Systematic error of the Gaia DR1 TGAS parallaxes from data for the red giant clump

Based on the Gaia DR1 TGAS parallaxes and photometry from the Tycho-2, Gaia, 2MASS, andWISE catalogues, we have produced a sample of ~100 000 clump red giants within ~800 pc of the Sun. The systematic variations of the mode of their absolute magnitude as a function of the distance, magnitude, and other parameters have been analyzed. We show that these variations reach 0.7 mag and cannot be explained by variations in the interstellar extinction or intrinsic properties of stars and by selection. The only explanation seems to be a systematic error of the Gaia DR1 TGAS parallax dependent on the square of the observed distance in kpc: 0.18R ² mas. Allowance for this error reduces significantly the systematic dependences of the absolute magnitude mode on all parameters. This error reaches 0.1 mas within 800 pc of the Sun and allows an upper limit for the accuracy of the TGAS parallaxes to be estimated as 0.2 mas. A careful allowance for such errors is needed to use clump red giants as “standard candles.” This eliminates all discrepancies between the theoretical and empirical estimates of the characteristics of these stars and allows us to obtain the first estimates of the modes of their absolute magnitudes from the Gaia parallaxes: mode(M _H ) = ?1.49 ^m ± 0.04 ^m , mode(M _Ks ) = ?1.63 ^m ± 0.03 ^m , mode(M _W1) = ?1.67 ^m ± 0.05 ^m mode(M _W2) = ?1.67 ^m ± 0.05 ^m , mode(M _W3) = ?1.66 ^m ± 0.02 ^m , mode(M _W4) = ?1.73 ^m ± 0.03 ^m , as well as the corresponding estimates of their de-reddened colors.     

Catalog of equatorial coordinates and <Emphasis Type="Italic">B</Emphasis>-magnitudes of stars of the Kitab part of the FON project

The processing of the plates of the Kitab part of the FON project has been completed. In total, 1963 plates were processed. The catalog of equatorial coordinates α, δ, and B-magnitudes for 13 413268 stars and galaxies up to B ≤ 17.5 ^m for the epoch 1984.97 is compiled. The Epson Expression 10000XL scanner with a 1200 dpi scanning mode and a plate size of 30 × 30 cm or 13000 × 13000 pel was used to digitize astronegatives. Coordinates of stars and galaxies are obtained in the Tycho-2 catalog system and B-magnitudes are obtained in the photovoltaic system. The catalog internal accuracy for all objects is σ_α,δ = 0.23" and σ _B = 0.15 ^m (for stars in the range B = 5 ^m …14 ^m , errors are σ_α,δ = 0.085" and σ _B = 0.054 ^m ) for equatorial coordinates and stellar B-magnitudes, respectively. Convergence between the calculated and reference positions is σ_α,δ = 0.042", and convergence between photoelectric B-magnitudes is σ _B = 0.16 ^m . Coordinate errors with respect to the UCAC-4 catalog are σ_α,δ = 0.26" (9892697 or 73.75% of stars and galaxies were identified).     

Outskirts of Galaxy Clusters A1139, A1314, A1656, A2040, A 2052, A2107: Star-Formation Rate

We investigate the variation of the fraction of galaxies with suppressed star formation (M_K < ?21 _. ^m 5) and early-type galaxies (frac_E) of the “red sequence” along the projected radius in six galaxy clusters:Coma (A1656), A1139, and A1314 in the Leo supercluster region (z ≈ 0.037) and A2040, A2052, A2107 in the Hercules supercluster region (z ≈ 0.036). According to SDSS (DR10) data, frac_E is the highest in the central regions of galaxy clusters and it is, on the average, equal to 0.62 ± 0.03, whereas in the 2–3R/R_200c interval and beyond the R_sp ≈ 0.95 ± 0.04 R_200m radius that we inferred from the observed profile frac_E is minimal and equal to 0.25 ± 0.02. This value coincides with the estimate frac_E = 0.24 ± 0.01 that we inferred for field galaxies located between the Hercules and Leo superclusters at the same redshifts. We show that the fraction of galaxies with suppressed star formation decreases continuously with cluster radius from 0.87 ± 0.02 in central regions down to 0.43 ± 0.03 in the 2–3 R/R_200c interval and beyond R_sp, but remains, on the average, higher than 26% than the corresponding fraction for field objects. This decrease is especially conspicuous in the galaxy mass interval log M_* [M_⊙] = 9.5–10. We found that galaxies with ongoing star formation have average clustercentric distances 1.5–2.5 R/R_200c and that their radial-velocity dispersions are higher than those of galaxies with suppressed star formation.     

Kinematics of B-F Stars as a Function of Their Dereddened Color from Gaia and PCRV Data

Parallaxes with an accuracy better than 10% and proper motions from the Gaia DR1 TGAS catalogue, radial velocities from the Pulkovo Compilation of Radial Velocities (PCRV), accurate Tycho-2 photometry, theoretical PARSEC, MIST, YaPSI, BaSTI isochrones, and the most accurate reddening and interstellar extinction estimates have been used to analyze the kinematics of 9543 thin-disk B-F stars as a function of their dereddened color. The stars under consideration are located on the Hertzsprung–Russell diagram relative to the isochrones with an accuracy of a few hundredths of a magnitude, i.e., at the level of uncertainty in the parallax, photometry, reddening, extinction, and the isochrones themselves. This has allowed us to choose the most plausible reddening and extinction estimates and to conclude that the reddening and extinction were significantly underestimated in some kinematic studies of other authors. Owing to the higher accuracy of TGAS parallaxes than that of Hipparcos ones, the median accuracy of the velocity components U, V, W in this study has improved to 1.7 km s^?1, although outside the range ?0.1 ^m < (B _T ? V _T )₀ < 0.5 ^m the kinematic characteristics are noticeably biased due to the incompleteness of the sample. We have confirmed the variations in the mean velocity of stars relative to the Sun and the stellar velocity dispersion as a function of their dereddened color known from the Hipparcos data. Given the age estimates for the stars under consideration from the TRILEGAL model and the Geneva–Copenhagen survey, these variations may be considered as variations as a function of the stellar age. A comparison of our results with the results of other studies of the stellar kinematics near the Sun has shown that selection and reddening underestimation explain almost completely the discrepancies between the results. The dispersions and mean velocities from the results of reliable studies fit into a ±2 km s^?1 corridor, while the ratios σ _V /σ _U and σ _W /σ _U fit into ±0.05. Based on all reliable studies in the range ?0.1 ^m < (B _T ? V _T )₀ < 0.5^m, i.e., for an age from 0.23 to 2.4 Gyr, we have found: W_⊙ = 7.15 km s^?1, \({\sigma _U} = 16.0{e^{1.29({B_T} - {V_T})o}}\), \({\sigma _V} = 10.9{e^{1.11({B_T} - {V_T})o}}\), \({\sigma _W} = 6.8{e^{1.46({B_T} - {V_T})o}}\), the stellar velocity dispersions in km s^?1 are proportional to the age in Gyr raised to the power β _U = 0.33, β _V = 0.285, and β _W = 0.37.     

3D stellar reddening map from 2MASS photometry: An improved version

An improved version of the 3D stellar reddening map in a space with a radius of 1200 pc around the Sun and within 600 pc of the Galactic midplane is presented. As in the previous 2010 and 2012 versions of the map, photometry with an accuracy better than 0.05 ^m in the J and Ks bands for more than 70 million stars from the 2MASS catalogue is used in the new version. However, the data reduction technique is considerably more complicated. As before, an analysis of the distribution of stars near the main-sequence turnoff on the (J ? Ks)?Ks diagram, where they form a distribution maximum, provides a basis for the method. The shift of this maximum, i.e., the mode (J ? Ks), along (J ? Ks) and Ks, given the spatial variations of the mean dereddened color (J ? Ks)₀ of these stars, is interpreted as a growth of the reddening with increasing distance. The main distinction of the new method is that instead of the fixed mean absolute magnitude, dereddened color, distance, and reddening for each cell, the individual values of these quantities are calculated for each star by iterations when solving the system of equations relating them. This has allowed one to increase the random accuracy of the map to 0.01 ^m and its spatial resolution to 20 pc in coordinates and distance and to 1° in longitude and latitude. Comparison with other reddening estimates for the same spatial cells and Gaia DR1 TGAS stars shows that the constructed map is one of the best maps for the space under consideration. Its systematic errors have been estimated to be σ(E(J ? Ks)) = 0.025 ^m , or σ(E(B ? V)) = 0.04 ^m . The main purpose of the map is to analyze the characteristics of Galactic structures, clouds, and cloud complexes. For this purpose, the reddening map within each spatial cell has also been computed by analyzing the reddening along each line of sight.     

KDG218, a nearby ultra-diffuse galaxy

We present properties of the low-surface-brightness galaxy KDG218 observed with the HST/ACS. The galaxy has a half-light (effective) diameter of a _e = 47″ and a central surface brightness of SB _V (0) = 24.^m4/□″. The galaxy remains unresolved with the HST/ACS, which implies its distance of D > 13.1 Mpc and linear effective diameter of A _e > 3.0 kpc. We notice that KDG218 is most likely associated with a galaxy group around the massive lenticular NGC4958 galaxy at approximately 22 Mpc, or with the Virgo Southern Extension filament at approximately 16.5 Mpc. At these distances, the galaxy is classified as an ultra-diffuse galaxy (UDG) similar to those found in the Virgo, Fornax, and Coma clusters. We also present a sample of 15 UDG candidates in the Local Volume. These sample galaxies have the following mean parameters: 〈D〉 = 5.1 Mpc, 〈A _e 〉 = 4.8 kpc, and 〈SB _B (e)〉 = 27.^m4/□″. All the local UDG candidates reside near massive galaxies located in the regions with the mean stellar mass density (within 1 Mpc) about 50 times greater than the average cosmic density. The local fraction of UDGs does not exceed 1.5% of the Local Volume population. We notice that the presented sample of local UDGs is a heterogeneous one containing irregular, transition, and tidal types, as well as objects consisting of an old stellar population.     

On Errors in Constructing the Polarization Phase Dependences for Solar System Bodies

In astrophysical studies of Solar System bodies, the measured values of the linear polarization degree P_obs and the position angle of the polarization plane θ are usually considered relative to the plane orthogonal to the scattering plane; and the resulting quantities are designated as P_r and θ_r, respectively. Parameters of the phase curve of polarization P_r = f(α) serve for determining the physical characteristics of grains composing the regolith surfaces of such bodies as, for example, the Moon, Mercury, asteroids, and planetary satellites, or the polydisperse media, such as cometary comae and tails. In this paper it has been shown that the error in the polarization degree grows \({\sigma _{{P_r}}}\) due to the error \({\sigma _{{\theta _{obs}}}}\) in determining the position angle. The interrelations between these errors were obtained, and the conditions, under which the values of the linear polarization degree P_r relative to the orthogonal system can be used to analyze the phase dependences of polarization, were formulated.     

One-meter Schmidt telescope of the Byurakan Astrophysical Observatory: New capabilities

In 2013–2015 the Laboratory of spectroscopy and photometry of extragalactic objects (LS-PEO) of the Special Astrophysical Observatory together with Armenian specialists upgraded the 1-m Schmidt telescope of the Byurakan Astrophysical Observatory of the National Academy of Sciences of Armenia. We completely redesigned the control system of the telescope: we replaced the actuating mechanisms, developed telescope control software, and made the guiding system. We reworked and prepared a 4k × 4k Apogee (USA) liquid-cooled CCD with RON ~ 11.1 e^?, a pixel size of 0.″868, and field of view of about 1□°, and in October 2015 mounted it in the focus of the telescope. The detector is equipped with a turret bearing 20 intermediate-band filters (FWHM = 250 Å) uniformly covering the 4000–9000 Å wavelength range, five broadband filters (u, g, r, i, z SDSS), and three narrow-band filters (5000 Å, 6560 Å and 6760 Å, FWHM = 100 Å). During the first year of test operation of the 1-m telescope we performed pilot observations within the framework of three programs: search for young stellar objects, AGNevolution, and stellar composition of galaxy disks.We confirmed the possibility of efficiently selecting of young objects using observations performed in narrow-band Hα and [SII] filters and the intermediate-band 7500 Å filter. Three-hours long exposures with SDSS g-, r-, and i-band filters allow us to reach the surface brightness level of 28^m/□″ when investigating the stellar content of galaxy disks for a sample of nine galaxies. We used observations performed with the 1-m telescope in five broadband (SDSS u, g, r, i, and z) and 15 intermediate-band filters (4000–7500 Å) to construct a sample of quasar candidates with 0.5 < z < 5 (330 objects) in about one-sq. degree SA68 field complete down to R_AB = 23^m. Spectroscopic observations of 29 objects (19.^m5 < R < 22^m) carried out at the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences confirmed the quasar nature of 28 objects.     

Nearby groups of galaxies in the Hercules–Bootes constellations

We consider a sample of 412 galaxies with radial velocities V _LG < 2500 kms^?1 situated in the sky region of RA = 13_. ^m 0–19_. ^m 0, Dec = +10?...+40? between the Local Void and the Supergalactic plane. One hundred and eighty-one of them have individual distance estimates. Peculiar velocities of the galaxies as a function of Supergalactic latitude SGB show signs of Virgocentric infall at SGB < 10? and motion from the Local Void at SGB > 60?. A half of the Hercules–Bootes galaxies belong to 17 groups and 29 pairs, with the richest group around NGC5353. A typical group is characterized by the velocity dispersion of 67 km s^?1, the harmonic radius of 182 kpc, the stellar mass of 4.3 × 10¹⁰ M _⊙ and the virialto- stellar mass ratio of 32. The binary galaxies have the mean radial velocity difference of 37 kms^?1, the projected separation of 96 kpc, the mean integral stellar mass of 2.6×109M _⊙ and the mean virial-to-stellar mass ratio of about 8. The total dark-matter-to-stellar mass ratio in the considered sky region amounts to 37 being almost the same as that in the Local Volume.     

Evolution of galaxy groups

We study the variations of the properties of groups of galaxies with dynamical masses of 10¹³ M _⊙<M ₂₀₀<10¹⁴ M _⊙, represented by two samples: one has redshifts of z < 0.027 and is located in the vicinity of the Coma cluster, the other has z > 0.027, and is located in the regions of the following superclusters of galaxies: Hercules, Leo, Bootes, Ursa Major, and Corona Borealis. Using the archived data of the SDSS and 2MASX catalogs, we determined the concentration of galaxies in the systems by measuring it as the inner density of the group within the distance of the fifth closest galaxy from the center brighter than M _K = ?23_. ^m 3. We also measured the magnitude gap between the first and the fourth brightest galaxies ΔM ₁₄ located within one half of the selected radius R ₂₀₀, the fraction of early-type galaxies, and the ratio of bright dwarf galaxies (Mr = [?18_. ^m 5,?16_. ^m 5]) to giant galaxies (M _r < ?18_. ^m 5) (DGR) within the radius R ₂₀₀. The main aim of the investigation is to find among these characteristics the ones that reflect the evolution of groups of galaxies.We determined that the ratio of bright dwarf galaxies to early-type giant galaxies on the red sequence depends only on the x-ray luminosity: the DGR increases with luminosity. The fraction of early-type galaxies in the considered systems is equal, on average, to 0.65 ± 0.01, and varies significantly for galaxies with σ₂₀₀ < 300 kms^?1. Based on the luminosity of the brightest galaxy, the magnitude gap between the first and the fourth brightest galaxies in the groups, and on model computations of these parameters, we selected four fossil group candidates: AWM4, NGC0533, NGC0741, and NGC6098 (where the brightest galaxy is a double).We observe no increase in the number of faint galaxies (the α parameter of the Schechter function is less than 1) in our composite luminosity function (LF) for galaxy systems with z < 0.027 in the M _K = [?26m,?21_. ^m 5] range, whereas earlier we obtained α > 1 for the LF of the Hercules and Leo superclusters of galaxies.     

On the Evolutionary State of High-Latitude Variable V534 Lyr

Based on the high spectral resolution monitoring conducted at the 6-m BTA telescope, we study the optical spectrum of the high-latitude variable V534 Lyr. Heliocentric radial velocities V_r corresponding to the positions of all metal absorption components, as well as the Na I D and Hα lines were measured during all the observational sets. The analysis of the velocity field examining the lines of various nature revealed a low-amplitude variability of V_r based on the lines with a high excitation potential, which are formed in deep layers of the stellar atmosphere, and allowed to estimate the systemic velocity of V_sys ≈ ?125 kms^?1 (V_lsr ≈ ?105 kms^?1). The distance estimate of d ≈ 6 kpc for the star leads to its absolute magnitude of \(M_V \approx - 5_ \cdot ^m 3\), what corresponds to the spectral classification. The previously undetected spectral phenomenon was revealed for this star: at certain times a splitting of the profiles of low-excited absorptions is observed, reaching ΔV_r = 20–50 kms^?1. A combination of the parameters: reduced metallicity [Met/H]_⊙ = ?0.28, high nitrogen abundance [N/Fe] = +1.10, large spatial velocity, high luminosity, a strong variability of the emission-absorption profiles of HI lines, splitting of metal absorptions at different times of observations and the variability of the velocity field in the atmosphere allow to classify V534 Lyr as a pulsating star in the thick disk of our Galaxy.     

Observational study of the candidate polar-ring galaxies NGC 304 and NGC 7625

We present the results of our photometric (BV R) and spectroscopic CCD observations of NGC 304 and NGC 7625, candidate polar-ring galaxies, performed with the 6-m Special Astrophysical Observatory telescope. For NGC 304, such a study has been carried out for the first time. We have obtained basic integrated characteristics of the galaxies and determined their morphological types (S0 for NGC 304 and Sa for NGC 7625). The absolute magnitudes of the galaxies, M _B = ?20^m.81 for NGC 304 and M _B = ?19^m.34 for NGC7625, are indicative of their fairly high luminosities. The disk and bulge parameters have been determined forNGC 304 (µ₀ = 20^m.60, h = 3.86 kpc, µ _e = 21^m.59, r _e = 1.26 kpc in the B band); these correspond to the parameters of S0-type objects. The rotation velocity for NGC 304 (200 km s^?1) reaches its maximum at a galactocentric distance of 3.1 kpc, which yields a mass estimate for the galaxy of 2.8 × 10¹⁰ \(\mathcal{M}_ \odot \). The observed photometric features at the center of NGC 304 indicate that it may have an inner ring structure, although we have failed to confirm the existence of two kinematic systems based on our spectroscopic observations. In NGC 7625, the disk makes a dominant contribution to the total brightness. The derived integrated color indices (B-V = 0^m.81 and V-R = 0^m.61) agree with previous determinations of other authors. We have estimated the учештсешщт in the inner galactic regions. In the outer regions, we have detected structures with bluer colors (B-V = 0^m.60), which may be indicative of a polar ring with a minor stellar component.     

Multicolor Photometry and Spectroscopy of the Yellow Supergiant with Dust Envelope HD 179821 = V1427 Aquilae

We present the results of multicolor (UBV JHKLM) photometry (2009–2017) and low-resolution spectroscopy (2016–2017) of the semi-regular variable V1427 Aql = HD 179821, a yellow supergiant with gas-dust envelope. The star displays low-amplitude (ΔV<0 _. ^m 2) semi-periodic brightness variations superimposed on a long-term trend. The light curve shape and timescale change from cycle to cycle. There are temperature variations characteristic for pulsations; brightness oscillations with no significant change of color are also observed. The UBV data for the 2009–2011 interval are well reproduced by a superposition of two periodic components with P = 170^d and 141^d (or P = 217^d—the one year alias of P = 141^d). The variation became less regular after 2011, the timescale increased and exceeded 250^d. Unusual photometric behavior was seen in 2015 when the star brightness increased by 0 _. ^m 25 in the V filter in 130 days and reached the maximum value ever observed in the course of our monitoring since 1990. In 2009–2016 the annual average brightness monotonically increased in V, J, K, whereas it decreased in U and B. The annual average U ? B, B ? V, and J ? K colors grew, the star was getting redder. The cooling and expanding of the star photosphere along with the increasing of luminosity may explain the long-term trend in brightness and colors. Based on our photometric data we suppose that the photosphere temperature decreased by ~400 K in the 2008–2016 interval, the radius increased by ~24%, and the luminosity grew by ~19%. We review the change of annual average photometric data for almost 30 years of observations. Low-resolution spectra in the λ4000?9000 Å wavelength range obtained in 2016–2017 indicate significant changes in the spectrum of V1427 Aql as compared with the 1994–2008 interval, i.e., the Ba II and near-infraredCa II triplet absorptions have gotten stronger while the OI λ7771-4 triplet blend has weakened that points out the decrease of temperature in the region where the absorptions are formed. The evolutionary stage of the star is discussed. We also compare V1427 Aql with post-AGB stars and yellow hypergiants.     

A Model of the Mira–Type Star T UMi

Stellar evolution calculations were carried out from the main sequence to the final stage of the asymptotic giant branch for stars with initial masses 1 M_⊙ ≤ M_ZAMS ≤ 2 M_⊙ and metallicity Z = 0.01. Selected models of evolutionary sequences were used as initial conditions for solution of the equations of radiation hydrodynamics and time–dependent convection describing radial stellar pulsations. The study was aimed to construct the hydrodynamic models of Mira–type stars that show the secular decrease in the pulsation period Π commenced in 1970th at Π = 315 day. We show that such a condition for the period change is satisfied with evolutionary sequences 1 M_⊙ ≤ M_ZAMS ≤ 1.2 M_⊙ and the best agreement with observations is obtained for M_ZAMS = 1.2 M_⊙. The pulsation period reduction is due to both the stellar radius decrease during the thermal pulse of the helium burning shell and mode switch from the fundamental mode to the first overtone. Theoretical estimates of the fundament parameters of the star at the onset of pulsation period reduction are as follows: the mass is M = 0.93 M_⊙, the luminosity is L = 4080 L_⊙, and the radius is R = 220 R_⊙. The mode switch occurs 35 years after the onset of period reduction.     

Pulsations of intermediate–mass stars on the asymptotic giant branch

Evolutionary tracks from the zero age main sequence to the asymptotic giant branch were computed for stars with initial masses 2 M _⊙ ≤ M _ZAMS ≤ 5 M _⊙ and metallicity Z = 0.02. Some models of evolutionary sequences were used as initial conditions for equations of radiation hydrodynamics and turbulent convection describing radial stellar pulsations. The early asymptotic giant branch stars are shown to pulsate in the fundamental mode with periods 30 day ? Π ? 400day. The rate of period change gradually increases as the star evolves but is too small to be detected (Π?/Π < 10^?5 yr^?1). Pulsation properties of thermally pulsing AGB stars are investigated on time intervals comprising 17 thermal pulses for evolutionary sequences with initial masses M _ZAMS = 2 M _⊙ and 3 M _⊙ and 6 thermal pulses for M _ZAMS = 4 M _⊙ and 5 M _⊙. Stars with initial masses M _ZAMS ≤ 3 M _⊙ pulsate either in the fundamental mode or in the first overtone, whereas more massive red giants (M _ZAMS ≥ 4 M _⊙) pulsate in the fundamental mode with periods Π ? 10³ day. Most rapid pulsation period change with rate ?0.02 yr^?1 ? Π?/Π ? ?0.01 yr^?1 occurs during decrease of the surface luminosity after the maximum of the luminosity in the helium shell source. The rate of subsequent increase of the period is Π?/Π ? 5 × 10^?3 yr^?1.     

A model of possible variations of the galactic cosmic ray intensity over the recent billion years

Based on the analysis of published data on exposure ages of iron meteorites determined with the ⁴⁰K/K method (T _K) and ages calculated using short-lived cosmogenic radionuclides (with the half-life T _1/2 < 1 Myr) in combination with stable cosmogenic isotopes of noble gases (T_RS), the following results have been obtained. (1) The distribution of T _RS ages (106 values) has an exponential shape, similar to that for ordinary chondrites, but different from the distribution of T _K ages (80 values). The difference is most likely due to small amounts of data for meteorites with low T _K ages (less than ~200–300 Myr). The latter can be ascribed to the difficulty of measurement of small concentrations of cosmogenic potassium isotopes. This circumstance makes the selection of meteorites with ⁴⁰K/K ages nonrepresentative and casts doubt on the correctness of conclusions about the variations of the intensity of galactic cosmic rays (GCR) based on the analysis of distribution of these ages. (2) The magnitude of the known effect (systematic overestimation of T _K ages in comparison with T _RS ages) has been refined. The value k = T _K/T _RS = 1.51 ± 0.03 is acquired for the whole population of data. We have shown the inefficiency of the explanation of this effect on account of an exponential change in the GCR intensity (I _T ) with time (T) according to the relation I _T = I ₀exp(–γT) over the whole range of ages of iron meteorites. (3) In order to explain the overestimation of T _K ages in comparison with T _RS ages, a model has been proposed, according to which the GCR intensity has exponentially increased in the interval of 0–1500 Myr governed by the relation: I _T = I _{T = 1500} (1 + αexp(–βT)). For one of the variants of this model, the GCR intensity has exponentially increased by a factor of two only over the recent ~300 Myr, remaining approximately constant for the rest of the time. The data acquired with the use of this model indicate that the measured T _K ages are close to the actual time that the meteorites existed in space; the data are in agreement with the observed exponential distribution of T _RS ages.     

Variability of hot supergiant IRAS 19336-0400 in the early phase of planetary nebula ionization

We present photoelectric and spectral observations of a hot candidate proto-planetary nebula—early B-type supergiant with emission lines in spectrum—IRAS 19336-0400. The light and color curves display fast irregular brightness variations with maximum amplitudes \(\Delta V = 0_ \cdot ^m 30\), \(\Delta B = 0_ \cdot ^m 35\), \(\Delta U = 0_ \cdot ^m 40\) and color-brightness correlations. By the variability characteristics IRAS 19336-0400 appears similar to other hot proto-planetary nebulae. Based on low-resolution spectra in the range λ4000–7500 Å we have derived absolute intensities of the emission lines Hα, Hβ, Hγ, [S II], [N II], physical conditions in gaseous nebula: n _e = 10⁴ cm^?3, T _e = 7000 ± 1000 K. The emission line Hα, Hβ equivalent widths are found to be considerably variable and related to light changes. By UBV-photometry and spectroscopy the color excess has been estimated: E _B-V = 0.50–0.54. Joint photometric and spectral data analysis allows us to assume that the star variability is caused by stellar wind variations.     

Inverse problem of central configurations and singular curve in the collinear 4-body problem

In this paper, we consider the inverse problem of central configurations of n-body problem. For a given \({q=(q_1, q_2, \ldots, q_n)\in ({\bf R}^d)^n}\), let S(q) be the admissible set of masses denoted \({ S(q)=\{ m=(m_1,m_2, \ldots, m_n)| m_i \in {\bf R}^+, q}\) is a central configuration for m}. For a given \({m\in S(q)}\), let S _m (q) be the permutational admissible set about m = (m ₁, m ₂, . . . , m _n ) denoted

$S_m(q)=\{m^\prime | m^\prime\in S(q),m^\prime \not=m \, {\rm and} \, m^\prime\,{\rm is\, a\, permutation\, of }\, m \}.$

The main discovery in this paper is the existence of a singular curve \({\bar{\Gamma}_{31}}\) on which S _m (q) is a nonempty set for some m in the collinear four-body problem. \({\bar{\Gamma}_{31}}\) is explicitly constructed by a polynomial in two variables. We proved:

1. (1)
   If \({m\in S(q)}\), then either ^# S _m (q) = 0 or ^# S _m (q) = 1.
    
2. (2)
   ^#S _m (q) = 1 only in the following cases:

   1. (i)
      If s = t, then S _m (q) = {(m ₄, m ₃, m ₂, m ₁)}.
       
   2. (ii)
      If \({(s,t)\in \bar{\Gamma}_{31}\setminus \{(\bar{s},\bar{s})\}}\), then either S _m (q) = {(m ₂, m ₄, m ₁, m ₃)} or S _m (q) = {(m ₃, m ₁, m ₄, m ₂)}.
       
    

     

Results of Complex Observations of Asteroid (596) Scheila at the Sanglokh International Astronomical Observatory

Results of astrometric and BVRI photometric observations of the active asteroid (596) Scheila are presented. The observations were carried out at the Zeiss-1000 telescope of the Sanglokh International Astronomical Observatory of the Institute of Astrophysics of the Academy of Sciences of the Republic of Tajikistan on June 16?17 and from July 30 to August 1, 2017. The coordinates of the object and its orbit were determined; and the apparent brightness in four filters, the absolute brightness in the V and R filters, and the color indices were obtained. The light curves suggest that no substantial changes in the asteroid’s brightness occurred during the observations. The absolute brightness of the asteroid in the V and R filters was (9.1 ± 0.05)^m and (8.8 ± 0.03)^m, respectively. The mean value of the asteroid diameter was (119 ± 2) km. The mean values of the color indices (B?V = (0.72 ± 0.05)^m, V?R = (0.29 ± 0.03)^m, and R?I = (0.31 ± 0.03)^m) agree well with the values for asteroids of the P- and D-types and its averages. The rotation period of the asteroid estimated from photometric observations was 16.1 ± 0.2 h. The analysis of the data has shown that the asteroid continues to exhibit the same values of absolute brightness and other characteristics as those before the collision with a small body in December 2010, though the latter resulted in the outburst event and cometary activity of the asteroid. Most likely, the collision of asteroid (596) Scheila with a small body did not lead to catastrophic changes in the surface of the asteroid or to its compete break-up.     

Variability of the period of the star DU Monocerotis,an RR Lyrae variable with the Blazhko effect

In 2012–2014 we obtained 3641 CCD frames of the fields of the RR Lyrae (AB subtype, P = 0.583 days) variable DU Mon with BV I _c filters using the 76-cm telescope of the South African Astronomical Observatory (SAAO) and the 1-m telescopes of the Las Cumbres Observatory Global Telescope Network (LCOGT). Our observations confirmed the presence of the Blazhko effect that we suspected previously and allowed its period to be determined, \({P_{Bl}} = 60_ \cdot ^d52 \pm 0_ \cdot ^d03\). Using all of the available observations, we constructed an O–C diagram spanning a time interval of 86 years that revealed at least one abrupt change in the pulsation period (a decrease by 15.26 s).