetic loop enters the corona. A sharp decrease in external pressure leads to the longitudinal magnetic field of a force-free flux rope tending to zero on the magnetic surface where the current changes sign, and the density of the azimuthal current and the force-free parameter begin to grow indefinitely near this surface, approaching a break. The current velocity of electrons here will inevitably exceed the speed of ion sound, and plasma instability will arise. Scattering of electrons on ion-acoustic plasmons will sharply decrease the plasma conductivity and cause rapid, flare dissipation of the magnetic energy of the rope, i.e. decrease in the amplitude of the field and currents and expansion of the rope cross-section. This is how the first peak of the flare radiation will be formed. In this case, the torque applied to each section of the rope will be greatly weakened in the energy release region. In equilibrium, the torque should be the same along the entire length of the loop, so there will be a transfer of the azimuthal flux by Alfven waves from the loop legs to the top. Alignment of the torque along the rope axis will return the rope to its original state, after which the second peak of the flare radiation is formed, and the process is repeated several times until the reserve of free magnetic energy associated with the currents in the entire loop decreases significantly. The oscillations of the rope cross-section accompanying the peaks of its radiation represent a specific type of fluctuations of a system with time-varying rigidity: in them the magnetic field intensity, providing the restoring force, changes greatly. Calculation of such oscillations allows achieving not only qualitative but also quantitative correspondence between the theoretical results and observational data.