Comparison of simple mass estimators for slowly rotating elliptical galaxies

We compare the performance of mass estimators for elliptical galaxies that rely on the directly observable surface brightness and velocity dispersion profiles, without invoking computationally expensive detailed modeling. These methods recover the mass at a specific radius where the mass estimate is expected to be least sensitive to the anisotropy of stellar orbits. One method (Wolf et al. 2010) uses the total luminosity-weighted velocity dispersion and evaluates the mass at a 3D half-light radius $r_{1/2}$, i.e., it depends on the GLOBAL galaxy properties. Another approach (Churazov et al. 2010) estimates the mass from the velocity dispersion at a radius $R_2$ where the surface brightness declines as $R^{-2}$, i.e., it depends on the LOCAL properties. We evaluate the accuracy of the two methods for analytical models, simulated galaxies and real elliptical galaxies that have already been modeled by the Schwarzschild's orbit-superposition technique. Both estimators recover an almost unbiased circular speed estimate with a modest RMS scatter ($\lesssim 10 \%$). Tests on analytical models and simulated galaxies indicate that the local estimator has a smaller RMS scatter than the global one. We show by examination of simulated galaxies that the projected velocity dispersion at $R_2$ could serve as a good proxy for the virial galaxy mass. For simulated galaxies the total halo mass scales with $\sigma_p(R_2)$ as $M_{vir} \left[M_{\odot}h^{-1}\right] \approx 6\cdot 10^{12} \left( \frac{\sigma_p(R_2)}{200\, \rm km\, s^{-1}} \right)^{4}$ with RMS scatter $\approx 40 \%$.Comment: 19 pages, 14 figures, 4 tables, accepted for publication in MNRA

Experience of Implementing Technology Liberal Arts Abroad in Russia

Образовательная модель Liberal Arts (либеральное образование, свободные искусства и науки) приобрела свою известность в США во второй половине XX в., затем получила свое распространение по всему миру. В статье рассматривается опыт внедрения технологий системы образования по Liberal Arts в США, странах Центральной, Центральной Азии, а также и в России. На основе рассмотренного опыта авторами выделяются основные проблемы внедрения технологий Liberal Arts в Россию.The educational model of Liberal Arts (liberal education, free arts and Sciences) gained its popularity in the United States in the second half of the XX century, and then spread around the world. The article discusses the experience of the introduction of technologies of the educational system of Liberal Arts in the United States, Central and Eastern Europe, Central Asia, as well as in Russia. On the basis of the considered experience, the authors highlight the main problems of the introduction of Liberal Arts technologies in Russia

Observations of Lensed Relativistic Jets as a Tool of Constraining Lens Galaxy Parameters

The possibility of using lensed relativistic jets on very small angular scales to construct proper models of spiral lens galaxies and to independently determine the Hubble constant is considered. The system B0218+357 is used as an example to illustrate that there exists a great choice of model parameters adequately reproducing its observed large-scale properties but leading to a significant spread in the Hubble constant. The jet image position angle is suggested as an additional parameter that allows the range of models under consideration to be limited. It is shown that the models for which the jet image position angles differ by at least $40^o$ can be distinguished between themselves during observations on very small angular scales. The possibility of observing the geometric properties of lensed relativistic jets and measuring the superluminal velocities of knot images on time scales of several months with very long baseline space interferometers is discussed.Comment: 11 pages, 3 figures, Will be published in the Astronomy Letters, V.37, PP.483-490, 201

Physical applications of second-order linear differential equations that admit polynomial solutions

Conditions are given for the second-order linear differential equation P3 y" + P2 y'- P1 y = 0 to have polynomial solutions, where Pn is a polynomial of degree n. Several application of these results to Schroedinger's equation are discussed. Conditions under which the confluent, biconfluent, and the general Heun equation yield polynomial solutions are explicitly given. Some new classes of exactly solvable differential equation are also discussed. The results of this work are expressed in such way as to allow direct use, without preliminary analysis.Comment: 13 pages, no figure

Modeling the Images of Relativistic Jets Lensed by Galaxies with Different Mass Surface Density Distributions

The images of relativistic jets from extragalactic sources produced by gravitational lensing by galaxies with different mass surface density distributions are modeled. In particular, the following models of the gravitational lens mass distribution are considered: a singular isothermal ellipsoid, an isothermal ellipsoid with a core, two- and three-component models with a galactic disk, halo, and bulge. The modeled images are compared both between themselves and with available observations. Different sets of parameters are shown to exist for the gravitationally lensed system B0218+357 in multicomponent models. These sets allow the observed geometry of the system and the intensity ratio of the compact core images to be obtained, but they lead to a significant variety in the Hubble constant determined from the modeling results.Comment: 26 pages, 9 figures, will be published in the Astronomy Letters, 2011, v.37, N4, pp. 233-24

Results of study of long-fiber flax’s collection material by the parameters of economically valuable traits

Cultivated common flax (Linum usitatissimum L.) is a traditional Russian technological crop of complex usage. Estimation of seasonal effects in economically valuable traits (productivity of straw and seeds; content of fiber and its quality) of long-fiber flax under conditions of Volga-Vyatka region (Kirov region) in 2014 - 2017 is presented in the article. Objects of study - 140 varieties of long-fiber flax different in ecological and geographic origin. Stable and plastic traits are selected according to correlation coefficient. Strong “genotype - environment” interactions were expressed by seed productivity, number of bolls and seed per plant; moderate interactions - by productivity of straw and fiber; weak interactions - by plant length, fiber content, 1000-grain mass. Strong correlation is pointed out between straw productivity and total and technical plant height (r = 0.71±0.09.. ,0.78±0.08) in average for years of study. Sources are selected for most important directions of long-fiber flax breeding: for straw productivity - Sinel, Vizit (Russia). Merilin (The Netherlands Soglasie (Belarus), Heiya 11, Heiyal2 (China); for seed productivity - Priboj, Sinichka, Er-27 (Russia), Ottawa (Canada), Soglasie (Belarus), Belinka, Merilin (The Netherlands); for fiber content- Mirazh, Peresvet, Tverskoj, Pskovsky-93, Dobrynya (Russia); Merilin (The Netherlands); Charivny, Zaryanka (Ukraine); for fiber durability - Soglasie (Belarus), Sinel, Pskovsky-93 (Russia), Kamenyar, Baltuchaj (Ukraine), B-179 (Lithuania); for fiber flexibility - Flax of Heilonjiang № 7, Huaguang 2, Heiya 11, Heiya 13 (China); Honkei-25 (Japan), Kamenyar (Ukraine), Priboj (Russia). By a complex of economically valuable traits the following genotypes are selected: Sinel, TOST 3, Peresvet (Russia), Flax of Heilonjiang № 13 and Heiya 12 (China), Merilin (The Netherlands)