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

Stellar kinematics of X-ray bright massive elliptical galaxies

We discuss a simple and fast method for estimating masses of early-type galaxies from optical data and compare the results with X-ray derived masses. The optical method relies only on the most basic observables such as the surface brightness $I(R)$ and the line-of-sight velocity dispersion $\sigma_p(R)$ profiles and provides an anisotropy-independent estimate of the galaxy circular speed $V_c$. The mass-anisotropy degeneracy is effectively overcome by evaluating $V_c$ at a characteristic radius $R_{\rm sweet}$ defined from {\it local} properties of observed profiles. The sweet radius $R_{\rm sweet}$ is expected to lie close to $R_2$, where $I(R) \propto R^{-2}$, and not far from the effective radius $R_{\rm eff}$. We apply the method to a sample of five X-ray bright elliptical galaxies observed with the 6-m telescope BTA-6 in Russia. We then compare the optical $V_c$-estimate with the X-ray derived value, and discuss possible constraints on the non-thermal pressure in the hot gas and configuration of stellar orbits. We find that the average ratio of the optical $V_c$-estimate to the X-ray one is equal to $\approx 0.98$ with $11 \%$ scatter, i.e. there is no evidence for the large non-thermal pressure contribution in the gas at $\sim R_{\rm sweet}$. From analysis of the Lick indices H$\beta$, Mgb, Fe5270 and Fe5335, we calculate the mass of the stellar component within the sweet radius. We conclude that a typical dark matter fraction inside $R_{\rm sweet}$ in the sample galaxies is $\sim 60\%$ for the Salpeter IMF and $\sim 75 \%$ for the Kroupa IMF.Comment: accepted for publication in MNRA

Prospects of detecting soft X-ray emission from typical WHIM filaments around massive clusters and the Coma cluster soft excess

While hot ICM in galaxy clusters makes these objects powerful X-ray sources, the cluster's outskirts and overdense gaseous filaments might give rise to much fainter sub-keV emission. Cosmological simulations show a prominent "focusing" effect of rich clusters on the space density of the Warm-Hot Intergalactic Medium (WHIM) filaments up to a distance of $\sim 10\,{\rm Mpc}$ ($\sim$ turnaround radius, $r_{ta}$) and beyond. Here, we use Magneticum simulations to characterize their properties in terms of integrated emission measure for a given temperature and overdensity cut and the level of contamination by the more dense gas. We suggest that the annuli $(\sim 0.5-1)\times \,r_{ta}$ around massive clusters might be the most promising sites for the search of the gas with overdensity $\lesssim 50$. We model spectral signatures of the WHIM in the X-ray band and identify two distinct regimes for the gas at temperatures below and above $\sim 10^6\,{\rm K}$. Using this model, we estimate the sensitivity of X-ray telescopes to the WHIM spectral signatures. We found that the WHIM structures are within reach of future high spectral resolution missions, provided that the low-density gas is not extremely metal-poor. We then consider the Coma cluster observed by SRG/eROSITA during the CalPV phase as an example of a nearby massive object. We found that beyond the central $r\sim 40'$ ($\sim 1100\,{\rm kpc}$) circle, where calibration uncertainties preclude clean separation of the extremely bright cluster emission from a possible softer component, the conservative upper limits are about an order of magnitude larger than the levels expected from simulations.Comment: Submitted to MNRA

Tempestuous life beyond R500: X-ray view on the Coma cluster with SRG/eROSITA. II. Shock & Relic

This is the second paper in a series of studies of the Coma cluster using the SRG/eROSITA X-ray data obtained during the calibration and performance verification phase of the mission. Here, we focus on the region adjacent to the radio source 1253+275 (radio relic, RR, hereafter). We show that the X-ray surface brightness exhibits its steepest gradient at $\sim 79'$ ($\sim 2.2\,{\rm Mpc}\approx R_{200c}$), which is almost co-spatial to the outer edge of the RR. As in the case of several other relics, the Mach number of the shock derived from the X-ray surface brightness profile ($M_X\approx 1.9$) appears to be lower than needed to explain the slope of the integrated radio spectrum in the diffusive shock acceleration (DSA) model ($M_R\approx 3.5$) if the magnetic field is uniform and the radiative losses are fast. However, the shock geometry is plausibly much more complicated than a spherical wedge centered on the cluster, given the non-trivial correlation between radio, X-ray, and SZ images. While the complicated shock geometry alone might cause a negative bias in $M_X$, we speculate on a few other possibilities that may affect the $M_X$-$M_R$ relation, including the shock substructure that might be modified by the presence of non-thermal filaments stretching across the shock and the propagation of relativistic electrons along the non-thermal filaments with a strong magnetic field. We also discuss the "history" of the radio galaxy NGC4789, which is located ahead of the relic in the context of the Coma-NGC4839 merger scenario.Comment: Replaced with the accepted versio

X-ray surface brightness and gas density profiles of galaxy clusters up to 3*R500c with SRG/eROSITA

Using the data of the SRG/eROSITA all-sky survey, we stacked a sample of ~40 galaxy cluster images in the 0.3--2.3 keV band, covering the radial range up to $10\times R_{\rm 500c}$. The excess emission on top of the galactic and extragalactic X-ray backgrounds and foregrounds is detected up to $\sim 3\times R_{\rm 500c}$. At these distances, the surface brightness of the stacked image drops below $\sim 1$% of the background. The density profile reconstructed from the X-ray surface brightness profile agrees well (within $\sim30$%) with the mean gas profile found in numerical simulations, which predict the local gas overdensity of $\sim$ 20--30 at $3\times R_{\rm 500c}$ and the gas fraction close to the universal value of $\frac{\Omega_b}{\Omega_m}\approx 0.15$ in the standard $\Lambda$CDM model. Taking at face value, this agreement suggests that up to $\sim 3\times R_{\rm 500c}$ the X-ray signal is not strongly boosted by the gas clumpiness, although a scenario with a moderately inhomogeneous gas cannot be excluded. A comparison of the derived gas density profile with the electron pressure profile based on the SZ measurements suggests that by $r\sim 3\times R_{\rm 500c}$ the gas temperature drops by a factor of $\sim$ 4--5 below the characteristic temperature of a typical cluster in the sample within $R_{\rm 500c}$, while the entropy keeps growing up to this distance. Better constraints on the gas properties just beyond $3\times R_{\rm 500c}$ should be possible with a sample larger than used for this pilot study.Comment: accepted by MNRA

Close-up view of an ongoing merger between the NGC 4839 group and the Coma cluster - a post-merger scenario

We study a merger of the NGC 4839 group with the Coma cluster using X-ray observations from the XMM–Newton and Chandra telescopes. X-ray data show two prominent features: (i) a long (∼600 kpc in projection) and bent tail of cool gas trailing (towards south-west) the optical centre of NGC 4839, and (ii) a ‘sheath’ region of enhanced X-ray surface brightness enveloping the group, which is due to hotter gas. While at first glance the X-ray images suggest that we are witnessing the first infall of NGC 4839 into the Coma cluster core, we argue that a post-merger scenario provides a better explanation of the observed features and illustrate this with a series of numerical simulations. In this scenario, the tail is formed when the group, initially moving to the south-west, reverses its radial velocity after crossing the apocenter, the ram pressure ceases and the ram pressure-displaced gas falls back towards the centre of the group and overshoots it. Shortly after the apocenter passage, the optical galaxy, dark matter, and gaseous core move in a north-east direction, while the displaced gas continues moving to the south-west. The ‘sheath’ is explained as being due to interaction of the re-infalling group with its own tail of stripped gas mixed with the Coma gas. In this scenario, the shock, driven by the group before reaching the apocenter, has already detached from the group and would be located close to the famous relic to the south-west of the Coma cluster

Accumulation and morphological properties of starch in tubers of new potato hybrids

The article presents the results of studying potato accessions according to the accumulation and morphological properties of starch in tubers in the nursery of dynamic testing in agroecological conditions of the Kirov region (Volga-Vyatka region) in 2022. The objects of the research were 11 new hybrids bred by the Falenki Breeding Station – branch of the Federal Agricultural Research Center of the North-East named N.V. Rudnitsky. The early-maturing variety Udacha, the middle-early variety Nevsky, and the mid-season variety Chaika were used as standards. There have been identified hybrids with increased starch content (19 % and higher) on the 80th day of vegetation: early-maturing 172-13, medium-early – 165-00, 27-07, 13-18, mid-season – 182-13, 580-13, 252-18. The hybrids of the middle early group had the largest average size of starch grains: 165-00 (34.3±2.6 microns), 132-18 (36.0±3.0 microns), 233-12 (39.2±3.3 microns). Most of the hybrids had starch grains of regular rounded shape, accessions 233-12 and 232-12 – mostly irregular (angular) shape. In the course of the research, it was found that storing potatoes at the temperature of 3...4 ° C led to a decrease in the fraction of starch grains of very large size: in early-maturing varieties from 9.2 to 2.7 %, in middle early – from 13.5 to 5.0 %, in mid-season – from 9.6 to 3.2 %, which was due to starch resynthesis. As a result of the breeding work, promising potato hybrids of various maturation periods have been identified for transfer to state variety testing with improved agronomic traits, including high potential productivity: early-maturing 172-13, middle-early 233-12, mid-season 182-13 and 580-13

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

Evalu ation of potato hybrids according to tuber flesh darkening and other useful agronomic characters under the conditions of Kirov Province

Background. Resistance of raw and boiled tuber flesh to darkening when potato is processed into potato-based products or consumed directly is an important requirement for new potato cultivars. Identification of hybrids resistant to tuber flesh darkening would contribute immensely to future breeding work.Materials and methods. Parent forms and hybrid progeny of potato were tested for five years (2016–2020) in Kirov Province using the methods and technologies approved for potato breeding process. The progeny of 10 cultivars used as pollinators was analyzed.Results and conclusions. Cultivars with high levels of resistance to the darkening of raw tuber flesh were selected in the collection nursery. A total of 62 accessions (or 24%) out of 256 were identified for the absence of darkening or only small traces thereof (8 points) in raw tubers. Medium and strong darkening of the flesh (4–5 points) was recorded for 45 accessions. Analyzing the progeny of pollinator cultivars showed an increased occurrence of hybrids resistant to tuber flesh darkening in the progeny of cv. ‘Manifest’: 71% of the studied hybrids had non-darkening flesh (9 points). Manifestation of tuber flesh darkening was found to depend on weather conditions during the growing season: the higher was the air temperature, the weaker was the darkening of raw tuber flesh, but when the soil moisture during tuberization was high, tuber flesh became more darkened. A statistically significant relationship was observed between the darkening of boiled tubers and the content of crude protein (r = 0.74) and vitamin C (r = 0.79). Hybrid 179-10 was identified for high productivity (32.5 t/ha) and crude protein content (1.54%), while the highest resistance to the darkening of raw and boiled potato tubers was registered in hybrid 72-13

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