Solar Wind Statistics at 1 AU: Alfven Speed and Plasma Beta

The phenomenon of MHD wave refraction is useful in interpreting the properties of the magnetic fluctuations in certain parcels of solar wind. In the physics of MHD wave refraction, variations in the Alfvén speed V_Alf play a dominant role. Here, we compile statistics of the 1-min averages of V_Alf at the location of the ACE spacecraft during its first 5 years of operation. We find that monthly distributions of V_Alf are close to log-normal, with standard deviations σ_V as small as 0.11 in the logarithm. Variations in the monthly mean V_Alf are correlated significantly with sunspot number. We also compile monthly distributions of the plasma β parameter. The distributions of both V_Alf and β are significantly narrower than they would be if the various solar wind parameters were statistically independent. In the T_p–V_Alf plane, we find a zone of avoidance at low V_Alf: for V_Alf ≤10 – 15 km/s, there are no samples in the 1-min data that are cooler than T_p = 10 000 – 15 000 K. This feature can be understood in the context of MHD wave refraction, although other explanations are also possible.     

Small-Amplitude Disturbances In A Radiating And Scattering Grey Medium Ii. Solutions Of Given Real Wave Number <Emphasis Type="BoldItalic">k</Emphasis>

We study the fundamental modes of radiation hydrodynamic waves arising from one-dimensional small-amplitude initial fluctuations with wave number k in a radiating and scattering grey medium using the Eddington approximation. The dispersion relation analyzed is the same as that of Paper I (Kaneko et al., 2000), but is solved as a quintic in angular frequency ω while a quadratic in k ² in Paper I. Numerical results reveal that wave patterns of five solutions are distinguished into three types of the radiation-dominated and type 1 and type 2 matter-dominated cases. The following wave modes appear in our problem: radiation wave, conservative radiation wave, entropy wave, Newtonian-cooling wave, opacity-damped and cooling-damped waves, constant-volume and constant-pressure diffusion modes, adiabatic sound wave, cooling-damped and drag–force-damped isothermal sound waves, isentropic radiation-acoustic wave, and gap mode. The radiation-dominated case is characterized by the gap between the isothermal sound and isentropic radiation-acoustic speeds within which there is not any acoustic wave propagating with real phase speed. One of the differences between type 1 and type 2 matter-dominated cases is the connectivity of the constant-volume diffusion mode, which originates from the radiative mode in the former case, while from the Newtonian-cooling wave in the latter case. Analytic solutions are derived for all wave modes to discuss their physical significance. The criterion, which distinguishes between radiation-dominated and type 1 matter-dominated cases, is given by Γ₀ = 9, where Γ₀ = C _p ^(tot)/C _V ^(tot) is the ratio of total specific heats at constant pressure and constant volume. Waves in a scattering grey medium are also analyzed, which provides us some hints for the effects of energy and momentum exchange between matter and radiation.     

Wave minimum of AR Lacertae

U, B, andV observations of AR Lacertae, obtained in 1981, have been presented alongwith the colour indices. A distortion wave minimum is found to lie at 0 _. ^P 21. The amplitude of the wave minimum inV filter is too weak, while it is stronger inU andV filters, the strongest being inV filter. The period of the migration wave turns out to be 2.53 yr.     

The characteristics of ion acoustic shock waves in non-Maxwellian plasmas with (G′/G)-expansion method

Korteweg-de-Vries-Burger (K-dVB) equation is derived for ion acoustic shock waves in electron-positron-ion plasmas. Electrons and positrons are considered superthermal and are effectively modeled by a kappa distribution in which ions are as cold fluid. The analytical traveling wave solutions of the K-dVB equation investigated, through the (G′/G)-expansion method. These traveling wave solutions are expressed by hyperbolic function, trigonometric functions are rational functions. When the parameters are taken special values, the shock waves are derived from the traveling waves. It is observed that the amplitude ion acoustic shock waves increase as spectral index κ and kinematic viscosity η _i,0 increases in which with increasing positron density β and electron temperature σ the shock amplitude decreases. Also, numerically the effect different parameters on the nonlinearity A and dispersive B terms and wave velocity V investigated.     

A closed-form solution to the minimum $${\Delta V_{\rm tot}^2}$$ Lambert’s problem

A closed form solution to the minimum DV_tot²{\Delta V_{\rm tot}^2} Lambert problem between two assigned positions in two distinct orbits is presented. Motivation comes from the need of computing optimal orbit transfer matrices to solve re-configuration problems of satellite constellations and the complexity associated in facing these problems with the minimization of DV_tot{\Delta V_{\rm tot}}. Extensive numerical tests show that the difference in fuel consumption between the solutions obtained by minimizing DV_tot²{\Delta V_{\rm tot}^2} and DV_tot{\Delta V_{\rm tot}} does not exceed 17%. The DV_tot²{\Delta V_{\rm tot}^2} solution can be adopted as starting point to find the minimum DV_tot{\Delta V_{\rm tot}}. The solving equation for minimum DV_tot²{\Delta V_{\rm tot}^2} Lambert problem is a quartic polynomial in term of the angular momentum modulus of the optimal transfer orbit. The root selection is discussed and the singular case, occurring when the initial and final radii are parallel, is analytically solved. A numerical example for the general case (orbit transfer “pork-chop” between two non-coplanar elliptical orbits) and two examples for the singular case (Hohmann and GTO transfers) are provided.     

The massive scalar field in a closed Friedmann universe model — new rigorous results

For the minimally coupled scalar field in Einstein's theory of gravitation we look for the space of solutions within the class of closed Friedmann universe models. We prove D ≥ 1, where D ≥ is the dimension of the set of solutions which can be integrated up to t → ∞ (D > 0 was conjectured by PAGE (1984)). We discuss concepts like “the probability of the appearance of a sufficiently long inflationary phase” and argue that it is primarily a probability measure μ in the space V of solutions (and not in the space of initial conditions) which has to be applied. μ is naturally defined for Bianchi-type I cosmological models because V is a compact cube. The problems with the closed Friedmann model (which led to controversial claims in the literature) will be shown to originate from the fact that V has a complicated non-compact non-Hausdorff Geroch topology: no natural definition of μ can be given. We conclude: the present state of our universe can be explained by models of the type discussed, but thereby the anthropic principle cannot be fully circumvented.     

High-resolution analysis of solar photospheric oscillations

The coherent 5-min photospheric pressure oscillations with spherical harmonic degrees in the range 100 <l< 1000 were directly imaged over the photosphere with the monochromatic solar telescope FPSS at Meudon Observatory. Movie films were obtained with images spatially filtered to select sizes of increasing wave numbers (or l). Areas with ephemeral concentrations of coherent waves evolve in shape and may move horizontally with velocities of several tenths of km s^–1. When a large number of waves are interacting, the maximum vertical velocity V _max of the pulsation reaches around 1000 m s^–1, irrespective of the size. Extrapolation to the ideal case of a single isolated wave gives V _max proportional to size. For the areas of the smallest scale measured (l = 1000), when about 100 waves are interacting, V _max is found to be 260 + 25 m s^–1 at an altitude of 210 km above the reference level ₅₀₀₀ = 1 and increases vertically with a scale height of 750 ± 400 km.     

Generation of waves by the solar magnetic field polarity reversal

In this paper an excitation of waves is considered during the time interval in which the undisturbed magnetic field changes its direction. If this interval is taken to be 2 years, which is shorter than the 11-year cycle, then the undisturbed components of the magnetic field may be linearly dependent on time and independent of the coordinates. The excitation of waves is due to the undisturbed stationaryV ₀ flow with divV ₀ = 0 and with (V ₀ rot₀) = constant.We use the local Cartesian coordinate system, which is immovable towards the solar centre, and consider the case when the toroidal component of the undisturbed magnetic field changes its sign simultaneously with one of the axial components. The third component does not change its direction.The efficiency of the enhancement of the magnetic field and velocity disturbances depends on the Alfvén wave frequency, _A. When _A = 0, the component of the disturbed velocity, which is directed along the constant component of the undisturbed magnetic field, increases. In this case the shear waves excite the carrier (high) frequency (KV ₀), whereK is the wave vector. Due to the shear instability the amplitude of the velocity increases during 1 year before the moment of reversal of the global magnetic field polarity (RGMFP) for an arbitrary latitude. It reaches a maximum at RGMFP and decreases in the next year. When _A > 0, then the amplitudes of the disturbed values reach maxima before the moment of RGMFP, and when _A < 0, they reach maxima after it.We argue that the shear waves propagate from middle latitudes to the pole and equator. Using the results of the analytical solutions and leaning on the evidence of the observational data (Gigolashvili and Japaridze, 1992), we derive the result that the component of the undisturbed magnetic field, which is perpendicular to the solar surface, changes its sign simultaneously with the toroidal component.     

Galactic Rotation Based on OB Stars from the Gaia DR2 Catalogue

We have studied a sample containing ~6000 OB stars with proper motions and trigonometric parallaxes from the Gaia DR2 catalogue. The following parameters of the angular velocity of Galactic rotation have been found: Ω₀ = 29.70 ± 0.11 km s^-1 kpc^-1, Ω'₀ = -4.035 ± 0.031 km s^-1 kpc^-2, and Ω ₀ = 0.620 ± 0.014 km s^-1 kpc^-3. The circular rotation velocity of the solar neighborhood around the Galactic center is V₀ = 238 ± 5 km s^-1 for the adopted Galactocentric distance of the Sun R₀ = 8.0 ± 0.15 kpc. The amplitudes of the tangential and radial velocity perturbations produced by the spiral density wave are f_θ = 4.4 ± 1.4 kms^-1 and f_R = 5.1 ± 1.2 kms^-1, respectively; the perturbation wavelengths are λ_θ = 1.9 ± 0.5 kpc and λ_R = 2.1 ± 0.5 kpc for the adopted four-armed spiral pattern. The Sun's phase in the spiral density wave is χ_⊙ = -178° ± 12°.

     

Ground Pc3–Pc5 wave power distribution and response to solar wind velocity variations

We examine the magnetospheric wave power in the Pc3–Pc5 range in terms of its growth and decay characteristics and its distribution in L shell in response to the interplanetary plasma bulk velocity, V_SW. We use linear and nonlinear (rank-order) correlation and filtering methods to quantify the effective coupling of the wave power to V_SW variations. These methods are applied to measurements from 26 ground magnetometers of the IMAGE array and NOAA's GOES-10 spacecraft at geosynchronous orbit, taken over 2 years of solar-maximum activity (2002–2003). We find that the ground ULF wave power is structured in the range 3.5<L<6.4 and distributed uniformly in the range 6.4<L<15 (uncertainties in L are estimated to be ±0.5). The response of the wave power to the V_SW is characterized by an increase starting 3 days before the V_SW peak, intensifying several hours before the peak, and is followed by a fast decrease in the next 2 days. The rapid decay of ULF waves has two stages: one at τ=−6±2 h before the solar wind velocity reaches its peak, and one at the V_SW peak, τ=0. We suggest that the first one is brought about by wave–particle interaction with inner-magnetospheric populations while the second one is a dV_SW/dt effect. The correlation results are confirmed by calculating the finite-impulse response, which shows clearly the decay of the ULF waves after the V_SW peak. The response of the wave power at geosynchronous orbit is remarkably similar to that of the ground wave power at comparable L shells. The above findings characterize the inner-magnetospheric response to interplanetary high-speed streams, as opposed to the more short-lived, higher-amplitude response to CMEs.     

Is the Asymmetric Cone Model for Halo Coronal Mass Ejections Correct?

A set of 106 limb CMEs which are wide and could be possible halo events, when directed towards Earth, are used to check the accuracy of the asymmetric cone model. For this purpose characteristics of CMEs (widths and radial speeds) measured for the possible halo CMEs are compared with these obtained for halo CMEs using the asymmetric cone model (Michalek, Solar Phys. 237, 101, 2006). It was shown that the width and speed distributions for both datasets are very similar and with a probability of p>0.93 (using the Kolmogorov – Smirnov test) were drawn from the same distribution of events. We also determined the accurate relationship between radial (V _rad) and expansion (V _exp) speeds of halo CMEs. This relation for the halo CMEs is simply V _rad=V _exp and could be very useful for space weather application.     

Ccd Photometry of Neglected Eclipsing Binaries – Kz Dra, Lr Cam and Im Vul

We present ephemerides and solutions of one Algol-type (KZ Dra) and two overcontact systems (LR Cam and IM Vul) based on V(RI)_C CCD observations obtained in the project Prosper (network of amateur observers).     

Optical depth effects on the formation of spectral lines in rotating and expanding spherical atmospheres

We have investigated the effects of increasing optical depths on spectral lines formed in a rotating and expanding spherical shell. We have assumed a shell whose outer radius is 3 times the inner radius, with the radial optical depths equal to 10, 50, 100, 500. We have employed a constant velocity with no velocity gradients in the shell. The shell is assumed to be rotating with velocities varying as 1/_ρ, where_ρ is the perpendicular distance from the axis of rotation, implying the conservation of angular momentum. Two expansion (radial) velocities are treated: (1)V = 0 (static case) and (2)V = 10 mean thermal units. The maximum rotational velocities areV _rot = 0, 5, 10 and 20. In the shell where there are no radial motions, we obtain symmetric lines with emission in the wings forV _rot = 0 and 5 while forV _rot ≥ 10 we obtain symmetric absorption lines. In the case of an expanding shell, we obtain lines with central emission.     

Intrinsic colour indices of Be stars obtained from 2MASS photometry

This paper is based on 2MASS photometry (J H K_s magnitudes) of 1172 Be stars. The observed mean intrinsic colours have been derived with aid of two‐colour diagrams for Be stars of luminosity classes Ie‐IIe, IIIe and IVe‐Ve. The obtained results are the first determinations of their intrinsic colours in the astronomical literature. The smoothed infrared colours are compared with those obtained for “normal” B stars. Several two‐colour diagrams and plots of observed and smoothed intrinsic colour versus spectral type of luminosity classes Ie‐IIe, IIIe and IVe‐Ve are presented. Generally the determined infrared intrinsic colours of Be stars (V – J)₀, (V – H)₀, and (V – K_s)_o differ substantially from those of “normal” B stars. It is found that the intrinsic colours of B stars are generally bluer than Be stars of corresponding spectral type and luminosity class. The mean absolute visual magnitude M_v of 528 Be stars for luminosity classes Iae, Ibe‐Iabe, IIe, IIIe and IVe‐Ve is derived from HIPPARCOS parallaxes. The M_v calibration is compared with the existing ones. The Be stars are generally brighter than “normal” B stars of corresponding spectral types. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The extinction curve in the visible and the value of RV

This article discusses the interstellar extinction curve in the visible and the value of the ratio of absolute to selective extinction R_V = A_V/E (B – V). It is concluded that the visible extinction curve is likely to be linear in the visible and that indirect estimates of R_V from tentative determinations of A_V or from infrared and UV observations are questionable. There is currently no evidence of any variation of R_V with direction. If R_V is close to 3, as it has been inferred from mid‐infrared data, starlight in the visible is extinguished by a factor F /F₀ = (2.5 e^–2μm/λ)^{E (B –V)}. But if the visible wavelength range alone is considered, 4 appears as its most natural and probable value and F /F₀ = e^{–2E (B –V)/λ} (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Flare-associated high-speed solar plasma streams

Characteristics of flare-associated high-speed solar plasma streams are investigated using measurements from space probes and Earth-orbiting spacecraft for the period 1964–1982. The maximum observed velocity (V _m) of these streams range from 400 to 850 km s^–1} with peak probability for 600 km s^–1}. These remain for the period of 1–10 days with the peak occurrence 3 days. The difference between the pre-stream velocity (V ₀) and the maximum velocity (V _m) of any high-speed stream serves as the measure of its intensity. For about 60% of the flare associated streams, (V _m-V ₀) is well in excess of 200 km s^–1} and in some cases becomes as large as 450 km s^–1}. The yearly percentage occurrence, total duration and the product of mean (V _m - V ₀) with total duration of the high-speed streams during the year correlates well with solar activity, e.g., maximum during high solar activity period and minimum during low solar activity. The study suggests that presence of sunspots plays a significant role in the generation of flare associated high-speed solar streams.     

The Spectrum of Torsional Oscillations of the Moon

The diagnostic potentialities of the torsional oscillations for probing the structure of the interiors of the Moon are investigated. Models with no core, a liquid core, and a solid core are considered. The profiles of compressional and shear wave velocities V _P and V _S for the lunar interior estimated by Bills and Ferrari (1977), Goins et al. (1981), and Nakamura (1983) from the Apollo lunar seismic network are used. For all these models, the periods of torsional oscillations for n = 2–100 and four overtones have been calculated. The derivatives of the dimensionless eigenfrequency with respect to the dimensionless shear modulus and density are calculated and tabulated for use. These data can be used to determine corrections to the model density and shear modulus distributions due to their small change. The damping of torsional oscillations is studied. Several trial radial distributions of the dissipative function Q are considered.     

Etude variationnelle des decalages spectraux

Sommaire L'auteur se propose d'établir une formulation générale non relativiste des décalages spectraux à partir d'une méthode variationnelle.Le premier pas consiste à établir pour l'espace euclidien ₃ une formulation duale de l'effet Doppler-Fizeau et à montrer que celle-ci peut s'interpréter comme un principe de moindre action. Nous faisons ressortir dans ce cas les hypothèses utilisées: isotropie de l'espace et uniformité du temps appliquées à un système lagrangien. Une telle façon d'opérer nécessite l'utilisation du groupe d'isométries de ₃, la comparaison des trajectoires naturelle et variée ne pouvant s'effectuer qu'au voisinage de l'observateur. Dans le cas où le groupe d'isométries de ₃ ne peut être utilisé, il y a surestimation systématique des décalages spectraux observés.La seconde étape est d'assimiler l'espace physique à une variété riemannienneV ₃ et à montrer que le temps peut être défini à partir des géodésiques de cette variété. Cela est possible en assimilant. pour un observateur donné, les surfaces isochrones (t) à une variété quotientV ₂ telle queV ₃ =V ₂ ×R. Cela implique l'existence de trajectoiresnon naturelles passant par deux points donnés deV ₃, de longueurs plus petites que celles des géodésiques riemanniennes correspondantes. D'où l'existence d'un temps propre local, mesuré le long des géodésiques, variable d'un point à l'autre selon les différences de symétries de l'espace au voisinage de ces points.Nous pouvons alors considérer dans un troisième temps l'espace physique comme un système lagrangien nanti de temps propres uniformes et tels que l'on passe du lagrangienG, définissant les conditions de symétries de la variétéV ₃, au lagrangien local G par une transformation conforme. Si l'on suppose que la fonction de transformationF(x,t) varie très lentement avec x ett, on est conduit à une relation entre les temps propres de deux points quelconques deV ₃.L'application d'un principe de moindre action, avec ces hypothèses permet alors une formulation non relativiste des décalages spectraux, contenant à la fois l'effet Doppler-Fizeau, un effet gravitationnel et un effet cosmologique. On peut alors considérer l'effet Doppler-Fizeau comme résultant d'un principe de Fermat généralisé.

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The aim of the author has been to establish a non-relativistic general formulation for the shift of spectral lines by means of a variational method.As a first step, we establish a dual formulation of the Doppler-Fizeau effect for Euclidean space ₃, and we show this can be interpreted as a principle of least action. In this case, the hypothesis can be clearly exhibited: isotropy of space and uniformity of time applied toaa Lagrangian system. The use of the isometries group of ₃ is required, since the comparison with the fiducial trajectory can be done only near the observer. A systematic overvaluation appears when incorrect use of this groups is made.The second step consists of an identification of the physical space with a Riemannian manifoldV ₃. The time can be defined by means of geodesics ofV ₃. This can be done by taking an isochronic surface (t) as aV ₂ quotient manifold such asV ₃ =V ₂ ×R. This implies the existence ofnonnatural trajectories of less extent than the corresponding geodesics. From that, we deduce the existence of a local proper time, measured along geodesics, which depends on the local conditions of symmetry.In a third step, we can consider the physical space as a Lagrangian system with uniform proper time allowing us to proceed from LagrangianG, describing the symmetry conditions of theV ₃ manifold, to a local Lagrangian G by means of a conformal transformation. If the transformation functionF(x,t) is supposed to be slowly variable with x andt, a relation between the proper times of any two points in the manifold can be found.With this hypothesis, the application of the principle of stationary action leads to a nonrelativistic formulation for shifts of spectral lines including, at the same time, the Doppler-Fizeau effect, the gravitational effect, and the cosmological effect. In this case, we can consider the Doppler-Fizeau effect as the result of a generalised Fermat principle.

     

The Plasma and Magnetic Field Characteristics of a Double Discontinuity in Interplanetary Space

A double discontinuity is a rarely observed compound structure composed of a slow shock layer and an adjoining rotational discontinuity layer in the downstream region. In this paper, we report the observations of a double discontinuity detected by Wind on May 15, 1997. This double discontinuity is found to be the front boundary of a magnetic cloud boundary layer. We strictly identify the shock layer and the rotational discontinuity layer by using the high-resolution plasma and magnetic field data from Wind. The observed jump conditions of the upstream and downstream region of the slow shock layer are in good agreement with the Rankine – Hugoniot relations. The flow speeds in the shock frame U _n <V _Acos θ _Bn on both sides of the slow shock layer. In the upstream region, the slow Mach number M _s1=U _n1/V _s1 is 1.95 (above unity), and in the downstream region, the slow Mach number M _s2=U _n2/V _s2 is 0.31 (below unity). Here V _A and V _s represent the Alfvén speed and the local slow magnetosonic speed, respectively, and θ _Bn is the angle between the direction of the magnetic field and the shock normal. The magnetic cloud boundary layer observed by Wind was also detected by Geotail 48 min later when the spacecraft was located outside the bow shock of the magnetosphere. However, Geotail observations showed that its front boundary was no longer a double discontinuity and the rotational discontinuity layer disappeared, indicating that this double discontinuity was unstable when propagating from Wind to Geotail.     

Galactic rotation curve from the space velocities of selected masers

Based on currently available observations of 28 maser sources in 25 star-forming regions with measured trigonometric parallaxes, proper motions, and radial velocities, we have constructed the rotation curve of the Galaxy. Taking different distances to the Galactic center R ₀, we have estimated the peculiar velocity of the Sun, the angular velocity of Galactic rotation, and its three derivatives. For R ₀ = 8 kpc, we have found the circular velocity of the Sun to be V ₀ = 243 ± 16 km s⁻¹, which corresponds to a revolution period of 202 ± 10 Myr. We have obtained the Oort constants A = 16.9 ± 1.2 km s⁻¹ kpc⁻¹ and B = −13.5 ± 1.4 km s⁻¹ kpc⁻¹. Our simulation of the influence of a spiral density wave has shown that the peculiar velocity of the Sun with respect to the local standard of rest and the component (V _⊙)_LSR depend significantly on the Sun’s phase in the spiral wave.