Article ID 0044 December 2019
Reconstruction of dynamical dark energy potentials: Quintessence, tachyon and interacting models
MANVENDRA PRATAP RAJVANSHI J. S. BAGLA
Dynamical models for dark energy are an alternative to the cosmological constant. It is important to investigate properties of perturbations in these models and go beyond the smooth FRLW cosmology. This allows us to distinguish different dark energy models with the same expansion history. For this, one oftenneeds the potential for a particular expansion history. We study how such potentials can be reconstructed by obtaining closed formulae for potential or reducing the problem to quadrature. We consider three classes of models here: tachyons, quintessence and interacting dark energy.We present results for the constant $\omega$ and the CPL parametrization. The method given here can be generalized to any arbitrary form of $\omega(z)$.
Article ID 0045 December 2019
Analysis of Manchuria astronomical almanacs of 1933–1945
G.-E. CHOI K.-W. LEE B.-H. MIHN Y. S. AHN
We investigate the astronomical almanacs of the Manchukuo state, which lasted for 14 years, from 1932 to 1945.We examine their contents and analyze the accuracy of the time data by using the almanacs for theyears from 1933 to 1945.We find that the calendar of the Qing dynasty in China, Shixianshu, provided the name of the almanac. In addition, the reference location of the time data was Xinjing (now known as Changchun) and the standard meridian was changed from 120$^{\circ}$E to 135$^{\circ}$E, starting with the almanac of 1937. We also find that sunrise and sunset times were recorded only on days of the 24 solar terms, for several cities, whereas moonrise and moonset times were recorded daily, but only for Xinjing. Moreover, only days were recorded (i.e., thehours are not recorded) in the almanacs of 1933 and 1934 for the 24 solar terms. To estimate the accuracy, we first extract 19 kinds of time data and classify them into four groups: rising and setting, solar term, phases of the Moon and eclipses. Then, we determine the mean absolute difference (MAD) of the time data between the almanacs and modern calculations performed using the DE405 ephemeris. Even though most of the time data are recorded in minutes, we compute the data in seconds. We find that the MAD values are 0.44, 0.42, 0.27and 0.44 min for the time data of the four respective groups. We believe that our findings will contribute to the study of the astronomical almanacs of Korea, Japan and Taiwan, which were published during this period.
Article ID 0046 December 2019
Neutral particle trajectory in the Kerr field
In this paper, the neutral particle trajectory around a rotating black hole in the four-dimensional Kerr space–time is studied. The equation of motion is derived by using the Kerr metric within the slowly rotating and weak-field limit. The stability conditions of the orbital motion of the neutral particle are deduced.For small amplitude of motion, the approximate solutions of the resulting differential equations are obtained by the perturbation method of Lindstedt and Poincar\'{e}. These are then expressed as power series for some smallperturbation parameters. The angular frequencies are also found in the corresponding order of the perturbation. By using angular frequencies, an expression of the perihelion advance is derived. To find the orbital equationsimilar to Newtonian orbit, the coordinate system is transformed into isotropic coordinates. The Newtonian orbital equation is derived and hence the eccentricity of the orbit is obtained. The resulting expression of circularmotion shows the relationship between energy and angular momentum of a spinning particle in the Kerr field.
Article ID 0047 December 2019
Cylindrical ionizing shock waves in a self-gravitating gas with magnetic field: Power series method
The propagation of cylindrical ionizing shock waves in a self-gravitating ideal gas with axial magnetic field is investigated. The density and magnetic pressure are assumed to be varying according to power law with distance in the undisturbed medium. Approximate analytical solutions are obtained by expanding the flow variables in power series. The zeroth order and first order approximate solutions are discussed. Solutions for zeroth order approximation are constructed in analytical form. Distributions of hydrodynamical quantities for zeroth order approximation are discussed. Also, the effect of various flow parameters, namely shock Cowling number, adiabatic exponent, gravitational parameter and ambient density variation exponent are studied on the flow variables.
Article ID 0048 December 2019
$\bar{A}$pa and Ap$\bar{a}$mvatsa – enigmatic stars catalogued in $S\bar{u}ryasiddh\bar{a}nta$
B. S. SHYLAJA R. VENKETESWARA PAI
Indian $siddh\bar{a}ntic$ texts are well known for their indigenous approach to solutions of problems in astronomy which also speaks of their expertise in mathematics. The text $S\bar{u}ryasiddh\bar{a}nta$ is considered as an authority and we come across a number of texts as commentaries on this text. They range from 8th Century CE to 19th century CE. The study of the stars that have been listed in the text appears relatively easy for the 27 stars of the zodiac. However, there are other stars for which optical identifications are not easy. Here we present possible identifications for two stars called $\bar{A}pa$ and $Ap\bar{a}mvatsa$, in the constellation of Virgo. We use the NASA Skyview Survey and other catalogues to see if these two correspond to variablestars.
Article ID 0049 December 2019
Day time whistlers observed at low latitude Varanasi ($L = 1.078$)
S. B. SINGH S. S. RAO A. K. SINGH
We present results of the first time observations of whistlers during day time (sunrise) on 4th January 2017 at 01 UT(UT$+$5.30 $=$ IST) at Indian low latitude ground station Varanasi (geomag. lat. 14$^{\prime}$55$^{\prime}$ N, geomag. long. 153$^{\prime}$54$^{\prime}$ E, L.1.078). The main goal of analysis is to study the propagation characteristic of the observed whistlers during the day time (sunrise). These whistlers were observed during the quiet geomagnetic conditions (Dst-index $=$ $–$8 nT). The dispersions of the observed whistlers are found between 11.16 and 14.78 s$^{1/2}$, which shows that the observed whistlers have propagated in the ducted mode and the whole propagation path of whistlers lies in the ionosphere. Their columnar ionospheric electron contents lie between 23.57 TECU and 39.44 TECU. The ionospheric parameters derived from whistler data at Varanasi compare well with othermeasurements made by other techniques.
Article ID 0050 December 2019
The propagation of cylindrical shock wave in rotational axisymmetric perfect gas under isothermal flow condition with azimuthal magnetic field is investigated. Distributions of gas dynamical quantities are discussed. The density, magnetic pressure, azimuthal fluid velocity and axial fluid velocity are assumed to bevarying according to power law with distance from the axis of symmetry in the undisturbed medium. Approximate analytical solutions are obtained by expanding flow variables in power series. Zeroth-order and first-order approximations are discussed with the aid of power series method. Solutions for zeroth-order approximation are constructed in approximate analytical form. The effect of flow parameters namely: shock Cowling number $C_0$, ambient density variation index $q$ and adiabatic exponent $\gamma$ are studied on the flow variables. Consideration of magnetic pressure increases the total energy of disturbance of zeroth order while with increase in ambient density variation index or adiabatic exponent, the total energy of disturbance decreases.
Volume 41, 2020
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