On the number and lifetime of 6.7-GHz methanol masers

A statistical estimate of the number of 6.7-GHz methanol masers in the Milky Way and their lifetime is presented. The estimate is based on the currently known number of masers, a realistic correction for sensitivity effects and generally accepted Galactic star formation rates and initial mass functions. The analysis suggests that the minimum number of masers in the Galaxy is of the order of 850 while a more realistic estimate of the total number of masers is of the order of 1200 ± 84. The lifetime is estimated to be between  2.5 × 10⁴  and  4.5 × 10⁴ yr  , with the variation being due to the use of different initial mass functions. The estimated lifetime agrees with that found from independent studies and agrees remarkably well with the time-scale for the chemical evolution of methanol in hot cores as well as with the dynamical time-scales of molecular outflows associated with high-mass star formation regions. It is shown that the hypothesis of the masers being associated with propagating planar shocks in cores or clumps results in lifetimes for the masers that are smaller by a factor of 2 or more compared with the lifetime of methanol masers as estimated here.     

On the initial cluster mass distribution inferred from synthesis models

In this contribution we examine the problem of inferring ages and initial cluster masses from synthesis models at the limit of low-mass clusters (M≤ a few ×10⁴ M_⊙). We show that it is not possible to apply directly synthesis models using standard methods to such clusters, since the basic hypothesis implicit in the models (a fixed proportionality between the number of stars in different evolutionary phases) is not fulfilled due to an insufficient number of stars for a reliable sampling of the stellar initial mass function. The consequence of this incomplete sampling is a non-Gaussian distribution of the mass–luminosity relation for clusters that share the same evolutionary conditions (age, metallicity and stellar initial mass distribution function). We review some tests, that can be performed before the start of the analysis, to estimate if the observed cluster can be analyzed with synthesis models following traditional procedures (like χ ² minimization) or if it is necessary make use of synthesis models in a probabilistic framework. Finally, we show the implications of these results for estimating the low-mass tail in the initial cluster mass distribution function.     

Some tests and improvements to the VFISV: Very Fast Inversion of the Stokes Vector for the Helioseismic and Magnetic Imager

Some experimental tests and improvements to the Very Fast Inversion of the Stokes Vector program, which is designed for the inversion calculation used by the Helioseismic and Magnetic Imager instrument on the Solar Dynamics Observatory,are given. On one hand, the interpolation for calculating the Voigt function is not smooth, which may occasionally cause the iteration process to converge to different minima although they are very close to initial values. This problem can be solved by a smoother interpolation. On the other hand, in order to improve the performance of this program, we have tried to abandon the randomly-jump-out strategy and set the initial value properly to avoid non-global minima. The resulting method costs only1/4 of the computational time, and will be very competitive when the users are only interested in the vectorial magnetic fields and the velocities along the line of sight.     

The minimum gap-opening planet mass in an irradiated circumstellar accretion disc

We consider the minimum mass planet, as a function of radius, that is capable of opening a gap in an α-accretion disc. We estimate that a half-Jupiter mass planet can open a gap in a disc with accretion rate     for viscosity parameter  α= 0.01  , and solar mass and luminosity. The minimum mass is approximately proportional to     . This estimate can be used to rule out the presence of massive planets in gapless accretion discs. We identify two radii at which an inwardly migrating planet may become able to open a gap and so slow its migration; the radius at which the heating from viscous dissipation is similar to that from stellar radiation in a flared disc, and the radius at which the disc becomes optically thin in a self-shadowed disc. In the inner portions of the disc, we find that the minimum planet mass required to open a gap is only weakly dependent on radius. If a migrating planet is unable to open a gap by the time it reaches either of the transition radii, then it is likely to be lost on to the star. If a gap-opening planet cuts off disc accretion allowing the formation of a central hole or clearing in the disc then we would estimate that the clearing radius would approximately be proportional to the stellar mass.     

Structure of Radiative Shock Waves in Stellar Atmospheres

A global iteration method to determine the self-consistent structure of steady plane-parallel radiative shock waves is shown to converge to the stable solution with upstream front velocities of 15 km/s ≤ U ₁≤ 60 km/s and for hydrogen gas of unperturbed temperature T= 3000 K and density ρ = 10⁻¹⁰gcm⁻³. This revised version was published online in July 2006 with corrections to the Cover Date.     

A comparative study of Newtonian,Kustaanheimo/Stiefel,and Sperling/Burdet optimal trajectories

An optimal trajectory problem is formulated in each of three sets of equations, and the resulting solutions are numerically compared. The three formulations are the classical Newtonian (N), the Kustaanheimo/Stiefel (K/S), and the Sperling/Burdet (S/B). The last two solutions are first regularized by the classical Sundman technique and the K/S solution is transformed before the optimization problem is posed. A novel technique is developed for generating initial control vectors for each solution. Numerically generated derivatives (central differences) are used by a type of gradient, Newton-Raphson iterator to converge the two-point boundary value problems. The results indicate that, although the K/S and S/B formulations are more difficult to express mathematically than the Newtonian formulation, the transformed solutions are significantly more numerically stable than the Newtonian solution when the perturbing acceleration is less than a minimum value (T/W _o=0.05 for the particular example problem treated).     

Orbital and physical parameters of the spectroscopic binary HD37737

We report the physical and orbital parameters of the visible component of the spectroscopic binary HD37737 (m _V = 8.03). The observations were performed with the 1.2-m telescope of the Kourovka Astronomical Observatory of the Ural Federal University in 2012 and the 6-m BTA telescope of the SAO RAS in 2007 and 2009. Radial velocities were measured separately from each spectral line of the list by the cross-correlation method with a synthetic spectrum. The latter was calculated using the grids of non-LTE model atmospheres with solar chemical compositions. A significant difference in the epochs of observations (2005–2012) allowed to refine the orbital period of the star (7 _· ^d 84705) and the orbital elements of the binary system. We obtained an estimate of the mass function f(m) = 0.23 ± 0.02M _⊙. The best agreement between the synthetic and observed spectra is achieved at T _eff = 30 000 K and log g = 3.50 according to the observations on both instruments. The obtained parameters correspond to a star of spectral type O9.5 III, with mass estimated at 26 ± 2M _⊙. The minimum mass estimate of the secondary component of the binary is 6.2 ± 0.5M _⊙. We have discovered a fact that the velocities, obtained from different spectral lines, differ, which is typical for giant stars. Engaging additional spectra, obtained in 2005 with the 2.1-m KPNO telescope, we investigated the effect of this fact on the estimate of the speed of the system’s center of mass. The difference in the velocities of various lines is approximately the same in the spectra, obtained at all the three instruments. The obtained ratios suggest that the deeper layers of the atmosphere of the star are moving with a greater velocity than the outer layers. Depending on the line, the estimate of the heliocentric velocity of the binary’s center of mass varies in the range from ?11 to 1 km/s.     

Phosphate control on the thorium/uranium variations in ordinary chondrites: Improving solar system abundances

Abstract— Isotope dilution thorium and uranium analyses by inductively‐coupled plasma mass spectrometry of 12 samples of Harleton (L6) show a much larger scatter than was previously observed in equilibrated ordinary chondrites. Th/U linearly correlates with 1/U in Harleton and in the total equilibrated ordinary chondrite data set as well. Such a correlation suggests a two component mixture and this trend can be quantitatively modeled as reflecting variations in the mixing ratio between two phosphate phases: chlorapatite and merrillite. The major effect is due to apatite variations, which strongly control the whole rock U concentrations. Phosphorous variations will tend to destroy the Th/U vs. 1/U correlation, and measured P concentrations on exactly the same samples as U and Th show a factor of 3 range. It appears that the P variations are compensated by inverse variations in U (a dilution effect) to preserve the Th/U vs. 1/U correlation. Because variations in whole rock Th/U are consequences of phosphate sampling, a weighted average of high accuracy Th/U measurements in equilibrated ordinary chondrites should converge to a significantly improved average solar system Th/U. Our best estimate of this ratio is 3.53 with σ_mean = 0.10.     

Forecast of the Decadal Average Sunspot Number

The forecast of the decadal average sunspot number (SN) becomes possible with an extension of telescopic observations based on proxy reconstructions using the tree ring radiocarbon data during the Holocene. These decadal numbers (SN_RC) provide a powerful statistic to verify the forecasting methods. Complicated dynamics of long-term solar activity and noise of proxy-based reconstruction make the one-step-ahead forecast challenging for any forecasting method. Here we construct a continuous data set of SN_RC which extends the group sunspot number and the international sunspot number. The known technique of nonlinear forecast, the local linear approximation, is adapted to estimate the coming SN. Both the method and the continuous data set were tested and tuned to obtain the minimum of a normalized average prediction error (E) during the last millennium using several past millennia as a training data set. E=0.58σ _D is achieved to forecast the SN successive differences whose standard deviation is σ _D=7.39 for the period of training. This corresponds to the correlation (r=0.97) between true and forecasted SN. This error is significantly smaller than the prediction error when the surrogate data were used for the training data set, and proves the nonlinearity in the decadal SN. The estimated coming SN is smaller than the previous one.     

Dynamical study of wide pairs of stars based on data from the WDS catalog

Using the method of apparent motion parameters, we have studied the relative motion of the components in 561 pairs of wide (ρ > 2″) and relatively nearby (Hipparcos parallaxes > 0.01″) visual double stars based on data from the WDS catalog. The minimum masses of the double stars have been calculated at given parallaxes. We have identified 358 optical pairs. For 11 stellar pairs, we have found the minimum mass to exceed the estimate corresponding to their spectral types and luminosities. This excess is 5–7 M _⊙ for two stars, ADS 7446 and 9701.     

The chemical variability at the surface of Mars: Implication for sediment formation and rock weathering

Compositional data analysis was performed on chemical compositions of martian surface materials in order to unravel scenarios of past and present weathering and to evaluate the role of meteoritic accumulation. The observed chemical variability is analyzed by means of principal component analysis. Potential reservoirs that may have contributed primary material to soil formation are assessed. Chemical alteration in the course of in situ weathering is described in terms of alteration vectors that link the compositions of fresh rocks and their weathering crusts. The interplay of localized chemical alteration and global scale re-distribution and mixing of fines material is documented through the identification of different soil forming branches. These branches emanate from distinct compositional domains, which comprise basaltic and basalt-andesitic primary materials, and they converge to a global dust composition, which represents the product of chemical and physical disintegration and subsequent global mixing. Mass balance considerations applied to localized weathering phenomena are in line with findings from experimental acid-sulfate weathering on olivine-bearing basalts and the persistence of secondary silica in evaporitic rocks. In addition the composition and oxidation state of involved volcanic gases is deduced. Our findings corroborate the past activity of volcanic exhalation products in combination with liquid water. We conclude that average martian crust is dominated by basaltic materials at its topmost level and that the amount of meteoritic accumulation may contribute about 6 wt% to the martian fines. From the meteoritic contribution minimum soil formation rates of 60±20 cm/Gyr are derived. Sequestration of atmospheric oxygen during weathering of primary materials may account for the oxygen deficiency of the martian atmosphere. A 4-14-m-thick layer of oxidized martian fines may account for the estimated deficit of 1.7×¹⁰¹⁸ mol O₂ in the martian atmosphere depending on the primary oxidation state of volatile volcanic emanations.     

A lower limit to the field strength in magnetic reconnection sites in solar flares inferred from hard X-ray bursts

It is shown how the hard X-ray burst count rate and itse-folding ime can be used to estimate the minimum magnetic fieldB _min required in a flare magnetic reconnection site for the burst to be interpreted in terms of a thick target model. Application of the method to data from the Solar Maximum Mission (HXRBS) indicates absolute minimum fields well in excess of 100 G, and impossibly high values for some reconnection geometries.     

The mass content in the region of the cluster NGC 1750

Kinematical information has been used to solve the Jeans’ equation to provide a mass estimate for the open cluster NGC 1750. Using published data we have also applied the Michie–King model to estimate the mass in the cluster. The comparison of these masses gives the best estimation of mass in the region of this cluster as 1.01×10⁴ M_⊙, which indicates that the cluster may be a massive cluster. Checks of the density distribution and isotropy of the stellar velocity distribution are given.     

Estimating the masses of Saturn’s A and B rings from high-optical depth N-body simulations and stellar occultations

We have completed a series of local N-body simulations of Saturn’s B and A rings in order to identify systematic differences in the degree of particle clumping into self-gravity wakes as a function of orbital distance from Saturn and dynamical optical depth (a function of surface density). These simulations revealed that the normal optical depth of the final configuration can be substantially lower than one would infer from a uniform distribution of particles. Adding more particles to the simulation simply piles more particles onto the self-gravity wakes while leaving relatively clear gaps between the wakes. Estimating the mass from the observed optical depth is therefore a non-linear problem. These simulations may explain why the Cassini UVIS instrument has detected starlight at low incidence angles through regions of the B ring that have average normal optical depths substantially greater than unity at some observation geometries [Colwell, J.E., Esposito, L.W., Srem?evi?, M., Stewart, G.R., McClintock, W.E., 2007. Icarus 190, 127-144]. We provide a plausible internal density of the particles in the A and B rings based upon fitting the results of our simulations with Cassini UVIS stellar occultation data. We simulated Cassini-like occultations through our simulation cells, calculated optical depths, and attempted to extrapolate to the values that Cassini observes. We needed to extrapolate because even initial optical depths of >4 (σ > 240 g cm⁻²) only yielded final optical depths no greater than 2.8, smaller than the largest measured B ring optical depths. This extrapolation introduces a significant amount of uncertainty, and we chose to be conservative in our overall mass estimates. From our simulations, we infer the surface density of the A ring to be , which corresponds to a mass of . We infer a minimum surface density of for Saturn’s B ring, which corresponds to a minimum mass estimate of . The A ring mass estimate agrees well with previous analyses, while the B ring is at least 40% larger. In sum, our lower limit estimate is that the total mass of Saturn’s ring system is 120-200% the mass of the moon Mimas, but significantly larger values would be plausible given the limitations of our simulations. A significantly larger mass for Saturn’s rings favors a primordial origin for the rings because the disruption of a former satellite of the required mass would be unlikely after the decay of the late heavy bombardment of planetary surfaces.     

Evolutionary processes in protoplanetary accretion disks: the propagation of axisymmetric shock waves

In this paper we investigate both the global and the local hydrodynamics of axisymmetric accretion disks around young stellar objects under the simultaneous action of viscosity, self-gravity and pressure forces. For simplicity, we take for the global model a polytropic equation of state, make the infinitely thin disk approximation and characterize the surface density and temperature profiles in the disk as power laws in the radial distance r from the protostar. We solve the problem of the general density profile of a Keplerian disk showing that self-gravity could not be an important factor for the fast formation of the rocky cores of giant gaseous planets in our solar system. Under the hypothesis that the unperturbed rotation curve of the disk is nearly Keplerian throughout the radial extent, we can estimate with our polytropic model a lower limit for the resulting masses M_d(r) of stable disks up to 100 AU. These masses are in the range of the so-called minimum mass solar nebular (_d/M_s ≈ 0.01–0.02).By adopting a simplified viscosity model, where the height-integrated turbulent dynamical viscosity ν is a function of the surface density σ like η ∝ σ^Γ, we derive in the local shearing sheet model linearized evolution equations for small density perturbations describing both a diffusion process and the propagation of acoustic density waves. We solve a special initial value problem and calculate the appropriate Green's function. The analytical solutions so obtained describe in the case Γ < 0 the successive formation of quasi-stationary ring-shaped density structures in a disk with a definite mode of maximum instability, whereas in the case Γ > Γ_c the density wave equation describes the propagation of an “overstable” ring-shaped acoustic density wavelet to the outer ranges of the accretion disk. Whereas the group velocity of the wave packet is subsonic, the phase velocities of individual wave crests in the wave packet are supersonic. The mode of maximum instability, the growth rate and the number of growing waves in the wavelet are controlled by Γ and α. Our present knowledge concerning turbulent viscosity in protoplanetary disks is not sufficient to decide whether or not the case Γ > Γ_c is realized.The suggested structuring processes in the linear theory should initiate in the non-linear regime the formation of narrow ring-shaped density shock waves moving through the protoplanetary disk. These non-linear waves could produce extremely spatially and temporally heterogeneous temperature regions in the disk. We speculate that ring-shaped density waves, excited by inner boundary conditions and which have dominated the disk's evolution at early times, are responsible both for the fast growth of dust to planetesimals and at least for the rapid accretion of the rocky cores of giant gaseous planets in the protoplanetary accretion disk (shock wave trigger hypothesis). We derive provisional scaling rules for planetary systems regarding the spacing of orbits as a function of the mass ratio of the protoplanetary disk to the protostar. However, further analytical work and linear as well as nonlinear numerical simulations of density waves excited by inner boundary conditions are needed to consolidate the results and speculations of our linear wave mechanics in the future.     

Monte Carlo simulations of star clusters – III. A million-body star cluster

A revision of Stodółkiewicz's Monte Carlo code is used to simulate the evolution of million-body star clusters. The new method treats each superstar as a single star and follows the evolution and motion of all individual stellar objects. The evolution of N -body systems influenced by the tidal field of a parent galaxy and by stellar evolution is presented. All models consist of 1 000 000 stars. The process of energy generation is realized by means of appropriately modified versions of Spitzer's and Mikkola's formulae for the interaction cross-section between binaries and field stars and binaries themselves. The results presented are in good agreement with theoretical expectations and the results of other methods. During the evolution, the initial mass function (IMF) changes significantly. The local mass function around the half-mass radius closely resembles the actual global mass function. At the late stages of evolution, the mass of the evolved stars inside the core can be as high as 97 per cent of the total mass in this region. For the whole system, the evolved stars can compose up to 75 per cent of the total mass. The evolution of cluster anisotropy strongly depends on initial cluster concentration, IMF and the strength of the tidal field. The results presented are the first step in the direction of simulating the evolution of real globular clusters by means of the Monte Carlo method.     

Chaotic behaviour in the newton iterative function associated with kepler's equation

The chaotic behaviour observed when Newton's method is used to solve Kepler's equation is analysed using methods borrowed from chaos theory. The result of the analysis is compared with previous results. A sufficient condition for convergence of a given iterative function is presented and yields ranges of eccentricity and mean anomaly such that Newton's method applied to Kepler's equation will converge from an initial guess of .     

The effect of metallicity on the minimum mass ratio of W Ursae Majoris-type systems

According to the prevenient theoretical study, the minimum mass ratio for tidal stability of W Ursae Majoris (W UMa) systems is q _min?=(M ₂/M ₁)～0.071–0.078. However, the mass ratios of some observed W UMa binaries are smaller than the theoretical minimum mass ratio. Using Eggleton’s stellar evolution code, we study the effects of metallicity and evolution on the minimum mass ratio of W UMa systems (M ₁=1.2M _⊙). We assume that $k_{1}^{2}=k_{2}^{2}$ for the component’s dimensionless gyration radii and that the contact degree is about 70 per cent. We find that the dynamical stability of W UMa binaries depends on the metallicity of W UMa systems. For the W UMa systems at age = 0 Gyr, the distribution of the minimum mass ratio has a fairly wide range, from 0.083 to 0.064, with the metallicity range from Z=0.0001 to 0.03. W UMa systems with Z=0.01 have the smallest value of the minimum mass ratio, which is about 0.064. The existence of low-q systems can be explained partly by the dependence of the dimensionless gyration radius on the metallicity. In addition, the dependence of the minimum mass ratio on the evolution, as suggested by previously work, is confirmed.     

Shear-induced instability and arch filament eruption: A magnetohydrodynamic (MHD) numerical simulation

We investigate, via a two-dimensional (nonplanar) MHD simulation, a situation wherein a bipolar magnetic field embedded in a stratified solar atmosphere (i.e., arch-filament-like structure) undergoes symmetrical shear motion at the footpoints. It was found that the vertical plasma flow velocities grow exponentially leading to a new type of global MHD-instability that could be characterized as a Dynamic Shearing Instability, with a growth rate of about 8{ovV} _A a, where {ovV} _A is the average Alfvén speed and a ^–1 is the characteristic length scale. The growth rate grows almost linearly until it reaches the same order of magnitude as the Alfvén speed. Then a nonlinear MHD instability occurs beyond this point. This simulation indicates the following physical consequences: the central loops are pinched by opposing Lorentz forces, and the outer closed loops stretch upward with the vertically-rising mass flow. This instability may apply to arch filament eruptions (AFE) and coronal mass ejections (CMEs).To illustrate the nonlinear dynamical shearing instability, a numerical example is given for three different values of the plasma beta that span several orders of magnitude. The numerical results were analyzed using a linearized asymptotic approach in which an analytical approximate solution for velocity growth is presented. Finally, this theoretical model is applied to describe the arch filament eruption as well as CMEs.