THE PROBLEM OF REDISTRIBUTION OF RADIO FREQUENCY USED IN THE ORGANIZATION DIVISIONS

The problem of radio frequency distribution is considered in the article, taking into account the regulations and geographical location of the operating units. The problem of assigning radio frequencies from among those assigned for corporate use is studied. Using conformal mapping, it was substantiated that any territory can be divided into zones, each of which will have a border with only three other zones. In this case, in each zone, you can assign frequencies in the amount of one quarter of the total number of available frequencies that do not overlap with frequencies assigned to adjacent zones. A mathematical model of the problem of radio frequency redistribution has been built, taking into account the regulations and the geographical location of the units. The implementation of algorithm allows taking into account the history of frequency distribution by zones, which allows you to completely update the used radio frequencies for a new period of operation. A software module has been compiled that generates frequencies at random from those available for assigning corporate use for each zone. The software module allows fast and frequent reallocation of frequencies by zones, thereby ensuring the safety, reliability and stability of communication between organizational units.

Fast and accurate approximation of the angle-averaged redistribution function for polarized radiation

Context. Modeling spectral line profiles taking frequency redistribution effects into account is a notoriously challenging problem from the computational point of view, especially when polarization phenomena (atomic polarization and polarized radiation) are taken into account. Frequency redistribution effects are conveniently described through the redistribution function formalism, and the angle-averaged approximation is often introduced to simplify the problem. Even in this case, the evaluation of the emission coefficient for polarized radiation remains computationally costly, especially when magnetic fields are present or complex atomic models are considered. Aims. We aim to develop an efficient algorithm to numerically evaluate the angle-averaged redistribution function for polarized radiation. Methods. The proposed approach is based on a low-rank approximation via trivariate polynomials whose univariate components are represented in the Chebyshev basis. Results. The resulting algorithm is significantly faster than standard quadrature-based schemes for any target accuracy in the range [10−6, 10−2].

Semi-empirical model atmospheres for the chromosphere of the sunspot penumbra and umbral flashes

Context. The solar chromosphere and the lower transition region are believed to play a crucial role in the heating of the solar corona. Models that describe the chromosphere (and the lower transition region), accounting for its highly dynamic and structured character are, so far, found to be lacking. This is partly due to the breakdown of complete frequency redistribution (CRD) in the chromospheric layers and also because of the difficulty in obtaining complete sets of observations that adequately constrain the solar atmosphere at all relevant heights. Aims. We aim to obtain semi-empirical model atmospheres that reproduce the features of the Mg II h&k line profiles that sample the middle chromosphere with focus on a sunspot. Methods. We used spectropolarimetric observations of the Ca II 8542 Å spectra obtained with the Swedish 1 m Solar Telescope and used NICOLE inversions to obtain semi-empirical model atmospheres for different features in and around a sunspot. These were used to synthesize Mg II h&k spectra using the RH1.5D code, which we compared with observations taken with the Interface Region Imaging Spectrograph (IRIS). Results. Comparison of the synthetic profiles with IRIS observations reveals that there are several areas, especially in the penumbra of the sunspot, where most of the observed Mg II h&k profiles are very well reproduced. In addition, we find that supersonic hot down-flows, present in our collection of models in the umbra, lead to synthetic profiles that agree well with the IRIS Mg II h&k profiles, with the exception of the line core. Conclusions. We put forward and make available four semi-empirical model atmospheres. Two for the penumbra, reflecting the range of temperatures obtained for the chromosphere, one for umbral flashes, and a model representative of the quiet surroundings of a sunspot.

Temperature constraints from inversions of synthetic solar optical, UV, and radio spectra

Context. High-resolution observations of the solar chromosphere at millimeter wavelengths are now possible with the Atacama Large Millimeter Array (ALMA), bringing with them the promise of tackling many open problems in solar physics. Observations from other ground and space-based telescopes will greatly benefit from coordinated endeavors with ALMA, yet the diagnostic potential of combined optical, ultraviolet and mm observations has remained mostly unassessed. Aims. In this paper we investigate whether mm-wavelengths could aid current inversion schemes to retrieve a more accurate representation of the temperature structure of the solar atmosphere. Methods. We performed several non-LTE inversion experiments of the emergent spectra from a snapshot of 3D radiation-MHD simulation. We included common line diagnostics such as Ca II H, K, 8542 Å and Mg II h and k, taking into account partial frequency redistribution effects, along with the continuum around 1.2 mm and 3 mm. Results. We find that including the mm-continuum in inversions allows a more accurate inference of temperature as function of optical depth. The addition of ALMA bands to other diagnostics should improve the accuracy of the inferred chromospheric temperatures between log τ ∼ [−6, −4.5] where the Ca II and Mg II lines are weakly coupled to the local conditions. However, we find that simultaneous multiatom, non-LTE inversions of optical and UV lines present equally strong constraints in the lower chromosphere and thus are not greatly improved by the 1.2 mm band. Nonetheless, the 3 mm band is still needed to better constrain the mid-upper chromosphere.