The nonlinear propagation of electrostatic perturbation modes in an unmagnetized, collisionless, relativistic, degenerate plasma (containing both nonrelativistic and ultrarelativistic
degenerate electrons, nonrelativistic degenerate ions, and arbitrarily charged static heavy ions) has been investigated theoretically. The Korteweg-de Vries (K-dV) equation has been derived by employing the reductive perturbation method. Their solitary wave solution is obtained and numerically analyzed in case of both planar and nonplanar (cylindrical and spherical) geometry. It has been observed that the ion-acoustic (IA) and modified ion-acoustic (mIA) solitary waves have been significantly changed due to the effects of degenerate plasma pressure and number densities of the arbitrarily charged heavy ions. It has been also found that properties of planar K-dV solitons are quite different from those of nonplanar K-dV solitons. There are numerous variations in case of mIA solitary waves due to the polarity of heavy ions. The basic features and the underlying physics of IA and mIA solitary waves, which are relevant to some astrophysical compact objects, are briefly discussed.

M. R. Hossen

L. Nahar

A. A. Mamun

Planar and Nonplanar Solitary Waves in a Four-Component Relativistic Degenerate Dense Plasma

The work concerns a problem of electron-induced contaminant at relatively low latitudes to high-energy astrophysical measurements on board the low-orbiting satellites. We show the results of a statistical analysis of the energetic electron enhancements in energy range 30&#x2013;300&#x2009;keV observed by a fleet of NOAA/POES low-orbiting satellites over the time period from 1999 to 2012. We demonstrate geographical distributions of great and moderate long-lasting enhancements caused by different type of the solar wind drivers.

Alla V. Suvorova

Alexei V. Dmitriev

Chien-Ming Huang

Energetic Electron Enhancements below the Radiation Belt and X-Ray Contamination at Low-Orbiting Satellites

The simulation of the Cherenkov light lateral distribution function (LDF) in extensive air showers (EAS) was performed using CORSIKA code for configuration of Yakutsk EAS array at high energy range for different primary particles (p, Fe, and O<sub>2</sub>) and different zenith angles. Depending on Breit-Wigner function a parameterization of Cherenkov light LDF was reconstructed on the basis of this simulation as a function of primary energy.  A comparison of the calculated Cherenkov light LDF with that measured on the Yakutsk EAS array gives the possibility of identification of the particle initiating the shower and determination of its energy in the knee region of the cosmic ray spectrum. The extrapolation of approximated Cherenkov light LDF for high energies was obtained for primary proton and iron nuclei.

A. A. Al-Rubaiee

Y. Al-Douri

U. Hashim

Extension of Cherenkov Light LDF Approximation  for Yakutsk EAS Array

We show that the superburst would be originated from thermonuclear burning ignited by accumulated fuels in the deep layers compared to normal X-ray bursts. Two cases are investigated for models related to superbursts by following thermal evolution of a realistic neutron star: helium flash and carbon flash accompanied with many normal bursts. For a helium flash, the burst shows the long duration when the accretion rate is low compared with the observation. The flash could become a superburst if the burning develops to the deflagration and/or detonation. For a carbon flash accompanied with many normal bursts, after successive 2786 normal bursts during 1.81&#x2009;&#xD7;&#x2009;10<sup>9</sup>&#x2009;s, the temperature reaches the deflagration temperature. This is due to the produced carbon which amount reaches to &#x2248;0.1 in the mass fraction. The flash will develop to dynamical phenomena of the deflagration and/or detonation, which may lead to a superburst.

Masa-aki Hashimoto

Reiko Kuromizu

Masaomi Ono

Tsuneo Noda

Masayuki Y. Fujimoto

Numerical Experiments for Nuclear Flashes toward Superbursts in an Accreting Neutron Star

Modulational instability of ion-acoustic waves  has been theoretically investigated in an unmagnetized collisionless plasma with nonthermal electrons, Boltzmann positrons, and warm positive ions. To describe the nonlinear evolution of the wave amplitude a nonlinear Schr&#xf6;dinger (NLS) equation has been derived by using multiple scale perturbation technique. The nonthermal parameter, positron concentration, and ion temperature are shown to play significant role in the modulational instability of ion-acoustic waves and the formation of envelope solitons.

Basudev Ghosh

Sreyasi Banerjee

Modulation Instability of Ion-Acoustic Waves in Plasma with Nonthermal Electrons

The difference between the Uniform Dynamical Time and Universal Time is referred to as <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.0pt;width:22.3375px;" id="M2" height="11.6125" version="1.1" viewBox="0 0 22.3375 11.6125" width="22.3375">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,11.55)"><path id="x394" d="M600 0h-557v24l268 633l28 8l261 -641v-24zM497 50l-194 489l-196 -489h390z"></path></g><g transform="matrix(.017,-0,0,-.017,10.959,11.55)"><use xlink:href="#x1D447"></use></g>

		
	
</svg> (delta <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.0pt;width:11.45px;" id="M3" height="11.6125" version="1.1" viewBox="0 0 11.45 11.6125" width="11.45">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,11.55)"><use xlink:href="#x1D447"></use></g>

		
	
</svg>). Delta <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.0pt;width:11.45px;" id="M4" height="11.6125" version="1.1" viewBox="0 0 11.45 11.6125" width="11.45">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,11.55)"><use xlink:href="#x1D447"></use></g>

		
	
</svg> is used in numerous astronomical calculations, that is, eclipses,and length of day. It is additionally required to reduce quantified positions of minor planets to a uniform timescale  for the purpose of orbital determination. Since Universal Time is established on the basis of the variable rotation of planet Earth, the quantity <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.0pt;width:22.3375px;" id="M5" height="11.6125" version="1.1" viewBox="0 0 22.3375 11.6125" width="22.3375">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,11.55)"><use xlink:href="#x394"></use></g><g transform="matrix(.017,-0,0,-.017,10.959,11.55)"><use xlink:href="#x1D447"></use></g>

		
	
</svg> mirrors the unevenness of that rotation, and so it changes slowly, but rather irregularly, as time passes. We have worked on empirical formulae for estimating <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.0pt;width:22.3375px;" id="M6" height="11.6125" version="1.1" viewBox="0 0 22.3375 11.6125" width="22.3375">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,11.55)"><use xlink:href="#x394"></use></g><g transform="matrix(.017,-0,0,-.017,10.959,11.55)"><use xlink:href="#x1D447"></use></g>

		
	
</svg> and have discovered a set of polynomials of the 4th order with nine intervals which is accurate within the range of ±0.6 seconds for the duration of years 1620–2013.

M. Khalid

Mariam Sultana

Faheem Zaidi

Delta <svg style="vertical-align:-0.0pt" height="11.6125" version="1.1" viewBox="0 0 11.45 11.6125" width="11.45" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.55)"><path id="x1D447" d="M649 676l-22 -187l-33 -2q3 56 -12 94q-8 20 -31.5 26.5t-86.5 6.5h-74l-90 -491q-4 -23 -6 -36.5t1 -25t7 -16.5t18 -9t27 -5t41 -3l-6 -28h-286l4 28q68 5 84 18.5t28 76.5l94 491h-55q-74 0 -100.5 -6t-41.5 -23q-24 -29 -54 -98l-32 1q32 98 53 188h22q7 -18 15 -22&#xA;t37 -4h417q23 0 33.5 5t25.5 21h23z" /></g></svg>: Polynomial Approximation of Time Period 1620&#x2013;2013

A statistical study on the properties of CMEs and flares associated with DH-type II bursts in the 23rd solar cycle during the period 1997–2008 is carried out. A sample of 229 events from our recent work is used for the present study (Vasanth and Umapathy, 2013). The collected events are divided into two groups as (i) solar cycle rise phase events and (ii) solar cycle decay phase events. The properties of CMEs in the two groups were compared and the results are presented. It is noted that there is no difference in the properties of type II burst like start frequency and end frequency between the solar cycle rise phase events and decay phase events. The mean CME speed of solar cycle decay phase events (1373 km s<sup>−1</sup>) is slightly higher than the solar cycle rise phase events (1058 km s<sup>−1</sup>). The mean CME acceleration of solar cycle decay phase events (−15.18 m s<sup>−2</sup>) is found to be higher than that of the solar cycle rise phase events (−1.32 m s<sup>−2</sup>). There exists good correlation between (i) CME speed and width and (ii) CME speed and acceleration for solar cycle decay phase events (<svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.27588pt;width:58.849998px;" id="M1" height="11.425" version="1.1" viewBox="0 0 58.849998 11.425" width="58.849998">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path id="x1D445" d="M627 18l-10 -26q-79 6 -116 27t-69 76q-41 71 -71 138q-13 29 -27.5 39t-42.5 10h-46l-27 -145q-13 -74 -2.5 -88.5t78.5 -20.5l-6 -28h-271l5 28q66 6 82.5 21.5t30.5 87.5l71 387q12 66 2 78.5t-77 19.5l8 28h233q102 0 147 -29q65 -43 65 -129q0 -69 -45.5 -117&#xA;t-115.5 -72q40 -86 66 -133q39 -68 65 -101q28 -37 73 -51zM491 483q0 67 -33.5 101t-91.5 34q-35 0 -51 -10q-13 -8 -20 -48l-45 -245h49q71 0 113 28q79 52 79 140z"></path></g><g transform="matrix(.017,-0,0,-.017,15.718,11.112)"><path id="x3D" d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z"></path></g><g transform="matrix(.017,-0,0,-.017,30.422,11.112)"><path id="x30" d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105&#xA;q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z"></path></g><g transform="matrix(.017,-0,0,-.017,38.582,11.112)"><path id="x2E" d="M113 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5t16 -40.5q0 -26 -16 -42t-41 -16z"></path></g><g transform="matrix(.017,-0,0,-.017,42.457,11.112)"><path id="x37" d="M447 623l8 -12l-283 -613l-74 -10l-7 11q174 283 297 551h-216q-48 0 -62.5 -12t-33.5 -63h-29q10 60 18 148h382z"></path></g><g transform="matrix(.017,-0,0,-.017,50.617,11.112)"><path id="x39" d="M244 635q90 0 143 -72t53 -177q0 -133 -65 -229.5t-171 -139.5q-79 -32 -140 -32l-5 30q109 18 185 91t101 186l-68 -36q-29 -16 -60 -16q-79 0 -129 51.5t-50 130.5q0 80 57 146.5t149 66.5zM228 602q-52 0 -78 -45.5t-26 -98.5q0 -69 36.5 -115.5t97.5 -46.5&#xA;q53 0 90 28q4 31 4 66q0 51 -9.5 95.5t-39 80.5t-75.5 36z"></path></g>

		
	
</svg>, <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.17555pt;width:68.824997px;" id="M2" height="11.375" version="1.1" viewBox="0 0 68.824997 11.375" width="68.824997">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><use xlink:href="#x1D445"></use></g><g transform="matrix(.017,-0,0,-.017,15.718,11.112)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,30.422,11.112)"><path id="x2212" d="M535 230h-483v50h483v-50z"></path></g><g transform="matrix(.017,-0,0,-.017,40.401,11.112)"><use xlink:href="#x30"></use></g><g transform="matrix(.017,-0,0,-.017,48.56,11.112)"><use xlink:href="#x2E"></use></g><g transform="matrix(.017,-0,0,-.017,52.436,11.112)"><path id="x38" d="M249 635q70 0 116 -43t46 -105q0 -46 -28 -80q-22 -25 -80 -64q62 -35 97 -75t35 -99q0 -81 -63 -131t-135 -50q-83 0 -137.5 45.5t-54.5 123.5q0 52 45 95q29 28 89 64q-109 62 -109 155q0 66 50.5 115t128.5 49zM238 603q-42 0 -67.5 -31t-25.5 -72q0 -50 32.5 -79.5&#xA;t98.5 -62.5q61 48 61 124q0 59 -29.5 90t-69.5 31zM248 20q46 0 76.5 33.5t30.5 89.5q0 50 -39 85.5t-110 71.5q-81 -54 -81 -137q0 -67 35.5 -105t87.5 -38z"></path></g><g transform="matrix(.017,-0,0,-.017,60.595,11.112)"><use xlink:href="#x30"></use></g>

		
	
</svg>) compared to solar cycle rise phase events (<svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.17555pt;width:58.849998px;" id="M3" height="11.375" version="1.1" viewBox="0 0 58.849998 11.375" width="58.849998">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><use xlink:href="#x1D445"></use></g><g transform="matrix(.017,-0,0,-.017,15.718,11.112)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,30.422,11.112)"><use xlink:href="#x30"></use></g><g transform="matrix(.017,-0,0,-.017,38.582,11.112)"><use xlink:href="#x2E"></use></g><g transform="matrix(.017,-0,0,-.017,42.457,11.112)"><path id="x36" d="M137 343l67 33q37 17 63 17q79 0 129.5 -53t50.5 -131q0 -92 -58 -156.5t-147 -64.5t-147 68t-58 182q0 63 17 119t43 95.5t61.5 72t69 52t67.5 31.5q62 22 128 33l6 -32q-56 -11 -108 -35q-149 -71 -184 -231zM227 337q-47 0 -95 -27q-6 -23 -6 -70q0 -93 36 -155.5&#xA;t96 -62.5q53 0 78 45.5t25 105.5q0 68 -35 116t-99 48z"></path></g><g transform="matrix(.017,-0,0,-.017,50.617,11.112)"><use xlink:href="#x30"></use></g>

		
	
</svg>, <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.17555pt;width:68.824997px;" id="M4" height="11.375" version="1.1" viewBox="0 0 68.824997 11.375" width="68.824997">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><use xlink:href="#x1D445"></use></g><g transform="matrix(.017,-0,0,-.017,15.718,11.112)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,30.422,11.112)"><use xlink:href="#x2212"></use></g><g transform="matrix(.017,-0,0,-.017,40.401,11.112)"><use xlink:href="#x30"></use></g><g transform="matrix(.017,-0,0,-.017,48.56,11.112)"><use xlink:href="#x2E"></use></g><g transform="matrix(.017,-0,0,-.017,52.436,11.112)"><path id="x35" d="M153 550l-26 -186q79 31 111 31q90 0 141.5 -51t51.5 -119q0 -93 -89 -166q-85 -69 -173 -71q-32 0 -61.5 11.5t-41.5 23.5q-18 17 -17 34q2 16 22 33q14 9 26 -1q61 -50 124 -50q60 0 93 43.5t33 104.5q0 69 -41.5 110t-121.5 41q-53 0 -102 -20l38 305h286l6 -8&#xA;l-26 -65h-233z"></path></g><g transform="matrix(.017,-0,0,-.017,60.595,11.112)"><use xlink:href="#x37"></use></g>

		
	
</svg>). These results indicate that the type II bursts parameters do not depend upon the time of appearance in the solar cycle.

V. Vasanth

S. Umapathy

Studies on Longer Wavelength Type II Radio Bursts Associated with Flares and CMEs during the Rise and Decay Phase of 23rd Solar Cycle

Possible modification in the velocity distribution in the nonresonant reaction rates leads to an extended reaction rate probability integral. The closed form representation for these thermonuclear functions is used to obtain the stellar luminosity and neutrino emission rates. The composite parameter <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.1881pt;width:13.675px;" id="M1" height="12.0625" version="1.1" viewBox="0 0 13.675 12.0625" width="13.675">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,11.738)"><path id="x1D49E" d="M449 645l-12 -19q-55 31 -136 31q-52 0 -103 -17t-85.5 -54.5t-34.5 -84.5q0 -60 41.5 -96.5t109.5 -43.5q81 125 216 216q137 92 240 92q46 0 71 -19.5t25 -55.5q0 -60 -67 -123q-66 -63 -177 -105q-109 -42 -225 -42q-69 -100 -69 -199q0 -49 31.5 -79.5t85.5 -30.5&#xA;q79 0 141 50q61 49 61 108q0 35 -20 54.5t-51 19.5q-53 0 -103 -53q-47 -52 -55 -131l-22 2q0 91 58 158t139 67q55 0 86.5 -26.5t31.5 -76.5q0 -81 -96 -148q-78 -54 -174 -54q-86 0 -141 46q-56 47 -56 127q0 81 48 171q-72 12 -121 55t-49 115q0 75 71 131q72 57 185 57&#xA;q91 0 156 -42zM331 355l1 -1q122 0 244 62q73 37 118.5 85.5t45.5 90.5q0 40 -50 40q-73 0 -174 -79q-102 -80 -185 -198z"></path></g>

		
	
</svg> that determines the standard nuclear reaction rate through the Maxwell-Boltzmann energy distribution is extended to <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.1881pt;width:21.275px;" id="M2" height="14" version="1.1" viewBox="0 0 21.275 14" width="21.275">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,13.688)"><use xlink:href="#x1D49E"></use></g>

			<g transform="matrix(.012,-0,0,-.012,13.612,5.525)"><path id="x2217" d="M471 153q-22 -15 -61 -13q-25 31 -45.5 49.5t-56.5 41.5q4 -71 28 -134q-17 -33 -42 -46q-24 12 -42 46q24 63 28 134q-36 -23 -56.5 -41.5t-45.5 -49.5q-36 -2 -61 13q0 28 19 59q65 10 130 43q-65 33 -130 43q-19 31 -19 59q22 15 61 13q25 -31 45.5 -49.5t56.5 -41.5&#xA;q-4 71 -28 134q17 33 42 46q24 -12 42 -46q-24 -63 -28 -134q36 23 56.5 41.5t45.5 49.5q36 2 61 -13q0 -28 -19 -59q-65 -10 -130 -43q65 -33 130 -43q19 -31 19 -59z"></path></g>

		
	
</svg> by the extended reaction rates through a more general distribution than the Maxwell-Boltzmann distribution. The new distribution is obtained by the pathway model introduced by Mathai (2005). Simple analytic models considered by various authors are utilized for evaluating stellar luminosity and neutrino emission rates and are obtained in generalized special functions such as Meijer's <i>G</i>-function and Fox's <i>H</i>-function. The standard and extended nonresonant thermonuclear functions are compared by plotting them. Behaviour of the new energy distribution, which is more general than the Maxwell-Boltzmann, is also studied.

Hans J. Haubold

Dilip Kumar

Analytical Results Connecting Stellar Structure Parameters and Extended Reaction Rates

When the Hall effect is included in the magnetohydrodynamics equations (Hall-MHD model) the wave propagation modes become coupled, but for propagation parallel to the ambient magnetic field the Alfv&#xe9;n mode decouples from the magnetosonic ones, resulting in circularly polarized waves that are described by the derivative nonlinear Schr&#xf6;dinger (DNLS) equation. In this paper, the DNLS equation is numerically solved using spectral methods for the spatial derivatives and a fourth order Runge-Kutta scheme for time integration. Firstly, the nondiffusive DNLS equation is considered to test the validity of the method by verifying the analytical condition of modulational stability. Later, diffusive and excitatory effects are incorporated to compare the numerical results with those obtained by a three-wave truncation model. The results show that different types of attractors can exist depending on the diffusion level: for relatively large damping, there are fixed points for which the truncation model is a good approximation; for low damping, chaotic solutions appear and the three-wave truncation model fails due to the emergence of new nonnegligible modes.

Gustavo Krause

Sergio Elaskar

Andrea Costa

Chaos and Intermittency in the DNLS Equation Describing the Parallel Alfv&#xe9;n Wave Propagation

The invariant imbedding technique is applied to the problems of radiation transfer in a plane-parallel inhomogeneous atmosphere. All the parameters which describe the elementary event of scattering and the distribution of the energy sources are allowed to vary with depth. Mathematically, the considered standard problems of the theory are reduced to initial-value problems which are better adapted to capabilities of the modern high speed computers. The reflectance of an atmosphere is shown to play a prominent role in describing the diffusion process since all the other characteristics of the radiation field are expressed through it. Three transfer problems frequently encountered in astrophysical applications are discussed: the radiation diffusion in the source-free medium, in a medium with arbitrarily distributed energy sources, as well as the problem of finding the statistical mean quantities, characteristics of the multiple scattering in the atmosphere.

Arthur G. Nikoghossian

Invariant Imbedding and the Radiation Transfer in a Plane-Parallel Inhomogeneous Atmosphere

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Journal of Astrophysics