Estimate of the black-hole mass and orbital inclination from the radial-velocity curve of the X-ray binary Cyg X-1

Astronomy Reports - The results of a statistical approach to interpreting a master radial-velocity curve for the X-ray binary Cyg X-1 are presented. The dependence of the mass of the X-ray...     

K-Corrections to radial-velocity curves of optical components in X-ray binaries. Massive systems with weak X-ray heating

The radial-velocity curves of optical components in X-ray binary systems can differ from the radial-velocity curves of their barycenters due to tidal distortion, gravitational darkening, X-ray heating, etc. This motivated us to investigate how the semi-amplitudes of the radial-velocity curves of these optical components can depend on the binary-system parameters in a Roche model. The K correction is taken to be the ratio of the radial velocity semi-amplitude for a star in the Roche model to the corresponding value for the stellar barycenter. K corrections are tabulated for the optical stars in the massive X-ray binaries Cen X-3, LMC X-4, SMC X-1, Vela X-1, and 4U 1538-52.     

Radial-velocity curves and theoretical spectral-line profiles of the components of low-mass close X-ray binary systems

We present the results of calculations of theoretical absorption-line profiles and radial-velocity curves for optical components in X-ray binary systems. Tidal distortion of the optical star and X-ray heating by incident radiation from the relativistic object are taken into account. An emission component forms whose intensity varies with orbital phase in the absorption-line profile in the presence of significant X-ray heating. As a result, the width of the line decreases rather than increases at quadrature. The line profiles and equivalent widths and the radial-velocity curves depend substantially on the parameters of the binary systems. This provides the possibility of directly determining component masses and orbital inclinations from high-resolution spectroscopic observations of X-ray binary systems.     

Microvariability of line profiles in the spectrum of the star ι Her

We present the results of a search for and analysis of line-profile variations in the spectrum of the star ι Her. The observations were acquired with the 1.8 m telescope of the Bohyunsan Optical Astronomy Observatory (Republic of Korea) in May–June 2004. We obtained 69 spectra of the star with signal-to-noise ratios ≈300 and a time resolution of 5–7 min. Profile variability was revealed for six lines of HI, HeI, and SiIII, in the central parts of the lines. The variability amplitude is ≈(1–2)% in units of the intensity of the adjacent continuum. Evidence was found for cyclic variations of the lines, with periods from ≈7^h to ≈2.9^d. We conclude that ι Her belongs to the group of slowly pulsating stars.     

Chemical,optical, and X-ray analysis of an unusual muscovite-biotite intergrowth

A specimen of intergrown biotite and muscovite from a pegmatite was subjected to detailed chemical, optical, and X-ray analysis. The crystals are intergrown in such a way that certain structural elements are common to both and that parts of the crystal structure must pass unbroken through the contact between them. Numerous ‘edge dislocations’ must occur at the boundary because of the different basal spacings. Partitioning of elements between the minerals, along with the structural observations, suggest that the crystals are an equilibrium intergrowth.     

Light curve and neutrino spectrum emitted during the collapse of a nonrotating,supermassive star

The formation of a neutrino pulse emitted during the relativistic collapse of a spherical supermassive star is considered. The free collapse of a body with uniform density in the absence of rotation and with the free escape of the emitted neutrinos can be solved analytically by quadrature. The light curve of the collapsing star and the spectrum of the emitted neutrinos at various times are calculated.     

Calculation of profiles of the CIV 1550 doublet formed in an accretion shock in a T Tauri star: Axially symmetric radial accretion

We have calculated profiles for the CIV 1550 doublet arising in an accretion shock in a T Tauri star assuming that (i) the accretion zone at the stellar surface is axially symmetric (a circular spot or spherical belt), (ii) the velocity and density of the gas in front of the shock do not vary within the accretion zone, and (iii) the gas falls radially inward toward the star. The calculated CIV 1550 profiles differ qualitatively from those observed in the spectra of T Tauri stars, probably because the velocity of the infalling gas in T Tauri stars has a tangential component of some tens of km/s due to the nonradial magnetic field near the stellar surface.     

The mass of the black hole in the X-ray binary LMC X-1

A dynamical estimate of the mass of the black hole in the LMC X-1 binary system is obtained in the framework of a Roche model for the optical star, based on fitting of the He I 4471 Å and He II 4200 Å absorption lines assuming LTE. The mass of the black hole derived from the radial-velocity curve for the He II 4200 Å line is m_x = 10.55 M_⊙, close to the value found earlier based on a model with two point bodies [1].     

Dependence of the diffuse X-ray luminosities of virialized systems on the masses of their central objects

Based on the available observational data on the diffuse X-ray emission from hot gas in virialized systems (the central regions of clusters of galaxies or the coronas of spherical galaxies) and the masses of the central objects in these systems (the central galaxies in clusters or massive compact objects—supermassive black holes—in the galactic nuclei), we show that the X-ray luminosity is proportional to the square of the mass of the central object. This is consistent with the dependence obtained earlier between X-ray luminosities of systems and the square of their optical luminosities (i.e., the luminosity of stars in these systems). The existence of such dependences for virialized systems on various scales may provide evidence that they are all formed by a single mechanism, such as hierarchical gravitational clustering. Although the times to achieve hydrostatic equilibrium between the gaseous and stellar components in systems on various scales differ, the relation between certain internal parameters of these systems may remain the same. This enables us to estimate certain parameters of virialized systems in terms of others, in particular, to estimate the masses of their central objects based on the diffuse X-ray luminosity of their coronas.     

Interpretation of the light curve of the eclipsing binary V444 Cyg on the set of convexo-concave functions

The narrow-band λ4244 Å continuum light curve of the eclipsing binary V444 Cyg, which has a Wolf-Rayet component, is interpreted assuming that the brightness distribution and absorption in the WN5 star's disk are monotonic, non-increasing, convexo-concave, non-negative functions. The convex and concave parts of these functions correspond to the core of the WN5 star and its extended photosphere and atmosphere, respectively. The radius and brightness temperature of the opaque core of the WN5 star are r _WN5 ^core ? 4R _⊙ and T _br ^core >52000 K, respectively. The stellar wind is characterized by an accelerated radial outflow. Acceleration of the wind persists at large distances from the center of the star. A crude Lamers-law fit to the reconstructed velocity field in the wind yields an acceleration parameter β=1.58–1.82.     

Variability of the HeI line profiles in the spectrum of the hot O9.5V star HD 93521

CCD spectra acquired with the PFES echelle spectrograph on the 6 m telescope of the Special Astrophysical Observatory (Russian Academy of Sciences) were used to study short-term variations in the HeI-line profiles in the spectrum of HD 93521. For all the lines, the variability pattern relative to the mean profile is the same, and can be described as a sinusoidal wave passing through the profiles, from the blue to the red wings. The variability amplitudes and time scales are different for different HeI lines. We studied variations of the radial velocities at the level of 0.5 R ₀ of the line residual intensity, for the absorption bisector and the blue and red halves of the absorption profile. The variation time scales and amplitudes for the line halves differ from one HeI line to another, and show good correlations with the line central depths. Going from the weak to the strong lines, the time scale of the radial-velocity variations measured for both halves of the absorption profile increases, and the amplitude decreases. The time scale of the radial-velocity variations for weak lines is, on average, twice the time scale for strong HeI lines. A variable absorption feature was detected in the profiles of strong HeI lines, which moves across the profile synchronously with the star’s axial rotation. Generally, the observed line variations are probably due to nonradial photospheric pulsations, together with the influence of the stellar wind on the profiles of the strong lines.     

Interstellar medium surrounding the WO star in the galaxy IC 1613: New optical and radio observations

Observations of the nebula S3 associated with the WO star in the galaxy IC 1613 and of an extended region surrounding S3 are reported. The star and bright core of the nebula were observed with a multipupil fiber spectrograph mounted on the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences. Images in the principle spectral lines and integrated spectra of the star and three compact clumps were obtained, and the radial-velocity field constructed. An extended region of the galaxy was observed with the Very Large Array at 21 cm. A giant ring or H I shell enclosing a large fraction of the stellar population in IC 1613 was discovered. The WO star and associated bipolar nebula, which we discovered earlier, lie at the inner edge of the H I ring. A local H I deficiency and two arclike H I ridges were also detected for the first time and probably represent the neutral component of the bipolar shell surrounding the WO star. The two arclike ridges may also have been produced by the collective stellar wind (and supernova explosions?) in OB association No. 9 from the list of Hodge. A scenario for the formation of the extended bipolar feature is discussed, based on the new data.     

Ar,N2, and CO2 in the structural cavities of cordierite,an optical and X-ray single-crystal study

Ar, N₂ and CO₂ were introduced into the structural cavities of channel-evacuated single-crystals of White Well cordierite with the composition: K_0.01Na_0.03(Mg_1.91Fe_0.09Mn_0.01)Al_3.98Si_5.01O₁₈. The gas refilling experiments were carried out in conventional hydrothermal bombs at 6–7 kbar and 600–700°C. The increase in the mean refractive indices for gas-treated crystals, as determined with a spindle-stage equipped microscope, was used along with point-dipole calculations to estimate the percentage of occupied structural cavities. The steep increase of the electronic polarizability parallel to the a-axis, which can be derived from the increase of the refractive index n _γ (Z∥a) upon introduction of volatiles, indicates that N₂ and CO₂ are preferentially aligned parallel to the a-axis of cordierite. Single-crystal structure refinements at room temperature confirm these predictions. Additionally, decreased C–O and N–N bond lengths suggest a librational motion with a mean rotary oscillation angle of 35° (N₂) and 25° (CO₂) about a, where c is the rotation axis. Mean libration angles of 40° (N₂) and 28° (CO₂) were estimated from the electronic polarizability tensors of CO₂ and N₂. Site occupancy refinements of the channel position are in good agreement with the optically derived values for the volatile concentrations, both indicating about 70% and 60% filled cavities for Ar- and N₂-cordierite, respectively. Chemical analyses and point-dipole calculations confirm that about 45% of the cavities are occupied in the CO₂-treated crystal. The structural framework of cordierite is slightly but specifically altered by the various channel occupants.     

The mass of the compact object in the X-ray binary 4U 1700-37

The results of a systematic analysis of master radial-velocity curves for the X-ray binary 4U 1700-37 are presented. The dependence of the mass of the X-ray component on the mass of the optical component is derived in a Roche model based on a fit of the master radial-velocity curve. The parameters of the optical star are used to estimate the mass of the compact object in three ways. The masses derived based on information about the surface gravity of the optical companion and various observational data are 2.25 _?0.24 ^+0.23 M_⊙ and 2.14 _?0.56 ^+0.50 M_⊙. The masses based on the radius of the optical star, 21.9R_⊙, are 1.76 _?0.21 ^+0.20 M_⊙ and 1.65 _?0.56 ^+0.78 M_⊙. The mass of the optical component derived from the mass-luminosity relation for X-ray binaries, 27.4M_⊙, yields masses for the compact object of 1.41 _?0.08 ⁺ M_⊙ and 1.35 _?0.18 ^+0.18 M_⊙.     

Velocity field of the stellar wind of the wolf-rayet star in the V 444 Cyg binary system: A parametric model

An analysis of the λ4244 Å continuum light curve of the eclipsing variable V444 Cyg is used to reconstruct the velocity law v(r) of the stellar wind of the WR star in terms of Lamers parametric and powerlaw models. Both models are inconsistent with the observed light curve, and can be rejected at the <2% significance level. Departures of the Lamers parametric relation from the empirical v(r) law reconstructed in previous papers from the same λ 4244 Å light curve on sets of concave and convexo-concave functions are statistically significant. The stellar wind of the WN5 star continues to accelerate at a considerable distance from the star’s center. This corresponds to an acceleration parameter β>1 in terms of a coarse Lamers-law approximation for the empirical v(r) field.     

Peculiarities and variations in the optical spectrum of the post-AGB star V448 Lac = IRAS 22223+4327

Multi-epoch observations with high spectral resolution acquired in 1998–2008 are used to study the time behavior of the spectral-line profiles and velocity fields in the atmosphere and circumstellar shell of the post-AGB star V448 Lac. Asymmetry of the profiles of the strongest absorption lines with lower-level excitation potentials χ _low < 1 eV and time variations of these profiles have been detected, most prominently the profiles of the resonance lines of BaII, YII, LaII, SiII. The peculiarities of these profiles can be explained using a superposition of stellar absorption line and shell emission lines. Emission in the (0; 1) 5635 Å Swan system band of the C₂ molecule has been detected in the spectrum of V448 Lac for the first time. The core of the Hα line displays radial-velocity variations with an amplitude of ΔV _r ≈ 8 km/s. Radial-velocity variations displayed by weak metallic lines with lower amplitudes, ΔV _r ≈ 1–2 km/s, may be due to atmospheric pulsations. Differential line shifts, ΔV _r = 0–8 km/s have been detected on various dates. The position of the molecular spectrum is stationary in time, indicating a constant expansion velocity of the circumstellar shell, V _exp = 15.2 km/s, as derived from the C₂ and NaI lines.     

The mass of the compact object in the low-mass X-ray binary 2S 0921-630

We interpret the observed radial-velocity curve of the optical star in the low-mass X-ray binary 2S 0921-630 using a Roche model, taking into account the X-ray heating of the optical star and screening of X-rays coming from the relativistic object by the accretion disk. Consequences of possible anisotropy of the X-ray radiation are considered. We obtain relations between the masses of the optical and compact (X-ray) components, m _v and m _x , for orbital inclinations i = 60°, 75°, and 90°. Including X-ray heating enabled us to reduce the compact object’s mass by ～0.5–1 M _⊙, compared to the case with no heating. Based on the K0III spectral type of the optical component (with a probable mass of m _v ? 2.9 M _⊙), we concluded that m _x ? 2.45?2.55 M _⊙ (for i = 75°?90°). If the K0III star has lost a substantial part of its mass as a result of mass exchange, as in the V404 Cyg and GRS 1905+105 systems, and its mass is m _v ? 0.65?0.75 M _⊙, the compact object’s mass is close to the standard mass of a neutron star, m _x ? 1.4 M _⊙ (for i = 75°?90°). Thus, it is probable that the X-ray source in the 2S 0921-630 binary is an accreting neutron star.     

The mass of the compact object in the X-ray binary her X-1/HZ her

We have obtained the first estimates of the masses of the components of the Her X-1/HZ Her X-ray binary system taking into account non-LTE effects in the formation of the H _γ absorption line: m _x = 1.8 M _⊙ and m _v = 2.5 M _⊙. These mass estimates were made in a Roche model based on the observed radial-velocity curve of the optical star, HZ Her. The masses for the X-ray pulsar and optical star obtained for an LTE model lie are m _x = 0.85 ± 0.15 M _⊙ and m _v = 1.87 ± 0.13 M _⊙. These mass estimates for the components of Her X-1/HZ Her derived from the radial-velocity curve should be considered tentative. Further mass estimates from high-precision observations of the orbital variability of the absorption profiles in a non-LTE model for the atmosphere of the optical component should be made.     

Variability of the planetary nebula NGC 6572 and its central star during the interval covered by optical observations

Estimates of relative line intensities available in the literature and integrated Hβ fluxes of the planetary nebula NGC 6572 during the time covered by optical observations (1938–2013) are compared to search for possible variations. Line intensities measured from observations obtained at the Crimean Station of the Sternberg Astronomical Institute in 2013 are presented, as well as previously unpublished photographic spectroscopic data obtained 1972–2005. Our analysis of all the available data shows that the line intensities do not vary within the observational uncertainties, with the possible exception of the [OIII] 4959 and 5007 Å lines, which show a tendency for their intensity increase with time. This can be interpreted as a manifestation of a temperature increase of the central star, or radial stratification of the [OIII] emission in the nebula, with the latter explanation being less probable. However, stratification is clearly visible in the [OII] and [NII] line intensities. The integrated Hβ flux is most probably constant at F(Hβ) = (1.50 ± 0.03) × 10^?10 erg cm^?2 s^?1. A refined estimate of the interstellar extinction toward NGC 6572 has been obtained from radio and optical data, c(Hβ) = 0.42 ± 0.03. The MAST spectroscopy data were used to derive the central star’s UBV magnitudes in 2004. Integrated photoelectric UBV observations of the nebula and central star for 1971–2005 are presented.