Equilibrium Structures of Differentially Rotating and Tidally Distorted White Dwarf Models of Stars

In this paper we present a method for computing the equilibrium structures and various physical parameters of a primary component of the binary system assuming that the primary is more massive than the secondary and is rotating differentially according to the law of the w² = b₀ + b₁ × s² + b₂ × s⁴, w being the angular velocity of rotation of a fluid element distant s from the axis of rotation and b₀, b₁, b₂ suitably chosen numerical constants. This method utilizes the averaging approach of Kippenhahn and Thomas (1997) and the concept of Roche equipotentials in a manner earlier used by Mohan et al. (1997) to incorporate the effects of rotation and tidal distortions on the equilibrium structures of certain rotationally and tidally distorted stellar models. The use of the method has been illustrated by applying it to obtain the structures and some observable parameters of certain differentially rotating and tidally distorted binary systems whose primary component is assumed to be a white dwarf star.     

Mariner 10 observations of hydrogen Lyman alpha emission from the venus exosphere: Evidence of complex structure

The Ultraviolet Spectrometer Experiment on the MARINER 10 spacecraft measured the hydrogen Lyman α emmission resonantly scattered in the Venus exosphere at several viewing aspects during the encounter period. Venus encounter occurred at 17:01 GMT on 5 February 1974. Exospheric emissions above the planet's limb were measured and were analyzed with a spherically symmetric, single scattering, two-temperature model. On the sunlit hemisphere the emission profile was represented by an exospheric hydrogen atmosphere with T_c = 275±50 K and n_c = 1.5 × 10⁵ cm^?3 and a non-thermal contribution represented by T_H = 1250±100 K with n_H = 500±100 cm^?3. The observations of the dark limb showed that the spherically symmetric model used for the sunlit hemisphere was inappropriate for the analysis of the antisolar hemisphere. The density of the non-thermal component had increased at low altitudes, < 12,000 km, and decreased at high altitudes, > 20,000 km, by comparison. We conclude that the non-thermal source is on the sunward side of the planet. Analysis of the dark limb crossing suggests that the exospheric temperature on the dark side is <125 K if the exospheric density remains constant over the planet; upper limits are discussed. An additional source of Lyman α emission, 70 ± 15 R, was detected on the dark side of the planet and is believed to be a planetary albedo in contrast to multiple scattering from the sunlit side. Our analysis of the MARINER 10 data is consistent when applied to the MARINER 5 data.     

The effect of solar pressure on the motion and stability of interconnected satellites in orbit

The paper deals with the effect of solar pressure on the motion and stability of two satellites connected by an inextensible string in a central gravitational field of force. A system of nonlinear, nonhomogeneous, and non-autonomous equations under the rotating frame of reference in Nechvíle's coordinate system have been obtained. The general solution of the above system of equations is beyond our reach. The particular solutions have been obtained.The particular solution in which the system lies, wholly along the radius vector joining the attracting centre and the centre of mass of the system under the central attracting force along was found to be stable (Singh, 1973). Naturally we got interested in examining the effect of solar radiation pressure on the stability of this particular solution.     

Variations in the Solar Coronal Rotation with Altitude – Revisited

Here we report an in-depth reanalysis of an article by Vats et al. (Astrophys. J. 548, L87, 2001) that was based on measurements of differential rotation with altitude as a function of observing frequencies (as lower and higher frequencies indicate higher and lower heights, respectively) in the solar corona. The radial differential rotation of the solar corona is estimated from daily measurements of the disc-integrated solar radio flux at 11 frequencies: 275, 405, 670, 810, 925, 1080, 1215, 1350, 1620, 1755, and 2800 MHz. We use the same data as were used in Vats et al. (2001), but instead of the twelfth maxima of autocorrelograms used there, we use the first secondary maximum to derive the synodic rotation period. We estimate synodic rotation by Gaussian fit of the first secondary maximum. Vats et al. (2001) reported that the sidereal rotation period increases with increasing frequency. The variation found by them was from 23.6 to 24.15 days in this frequency range, with a difference of only 0.55 days. The present study finds that the sidereal rotation period increases with decreasing frequency. The variation range is from 24.4 to 22.5 days, and the difference is about three times larger (1.9 days). However, both studies give a similar rotation period at 925 MHz. In Vats et al. (2001) the Pearson’s factor with trend line was 0.86, whereas present analysis obtained a \({\sim}\,0.97\) Pearson’s factor with the trend line. Our study shows that the solar corona rotates more slowly at higher altitudes, which contradicts the findings reported in Vats et al. (2001).     

Fisher Matrix-based Predictions for Measuring the <Emphasis Type="Italic">z</Emphasis> = 3.35 Binned 21-cm Power Spectrum using the Ooty Wide Field Array (OWFA)

We use the Fisher matrix formalism to predict the prospects of measuring the redshifted 21-cm power spectrum in different k-bins using observations with the upcoming Ooty Wide Field Array (OWFA) which will operate at 326.5 MHz. This corresponds to neutral hydrogen (HI) at z = 3.35, and a measurement of the 21-cm power spectrum provides a unique method to probe the large-scale structures at this redshift. Our analysis indicates that a 5σ detection of the binned power spectrum is possible in the k range 0.05 ≤ k ≤ 0.3 Mpc^?1 with 1000 hours of observation. We find that the signal- to-noise ratio (SNR) peaks in the k range 0.1?0.2 Mpc^?1 where a 10σ detection is possible with 2000 hours of observations. Our analysis also indicates that it is not very advantageous to observe beyond 1000 h in a single field-of-view as the SNR increases rather slowly beyond this in many of the small k-bins. The entire analysis reported here assumes that the foregrounds have been completely removed.     

Planning and Scheduling of Payloads of AstroSat During Initial and Normal Phase Observations

On 28th September 2015, India launched its first astronomical space observatory AstroSat, successfully. AstroSat carried five astronomy payloads, namely, (i) Cadmium Zinc Telluride Imager (CZTI), (ii) Large Area X-ray Proportional Counter (LAXPC), (iii) Soft X-ray Telescope (SXT), (iv) Ultra Violet Imaging Telescope (UVIT) and (v) Scanning Sky Monitor (SSM) and therefore, has the capability to observe celestial objects in multi-wavelength. Four of the payloads are co-aligned along the positive roll axis of the spacecraft and the remaining one is placed along the positive yaw axis direction. All the payloads are sensitive to bright objects and specifically, require avoiding bright Sun within a safe zone of their bore axes in orbit. Further, there are other operational constraints both from spacecraft side and payloads side which are to be strictly enforced during operations. Even on-orbit spacecraft manoeuvres are constrained to about two of the axes in order to avoid bright Sun within this safe zone and a special constrained manoeuvre is exercised during manoeuvres. The planning and scheduling of the payloads during the Performance Verification (PV) phase was carried out in semi-autonomous/manual mode and a complete automation is exercised for normal phase/Guaranteed Time Observation (GuTO) operations. The process is found to be labour intensive and several operational software tools, encompassing spacecraft sub-systems, on-orbit, domain and environmental constraints, were built-in and interacted with the scheduling tool for appropriate decision-making and science scheduling. The procedural details of the complex scheduling of a multi-wavelength astronomy space observatory and their working in PV phase and in normal/GuTO phases are presented in this paper.     

Effect of solar pressure on the motion and stability of the system of two inter-connected satellites in an elliptical orbit

The effect of solar pressure on the two-dimensional motion of two cable-connected satellites in the Earth's central gravitational field of force for the elliptical orbit of the centre-of-mass of the system has been analysed. The equations of motion obtianed are nonlinear and non-autonomous.It is concluded with the aid of non-resonant solution that the system experiences resonance main as well as parametric. If the eccentricity is small, the system will always oscillate about the position of equilibrium with tight string like dumb-bell satellite with changing phase and constant amplitude.     

Revisiting Noether gauge symmetry for F(R) theory of gravity

Noether gauge symmetry for F(R) theory of gravity has been explored recently. The fallacy is that, even after setting gauge to vanish, the form of F(R)∝R ⁿ (where n≠1 is arbitrary) obtained in the process, has been claimed to be an outcome of gauge Noether symmetry. On the contrary, earlier works proved that any nonlinear form other than $F(R) \propto R^{\frac{3}{2}}$ is obscure. Here, we show that, setting gauge term zero, Noether equations are satisfied only for n=2, which again does not satisfy the field equations. Thus, as noticed earlier, the only form that Noether symmetry admits is $F(R) \propto R^{\frac{3}{2}}$ . Noether symmetry with non-zero gauge has also been studied explicitly here, to show that it does not produce anything new.     

Study of the Diurnal Variation of Cosmic Rays during Different Phases of Solar Activity

The pressure-corrected hourly counting rate data of ground-based super neutron monitor stations, situated in different latitudes, have been employed to study the characteristics of the long-term variation of cosmic-ray diurnal anisotropy for a long (44-year) period (1965?–?2008). Some of these super neutron monitors are situated in low latitudes with high cutoff rigidity. Annual averages of the diurnal amplitudes and phases have been obtained for each station. It is found that the amplitude of the diurnal anisotropy varies with a period of one solar activity cycle (11 years), whereas the diurnal phase varies with a period of 22 years (one solar magnetic cycle). The average diurnal amplitudes and phases have also been calculated by grouping the days on the basis of ascending and descending periods of each solar cycle (Cycles 20, 21, 22, and 23). Systematic and significant differences are observed in the characteristics of the diurnal variation between the descending periods of the odd and even solar cycles. The overall vector averages of the descending periods of the even solar cycles (20 and 22) show significantly smaller diurnal amplitudes compared to the vector averages of the descending periods of the odd solar cycles (21 and 23). In contrast, we find a large diurnal phase shift to earlier hours only during the descending periods of even solar cycles (20 and 22), as compared to almost no shift in the diurnal phase during the descending periods of odd solar cycles. Further, the overall vector average diurnal amplitudes of the ascending period of odd and even solar cycles remain invariant from one ascending period to the other, or even between the even and odd solar cycles. However, we do find a significant diurnal phase shift to earlier hours during the ascending periods of odd solar cycles (21 and 23) in comparison to the diurnal phase in the ascending periods of even solar cycles (20 and 22).     

Uncertainty propagation in orbital mechanics via tensor decomposition

Uncertainty forecasting in orbital mechanics is an essential but difficult task, primarily because the underlying Fokker–Planck equation (FPE) is defined on a relatively high dimensional (6-D) state–space and is driven by the nonlinear perturbed Keplerian dynamics. In addition, an enormously large solution domain is required for numerical solution of this FPE (e.g. encompassing the entire orbit in the \(x-y-z\) subspace), of which the state probability density function (pdf) occupies a tiny fraction at any given time. This coupling of large size, high dimensionality and nonlinearity makes for a formidable computational task, and has caused the FPE for orbital uncertainty propagation to remain an unsolved problem. To the best of the authors’ knowledge, this paper presents the first successful direct solution of the FPE for perturbed Keplerian mechanics. To tackle the dimensionality issue, the time-varying state pdf is approximated in the CANDECOMP/PARAFAC decomposition tensor form where all the six spatial dimensions as well as the time dimension are separated from one other. The pdf approximation for all times is obtained simultaneously via the alternating least squares algorithm. Chebyshev spectral differentiation is employed for discretization on account of its spectral (“super-fast”) convergence rate. To facilitate the tensor decomposition and control the solution domain size, system dynamics is expressed using spherical coordinates in a noninertial reference frame. Numerical results obtained on a regular personal computer are compared with Monte Carlo simulations.