Evolution of the dust envelope of Sakurai’s star (V4334 Sgr) in 1997–1999

We have studied the structural evolution of the dust envelope of V4334 Sgr, starting with the onset of its condensation in 1997. A model with complete cloud cover, with the optical depth growing until the end of 1999, gives the best fit to the photometric data in the optical and IR. The inner radius of the dust layer remained virtually constant, whereas its thickness increased due to expansion. The deep minimum in the visual light curve of V4334 Sgr in October 1998 is attributed to the arrival at the dust-grain condensation zone of a density discontinuity in the circumstellar envelope. The discontinuity was probably formed early in 1997 due to an increase in the mass-loss rate by a factor of about four, possibly associated with an increase in the luminosity of V4334 Sgr during its transformation into a carbon star. After this luminosity increase, the mass-loss rate was $\dot M \approx 2 \times 10^{ - 6} M_ \odot /yr$ . In the summer of 1999, the mass of the dust envelope was $M_{dust} \approx 2 \times 10^{ - 7} M_ \odot (M_{gas} \approx 4 \times 10^{ - 6} M_ \odot)$ . In the complete-cloud-cover model, the envelope consists of graphite grains with a _gr=0.05 µm, to ～85% per cent in terms of the number of grains. The remaining ～15 per cent of the grains have sizes a _gr=0.1 and 0.25 µm. To reproduce the small hump in the spectral energy distribution of V4334 Sgr near 11 µm, some silicon carbide grains must be added to the graphite mixture. Their contribution to the V optical depth is ≤4%. The first deep minimum in the visual light curve could also be reproduced using a model in which the dust cloud has condensed along the line of sight, but a detailed analysis of the resulting characteristics of the cloud and envelope indicates that this model is improbable.     

Photometric observations of R Coronae Borealis in the optical and infrared

The results of long-term photometric observations of R CrB in the UBV JHKLM bands are presented. The temporal and color characteristics of the emission of the star itself and of its extended dust envelope are analyzed in detail. No stable harmonic has been found in the semiregular variations of the optical brightness of R CrB. Two harmonics with periods P≈3.3 and 11.3 yrs have been detected in the brightness variations of the dust envelope; the minima of these variations coincided in 1999, resulting in a record decrease in the LM brightness of the envelope. This by chance coincided in time with a deep minimum of the visual brightness of the star, resulting in a unique decrease in the total brightness of the star and dust envelope. This enabled estimation of the bolometric flux of the hot dust clouds, which made up only a few per cent of the bolometric flux of the dust envelope. The brightness variations of the dust envelope are not accompanied by appreciable color changes and are associated with variations of its optical depth τ(V) in the range 0.2–0.4. The dust envelope forms at a large and fairly constant distance from the star $(r_{in} \approx 110R_* ,T_{gr} \approx 860 K)$ , from material in its stellar wind, whose intensity $(\dot M_{gas} \approx 2.1 \times 10^{ - 7} M_ \odot /year)$ obeys a Reimers law. No variations synchronous with those of the optical depth of the dust envelope, in particular, with the period P≈3.3 yrs, have been found in the optical emission of R CrB, suggesting that the stellar wind is not spherically symmetric. The dust envelope consists of small grains (a _gr≤0.01 µm), while the clouds screening the star from the observer are made up of large grains (a _gr≈0.1 µm). The activity of R CrB, whose nature is unclear, is reflected in variations of the stellar-wind intensity and the appearance of dust clouds in the line of sight: these variations are repeated by corresponding changes in the optical depth of the dust envelope with a delay of ～4 years (the time for a particle moving at V _env≈45 km/s to move from the star to the boundary of the dust envelope).     

Infrared photometry of the unique object FG Sge in 1985–2001

Our analysis of many years of infrared photometry of the unique object FG Sge indicates that the dust envelope formed around the supergiant in August 1992 is spherically symmetrical and contains compact, dense dust clouds. The emission from the spherically symmetrical dust envelope is consistent with the observed radiation from the star at 3.5–5 µm, and the presence of the dust clouds can explain the radiation observed at 1.25–2.2 µm. The mean integrated flux from the dust envelope in 1992–2001 was ～(1.0±0.2)×10^?8 erg s^?1cm^?2. The variations of its optical depth in 1992–2001 were within 0.5–1.0. The maximum density of the dust envelope was recorded in the second half of 1993 and corresponded to mean optical depths as high as unity. Several times in the interval from 1992 to 2001, the dusty material of the envelope partially dissipated and was then replenished. For example, the optical depth of the dust cloud at λ=1.25 µm during the last brigthness minimum in the J band was τ_1.25≈4.3, which is much higher than the optical depth of the dust envelope of FG Sge. During maxima of the J brightness, the mean spectral energy distribution at 0.36–5 µm can be represented as a combination of radiation from a G0 supergiant that is attenuated by a dust envelope with a mean optical depth of 0.65±0.15 and emission from the spherically symmetrical dust envelope itself, with the temperature of the graphite grains being 750±150 K. At minima of the J brightness, only radiation from the dust envelope is observed at 1.65–5 µm, with the radiation from the supergiant barely detectable at 1.25 µm. As a result, the integrated flux during J minima is almost half that during J maxima. The mean mass of the spherically symmetrical dust envelope of FG Sge in 1992–2001 was (3 ± 1) × 10^?7M_⊙. This envelope’s mass varied by nearly a factor of two during 1992–2001, in the range (2 – 4) × 10^?7M_⊙. In Autumn 1992, the mass-loss rate from the supergiant exceeded 2 × 10^?7M_⊙/yr. The average rate at which matter was injected into the envelope during 1993–2001 was 10^?8M_⊙/yr. The mean rate of dissipation of the dust envelope was about 1 × 10^?8M_⊙/yr. During 1992–2001, the supergiant lost about 8.7 × 10^?7M_⊙. The parameters of the dust envelope were relatively constant from 1999 until the middle of 2001.     

The dust envelope of R Cas

The spectral energy distribution in the far infrared and the shape of a broad emission band in the spectrum of R Cas at 9–13 µm can be reproduced in a model with a dust envelope consisting of approximately half amorphous olivine (Mg_0.8Fe_1.2SiO₄) and half amorphous aluminum-oxide grains (Al₂O₃), with a small admixture of spinel grains (MgAl₂O₄). The dust envelope’s optical depth τ(50 µm) is ≈5×10^?3 [τ(1.25 µm)≈0.07 for a _gr≈0.05 µm], and its mass within r≤0.025 pc M _dust is ≈8×10^?6 M _⊙. The index α in the power-law radial dust distribution, n _d ∝(R ₊/r)^α, is ≈1.8. Over the last several thousand years, the mass-loss rate of R Cas has been decreasing as $\dot M(t) \propto t^{0.2} $ (where time is measured backward from the present). This probably implies that R Cas experienced a thermal helium flare several thousand years ago. If M _gas/M _dust≈200 (where M _gas is the gas mass), the mean mass-loss rate of the star is $\dot M \approx 6 \times 10^{ - 7} M_ \odot /yr$ .     

Pulsed optical emission by radio pulsars

The luminosity L of radio pulsars due to synchrotron radiation by the primary beam at the magnetosphere periphery is derived. There is a strong correlation between the observed optical luminosities of radio pulsars and the parameter $\dot P/P^4$ (where P is the pulsar period). This correlation predicts appreciable optical emission from several dozen pulsars, in particular, from all those with P<0.1 s. Agreement with optical observations can be achieved for Lorentz factors of the secondary plasma γ_p=2–13. Plasma with such energies can be produced only when the magnetic-field structure near the neutron-star surface deviates substantially from a dipolar field. The peak frequency of the synchrotron spectrum should shift toward higher values as the pulsar period P decreases; this is, in agreement with observational data for 27 radio pulsars for which emission has been detected outside the radio band.     

Variations of the parameters of the dust envelope of the symbiotic star CH Cygni

The results of JHKLM photometry of the symbiotic star CH Cyg are presented. These demonstrate that, in Autumn 2006, the state of maximum near-IR brightness observed in 2003–2006 was replaced by a sharp brightness decline in all wavebands. One possible explanation is a sharp increase in the density of circumstellar dust envelope. The JHKLM photometry data together with ISO far-IR flux measurements are used to calculate spherically symmetric dust-envelope models for the maximum and minimum brightness states. The optical depth, expansion rate, and mass-loss rate of the envelope are calculated for both states, as well as an upper limit for the mass of the central source. Comparison with earlier models suggests that the rate of growth of the envelope optical depth and the mass-loss rate by the star are accelerating with time.     

Rethinking communication in risk interpretation and action

We have studied the attenuation characteristics of eastern Himalaya and southern Tibet by using local earthquake data set that consists of 123 well-located events, recorded by the Himalayan Nepal Tibet Seismic Experiment operated during 2001–2003. We have used single backscattering model to calculate frequency-dependent values of coda Q (\(Q_\mathrm{c}\)). The estimation of \(Q_\mathrm{c}\) is made at central frequencies 2, 4, 8 and 12 Hz through five lapse time windows from 10 to 50 s starting at double the travel time of the S-wave. The observed \(Q_\mathrm{c}\) is found to be strongly frequency-dependent and follows a similar trend as observed in other tectonically active parts of the Himalaya. The trend of variation of \(Q_\mathrm{c}\) with lapse time and the corresponding apparent depths is also studied. Increase in \(Q_\mathrm{c}\) values with the lapse time suggests that the deeper part of the study region is less heterogeneous than the shallower part. The observed values of \(Q_0\) (\(Q_\mathrm{c}\) at 1 Hz) and frequency parameter n indicate that the medium beneath the study area is highly heterogeneous and tectonically very active. A regionalization of the estimated \(Q_0\) is carried out, and a contour map is prepared for the whole region. Some segments of Lesser Himalaya and Sub-Himalaya exhibit very low \(Q_0\) , while the whole Tethyan Himalaya and some parts of Greater Himalaya are characterized by low \(Q_0\) values. Our results are comparable with those obtained from tectonically active regions in the world.     

Light curve interpretation for “Quiescent” X-ray novae in a model with noncollisional interaction between the flow and disk. The system GU Mus = GRS 1124-68

We have analyzed optical and infrared light curves of GU Mus obtained during the system's quiescent state and carried out computations for “hot-line” and “hot-spot” models. The hot-line model describes the optical variability of GU Mus better than the hot-spot model. Season-to-season variations of the shape, amplitude, and mean levels of the optical and infrared light curves of GU Mus are due to changing parameters of the hot line and, to a lesser degree, of the accretion disk. Taking into account the contribution of the variability of the disk + hot line system to the variability of the system as a whole, we are able to reliably estimate the orbital inclination, \(i = 54^\circ \pm 1^\circ .3\), and the mass of the black hole, M _X =(6.7–7.6)M_⊙.     

Effect of $$\hbox {CO}_2$$ solubility on dissolution rate of calcite in saline aquifers for temperature range of 50–100 $$^{\circ } \hbox {C}$$∘C and pressures up to 600 bar: alterations of fractures geometry in carbonate rocks by $$\hbox {CO}_2$$-acidified brines

An empirical model is developed to predict the dissolution rate of calcite in saline solutions that are saturated with respect to dissolved \(\hbox {CO}_2\) over a broad range of both subcritical and supercritical conditions. The focus is on determining the rate of calcite dissolution within a temperature range of 50–100 \(^\circ \hbox {C}\) and pressures up to 600 bar, relevant for \(\hbox {CO}_2\) sequestration in saline aquifers. A general reaction kinetic model is used that is based on the extension of the standard Arrhenius equation with an added, solubility-dependent, pH term to account for the saturated concentration of dissolved \(\hbox {CO}_2\). On the basis of this kinetic model, a new rate equation is obtained using multi-parameter, nonlinear regression of experimental data to determine the dissolution of calcite as a function of temperature, pressure and salinity. Different models for the activity coefficient of \(\hbox {CO}_2\) dissolved in saline solutions are accounted for. The new rate equation helps us obtain good agreement with experimental data, and it is applied to study the geochemically induced alterations of fracture geometry due to calcite dissolution.     

<Emphasis Type="Italic">UBVJHKLM</Emphasis> photometry of the symbiotic Mira V407 Cyg in 1998–2002

New results of UBV JHKLM photometry of the symbiotic Mira V407 Cyg performed in 1998–2002 are reported. In 2002, these observations were supplemented with RI observations and a search for rapid variability in the V band. The hot component of V407 Cyg experienced a strong flare in 1998, which was the second in the history of photometric observations of this star; this flare is still continuing. During the flare, the spectral energy distribution of the hot component can be approximated by blackbody radiation with a temperature of ～7200 K. At the maximum brightness, the bolometric flux from the hot component did not exceed 3% of the Mira's mean bolometric flux, while its bolometric luminosity was ～400L_⊙. Appreciable variations of the star's BV brightness \((\tilde0\mathop m\limits_. 7)\) on a timescale of several days have been observed. These variations are not correlated with variations of B-V. Flickering on a timescale of several minutes with an amplitude of \(\tilde0\mathop m\limits_. 2\) has been detected in the V band. The observations suggest that the hot component can be in three qualitatively different states. In a model with a rapidly rotating white dwarf, these states can be associated with (i) the quiescent state of the white dwarf (with a very low accretion rate), (ii) an ejection state, and (iii) an accretion state. The Mira pulsation period P is \( \approx 762\mathop d\limits_. 9\), with its infrared maximum occurring ～0.15P after the visual maximum. A “step” is observed on the ascending branch of the Mira infrared light curves. In 1998, the gradual increase of the mean K brightness of the Mira that had been observed since 1984 was interrupted by an unusually deep minimum, after which the mean level of the K brightness considerably decreased.     

Wolf-Rayet stars,black holes,and gamma-ray bursters in close binaries

We consider the evolutionary status of observed close binary systems containing black holes and Wolf-Rayet (WR) stars. When the component masses and the orbital period of a system are known, the reason for the formation of a WR star in an initial massive system of two main-sequence stars can be established. Such WR stars can form due to the action of the stellar wind from a massive OB star (M_OB≥50M_⊙), conservative mass transfer between components with close initial masses, or the loss of the common envelope in a system with a large (up to ～25) initial component mass ratio. The strong impact of observational selection effects on the creation of samples of close binaries with black holes and WR stars is demonstrated. We estimate theoretical mass-loss rates for WR stars, which are essential for our understanding the observed ratio of the numbers of carbon and nitrogen WR stars in the Galaxy \(\dot M_{WR} (M_ \odot yr^{ - 1} ) = 5 \times 10^{ - 7} (M_{WR} /M_ \odot )^{1.3} \). We also estimate the minimum initial masses of the components in close binaries producing black holes and WR stars to be ～25M_⊙. The spatial velocities of systems with black holes indicate that, during the formation of a black hole from a WR star, the mass loss reaches at least several solar masses. The rate of formation of rapidly rotating Kerr black holes in close binaries in the Galaxy is ～3×10^?6 yr^?1. Their formation may be accompanied by a burst of gamma radiation, possibly providing clues to the nature of gamma-ray bursts. The initial distribution of the component mass ratios for close binaries is dN～dq=dM₂/M₁ in the interval 0.04?q₀≤1, suggesting a single mechanism for their formation.     

Stochastic analysis of bed-thickness distribution of sediments

On formation of a bed and distribution of bed thickness, A. N. Kolmogorov presented a mathematical explanation that if repetitive alternations of material accumulation and erosion form a sequence of beds, the resultant bed-thickness distribution curve takes a shape truncated by the ordinate at zero thickness. In this truncated distribution curve, its continuation and extension from positive to negative thickness represents the distribution of beds with negative thickness, that is, the depth of erosion. When a distribution curve, including both positive and negative parts, is expressed by a function f(x),the ratio \(\int_0^\infty {f(x)dx to} \int_{ - \infty }^\infty {f(x)dx} \) ,called Kolmogorov's coefficient and designated as p,is a parameter representing the degree of accumulation in the depositional environment. On the assumption that f(x)is described by the Gaussian distribution function, the coefficient pfor Permian and Pliocene sequences in central Japan was calculated. The coefficients also were obtained from published data for different types of sediments from other areas. It was determined that they are more or less different depending on their depositional environments. The calculated results are summarized as follows: $$\begin{gathered} p = 0.80 - 1.0for{\text{ }}alluvial{\text{ }}or{\text{ }}fluvial{\text{ }}deposits \hfill \\ p = 0.65 - 0.95for{\text{ }}nearshore{\text{ }}sediments \hfill \\ p = 0.55 - 0.95for{\text{ }}geosynclinal{\text{ }}sediments \hfill \\ p = 0.90 - 1.0for{\text{ }}varves \hfill \\ \end{gathered} $$ In addition, a ratio \(q = \int_0^\infty {xf(x)dx/} \int_{ - \infty }^\infty {|x|f(x)dx} \) ,called Kolmogorov's ratio in this paper, is introduced for estimating a degree of total thickness actually observed in the field relative to total thickness once present in a basin. The calculated results of Kolmogorov's ratio are as follows: $$\begin{gathered} q = 0.88 - 1.0for{\text{ }}alluvial{\text{ }}or{\text{ }}fluvial{\text{ }}deposits \hfill \\ q = 0.68 - 0.98for{\text{ }}nearshore{\text{ }}sediments \hfill \\ q = 0.55 - 0.96for{\text{ }}geosynclinal{\text{ }}sediments \hfill \\ q = 0.92 - 1.0for{\text{ }}varves \hfill \\ \end{gathered} $$ The sedimentological significance of these values is discussed.     

H-bonding scheme and cation partitioning in axinite: a single-crystal neutron diffraction and Mössbauer spectroscopic study

The crystal chemistry of a ferroaxinite from Colebrook Hill, Rosebery district, Tasmania, Australia, was investigated by electron microprobe analysis in wavelength-dispersive mode, inductively coupled plasma–atomic emission spectroscopy (ICP–AES), ⁵⁷Fe Mössbauer spectroscopy and single-crystal neutron diffraction at 293 K. The chemical formula obtained on the basis of the ICP–AES data is the following: \( ^{X1,X2} {\text{Ca}}_{4.03} \,^{Y} \left( {{\text{Mn}}_{0.42} {\text{Mg}}_{0.23} {\text{Fe}}^{2 + }_{1.39} } \right)_{\varSigma 2.04} \,^{Z1,Z2} \left( {{\text{Fe}}^{3 + }_{0.15} {\text{Al}}_{3.55} {\text{Ti}}_{0.12} } \right)_{\varSigma 3.82} \,^{T1,T2,T3,T4} \left( {{\text{Ti}}_{0.03} {\text{Si}}_{7.97} } \right)_{\varSigma 8} \,^{T5} {\text{B}}_{1.96} {\text{O}}_{30} \left( {\text{OH}} \right)_{2.18} \). The ⁵⁷Fe Mössbauer spectrum shows unambiguously the occurrence of Fe²⁺ and Fe³⁺ in octahedral coordination only, with Fe²⁺/Fe³⁺ = 9:1. The neutron structure refinement provides a structure model in general agreement with the previous experimental findings: the tetrahedral T1, T2, T3 and T4 sites are fully occupied by Si, whereas the T5 site is fully occupied by B, with no evidence of Si at the T5, or Al or Fe³⁺ at the T1–T5 sites. The structural and chemical data of this study suggest that the amount of B in ferroaxinite is that expected from the ideal stoichiometry: 2 a.p.f.u. (for 32 O). The atomic distribution among the X1, X2, Y, Z1 and Z2 sites obtained by neutron structure refinement is in good agreement with that based on the ICP–AES data. For the first time, an unambiguous localization of the H site is obtained, which forms a hydroxyl group with the oxygen atom at the O16 site as donor. The H-bonding scheme in axinite structure is now fully described: the O16–H distance (corrected for riding motion effect) is 0.991(1) Å and an asymmetric bifurcated bonding configuration occurs, with O5 and O13 as acceptors [i.e. with O16···O5 = 3.096(1) Å, H···O5 = 2.450(1) Å and O16–H···O5 = 123.9(1)°; O16···O13 = 2.777(1) Å, H···O13 = 1.914(1) Å and O16–H···O13 = 146.9(1)°].     

The evolution of GRS 1915+105—an X-ray binary with a black hole

A brief review of the observed parameters of binary systems with black holes is presented. We discuss in detail the evolutionary status of the X-ray binary GRS 1915+105, which contains a massive black hole. Numerical simulations of the evolution of GRS 1915+105 at the X-ray stage indicate that the most probable initial mass of the optical component (donor star) is (1.5–)M_⊙. Two possible scenarios are suggested for the evolution of the system prior to the formation of the black hole. If the initial mass of the optical component was (2.5–)M_⊙, the system underwent a common-envelope phase; in this case, the initial mass of the black hole progenitor did not exceed ～50M_⊙. If the initial mass of the donor was (1.5–2.5)M_⊙, a scenario without a common envelope is possible, with the initial mass of the black hole progenitor being smaller than ～50M_⊙. The lack of information about the initial mass-ratio distribution for binary components for small q and the uncertainty of the system parameters make it impossible to give preference to a particular scenario for the system's prior evolution.     

Manganese thermometer for mantle peridotites

The temperature dependence of the Mn-Mg distribution between garnet and clinopyroxene, originally proposed by Carswell, was confirmed by Shimizu and Allègre (1978) using ion microprobe and electron microprobe data. High precision electron microprobe analyses of a larger set of 52 Iherzolites from S. Africa and Malaita, Solomon Islands show considerable scatter in the temperature dependence of this distribution, and correlation with the CaO content of the garnet is indicated. A new distribution coefficient is based on the reaction: $$\begin{gathered} \operatorname{Mn} _{\text{2}} \operatorname{Si} _2 \operatorname{O} _6 {\text{ + }}\operatorname{CaAl} _{2/3} \operatorname{SiO} _4 {\text{ + }}\operatorname{MgAl} _{2/3} \operatorname{SiO} _4 \hfill \\ {\text{Mn - pyroxene grossular pyrope}} \hfill \\ {\text{ }} \rightleftharpoons \operatorname{CaMgSi} _2 \operatorname{O} _6 {\text{ + }}2\operatorname{MnAl} _{2/3} \operatorname{SiO} _4 \hfill \\ {\text{ diopside spessartine}} \hfill \\ \end{gathered} $$ It was calibrated against temperature determined from two independent thermometers (Wells pyroxene and O'Neill-Wood garnet-olivine) for Iherzolitic assemblages, and shown to to be sensitive to within + 50 °C for most specimens in the range 900 °– 1,300 ° C. This distribution coefficient appears independent of pressure within the uncertainty of the available data, and has the potential to be a third independent thermometer for use in garnet Iherzolites and possibly eclogites.     

The dilatant behaviour of sand–pile interface subjected to loading and stress relief

Property and behaviour of sand–pile interface are crucial to shaft resistance of piles. Dilation or contraction of the interface soil induces change in normal stress, which in turn influences the shear stress mobilised at the interface. Although previous studies have demonstrated this mechanism by laboratory tests and numerical simulations, the interface responses are not analysed systematically in terms of soil state (i.e. density and stress level). The objective of this study is to understand and quantify any increase in normal stress of different pile–soil interfaces when they are subjected to loading and stress relief. Distinct element modelling was carried out. Input parameters and modelling procedure were verified by experimental data from laboratory element tests. Parametric simulations of shearbox tests were conducted under the constant normal stiffness, constant normal load and constant volume boundary conditions. Key parameters including initial normal stress ( $ \sigma_{{{\text{n}}0}}^{\prime } $ ), initial void ratio (e ₀), normal stiffness constraining the interface and loading–unloading stress history were investigated. It is shown that mobilised stress ratio ( $ \tau /\sigma_{\text{n}}^{\prime } $ ) and normal stress increment ( $ \Updelta \sigma_{\text{n}}^{\prime } $ ) on a given interface are governed by $ \sigma_{{{\text{n}}0}}^{\prime } $ and e ₀. An increase in $ \sigma_{{{\text{n}}0}}^{\prime } $ from 100 to 400 kPa leads to a 30 % reduction in $ \Updelta \sigma_{\text{n}}^{\prime } $ . An increase in e ₀ from 0.18 to 0.30 reduces $ \Updelta \sigma_{\text{n}}^{\prime } $ by more than 90 %, and therefore, shaft resistance is much lower for piles in loose sands. A unique relationship between $ \Updelta \sigma_{\text{n}}^{\prime } $ and normal stiffness is established for different soil states. It can be applied to assess the shaft resistance of piles in soils with different densities and subjected to loading and stress relief. Fairly good agreement is obtained between the calculated shaft resistance based on the proposed relationship and the measured results in centrifuge model tests.     

Estimation of the accuracy of methods for determining component masses for low-mass X-ray binary systems

Modern modeling of the population of low-mass X-ray binary systems containing black holes applying standard assumptions leads to a lack of agreement between the modeled and observed mass distributions for the optical components, with the observed masses being lower. This makes the task of estimating the systematic errors in the derived component masses due to imperfect models relevant. To estimate the influence of systematic errors in the derived masses of stars in X-ray binary systems, we considered two approximations for the tidally deformed star in a Roche model. Approximating the star as a sphere with a volume equal to that of the Roche lobe leads to slight overestimation of the equatorial rotational velocity V _rot sin i, and hence to slight underestimation of the mass ratio q = M _x /M _v . Approximating the star as a flat, circular disk with constant local line profiles and a linear limb-darkening law (a classical rotational broadeningmodel) is an appreciably cruder approach, and leads to overestimation of V _rot sin i by about 20%. In the case of high values of q = M _x /M _v , this approximation leads to substantial underestimation of the mass ratio q, which can reach several tens of percent. The mass of the optical star is overestimated by a factor of 1.5 in this case, while the mass of the black hole is changed only slightly. Since most estimates of component mass ratios for X-ray binary systems are carried out using a classical rotational broadening model for the lines, this leads to the need for appreciable corrections to (reductions of) previously published masses for the optical stars, which enhances the contradiction with the standard evolutionary scenario for low-mass X-ray binaries containing black holes.     

Magnetic fields and the $$\dot P - P$$ diagram for radio pulsars

Various mechanisms for the loss of angular momentum of neutron stars are analyzed. Theoretical predictions about the evolution of the period are compared with the observed distribution of pulsars on the log\(\dot P\)log(P) diagram. Pulsars with short periods (P≤0.1 s) cannot be fit well by any of the models considered. Their braking index is n=?1, which requires the development of a new braking mechanism. The evolution of pulsars with P>1.25 s is described by the law \(\dot P \propto P^2\), probably due to processes internal to the neutron stars. The observational data for pulsars with 0.1<P≤1.25 s can be fit with a hybrid model incorporating internal processes and magnetic-dipole losses. The magnetic fields in pulsar catalogs should be recomputed in accordance with the results obtained. For example, the magnetic fields obtained for two magnetars with P=5.16 s and P=7.47 s are B _s =1.7×10¹³ and 2.9×10¹³ G, which are lower than the critical field B_cr=4.4×10¹³ G. For a substantial fraction of pulsars, their characteristic ages \(\tau = P/2\dot P\) cannot serve as measures of their real ages.     

Earthquake hazard and risk assessment based on unified scaling law for earthquakes: Altai–Sayan Region

We apply the general concept of seismic risk analysis based on morphostructural analysis of the territory, pattern recognition of earthquake-prone nodes, and the Unified Scaling Law for Earthquakes, USLE, in another seismic region of Russia to the west from Lake Baikal, i.e., Altai–Sayan Region. The USLE generalizes the empirical Gutenberg–Richter relationship making use of apparently fractal distribution of earthquake sources of different size: \( \log_{10} N\left( {M,L} \right)\, = \,A\, + \,B \cdot \left( {5\, - \,M} \right)\, + \,C \cdot \log_{10} L, \) where N (M, L) is the expected annual number of earthquakes of a certain magnitude M within an seismically prone area of linear dimension L. The local estimates of A, B, and C allow determination of the expected maximum credible magnitude in a given time interval and the associated spread around ground shaking parameters (e.g., peak ground acceleration, PGA, or macroseismic intensity, I₀). Compilation of the corresponding seismic hazard map of Altai–Sayan Region and its rigorous testing against the available seismic evidences in the past is used to model regional maps of specific earthquake risks for population, cities, and infrastructures.