Spectroscopic Orbit of the Eclipsing Binary AI Draconis

New radial velocity measurements of the Algol-type eclipsing binary AI Dra, based on Reticon observations, are presented. The velocity measures themselves are based on fitting theoretical profiles, generated by a physical model of the binary, to the observed cross-correlation function (ccf). Such profiles match this function very well, much better in fact that Gaussian profiles which are generally used. Measuring the ccf's with Gaussian profiles yields following results: m_p sin³ i=2.55± 0.05m_⊙, m_s sin³ i = 1.14 ± 0.03m_⊙, (a_p + a_s) sin i=7.34 ±0.05R_⊙, and m_p/m_s =2.23± 0.05. Where as measuring the ccf's with theoretical profiles yields a mass ratio of 2.33 and following results: m_p sin³ i=2.84± 0.05m_⊙, m_s sin³ i=1.22 ± 0.03m_⊙, (a_p +a_s) sin i=7.56± 0.05R_⊙. The system comprising a semi-detached configuration. From the solution of a previously published light curved and combining it's results with the spectroscopic orbit, one can lead to the following physical parameters: m_p =2.99m_⊙, m_s =1.28m_⊙, > T_p < =9600 K, > T_s < =5400 K, > R_p < =2.35R_⊙, > R_s < =2.12R_⊙. The system comprising an AO primary and a secondary of G2 spectral type. This revised version was published online in July 2006 with corrections to the Cover Date.     

Heat flow of the Earth and resonant capture of solar <Superscript>57</Superscript>Fe axions

In a very conservative approach, supposing that all heat flow of the Earth is exclusively due to resonant capture inside the Earth of axions emitted by ⁵⁷Fe nuclei on Sun, we obtain limit on the mass of hadronic axion: m _a < 1.8 keV. Taking into account release of heat from decays of ⁴⁰K, ²³²Th, ²³⁸U inside the Earth, this estimation could be improved to the value: m _a < 1.6 keV. Both the values are less restrictive than limits set in devoted experiments to search for ⁵⁷Fe axions (m _a < 216–745 eV), but are much better than limits obtained in experiments with ⁸³Kr (m _a < 5.5 keV) and ⁷Li (m _a < 13.9–32 keV). Published in Ukrainian in Kinematika i Fizika Nebesnykh Tel, 2009, Vol. 25, No. 2, pp. 143–149. The article was translated by the authors.     

Existence and uniqueness of stellar equilibrium models

The stellar equilibrium equations for given surface pressureP _* and temperatureT _*, and in the absence of convection, are translated into a nonlinear integral equation, in which the radiusR of the star enters as an eigenvalue. We show that under broad mathematical assumptions on the constitutive equations (equation of state, opacity and energy generation) a global existence and uniqueness property can be formulated. If a valueP _M is selected, which restricts the allowed pressure and temperature range |P(r)–P _*|+E|T(r)–T _*P _M (E, arbitrary constant of dimensions of a pressure over temperature), thenat least one solutionP(r),T(r) exists in the pressure-temperature range chosen, for anyR<R _E . This solution isunique forR<R _c .R _E andR _c are expressed in terms of the constitutive equations, and of the pressure-temperature range adopted. A physical argument in favour of the stability of this solution is presented.     

Robe’s problem: its extension to 2+2 bodies

In the problem of 2+2 bodies in the Robe’s setup, one of the primaries of mass m^*₁m^{*}_{1} is a rigid spherical shell filled with a homogeneous incompressible fluid of density ρ ₁. The second primary is a mass point m ₂ outside the shell. The third and the fourth bodies (of mass m ₃ and m ₄ respectively) are small solid spheres of density ρ ₃ and ρ ₄ respectively inside the shell, with the assumption that the mass and the radius of third and fourth body are infinitesimal. We assume m ₂ is describing a circle around m^*₁m^{*}_{1}. The masses m ₃ and m ₄ mutually attract each other, do not influence the motion of m^*₁m^{*}_{1} and m ₂ but are influenced by them. We also assume masses m ₃ and m ₄ are moving in the plane of motion of mass m ₂. In the paper, the equations of motion, equilibrium solutions, linear stability of m ₃ and m ₄ are analyzed. There are four collinear equilibrium solutions for the given system. The collinear equilibrium solutions are unstable for all values of the mass parameters μ,μ ₃,μ ₄. There exist an infinite number of non collinear equilibrium solutions each for m ₃ and m ₄, lying on circles of radii λ,λ′ respectively (if the densities of m ₃ and m ₄ are different) and the centre at the second primary. These solutions are also unstable for all values of the parameters μ,μ ₃,μ ₄, φ, φ′. Such a model may be useful to study the motion of submarines due to the attraction of earth and moon.     

Search for LBV candidates in the M33 galaxy

A total of 185 luminous blue variable star (LBV) candidates with V<18_·^m 5 are selected based on the results of aperture photometry. The primary selection criterion is that the prospective candidate should be a blue star with Hα emission. In order not to overlook appreciably reddened LBV candidates, we compose an additional list of 25 red (0_·^m35< B − V < 1_·^m2, V < 18_·^m5) emission star candidates. A comparison with the list of known variables in the M33 galaxy showed 29% of our selected candidates to be photometrically variable. We also find our list to agree well with the lists of emission-line objects obtained in earlier papers using different methods.     

Distribution of stars perpendicular to the plane of the galaxy

We present here rigorous analytical solutions for the Boltzmann-Poisson equation concerning the distribution of stars above the galactic plane. The number density of stars is considered to follow a behaviour n(m,0) ∼H(m - m₀)m^−x, wherem is the mass of a star andx an arbitrary exponent greater than 2 and also the velocity dispersion of the stars is assumed to behave as < v²(m)> ∼ m^−θ the exponent θ being arbitrary and positive. It is shown that an analytic expression can be found for the gravitational field K_z, in terms of confluent hypergeometric functions, the limiting trends being K_z∼z for z →0, while K_z → constant for z → infinity. We also study the behaviour of < |z(m)|²>,i.e. the dispersion of the distance from the galactic disc for the stars of massm. It is seen that the quantity < |z(m)|²>∼ m^t-θ, for m→ t, while it departs significantly from this harmonic oscillator behaviour for stars of lighter masses. It is suggested that observation of < |z(m)|²> can be used as a probe to findx and hence obtain information about the mass spectrum.     

Estimating the Luminosity Function of M51-Type Galaxies

A new sample of M51-type galaxies consisting of 46 systems is used to estimate the B-band luminosity function. The luminosity function for the primary components of the systems can be described by a Schechter function with the parameters _* = (1.4±0.3)×10^-5 Mpc^-3, = -1.3^+0.4 _-0.3, and M _* = -20.3^+0.2 _-0.1. The values of the latter two parameters are comparable to those for isolated galactic pairs. The resulting estimate of the average density of M51-type galaxies is (4±3)% of the average density of isolated pairs for luminosities in the range -22^m.0<M<-16^m.0     

VV Orionis – improved elements

TheUBV light curves obtained by Duerbeck (1975) andHa (wide) and Ha (narrow) light curves obtained by Chambliss & Davan (1987) of the detached eclipsing binary VV Orionis (VV Ori) were analysed using the Wilson-Devinney method fixing the two parametersT _h (25,000 K) and q(0.4172), resulting in the following absolute elements:A = 13.605 ± 0.03 LR_⊙,R _h = 5.03 ±0.03R _⊙, R_c = 2.43 ±0.02R _⊙,M _bol,h = -5.18 ± 0.11,M _bol,c = -1.54 ± 0.06,m _h =10.81 + 0.42m _⊙ andm _c = 4.51 ± 0.41m _⊙. The de-reddened colours obtained from applying the reddening corrections ofE(B-V) = 0^m.05 andE(U-B) = O ^m .04, and the derived temperatures of the components, gave spectral types ofB 1.5V for the primary and 54-5V with anUV excess of 0 ^m ·3 for the secondary component. A comparison of the logL and logT _e of the components with the observed ZAMS shows the primary component to be a little above and the secondary component to be a little below/or on the ZAMS. A comparison of the properties of the components of VV Ori and a few other detached systems with the normal stars in the logL, logR and logT _e versus logm planes, indicated a need for either a readjustment of the scales of the above parameters or modifications in the theoretical models. From the position of the components on the evolutionary tracks of Pop I composition computed by Schaller et al. (1992) it is noticed that while the primary component of W Ori had slightly evolved along the main-sequence, its secondary is still unevolved. The age of VV Ori is found to be 10 ± 1 million years and it is at a distance of 368 ± 10 pc.     

Dirac neutrino magnetic moment and possible time evolution of the neutrino signal from a supernova

We analyze the influence of neutrino helicity conversion, ν _L → ν _R, on the neutrino flux from a supernova attributable to the interaction of the Dirac neutrino magnetic moment with a magnetic field.We show that if the neutrino has a magnetic moment in the interval 10⁻¹³μ_B < μ_ν < 10⁻¹²μ_B and provided that a magnetic field of ∼10¹³–10¹⁴ G exists in the supernova envelope, a peculiar kind of time evolution of the neutrino signal from the supernova attributable to the resonance transition ν _L → ν _R in the magnetic field of the envelope can appear.     

The Relationship between Prediction Accuracy and Correlation Coefficient

The correlation coefficient (r) between the maximum amplitude (R _m) of a sunspot cycle and the preceding minimum aa geomagnetic index (aa _min), in terms of geomagnetic cycle, can be fitted by a sinusoidal function with a four-cycle periodicity superimposed on a declining trend. The prediction index (χ) of the prediction error relative to its estimated uncertainty based on a geomagnetic precursor method can be fitted by a sinusoidal function with a four-and-half-cycle periodicity. A revised prediction relationship is found between the two quantities: χ<1.2 if r varies in a rising trend, and χ>1.2 if r varies in a declining trend. The prediction accuracy of R _m depends on the long-term variation in the correlation. These results indicate that the prediction for the next cycle inferred from this method, R _m(24)=87±23 regarding the 75% level of confidence (1.2-σ), is likely to fail. When using another predictor of sunspot area instead of the geomagnetic index, similar results can be also obtained. Dynamo models will have better predictive powers when having considered the long-term periodicities.     

Notes on Hori Method for Canonical Systems

In this paper a slightly different approach is proposed for the process of determining the functions S _m and H _m ^* of the algorithm of the canonical version of Hori method. This process will be referred to as integration theory of the mth order equation of the method. It will be shown that the ordinary differential equation with an auxiliary parameter t ^* as independent variable, introduced through Hori auxiliary system, can be replaced by a partial differential equation in the time t. In this way, the mth order equation of the algorithm assumes a form very similar to the one of other perturbation methods. In virtue of this new approach of the integration theory for Hori method, Lagrange's variational equations introduced by Sessin are revised. As an example, the Duffing equation is solved through this new approach.     

WR 140 (=V1687 Cyg): Infrared photometry, 2001–2010

We present the results of our infrared observations of WR 140 (=V1687 Cyg) in 2001–2010. Analysis of the observations has shown that the J brightness at maximum increased near the periastron by about 0 ^m .3; the M brightness increased by ∼2 ^m in less than 50 days. The minimum J brightness and the minimum L and M brightnesses were observed 550–600 and 1300–1400 days after the maximum, respectively. The JHKLM brightness minimum was observed in the range of orbital phases 0.7–0.9. The parameters of the primary O5 component of the binary have been estimated to be the following: R(O5) ≈ 24.7R _⊙, L(O5) ≈ 8 × 10⁵ L _⊙, and M _bol(O5) ≈ −10 ^m . At the infrared brightness minimum, T _g ∼ 820–880 K, R _g ≈ 2.6 × 10⁵ R _⊙, the optical depth of the shell at 3.5 μm is ∼5.3 × 10⁻⁶, and its mass is ≈1.4 × 10⁻⁸ M _⊙. At the maximum, the corresponding parameters are ∼1300 K, 8.6 × 10⁴ R _⊙, ∼2 × 10⁻⁴, and ∼6 × 10⁻⁸ M _⊙; the mean rate of dust inflow (condensation) into the dust structure is ∼3.3 × 10⁻⁸ M _⊙ yr⁻¹. The mean escape velocity of the shell from the heating source is ∼10³ km s⁻¹ and the mean dispersal rate of the shell is ∼1.1 × 10⁻⁸ M _⊙ yr⁻¹.     

V792 Her=HD 155638: A totally eclipsing RS CVn binary

Photometry of HD 155638=V792 Her has been analyzed to determine the elements of this totally eclipsing RS CVn binary. The light variation outside eclipse was found to have a period of 27^d.07±0^d.07, which is slightly different from the 27^d.5384±0^d.0045 orbital period. Analysis of the eclipses was achieved by a modification of the Russell-Merrill technique. With the aid of radial velocity measures, absolute elements were obtained for the hot and cool stars, respectively;R _h=2.58R ,R _c=12.28R ,M _h=1.40M ,M _c=1.46M ,i=80^o.61 and velocity semi-amplitudesK _c=48.36 km s^–1±0.79 km s^–1, andK _h=50.50 km s^–1±0.33 km s^–1. The apparent magnitudes areV _h=9 ^m .73 andV _c=8 ^m .48. The distance to HD 155638 was estimated to be 310 parsecs.     

Rosette Central Configurations, Degenerate Central Configurations and Bifurcations

In this paper we find a class of new degenerate central configurations and bifurcations in the Newtonian n-body problem. In particular we analyze the Rosette central configurations, namely a coplanar configuration where n particles of mass m₁ lie at the vertices of a regular n-gon, n particles of mass m₂ lie at the vertices of another n-gon concentric with the first, but rotated of an angle π /n, and an additional particle of mass m₀ lies at the center of mass of the system. This system admits two mass parameters μ = m₀/m₁ and ε = m₂/m₁. We show that, as μ varies, if n > 3, there is a degenerate central configuration and a bifurcation for every ε > 0, while if n = 3 there is a bifurcation only for some values of ε.     

Do Average Hamiltonians Exist?

The word "average" and its variations became popular in the sixties and implicitly carried the idea that "averaging" methods lead to "average" Hamiltonians. However, given the Hamiltonian H = H₀(J) + ∈R(θ, J), (∈ < < 1), the problem of transforming it into a new Hamiltonian H^* (J^*) (dependent only on the new actions J^*), through a canonical transformation given by zero-average trigonometrical series has no general solution at orders higher than the first. This revised version was published online in July 2006 with corrections to the Cover Date.     

The azimuthal magnetorotational instability (AMRI)

We consider the flow of an electrically conducting fluid between differentially rotating cylinders, in the presence of an externally imposed current-free toroidal field B₀(R_in/R) ê _ϕ . It is known that the classical, axisymmetric magnetorotational instability does not exist for such a purely toroidal imposed field.We show here that a nonaxisymmetric magnetorotational instability does exist, having properties very similar to the axisymmetric magnetorotational instability in the presence of an axial field. In the nonlinear regime the magnetic energy of the perturbances is shifted (in the sense of an inverse cascade) to the axisymmetric mode rather than to the modes with m > 1. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The ultraviolet extinction by hollow spherical particles of graphite

Using the discrete dipole approximation, we have calculated the extinction efficiency of hollow spherical particles of graphite as a possible constituent of interstellar grains. The particles had a shell structure with the basal plane perpendicular to the radius. The calculations were made on the particles having the outer radiusR ₀=10 and 5nm in the wave number region from 0.8 to 8.0 m^–1 using the anisotropic optical constants. It was found that the hollow particles with the inner radiusR ₁0.65R ₀ yield an extinction feature at 4.6 m^–1, which fits fairly well to one observed in the interstellar extinction.     

Statistical Characteristics on SEPs,Radio-Loud CMEs,Low Frequency Type II and Type III Radio Bursts Associated with Impulsive and Gradual Flares

We have statistically analyzed a set of 115 low frequency (Deca-Hectometer wavelengths range) type II and type III bursts associated with major Solar Energetic Particle (SEP: E_p?>?10 MeV) events and their solar causes such as solar flares and coronal mass ejections (CMEs) observed from 1997 to 2014. We classified them into two sets of events based on the duration of the associated solar flares:75 impulsive flares (duration <?60 min) and 40 gradual flares (duration >?60 min).On an average, the peak flux (integrated flux) of impulsive flares?×?2.9 (0.32 J m^?2) is stronger than that of gradual flares M6.8 (0.24 J m^?2). We found that impulsive flare-associated CMEs are highly decelerated with larger initial acceleration and they achieved their peak speed at lower heights (??27.66 m s^?2 and 14.23 R_o) than the gradual flare-associated CMEs (6.26 m s^?2 and 15.30 R_o), even though both sets of events have similar sky-plane speed (space speed) within LASCO field of view. The impulsive flare-associated SEP events (R_t?=?989.23 min: 2.86 days) are short lived and they quickly reach their peak intensity (shorter rise time) when compared with gradual flares associated events (R_t?=?1275.45 min: 3.34 days). We found a good correlation between the logarithmic peak intensity of all SEPs and properties of CMEs (space speed: cc?=?0.52, SE_cc?=?0.083), and solar flares (log integrated flux: cc?=?0.44, SE_cc?=?0.083). This particular result gives no clear cut distinction between flare-related and CME-related SEP events for this set of major SEP events. We derived the peak intensity, integrated intensity, duration and slope of these bursts from the radio dynamic spectra observed by Wind/WAVES. Most of the properties (peak intensity, integrated intensity and starting frequency) of DH type II bursts associated with impulsive and gradual flare events are found to be similar in magnitudes. Interestingly, we found that impulsive flare-associated DH type III bursts are longer, stronger and faster (31.30 min, 6.43 sfu and 22.49 MHz h^?1) than the gradual flare- associated DH type III bursts (25.08 min, 5.85 sfu and 17.84 MHz h^?1). In addition, we also found a significant correlation between the properties of SEPs and key parameters of DH type III bursts. This result shows a closer association of peak intensity of the SEPs with the properties of DH type III radio bursts than with the properties DH type II radio bursts, atleast for this set of 115 major SEP events.

     

Twenty-Seven-Day Variation of Galactic Cosmic Rays

Neutron monitor data observed at Climax (CL) and Huancayo/Haleakala (HU/HAL) have been used to calculate the amplitude A of the 27-day variation of galactic cosmic rays (CRs). The median primary rigidity of response, R _m, for these detectors encompasses the range 18 ≤R _m≤46 GV and the threshold rigidity R ₀ covers the range 2.97≤R ₀≤12.9 GV. The daily average values of CR counts have been harmonically analyzed for each Bartels solar rotation (SR) during the period 1953 – 2001. The amplitude of the 27-day CR variation is cross-correlated to solar activity as measured by the sunspot number R, the interplanetary magnetic field (IMF) strength B, the z-component B _z of the IMF vector, and the tilt angle ψ of the heliospheric current sheet (HCS). It is anticorrelated to the solar coronal hole area (CHA) index as well as to the solar wind speed V. The wind speed V leads the amplitude by 24 SRs. The amplitude of the 27-day CR variation is better correlated to each of the these parameters during positive solar polarity (A>0) than during negative solar polarity (A<0) periods. The CR modulation differs during A>0 from that during A<0 owing to the contribution of the z-component of the IMF. It differs during A ₁>0 (1971 – 1980) from that during A ₂>0 (1992 – 2001) owing to solar wind speed.     

Photometry of the poorly studied galactic open star clusters King 13, King 18, King 19, King 20, NGC 136, and NGC 7245

We present the results of our BV R _c I _c CCD photometry for six Galactic open star clusters toward the Perseus spiral armperformed at the Special Astrophysical Observatory of the Russian Academy of Sciences. Based on these data and using JHK _s photometry from the 2MASS catalog, we have determined the ages, distances, and color excesses for the clusters: 710 Myr, 2960₋₃₄₀⁺⁴⁰⁰ pc, 0_· ^m 56 ± 0_· ^m 04 (King 13); 130 Myr, 3010₋₂₈₀⁺³⁰⁰ pc, 0_· ^m 69 ± 0_· ^m 04 (King 18); 560 Myr, 2630₋₂₇₀⁺³¹⁰ pc, 0_· ^m 69 ± 0_· ^m 08 (King 19); 160 Myr, 1750₋₇₀⁺⁸⁰ pc, 0_· ^m 77 ± 0_· ^m 05 (King 20); 250 Myr, 5220₋₃₂₀⁺³⁵⁰ pc, 0_· ^m 70 ± 0_· ^m 09 (NGC 136); 320 Myr, 3390₋₂₀₀⁺²¹⁰ pc, 0_· ^m 43 ± 0_· ^m 03 (NGC 7245).