Diffuse reflection and transmission in accordance with the phase function 3/4(1+cos2Θ)

We have considered the transport equation for the problem of diffuse reflection and transmission on Rayleigh's phase function and obtained the exact solution of this equation for angular distributions of the intensities diffusely reflected from the surfacet=0 and diffusely transmitted below the surfacet=t ₀ of a finite atmosphere of optical deptht=t ₀ using the Laplace transform and the theory of singular operators. This is an exact method.     

Predicting the maximum amplitude for the sunspot cycle from the rate of rise in sunspot number

Examined are associational aspects as they relate the maximum amplitude R _M for the sunspot cycle to the rate of rise R _t during the ascending phase, where R _M is the smoothed sunspot number at cycle maximum and R _t is the sum of the monthly mean sunspot numbers for selected 6-month intervals (t) measured from cycle onset. One finds that, prior to about 2 yr into the cycle, the rate of rise is not a reliable predictor for maximum amplitude. Only during the latter half of the ascent do the fits display strong linearity, having a coefficient of correlation r 0.9 and a standard error S _yx 20. During the first four intervals, the expected R _M and the observed R _M were found to differ by no more than 20 units of smoothed sunspot number only 25, 42, 50, and 58 % of the time; during the latter four intervals, they differed by no more than 20 units 67, 83, 92, and 100% of the time.     

Velocity structure of the shallow lunar crust

The data from the Apollo-14 and Apollo-16 Active Seismic Experiments have been reanalyzed and show that a power-law velocity variation with depth,v(z)110z ^1/6 m s^–1 (0<z<10 m), is consistent with both the travel times and amplitudes of the first arrivals for source-to-geophone separations up to 32 m. The data were improved by removing spurious glitches, by filtering and stacking. While this improved the signal-to-noise ratios, it was not possible to measure the arrival times or amplitudes of the first arrivals beyond 32 m. The data quality precludes a definitive distinction between the power-law velocity variation and the layered-velocity model proposed previously. However, the physical evidence that the shallow lunar regolith is made up of fine particles adds weight to the 1/6-power velocity model because this is the variation predicted theoretically for self-compacting spheres.The 1/6-power law predicts the travel time,t(x), varies with separation,x, ast(x)=t ₀(x/x ₀)^5/6 and, using a first-order theory, the amplitude,A(x), varies asA(x)=A ₀(x/x ₀)^{–(13–m)/12},m>1; the layervelocity model predictst(x)=t ₀(x/x ₀) andA(x)=A ₀(x/x ₀)^–2, respectively. The measured exponents for the arrival times were between 0.63 and 0.84 while those for the amplitudes were between –1.5 and –2.2. The large variability in the amplitude exponent is due, in part, to the coarseness with which the amplitudes are measured (only five bits are used per amplitude measurement) and the variability in geophone sensitivity and thumper-shot strengths.A least-squares analysis was devised which uses redundancy in the amplitude data to extract the geophone sensitivities, shot strengths and amplitude exponent. The method was used on the Apollo-16 ASE data and it indicates there may be as much as 30 to 40% variation in geophone sensitivities (due to siting and coupling effects) and 15 to 20% variability in the thumper-shot strengths. However, because of the low signal-to-noise ratios in the data, there is not sufficient accuracy or redundancy in the data to allow high confidence in these results.     

Dependence of the meridional motions of sunspot groups on life spans and age of the groups,and on the phase of the solar cycle

We have analyzed data on sunspot groups compiled during 1874–1981 and investigated the following: (i) dependence of the `initial' meridional motion (v <sub>ini</sub>()) of sunspot groups on the life span () of the groups in the range 2–12 days, (ii) dependence of the meridional motion (v(t)) of sunspot groups of life spans 10–12 days on the age (t) of the spot groups, and (iii) variations in the mean meridional motion of spot groups of life span 2–12 days during the solar cycle. In each of the latitude intervals 0°–10°, 10°–20° and 20°–30°, the values of both v <sub>ini</sub>() and v(t) often differ significantly from zero. In the latitude interval 20°–30°, the forms of v <sub>ini</sub>() and v(t) are largely systematic and mutually similar in both the north and south hemispheres. The form of v(t) suggests existence of periodic variation in the solar meridional motion with period of 4 days and amplitude 10–20 m s<sup>–1</sup>. Using the anchoring depths of magnetic structures for spot groups of different and testimated earlier, (Javaraiah and Gokhale, 1997), we suggest that the forms of v <sub>ini</sub>() and v(t) may represent radial variation of meridional flow in the Sun's convection zone, rather than temporal variation of the flow. The meridional flows (v <sub>e</sub>(t)) determined from the data during the last few days (i.e., age t: 10–12 days) of spot groups of life spans of 10–12 days are found to have magnitudes (10–20 m s<sup>–1</sup>) and directions (poleward) similar to the those of the surface meridional plasma flows determined from the Dopplergrams and magnetograms. The mean meridional velocity of sunspot groups living 2–12 days seems to vary during the solar cycle. The velocity is not significantly different from zero during the rising phase of the cycle and there is a suggestion of equatorward motion (a few m s<sup>–1</sup>at lower latitudes and 10 m s<sup>–1</sup>at higher latitudes) during the declining phase (last few years) of the cycle. The variation during the odd numbered cycles seems to anticorrelate with the variation during the even numbered cycles, suggesting existence of 22-year periodicity in the solar meridional flow. The amplitude of the anticorrelation seems to be depending on latitude and the cycle phase. In the latitude interval 20°–30° the `surface plasma meridional motion', v _e(t), is found to be poleward during maximum years (v _e(t) 20 m s^–1at 4th year) and equatorward during ending years of the cycle (v _e(t) –17 m s^–1at 10th year).     

The Shape of Solar Cycle Described by a Modified Gaussian Function

The shape of each sunspot cycle is found to be well described by a modified Gaussian function with four parameters: peak size A, peak timing t _m, width B, and asymmetry α. The four-parameter function can be further reduced to a two-parameter function by assuming that B and α are quadratic functions of t _m, computed from the starting time (T ₀). It is found that the shape can be better fitted by the four-parameter function, while the remaining behavior of the cycle can be better predicted by the two-parameter function when using the data from a few (about two) months after the starting time defined by the smoothed monthly mean sunspot numbers. As a new solar cycle is ongoing, its remaining behavior can be constructed by the above four- or two-parameter function. A running test shows that the maximum amplitude of the cycle can be predicted to within 15% at about 25 months into the cycle based on the two-parameter function. A preliminary modeling to the first 24 months of data available for the current cycle indicates that the peak of cycle 24 may probably occur around June 2013±7 months with a size of 72±11. The above results are compared to those by quasi-Planck functions.     

Study of the Cosmic Ray Diurnal Anisotropy During Different Solar and Magnetic Conditions

The pressure-corrected hourly counting rate data of four neutron monitor stations have been employed to study the variation of cosmic ray diurnal anisotropy for a period of about 50 years (1955–2003). These neutron monitors, at Oulu ( R _c = 0.78 GV), Deep River ( R _c = 1.07 GV), Climax ( R _c = 2.99 GV), and Huancayo ( R _c = 12.91 GV) are well distributed on the earth over different latitudes and their data have been analyzed. The amplitude of the diurnal anisotropy varies with a period of one solar cycle (∼11 years), while the phase varies with a period of two solar cycles (∼22 years). In addition to its variation on year-to-year basis, the average diurnal amplitude and phase has also been calculated by grouping the days for each solar cycle, viz. 19, 20, 21, 22, and 23. As a result of these groupings over solar cycles, no significant change in the diurnal vectors (amplitude as well as phase) from one cycle to other has been observed. Data were analyzed by arranging them into groups on the basis of the polarity of the solar polar magnetic field and consequently on the basis of polarity states of the heliosphere ( A > 0 and A < 0). Difference in time of maximum of diurnal anisotropy (shift to earlier hours) is observed during A < 0 (1970s, 1990s) polarity states as compared to anisotropy observed during A > 0 (1960s, 1980s). This shift in phase of diurnal anisotropy appears to be related to change in preferential entry of cosmic ray particles (via the helioequatorial plane or via solar poles) into the heliosphere due to switch of the heliosphere from one physical/magnetic state to another following the solar polar field reversal.     

Investigation of the Neupert Effect in the Various Intervals of Solar Flares

The Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) gives us a chance to investigate the theoretical Neupert effect using the correlation between the thermal-energy derivative and the nonthermal energy, or the thermal energy and the integral nonthermal energy. Based on this concept, we analyze four M-class RHESSI flares on 13 November 2003, 4 November 2004, 3 and 25 August 2005. According to the evolution of the temperature [T], emission measure [EM], and thermal energy [E _th], each event is divided into three phases during the nonthermal-energy input [ \frac dE_nthdt\frac {\mathrm{d}E_{\mathrm{nth}}}{\mathrm{d}t} in the units of erg s⁻¹]. Phase 1 is identified as the interval before the temperature maximum, while after the thermal-energy maximum is phase 3, between them is phase 2. We find that these four flares show the Neupert effect in phase 1, but not in phase 3. The Neupert effect still works well in the second phase, although the cooling becomes slightly important. We define the parameter μ in the relation of \fracdE_thdt=m\fracdE_nth(t)dt\frac{\mathrm {d}E_{\mathrm{th}}}{\mathrm{d}t}=\mu\frac{\mathrm{d}E_{\mathrm {nth}}(t)}{\mathrm{d}t} or E_th(t₀)=mò₀^t₀\fracdE_nth(t)dt dtE_{\mathrm{th}}(t_{0})=\mu\int_{0}^{t_{0}}\frac{\mathrm{d}E_{\mathrm{nth}}(t)}{\mathrm{d}t}\,\mathrm{d}t when the cooling is ignored in phase 1. Considering the uncertainties in estimating the energy from the observations, it is not possible to precisely determine the fraction of the known energy in the nonthermal electrons transformed into the thermal energy of the hottest plasma observed by RHESSI. After a rough estimate of the flare volume and the assumption of the filling factor, we investigate the parameter μ in these four events. Its value ranges from 0.02 to 0.20, indicating that a small fraction (2% – 20%) of the nonthermal energy can be efficiently transformed into thermal energy, which is traced by the soft X-ray emission, and the bulk of the energy is lost possibly due to cooling.     

Errors in calculated values of electron temperatures in H II regions

This paper considers the classical method to determine the electron temperatures t _3,O, t _2,O and t _2,N from forbidden lines of the ions O⁺⁺, O⁺, and N⁺, and investigates the influence of uncertainties in atomic data on the accuracy of the determined electron temperatures. The uncertainties in atomic data (the Einstein coefficients for spontaneous transitions and electron ionization cross-sections) are estimated as discrepancies between the values computed by various authors. The error in the electron temperature caused by uncertainties in the atomic data is found to increase with the growth in the electron temperature. At a temperature 10000 K, the errors in the electron temperatures t _3,O, t _2,N, and t _2,O do not exceed 1, 3, and 7%, respectively.     

Free molecular flow of rarefied gas over an oscillating plate under a periodic external force

The free molecular flow over an infinite oscillating plane wall under external periodic force is considered. The Boltzmann equation is solved by using moments method with two-stream distribution functions. The boundary condition is obtained by assuming that the reflection of the particles from the solid surface takes place with complete energy accommodation. An analytical form for the velocity (X) and shear stress (Y) at any point is obtained. The results show that the amplitude of both the velocity change (X ₁) and the shear stress change (Y ₁) due to the periodic external force at the boundary (y=0) is an increasing function of time (t).     

Flare Plasma Cooling from 30 MK down to 1 MK modeled from Yohkoh,GOES, and TRACE observations during the Bastille Day Event (14 July 2000)

We present an analysis of the evolution of the thermal flare plasma during the 14 July 2000, 10 UT, Bastille Day flare event, using spacecraft data from Yohkoh/HXT, Yohkoh/SXT, GOES, and TRACE. The spatial structure of this double-ribbon flare consists of a curved arcade with some 100 post-flare loops which brighten up in a sequential manner from highly-sheared low-lying to less-sheared higher-lying bipolar loops. We reconstruct an instrument-combined, average differential emission measure distribution dEM(T)/dT that ranges from T=1 MK to 40 MK and peaks at T ₀=10.9 MK. We find that the time profiles of the different instrument fluxes peak sequentially over 7 minutes with decreasing temperatures from T≈30 MK to 1 MK, indicating the systematic cooling of the flare plasma. From these temperature-dependent relative peak times t _peak(T) we reconstruct the average plasma cooling function T(t) for loops observed near the flare peak time, and find that their temperature decrease is initially controlled by conductive cooling during the first 188 s, T(t)∼[1+(t/τ_cond)]^−2/7, and then by radiative cooling during the next 592 s, T(t)∼[1−(t/τ_rad)]^3/5. From the radiative cooling phase we infer an average electron density of n _e=4.2×10¹¹ cm⁻³, which implies a filling factor near 100% for the brightest observed 23 loops with diameters of ∼1.8 Mm that appear simultaneously over the flare peak time and are fully resolved with TRACE. We reproduce the time delays and fluxes of the observed time profiles near the flare peak self-consistently with a forward-fitting method of a fully analytical model. The total integrated thermal energy of this flare amounts to E _thermal=2.6×10³¹ erg. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1014257826116     

Determining the fundamental parameters of F and G supergiants

A technique for determining the effective temperature T _eff and the acceleration of gravity log g of F and G supergiants is discussed using four bright stars as examples, specifically two F supergiants, α Lep(F0 Ib) and π Sgr (F2 II), and two G supergiants, β Aqr (G0 Ib) and α Aqr (G2 Ib). In all four cases the parameter log g was derived from the high precision parallaxes recently obtained by van Leeuwen in a new reduction of data from Hipparcos. Because of this, the accuracy of the determinations of log g is much greater than before. Estimates of the parameter T _eff were checked using accurate values of T _eff obtained previously by the infrared flux method (IRFM). In the case of the early F supergiants, this method confirms the good accuracy of the T _eff values derived from the Balmer lines and the β-index. Measurements of the Balmer lines for the G supergiants are difficult because of strong blending, so the indices [c ₁] and β serve as indicators of T _eff . It is shown that the indices [c ₁] and β yield a systematic difference in the values of T _eff ; the IRFM confirms that deriving T _eff from the index [c ₁] is more accurate. Based on the values of T _eff and log g that have been found here, with the aid of the evolutionary tracks, we estimate the mass M and age t of each star. The Fe II lines, which are insensitive to departures from LTE, have been used to determine the microturbulence parameter V _t and the iron abundance. The latter is close to the solar iron abundance. Some problems concerning the chemical composition of these stars are discussed using the supergiant α Lep as an example. Translated from Astrofizika, Vol. 52, No. 2, pp. 237–257 (May 2009).     

Worldwide photometry and lightcurve observations of 16 Psyche during the 1975–1976 apparition

We present 26 lightcurves of 16 Psyche from 1975 and 1976. The synodic period during this apparition was 4^h.1958. Combining photometric data from this opposition with those from previous apparitions allowed us to derive a mean phase coefficient in V of 0.026 ± 0.002 mag/deg and to establish that Psyche's absolute V₀ magnitude and rotational amplitude vary with aspect; at 90° aspect, V₀(1, 0) = 6.27 ± 0.05 and the lightcurve amplitude is 0.30 mag, while at 0° or 180° aspect, V₀(1, 0) = 6.02 ± 0.02 and the amplitude is ?0.03 mag. This behavior is accounted for if, to first order, Psyche's shape is that of a triaxial ellipsoid with axial ratios near 5:4:3. Colors at zero phase are U-B = 0.26 ± 0.01 and B-V = 0.71 ± 0.01. Color phase coefficients are <0.001 mag/deg in U-B and 0.0010 ± 0.0004 mag/deg in B-V.     

An integrable case of a rotational motion analogous to that of Lagrange and Poisson for a gyrostat in a Newtonian force field

The scope of the present paper is to provide analytic solutions to the problem of the attitude evolution of a symmetric gyrostat about a fixed point in a central Newtonian force field when the potential function isV ⁽²⁾.We assume that the center of mass and the gyrostatic moment are on the axis of symmetry and that the initial conditions are the following: (t ₀)=₀, (t ₀)=₀, (t ₀)=(t ₀)=₀, ₁(t ₀)=0, ₂(t ₀)=0 and ₃(t ₀)= ₃ ⁰ .The problem is integrated when the third component of the total angular momentum is different from zero (B ₁ 0). There now appear equilibrium solutions that did not exist in the caseB ₁=0, which can be determined in function of the value ofl ₃ ^r (the third component of the gyrostatic momentum).The possible types of solutions (elliptic, trigonometric, stationary) depend upon the nature of the roots of the functiong(u). The solutions for Euler angles are given in terms of functions of the timet. If we cancel the third component of the gyrostatic momentum (l ₃ ^r =0), the obtained solutions are valid for rigid bodies.     

Anisotropic solar cosmic ray propagation in an inhomogeneous medium,II

The author's model for anisotropic solar cosmic ray propagation gives 2 coupled, partial differential equations for the intensity and anisotropy of solar cosmic rays propagating with finite speed V in an inhomogeneous medium. The model is used to study the effect of the solar shell on solar cosmic ray propagation. It predicts an exponential decay, regardless of the observer's position. It predicts that when the observer is near the center of the shell, t _D/t ₀ 20 to 30, (t _D= decay time, t ₀ = onset time) and A _m(anisotropy) 15%, if t _m/t ₀ 3 to 5 (t _m= time of maximum), consistent with observations of relativistic particles on Feb. 23, 1956. When the observer is between the shell and the sun, the model predicts that oscillations might be observed near maximum intensity. When the observer moves away from the sun and the shell, the propagation is diffusive, but there is an increasingly large persistent anisotropy which serves as a measure of the width of the shell.     

Radiative cooling flows of self-gravitating filamentary clouds

We study the dynamics of a self-gravitating cooling filamentary cloud using a simplified model. We concentrate on the radial distribution and restrict ourselves to quasi-hydrostatic, cylindrically symmetric cooling flows. For a power-law dependence of cooling function on the temperature, self-similar solutions which describe quasi-hydrostatic cooling flows are derived. We consider obtically thin filaments with a constant mass per unit length and the solutions are parameterized by their line masses. There is no polytropic relation between the density and the pressure. The filament experiences radiative condensation, irrespective of the γ,the gas specific heat ratio. So, the filament becomes denser due to the quasi-hydrostatic flows and the density at the center (ρ_c) increases in proportion to (t ₀-t)^-1, where t denotes the time. The term,t ₀, denotes an epoch at which the central density increases infinitely. We also found that the radius of the filament (r _c) decreases in proportion to (t ₀-t)^1/2. This revised version was published online in July 2006 with corrections to the Cover Date.     

Classical Meteor Light Curve Morphology

We investigate the morphological variation of classical meteor light curves, under the constant velocity assumption, for a series of idealized atmospheric density profiles. We look specifically at the t _rise /t _fall ratio, which compares the rise time to maximum brightness against the time to fall from maximum brightness. We demonstrate that for a classical meteoroid undergoing rapid ablation in an isothermal atmosphere that t _rise/t _fall > 1, indicating that all such light curves are late peaked. For a classical meteoroid ablating in a region over which the density is constant, t _rise/t _fall≡ 0, and the light curve is necessarily downward concave in the height vs. intensity diagram. If ablation occurs over a region in which the density increases linearly with decreasing height, then t _rise/t _fall=1/(√5 – 1) ≈ 0.81, indicative of an early peaked, near symmetric light curve.     

Observational background of TREDER'S gravitation theory in cosmology and the role of viscosity

Starting from solutions of TREDER'S field equations for a homogeneous and isotropic universe filled with incoherent matter (p = 0) relations between observation quantities are derived and discussed. The FRIEDMANN time is of the order of HUBBLE age, the deceleration parameter may principally possess any positive or negative value, hence it is also possible to explain any m,z-relation completely in the frame of this theory. A decision between EINSTEIN'S theory and TREDER'S by cosmological observations is impossible. – Considering a realistic medium which consists of particles and radiation, energy dissipation originating from bulk viscosity (due to the interaction of particles and quanta) prevents cosmological singularities. Thereby entropy, now present in form of relict radiation, is produced. This process generates large amounts of restmass-free energy in the phase of maximum contraction and therefore could as well explain the large luminosity of compact single objects (quasars?). Models with energy dissipation are not invariant with respect to time reflection t→ – t in contrast to EINSTEIN'S theory. If demanding the universe to be free from singularities the direction of cosmic time is uniquely determined. This demand then restricts the possible relations between observation data to the case q₀ = + 1 being in accord with the latest determination by SANDAGE .     

Oxygen abundance methods in SDSS: View from modern statistics

Our purpose is to find which is the most reliable one among various oxygen abundance determination methods. We will test the validity of several different oxygen abundance determination methods using methods of modern statistics. These methods include Bayesian analysis and information scoring. We will analyze a sample of ∼ 6000 Hii galaxies from the Sloan Digital Sky Survey (SDSS) spectroscopic observations data release four. All methods that we used drew the same conclusion that the T _e method is a more reliable oxygen abundance determination method than the Bayesian metallicity method under the existing telescope ability. The ratios of the likelihoods between the different kinds of methods tell us that the T _e , P, and O3N2 methods are consistent with each other because the P and O3N2 methods are calibrated by T _e method. The Bayesian and R ₂₃ methods are consistent with each other because both are calibrated by a galaxy model. In either case, the N2 method is an unreliable method.     

Evaluating Mean Magnetic Field in Flare Loops

We analyze multiple-wavelength observations of a two-ribbon flare exhibiting apparent expansion motion of the flare ribbons in the lower atmosphere and rising motion of X-ray emission at the top of newly-formed flare loops. We evaluate magnetic reconnection rate in terms of V _r B _r by measuring the ribbon-expansion velocity (V _r) and the chromospheric magnetic field (B _r) swept by the ribbons. We also measure the velocity (V _t) of the apparent rising motion of the loop-top X-ray source, and estimate the mean magnetic field (B _t) at the top of newly-formed flare loops using the relation 〈V _t B _t〉≈〈V _r B _r〉, namely, conservation of reconnection flux along flare loops. For this flare, B _t is found to be 120 and 60 G, respectively, during two emission peaks five minutes apart in the impulsive phase. An estimate of the magnetic field in flare loops is also achieved by analyzing the microwave and hard X-ray spectral observations, yielding B=250 and 120 G at the two emission peaks, respectively. The measured B from the microwave spectrum is an appropriately-weighted value of magnetic field from the loop top to the loop leg. Therefore, the two methods to evaluate coronal magnetic field in flaring loops produce fully-consistent results in this event.     

Spherical variable-energy blast wave in self-gravitating gas

Modified similarity method has been used to study the propagation of spherical-variable energy blast waves through a self-gravitating gas. For an energy inputE =E ₀t^4/3, whereE is the energy released up to timet andE ₀ is a functional constant, the similarity solutions correct up to third approximation have been obtained. It is found that the effects of self-gravitational forces are of third order. An increase in the parameterA ² (characterising the gravitational field) increases the shock velocity.