KBO binaries: how numerous were they?

Given the large orbital separation and high satellite-to-primary mass ratio of all known Kuiper Belt Object (KBO) binaries, it is important to reassess their stability as bound pairs with respect to several disruptive mechanisms. Beside the classical shattering and dispersing of the secondary due to a high-velocity impact, we consider the possibility that the secondary is kicked off its orbit by a direct collision of a small impactor, or that it is gravitationally perturbed due to the close approach of a somewhat larger TNO. Depending on the values for the size/mass/separation of the binaries that we used, 2 or 3 of the 9 pairs can be dispersed in a timescale shorter than the age of the Solar System in the current rarefied environment. A contemporary formation scenario could explain why we still observe these binaries, but no convincing mechanism has been proposed to date. The primordial formation scenarios, which seem to be the only viable ones, must be revised to increase the formation efficiency in order to account for this high dispersal rate. For the reference current KBO population, objects like the large-separation KBO binaries 1998 WW₃₁ or 2001 QW₃₂₂ must have been initially an order of magnitude more numerous. If the KBO binaries are indeed primordial, then we show that the mass depletion of the Kuiper belt cannot result from collisional grinding, but must rather be due to dynamical ejection.     

New class of Well behaved exact solutions of relativistic charged <Emphasis Type="Italic">white-dwarf</Emphasis> star with perfect fluid

The paper presents a class of interior solutions of Einstein-Maxwell field equations of general relativity for a static, spherically symmetric distribution of the charged fluid. This class of solutions describes well behaved charged fluid balls. The class of solutions gives us wide range of parameter K (0.3277≤K≤0.49), for which the solution is well behaved hence, suitable for modeling of super dense star. For this solution the mass of a star is maximized with all degree of suitability and by assuming the surface density ρ _b =2×10¹⁴ g/cm³. Corresponding to K=0.3277 with X=−0.15, the maximum mass of the star comes out to be M=0.92M _Θ with radius r _b ≈17.15 km and the surface red shift Z _b ≈0.087187. It has been observed that under well behaved conditions this class of solutions gives us the mass of super dense object within the range of white-dwarf.     

Migration of Comets

Based on one of the particular cases of twice averaged model Hill problem with the allowance for the oblateness of the central body a quadrature is derived for the determination of the migration time of cometary nuclei from various cometary reservoirs and a (14-th order) algebraic equation for the determination of the initial conditions that allow the escape of the cometary nucleus (which at the initial instant of time moves in an orbit with arbitrary eccentricity (0 < e < 1) and inclination (0° < i < 180°) deeply inside the sphere o f action of the central body) from the sphere of action of the central body or its impact onto the central body. We analyze the shape of the boundaries of the hypothetical cometary reservoirs and the method of searching for regions of high concentration of interstellar particles in the Solar System.     

The round chroms of contact binaries

It is shown that the formation of a roundchrom, i.e. a common chromosphere,in W UMa type contact binaries is inevitable. The geometrical forms of roundchroms for ten contact binaries are obtained. For contact binaries the round-chroms of open type are predicted along with a possibility of outflow of round-chrom's gaseous matter from the outer Lagrangian point L₂. The main parameters of roundchroms, the electron concentration n _e, efficient emission volume V, power of emission in magnesium doublet 2800 MgII etc. are obtained for the ten contact binaries. The decrease of the mean electron concentration in roundchrom n _e with the increase of the intercomponent distance a is discovered: n _e ∼ a ^-1. This revised version was published online in July 2006 with corrections to the Cover Date.     

Accretion activity of young binary systems with low-mass secondary components

The accretion activity of young binaries with low-mass (q = M ₂/M ₁ ≤ 0.1) secondary components is studied. The source of accreted matter is a common disk surrounding the binary system and coplanar with its orbit. Gas dynamic models of these systems are used to calculate the rates of accretion to the components and their dependence on the phase of the orbital period is studied. It is shown that, despite its low mass, the secondary accretes matter at a relatively higher rate than the primary. This result can be regarded as an extension of the work of Artymowicz and Lubow for young binaries with components that have unequal masses. Possible astrophysical applications of the theory are discussed.     

Solving Kepler’s Equation using Bézier curves

This paper presents a non-iterative approach to solve Kepler’s Equation, M = E − e sin E, based on non-rational cubic and rational quadratic Bézier curves. Optimal control point coordinates are first shown to be linear with respect to orbit eccentricity for any eccentric anomaly range. This property yields the development of a piecewise (e.g., 3, 4) solving technique providing accuracies better than 10⁻¹³ degree for orbit eccentricity e ≤ 0.99. The proposed method does not require large pre-computed discretization data, but instead solves a cubic/quadratic algebraic equation and uses a single final Halley iteration in only a few lines of code. The method still provides accuracies better than 10⁻⁵ degree for the near parabolic worst case (e = 0.9999) with very small mean anomalies (M < 0.0517 deg). The complexity of the proposed algorithm is constant, independent of the parameters e and M. This makes the method suitable for extensive orbit propagations. Presented at the 7th Dynamics and Control of Systems and Structures in Space Conference, July 18–22, 2006, Greenwich, England.     

The Hill stability of low mass binaries in hierarchical triple systems

The Hill stability of the low mass binary system in the presence of a massive third body moving on a wider inclined orbit is investigated analytically. It is found that, in the case of the third body being on a nearly circular orbit, the region of Hill stability expands as the binary/third body mass ratio increases and the inclination (i) decreases. This i-dependence decreases very quickly with increasing eccentricity (e ₂) of the third body relative to the binary barycentre. In fact, if e ₂ is not extremely small, the Hill stable region can be approximately expressed in a closed form by setting i = 90°, and it contracts with increasing e ₂ as ${e_2^2}$ for sufficiently low mass binary. Our analytic results are then applied to the observed triple star systems and the Kuiper belt binaries.     

Evolution of massive binary stars in the LMC and its implications for radio pulsar population

The Hertzsprung-Russell diagram of the Large Magellanic Cloud compiled recently by Fitzpatrick & Garmany (1990) shows that there are a number of supergiant stars immediately redward of the main sequence although theoretical models of massive stars with normal hydrogen abundance predict that the region 4.5 ≤ logT _eff ≤ 4.3 should be un-populated (“gap”). Supergiants having surface enrichment of helium acquired for example from a previous phase of accretion from a binary companion, however, evolve in a way so that the evolved models and observed data are consistent — an observation first made by Tuchman & Wheeler (1990). We compare the available optical data on OB supergiants with computed evolutionary tracks of massive stars of metallicity relevant to the LMC with and without helium-enriched envelopes and conclude that a large fraction (≈ 60 per cent) of supergiant stars may occur in binaries. As these less evolved binaries will later evolve into massive X-ray binaries, the observed number and orbital period distribution of the latter can constrain the evolutionary scenarios of the supergiant binaries. The distributions of post main sequence binaries and closely related systems like WR + O stars are bimodal-consisting of close and wide binaries in which the latter type is numerically dominating. When the primary star explodes as a supernova leaving behind a neutron star, the system receives a kick and in some cases can lead to runaway O-stars. We calculate the expected space velocity distribution for these systems. After the second supernova explosion, the binaries in most cases, will be disrupted leading to two runaway neutron stars. In between the two explosions, the first born neutron star’s spin evolution will be affected by accretion of mass from the companion star. We determine the steady-state spin and radio luminosity distributions of single pulsars born from the massive stars under some simple assumptions. Due to their great distance, only the brightest radio pulsars may be detected in a flux-limited survey of the LMC. A small but significant number of observable single radio pulsars arising out of the disrupted massive binaries may appear in the short spin period range. Most pulsars will have a low velocity of ejection and therefore may cluster around the OB associations in the LMC.     

Classical and relativistic node precessional effects in WASP-33b and perspectives for detecting them

WASP-33 is a fast rotating, main sequence star which hosts a hot Jupiter moving along a retrograde and almost polar orbit with semi-major axis a=0.02 au and eccentricity provisionally set to e=0. The quadrupole mass moment J₂^*J_{2}^{\star} and the proper angular momentum S _⋆ of the star are 1900 and 400 times, respectively, larger than those of the Sun. Thus, huge classical and general relativistic non-Keplerian orbital effects should take place in such a system. In particular, the large inclination Ψ_⋆ of the orbit of WASP-33b to the star’s equator allows to consider the node precession [(W)\dot]\dot{\Omega} and the related time variation dt _d /dt of the transit duration t _d . The WASP-33b node rate due to J₂^*J_{2}^{\star} is 9×10⁹ times larger than the same effect for Mercury induced by the Sun’s oblateness, while the general relativistic gravitomagnetic node precession is 3×10⁵ times larger than the Lense-Thirring effect for Mercury due to the Sun’s rotation. We also consider the effect of the centrifugal oblateness of the planet itself and of a putative distant third body X. The magnitudes of the induced time change in the transit duration are of the order of 3×10⁻⁶,2×10⁻⁷,8×10⁻⁹ for J₂^*J_{2}^{\star}, the planet’s rotational oblateness and general relativity, respectively. A yet undiscovered planet X with the mass of Jupiter orbiting at more than 1 au would induce a transit duration variation of less than 4×10⁻⁹. A conservative evaluation of the accuracy in measuring dt _d /dt over 10 yr points towards ≈10⁻⁸. The analysis presented here will be applicable also to other exoplanets with similar features if and when they will ne discovered.     

Measurement of the orbital period of the X-ray burster GS 1826-238 based on observations of its optical brightness variations

The variability of the optical and X-ray fluxes from the binary GS 1826-238 is investigated. An epoch-folding analysis of the optical data obtained with the RTT-150 telescope in 2003–2004 has revealed periodic brightness variations in the source with a period P _orb = 2.24940 ± 0.00015 h with a high statistical significance. When estimating the detection significance of the periodic signal, we have specially taken into account the presence of a powerful aperiodic component (“red noise”) in the source’s brightness variability. The source’s power density spectra in the frequency range ∼10⁻⁵–0.01 Hz have been obtained. We have detected a statistically significant break in the power density spectrum of GS 1826-238 at a frequency ν _br ≈ (8.48 ± 0.14) × 10⁻⁵ Hz in both optical and X-ray energy bands. We have estimated the orbital period of the binary GS 1826-238 using the correlation between the break frequency in the power density spectrum and the orbital period of binaries, P _orb ∝ 1/ν _br, found by Gilfanov and Arefiev (2005): P _orb = 3.7 ± 0.8 h and P _orb = 11.3 ± 5.9 h when using Sco X-1 and 1H 16267-273, respectively, as reference sources. It seems to us that the method for estimating the orbital periods of low-mass X-ray binaries using the correlation P _orb ∝ 1/ν _br may turn out to be very promising, especially for persistent low-luminosity X-ray binaries.     

Streamer Belt and Chains as the Main Sources of Quasi-Stationary Slow Solar Wind

Synoptic maps of white-light coronal brightness from SOHO/LASCO C2 and distributions of solar wind velocity obtained from interplanetary scintillation are studied. Regions with velocity V≈300 – 450 km s⁻¹ and increased density N>10 cm⁻³, typical of the “slow” solar wind originating from the belt and chains of streamers, are shown to exist at Earth’s orbit, between the fast solar wind flows (with a maximum velocity V _max≈450 – 800 km s⁻¹). The belt and chains of streamers are the main sources of the “slow” solar wind. As the sources of “slow” solar wind, the contribution from the chains of streamers may be comparable to that from the streamer belt.     

Well-behaved relativistic charged super-dense star models

A new class of charged super-dense star models is obtained by using an electric intensity, which involves a parameter, K. The metric describing the model shares its metric potential g ₄₄ with that of Durgapal’s fourth solution (J. Phys. A, Math. Gen. 15:2637, 1982). The pressure-free surface is kept at the density ρ _b =2×10¹⁴ g/cm³ and joins smoothly with the Reissner-Nordstrom solution. The charge analogues are well-behaved for a wide range, 0≤K≤59, with the optimum value of X=0.264 i.e. the pressure, density, pressure–density ratio and velocity of sound are monotonically decreasing and the electric intensity is monotonically increasing in nature for the given range of the parameter K. The maximum mass and the corresponding radius occupied by the neutral solution are 4.22M _Θ and 20 km, respectively for X=0.264. For the charged solution, the maximum mass and radius are defined by the expressions M≈(0.0059K+4.22)M _Θ and r _b ≈−0.021464K+20 km respectively.     

Chromospheric Height and Density Measurements in a Solar Flare Observed with RHESSI – II. Data Analysis

We present an analysis of hard X-ray imaging observations from one of the first solar flares observed with the Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI) spacecraft, launched on 5 February 2002. The data were obtained from the 22 February 2002, 11:06 UT flare, which occurred close to the northwest limb. Thanks to the high energy resolution of the germanium-cooled hard X-ray detectors on RHESSI we can measure the flare source positions with a high accuracy as a function of energy. Using a forward-fitting algorithm for image reconstruction, we find a systematic decrease in the altitudes of the source centroids z(ε) as a function of increasing hard X-ray energy ε, as expected in the thick-target bremsstrahlung model of Brown. The altitude of hard X-ray emission as a function of photon energy ε can be characterized by a power-law function in the ε=15–50 keV energy range, viz., z(ε)≈2.3(ε/20 keV)^−1.3 Mm. Based on a purely collisional 1-D thick-target model, this height dependence can be inverted into a chromospheric density model n(z), as derived in Paper I, which follows the power-law function n _e(z)=1.25×10¹³(z/1 Mm)^−2.5 cm⁻³. This density is comparable with models based on optical/UV spectrometry in the chromospheric height range of h≲1000 km, suggesting that the collisional thick-target model is a reasonable first approximation to hard X-ray footpoint sources. At h≈1000–2500 km, the hard X-ray based density model, however, is more consistent with the `spicular extended-chromosphere model' inferred from radio sub-mm observations, than with standard models based on hydrostatic equilibrium. At coronal heights, h≈2.5–12.4 Mm, the average flare loop density inferred from RHESSI is comparable with values from hydrodynamic simulations of flare chromospheric evaporation, soft X-ray, and radio-based measurements, but below the upper limits set by filling-factor insensitive iron line pairs.     

Energy-Dependent Timing of Thermal Emission in Solar Flares

We report solar flare plasma to be multi-thermal in nature based on the theoretical model and study of the energy-dependent timing of thermal emission in ten M-class flares. We employ high-resolution X-ray spectra observed by the Si detector of the “Solar X-ray Spectrometer” (SOXS). The SOXS onboard the Indian GSAT-2 spacecraft was launched by the GSLV-D2 rocket on 8 May 2003. Firstly we model the spectral evolution of the X-ray line and continuum emission flux F(ε) from the flare by integrating a series of isothermal plasma flux. We find that the multi-temperature integrated flux F(ε) is a power-law function of ε with a spectral index (γ)≈−4.65. Next, based on spectral-temporal evolution of the flares we find that the emission in the energy range E=4 – 15 keV is dominated by temperatures of T=12 – 50 MK, while the multi-thermal power-law DEM index (δ) varies in the range of −4.4 and −5.7. The temporal evolution of the X-ray flux F(ε,t) assuming a multi-temperature plasma governed by thermal conduction cooling reveals that the temperature-dependent cooling time varies between 296 and 4640 s and the electron density (n _e) varies in the range of n _e=(1.77 – 29.3)×10¹⁰ cm⁻³. Employing temporal evolution technique in the current study as an alternative method for separating thermal from nonthermal components in the energy spectra, we measure the break-energy point, ranging between 14 and 21±1.0 keV.     

Constraining the cosmological time variation of the fine - structure constant

The variation of the fine-structure constant α = e ² / ħc can be probed by comparing the wavelength of atomic transitions from the redshift of quasars in the Universe and laboratory over cosmological time scales t ~ 10¹⁰ yr. After a careful selection of pairs of lines, the Thong method with a derived analytical expression for the error analysis was applied to compute the α variation. We report a new constraint on the variation of the fine-structure constant based on the analysis of the C_IV, N_V, Mg_II, Al_III, and Si_IV doublet absorption lines. The weighted mean value of the variation in α derived from our analysis over the redshift range 0.4939 ≤ z ≤ 3.7 is = ( 0.09 ± 0.07)×10⁻⁵. This result is three orders of magnitude better than the results obtained by earlier analysis of the same data on the constraint on Δα/α .     

Helicity Measurements from Two Magnetographs

We use 270 pairs of vector magnetograms observed by Haleakala Stokes Polarimeter (HSP) and Solar Magnetic Field Telescope (SMFT) of Huairou Solar Observing Station from 1997 to 2000 to compare current helicity derived by these two instruments. We apply the same approach to both data sets to resolve 180^∘ azimuth ambiguity and compute α coefficient of linear force-free field. After careful consideration of various aspects of both data sets, we find that in ≈80% of cases SMFT and HSP data result in the same sign of α, and the Pearson linear correlation coefficient between two data sets is r_p = 0.64. Operated by the Association of Universities for Research in Astronomy (AURA, Inc) under cooperative agreement with the National Science Foundation (NSF).     

High-Resolution Infrared Measurements of H2O and SiO in Sunspots

Ultra-high-resolution spectroscopic measurements (R ≈ 10⁷) of water vapor and silicon monoxide in sunspots are presented. Observations were performed using the Cologne Tunable Heterodyne Infrared Spectrometer (THIS) at the McMath–Pierce Solar Observatory. Mid-infrared molecular absorption lines around 10 μm were recorded and resolved in full detail. The linewidth and shape can thus be determined with high precision and were used to calculate kinetic temperatures which are much higher than the physical temperatures of the sunspot. Only 15% of the wavelengths between 9 and 12μ can be covered using CO₂ and all its isotopologues as laser gases (Kostiuk and Mumma, 1983).     

Astrometric study of the relative motion of three stars with possible invisible companions based on homogeneous series obtained at Pulkovo with a 26-inch refractor

We investigate the relative motion of three stars, ADS 7446, 9346, and 9701, based on long-term observations with the Pulkovo 26-inch refractor. The relative motion of all three stars shows a perturbation that could be produced by the gravitational influence of an invisible companion. For ADS 7446, we have determined the orbit of the photocenter with a period of 7.9 yr; the mass of the companion is more than 0.4M _⊙. For ADS 9346, we have determined the radial velocities of the components: −14.60 km s⁻¹ for A and −13.94 km s⁻¹ for B. For ADS 9346 and 9701, we have determined the dynamical parallaxes, 24 and 20 mas, respectively, which are larger than those in the Hipparcos catalog by 5 mas, and calculated the orbits by the apparent motion parameter (AMP) method. The new orbit of ADS 9346 is: a = 5″.2, P = 2035 yr, and e = 0.46 at the system’s mass M = 2.5M _⊙. The new orbits of ADS 9701 are: (a = 2″.9, P = 829 yr, e = 0.54, M = 4.3M _⊙) and (a = 3″.8, P = 1157 yr, e = 0.53, M = 5.0M _⊙).     

Relativistic model of radiating massive fluid sphere

In this paper we present a new class of nonsingular solutions representing time dependent balls of perfect fluid with matter-radiation in general relativity. The solution of the class is suitable for interior modeling of a quasar i.e. a massive radiating star. The interior solution is matched with a zero pressure Vaidya metric. From this solution we constructed a quasar model by assuming the life time of the quasar of ≈10⁷ year. We obtained a mass of the quasar of ≈10⁹ M _θ , linear dimension ≈10¹⁷ km and a rate of emission L _∞≈10⁴⁷ erg/s.     

Five new and three improved mutual orbits of transneptunian binaries

We present three improved and five new mutual orbits of transneptunian binary systems (58534) Logos-Zoe, (66652) Borasisi-Pabu, (88611) Teharonhiawako-Sawiskera, (123509) 2000 WK₁₈₃, (149780) Altjira, 2001 QY₂₉₇, 2003 QW₁₁₁, and 2003 QY₉₀ based on Hubble Space Telescope and Keck II laser guide star adaptive optics observations. Combining the five new orbit solutions with 17 previously known orbits yields a sample of 22 mutual orbits for which the period P, semimajor axis a, and eccentricity e have been determined. These orbits have mutual periods ranging from 5 to over 800 days, semimajor axes ranging from 1600 to 37,000 km, eccentricities ranging from 0 to 0.8, and system masses ranging from 2 × 10¹⁷ to 2 × 10²² kg. Based on the relative brightnesses of primaries and secondaries, most of these systems consist of near equal-sized pairs, although a few of the most massive systems are more lopsided. The observed distribution of orbital properties suggests that the most loosely-bound transneptunian binary systems are only found on dynamically cold heliocentric orbits. Of the 22 known binary mutual orbits, orientation ambiguities are now resolved for 9, of which 7 are prograde and 2 are retrograde, consistent with a random distribution of orbital orientations, but not with models predicting a strong preference for retrograde orbits. To the extent that other perturbations are not dominant, the binary systems undergo Kozai oscillations of their eccentricities and inclinations with periods of the order of tens of thousands to millions of years, some with strikingly high amplitudes.