Calculation of effective optical depth of absorption line formation in homogeneous semi-infinite planetary atmosphere during anisotropic scattering

The algorithm for determining effective optical thickness of absorption line formation in a plane-parallel homogeneous planetary atmosphere is presented. The case of anisotropic scattering is considered. The results of numerical calculations of τ _e (μ₀) at the scattering angle γ = π for some values of the single scattering albedo λ and the parameter of the Heyney-Greenstein scattering indicatrix g are given. The refined equation for the function T ^m (−μ, μ₀) is presented.     

Non-vacuum solutions of Bianchi type VI0 universe in f(R) gravity

In this paper, we solve the field equations in metric f(R) gravity for Bianchi type VI ₀ spacetime and discuss evolution of the expanding universe. We find two types of non-vacuum solutions by taking isotropic and anisotropic fluids as the source of matter and dark energy. The physical behavior of these solutions is analyzed and compared in the future evolution with the help of some physical and geometrical parameters. It is concluded that in the presence of isotropic fluid, the model has singularity at [(t)\tilde]=0\tilde{t}=0 and represents continuously expanding shearing universe currently entering into phantom phase. In anisotropic fluid, the model has no initial singularity and exhibits the uniform accelerating expansion. However, the spacetime does not achieve isotropy as t→∞ in both of these solutions.     

Singularitäten in der Allgemeinen Relativitätstheorie

“Regular solutions of EINSTEIN 's equations” mean very different things. In the case of the empty-space equations, R_ik = 0, such solutions must be metrics g_ik(x^l) without additionaly singular “field sources” (EINSTEIN 's “Particle problem”). – However the “phenomenological matter” is defined by the EINSTEIN equations R_ik – 1/2g_ikR =–xT_ik itselves. Therefore if 10 regular functions g_ik(x^l) are given (which the inequalities of LORENTZ -signature fulfil) then these g_ik define 10 functions T_ik(x^l) without singularities. But, the matter-tensor T_ik must fulfil the two inequalities T ≥ 0, T ≥ 1/2 T only and therefore the EINSTEIN -equations with “phenomenological matter” mean the two inequalities R ≥ 0, R ≤ 0 which are incompatible with a permanently regular metric with LORENTZ -signature, generally.     

40Ar‐39Ar and cosmic‐ray exposure ages of nakhlites—Nakhla,Lafayette, Governador Valadares—and Chassigny

Abstract– We present ⁴⁰Ar‐³⁹Ar dating results of handpicked mineral separates and whole‐rock samples of Nakhla, Lafayette, and Chassigny. Our data on Nakhla and Lafayette and recently reported ages for some nakhlites and Chassigny ( Misawa et al. 2006 ; Park et al. 2009 ) point to formation ages of approximately 1.4 Ga rather than 1.3 Ga that is consistent with previous suggestions of close‐in‐time formation of nakhlites and Chassigny. In Lafayette mesostasis, we detected a secondary degassing event at approximately 1.1 Ga, which is not related to iddingsite formation. It may have been caused by a medium‐grade thermal event resetting the mesostasis age but not influencing the K‐Ar system of magmatic inclusions and the original igneous texture of this rock. Cosmic‐ray exposure ages for these meteorites and for Governador Valadares were calculated from bulk rock concentrations of cosmogenic nuclides ³He, ²¹Ne, and ³⁸Ar. Individual results are similar to literature data. The considerable scatter of T₃, T₂₁, and T₃₈ ages is due to systematic uncertainties related to bulk rock and target element chemistry, production rates, and shielding effects. This hampers efforts to better constrain the hypothesis of a single ejection event for all nakhlites and Chassigny from a confined Martian surface terrain ( Eugster 2003 ; Garrison and Bogard 2005 ). Cosmic‐ray exposure ages from stepwise release age spectra using ³⁸Ar and neutron induced ³⁷Ar from Ca in irradiated samples can eliminate errors induced by bulk chemistry on production rates, although not from shielding conditions.     

Dynamics of Kantowski-Sachs universe with magnetized anisotropic Dark Energy

Kantowski-Sachs cosmological model in the presence of magnetized anisotropic dark energy is investigated. The energy-momentum tensor consists of anisotropic fluid with anisotropic EoS p=ωρ and a uniform magnetic field of energy density ρ _B . We obtain exact solutions to the field equations using the condition that expansion is proportional to the shear scalar. The physical behavior of the model is discussed with and without magnetic field. We conclude that universe model as well as anisotropic fluid does not approach isotropy through the evolution of the universe.     

Cosmological Models with ‘Some’ Variable Constants

Various models are considered with metric type flat FRW i.e. with k = 0 whose energy-momentum tensor is described by a perfect fluid whose generic equation of state is p = ωρ and taking into account the conservation principle div(T _i ^j ) = 0, but considering some of the‘constants’ as variable. A set of solutions through dimensional analysis is trivially found. The numeric calculations carried out show that the results obtained are not discordant with those presently observed for cosmological parameters together with the electromagnetic and quantum quantities. This revised version was published online in July 2006 with corrections to the Cover Date.     

Dynamics of a magnetized Bianchi VI 0 universe with anisotropic fluid

We discuss spatially homogeneous and anisotropic Bianchi type VI ₀ cosmological model with anisotropic fluid and magnetic field. The energy-momentum tensor consists of anisotropic fluid with anisotropic EoS and a uniform magnetic field of energy density ρ _B . Exact solution of the field equations is obtained by using the condition that expansion is proportional to the shear scalar. We focus on the future evolution of the model both in the presence and absence of magnetic field. In particular, we address the question whether these models approach to isotropy.     

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     

Effects of viscous dissipation and free convection currents on the flow of an electrically conducting fluid past an accelerated vertical porous plate

In the present paper, the effects of free convection currents and the viscous dissipation on the unsteady flow of an electrically conducting and viscous incompressible fluid around an uniformly accelerated vertical porous plate subjected to a suction or injection velocity inversely proportional to the square root of time, in presence of a transverse magnetic field, have been investigated. Analytical solutions for the velocity and the temperature distributions, the skin-friction and the rate of heat transfer are obtained for small magnetic parameterM. During the course of discussion the effects of the Grashof number Gr, the Eckert number Ec, the suction/injection parametera have been considered for unit value of the Prandtl number Pr.Nomenclature a suction/injection parameter - C _p specific heat at constant pressure - B ₀ magnetic induction - g acceleration due to gravity - Gr Grashof number (g(T _w –T )/U ₀ ³ ) - K thermal conductivity - M magnetic field parameter (B ₀ ² /U ₀ ² ) - Pr Prandtl number (C _p/K) - T temperature of the fluid near the plate - T _w temperature of the plate - T temperature of the fluid at infinity - t time - t dimensionless time (tU ₀ ² /) - u velocity of the fluid - u non-dimensional velocity (u/U ₀) - U velocity of the plate - U dimensionless velocity of the plate (U/U ₀) - U ₀ reference velocity - v ₀ suction velocity - v ₀ non-dimensional suction velocity (v ₀/U ₀)=at ^–1/2 - Ec Eckert number ((U ₀)^2/3/C _p(T _w –T )) - T dimensionless temperature of the fluid near the plate ((T–T )/(T _w ^–T )) - x, y coordinates along and normal to the plate - x, y dimensionless coordinates (y=yU ₀/) - kinematic viscosity - coefficient of volume expansion - electric conductivity of the fluid - y/2t ^1/2 - density of the fluid - skin-friction - dimensionless skin-friction - q rate of heat transfer - q non-dimensional rate of heat transfer - coefficient of viscosity - _e magnetic permeability On leave of absence from Department of Mathematics, University of Dhaka, Bangladesh     

Thermal history of ALH 84001 meteorite by Fe2+‐Mg ordering in orthopyroxene

Abstract— A single orthopyroxene crystal from the Martian meteorite Allan Hills (ALH) 84001 was studied by X‐ray diffraction (XRD) and electron microprobe analysis (EMPA) to retrieve information about its thermal history. Both sets of data were used to measure the Fe²⁺‐Mg order degree between the M1 and M2 sites expressed by the distribution coefficient k_D. The 529 ± 30°C closure temperature (T_c) of the Fe²⁺‐Mg ordering process of ALH 84001 orthopyroxene (Fs₂₈) was calculated using Stimpfl (2005a, 2005b) ln k_D versus 1/T equation obtained for intermediate iron sample. At this T_c, the orthopyroxene cooling rate, calculated by Ganguly's (1982) numerical method, was 0.1 °C/day. This study puts new constraints on the last high‐temperature thermal episode recorded by orthopyroxene. With reference to the geological history (Treiman 1998), we ascribe this episode to the I3 event, and we interpret the T_c of 529 °C as a lower limit for this impact heating. Our data confirm that experimentally defined physical conditions for the formation of magnetite from decomposition of carbonates took place on the Martian surface during event I3.     

Comment on “Non-vacuum conformally flat space-times: dark energy”

Ibohal, Ishwarchandra and Singh (Ibohal et al., Astrophys. Space Sci. 335, 581, 2011) proposed a class of exact, non-vacuum and conformally flat solutions of Einstein’s equations whose stress tensor T _ab has negative pressure. We show that T _ab corresponds to an anisotropic fluid and the equation of state parameter seems not to be ω=?1/2. We consider the authors’ constant cannot be the mass of a test particle but is related to a Rindler acceleration of a spherical distribution of uniformly accelerating observers.     

Further considerations on contracting solar nebula

Prentice (1978a) in his modern Laplacian theory of the origin of the solar system has established the scenario of the formation of the solar system on the basis of the usual laws of conservation of mass and angular momentum and the concept of supersonic turbulent convection that he has developed. In this, he finds the ratio of the orbital radii of successively disposed gaseous rings to be a constant - 1.69. This serves to provide a physical understanding of the Titius-Bode law of planetary distances. In an attempt to understand the law in an alternative way, Rawal (1984) starts with the concept of Roche limit. He assumes that during the collapse of the solar nebula, the halts at various radii are brought about by the supersonic turbulent convection developed by Prentice and arrives at the relation: R _p= Ra^p, where R _pare the radii of the solar nebula at various halts during the collapse, R the radius of the present Sun and a = 1.442. a is referred here as the Roche constant. In this context, it is shown here that Kepler's third law of planetary system assumes the form: T _p = T ₀(a^3/2)^p, where T _p are the orbital periods at the radii R _p, T ₀ - 0.1216d - 3 h, and a the Roche constant. We are inclined to interpret T ₀' to be the rotation period of the Sun at the time of its formation when it attained the present radius. It is also shown that the oribital periods T _pcorresponding to the radii R _psubmit themselves to the Laplace's resonance relation.     

A quantitative analysis of the surge of March 19, 1989

A large surge event appearing in AR 5395 was observed at the Yunnan Observatory on March 19, 1989. H spectral profiles of the event are interpreted by using a two-cloud model and the contours of three parameters: excitation temperature, T _exc, microturbulent velocity, V _t ,and column density of hydrogen atoms at the second level, N _0,2, are obtained, respectively. The question about the unique feature of the solution obtained by the fitting method is also discussed. The results show that the surge is composed of some conglomerated materials with higher temperature and density; the mass ejection is probably intermittent. Neither T _exc nor N _0,2 vary with the height over the solar limb but decrease from the center to the periphery of the surge. V _t varies from 10 to 30 km s^-1 and decreases with height. Some other important parameters, such as electron density, n _e ,and electron pressure, P _e ,etc., have also been estimated. In the surge, with N _0,2 about 2.0 × 10¹² cm^-2 and T _exc about 8500 K on average, we obtained n _e = 1.80 × 10¹⁰ cm^-3 and P _e = 0.023 dyn cm^-2. The energy variations of the surge during the ascending phase are estimated.     

The spectrum of Cyg X-1 — A theoretical model

We have calculated the spectrum of Cyg X-1 under the assumption that the radiation orginates in a disk around a 11M black-hole. Supersonic turbulence prevails in the outer parts of the disk and electron-electron bremsstrahlung appears to be resonsible for the maintenance of the temperature at a level less than 10¹⁰ K near the inner edge of the disk. The theoretical spectrum gives the best fit with the observations if the Reynolds number is about 1200.     

The problem of the maximum volumes and particle horizon in the Friedmann universe model

The maximum volume of the closed Friedmann universe is further investigated and is shown to be 2² R ³ (t), instead of ² R ³ (t) as found previously. This discrepancy comes from the incomplete use of the volume formula of 3-dimensional spherical space in the astronomical literature. Mathematically, there exists the maximum volume at any cosmic timet in a 3-dimensional spherical case. However, the Friedmann closed universe in expansion reaches its maximum volume only at the timet _m of the maximum scale factorR(t _m ). The particle horizon has no limitation for the farthest objects in the closed Friedmann universe if the proper distance of objects is compared with the particle horizon as it should be. It will lead to absurdity if the luminosity distance of objects is compared with the proper distance of the particle horizon.     

Heavy Ions From the 6 November 1997 sep Event: a Charge-Consistent Acceleration Model

Based on the observed dependence of the mean charge of several elements (C, O, Ne, Mg, Si and Fe) on energy for the gradual event of 6 November 1997 we deduce plasma parameters in the accelerating site. This is done in the framework of a charge-consistent acceleration model which incorporates ionisation and recombination processes during heavy ion energization by a parallel shock wave. To obtain good fits to observations we have to assume for the product of the characteristic acceleration time and number density T ^q _ac N (3–10) ×10⁹ s cm^–3 and temperature T=10⁶ K of a plasma where all the elements under consideration originated.     

Thermal bremsstrahlung hard X-rays and primary energy release in flares

Various methods are explored for obtaining regularized solutions of the severely ill-posed Laplace inversion problem involved in deriving plasma temperature (T) structure (differential emission measure(T)) from bremsstrahlung spectra. Inversions of simulated data show that zero-order regularisation (Tikhonov regularisation inL ² space) is very unsatisfactory even with weighting, while first-order regularisation (Tikhonov regularisation in Sobolev space) yields reasonable results.The method is applied to a high-resolution hard X-ray flare spectrum observed by Lin and Schwartz (1987) and yields a positive solution for(T) showing that a purely thermal interpretation is possible for that event. The form of(T) found has two broad features: one peaking at around 10⁷ K and falling off steeply toward 2 × 10⁸ K; a second spread around a peak near 4.5 × 10⁸ K. The interpretation of such(T) in terms of plasma heating and conductive flux is discussed in terms of plasma heat fluxes and heating rates. For 1-D geometry, the distribution of the plasma heating rateH(T) per unit volume is inferred from(T) in the limits of classical diffusive conduction and of saturated heat flux, the former being relevant atT below around 5 × 10⁷ K and the latter at much higherT. We find there exists a maximum inH(T) around 2 × 10⁸ K, a fact which may be important for energy release theories.     

Well behaved parametric class of relativistic charged fluid ball in?general relativity

The paper presents a class of interior solutions of Einstein–Maxwell field equations of general relativity for a static, spherically symmetric distribution of the charged fluid. This class of solutions describes well behaved charged fluid balls. The class of solutions gives us wide range of parameter K (0≤K≤42) for which the solution is well behaved hence, suitable for modeling of super dense star. For this solution the mass of a star is maximized with all degree of suitability and by assuming the surface density ρ _b =2×10¹⁴ g/cm³. Corresponding to K=2 and X=0.30, the maximum mass of the star comes out to be 4.96 M _Θ with linear dimension 34.16 km and central redshift and surface redshift 2.1033 and 0.683 respectively. In absence of the charge we are left behind with the well behaved fourth model of Durgapal (J. Phys., A, Math. Gen. 15:2637, 1982).     

Thermalization of solar wind

Three kinetic equations describing the linear and non-linear wave-particle interaction for an anisotropic solar wind plasma have been developed. These equations have been solved numerically to find the variation inT /T with respect to time, whereT andT are the perpendicular and parallel temperatures with respect to the ambient magnetic field of the solar wind. For wave energy greater than a critical value (strong turbulence), non-linear wave-particle interactions are important but do not lead to thermalization. On the other hand, weak nonlinear interactions tend to increaseT /T , but make only a negligible contribution in the quantitative sense. Thus, only the linear wave-particle interaction remains as the significant contributer to the increase ofT /T .