Radio variability of the blazar S5 0716+714: a ∼6.1 year quasi-periodicity

We report a ～6.1 yr quasi-periodicity for the blazar S5 0716+714 using the radio light curves at 4.8, 8 and 14.5 GHz observed by the University of Michigan Radio Astronomical Observatory (UMRAO) from 1981 to 2012, by means of the Jurkevich, discrete correlation function (DCF) and power spectral analysis techniques. There are a general correlation among light curves at different frequencies and a time lag of \(170\pm 10\) days between 4.8 and 14.5 GHz light curves can be confirmed. We also estimate the orbit parameters assuming a binary black hole system, and the magnetic field strength under the jet comoving frame.     

Fine-resolution analysis of exoplanetary distributions by wavelets: hints of an overshooting iceline accumulation

We investigate 1D exoplanetary distributions using a novel analysis algorithm based on the continuous wavelet transform. The analysis pipeline includes an estimation of the wavelet transform of the probability density function (p.d.f.) without pre-binning, use of optimized wavelets, a rigorous significance testing of the patterns revealed in the p.d.f., and an optimized minimum-noise reconstruction of the p.d.f. via matching pursuit iterations.In the distribution of orbital periods, \(P\), our analysis revealed a narrow subfamily of exoplanets within the broad family of “warm Jupiters”, or massive giants with \(P\gtrsim 300~\mbox{d}\), which are often deemed to be related with the iceline accumulation in a protoplanetary disk. We detected a p.d.f. pattern that represents an upturn followed by an overshooting peak spanning \(P\sim 300\mbox{--}600~\mbox{d}\), right beyond the “period valley”. It is separated from the other planets by p.d.f. concavities from both sides. It has at least 2-sigma significance.In the distribution of planet radii, \(R\), and using the California Kepler Survey sample properly cleaned, we confirm the hints of a bimodality with two peaks about \(R=1.3R_{\oplus }\) and \(R=2.4R_{ \oplus }\), and the “evaporation valley” between them. However, we obtain just a modest significance for this pattern, 2-sigma only at the best. Besides, our follow-up application of the Hartigan and Hartigan dip test for unimodality returns 3 per cent false alarm probability (merely 2.2-sigma significance), contrary to 0.14 per cent (or 3.2-sigma), as claimed by Fulton et al. (2017).     

A satellite relative motion model including $$J_2$$ and $$J_3$$J3 via Vinti’s intermediary

Vinti’s potential is revisited for analytical propagation of the main satellite problem, this time in the context of relative motion. A particular version of Vinti’s spheroidal method is chosen that is valid for arbitrary elliptical orbits, encapsulating \(J_2\), \(J_3\), and generally a partial \(J_4\) in an orbit propagation theory without recourse to perturbation methods. As a child of Vinti’s solution, the proposed relative motion model inherits these properties. Furthermore, the problem is solved in oblate spheroidal elements, leading to large regions of validity for the linearization approximation. After offering several enhancements to Vinti’s solution, including boosts in accuracy and removal of some singularities, the proposed model is derived and subsequently reformulated so that Vinti’s solution is piecewise differentiable. While the model is valid for the critical inclination and nonsingular in the element space, singularities remain in the linear transformation from Earth-centered inertial coordinates to spheroidal elements when the eccentricity is zero or for nearly equatorial orbits. The new state transition matrix is evaluated against numerical solutions including the \(J_2\) through \(J_5\) terms for a wide range of chief orbits and separation distances. The solution is also compared with side-by-side simulations of the original Gim–Alfriend state transition matrix, which considers the \(J_2\) perturbation. Code for computing the resulting state transition matrix and associated reference frame and coordinate transformations is provided online as supplementary material.     

On the energy integral for first post-Newtonian approximation

The post-Newtonian approximation for general relativity is widely adopted by the geodesy and astronomy communities. It has been successfully exploited for the inclusion of relativistic effects in practically all geodetic applications and techniques such as satellite/lunar laser ranging and very long baseline interferometry. Presently, the levels of accuracy required in geodetic techniques require that reference frames, planetary and satellite orbits and signal propagation be treated within the post-Newtonian regime. For arbitrary scalar W and vector gravitational potentials \(W^j (j=1,2,3)\), we present a novel derivation of the energy associated with a test particle in the post-Newtonian regime. The integral so obtained appears not to have been given previously in the literature and is deduced through algebraic manipulation on seeking a Jacobi-like integral associated with the standard post-Newtonian equations of motion. The new integral is independently verified through a variational formulation using the post-Newtonian metric components and is subsequently verified by numerical integration of the post-Newtonian equations of motion.     

Capture into first-order resonances and long-term stability of pairs of equal-mass planets

Massive planets form within the lifetime of protoplanetary disks, and therefore, they are subject to orbital migration due to planet–disk interactions. When the first planet reaches the inner edge of the disk, its migration stops and consequently the second planet ends up locked in resonance with the first one. We detail how the resonant trapping works comparing semi-analytical formulae and numerical simulations. We restrict to the case of two equal-mass coplanar planets trapped in first-order resonances, but the method can be easily generalized. We first describe the family of resonant stable equilibrium points (zero-amplitude libration orbits) using series expansions up to different orders in eccentricity as well as a non-expanded Hamiltonian. Then we show that during convergent migration the planets evolve along these families of equilibrium points. Eccentricity damping from the disk leads to a final equilibrium configuration that we predict precisely analytically. The fact that observed multi-exoplanetary systems are rarely seen in resonances suggests that in most cases the resonant configurations achieved by migration become unstable after the removal of the protoplanetary disk. Here we probe the stability of the resonances as a function of planetary mass. For this purpose, we fictitiously increase the masses of resonant planets, adiabatically maintaining the low-amplitude libration regime until instability occurs. We discuss two hypotheses for the instability, that of a low-order secondary resonance of the libration frequency with a fast synodic frequency of the system, and that of minimal approach distance between planets. We show that secondary resonances do not seem to impact resonant systems at low amplitude of libration. Resonant systems are more stable than non-resonant ones for a given minimal distance at close encounters, but we show that the latter nevertheless play the decisive role in the destabilization of resonant pairs. We show evidence that as the planetary mass increases and the minimal distance between planets gets smaller in terms of mutual Hill radius, the region of stability around the resonance center shrinks, until the equilibrium point itself becomes unstable.     

Development of a Lunar Scintillometer as part of the national large optical telescope site survey

Ground layer turbulence is a very important site characterization parameter used to assess the quality of an astronomical site. The Lunar Scintillometer is a simple and effective site-testing device for measuring the ground layer turbulence. It consists of a linear array of photodiodes which are sensitive to the slight variations in the moon’s brightness due to scintillation by the lower layers of the Earth’s atmosphere. The covariance of intensity values between the non-redundant photodiode baselines can be used to measure the turbulence profile from the ground up to a height determined by the furthest pair of detectors. The six channel lunar scintillometer that has been developed at the Indian Institute of Astrophysics is based closely on an instrument built by the team led by Andrei Tokovinin of Cerro Tololo Inter-American Observatory (CTIO), Chile (Tokovinin et al., Mon. Not. R. Astron. Soc. 404(3), 1186–1196 2010). We have fabricated the instrument based on the existing electronic design, and have worked on the noise analysis, an EMI (Electromagnetic Induction) resistant PCB design and the software pipeline for analyzing the data from the same. The results from the instrument’s multi-year campaign at Mount Saraswati, Hanle is also presented.     

On the use of logistic regression for stellar classification

We are totally immersed in the Big Data era and reliable algorithms and methods for data classification are instrumental for astronomical research. Random Forest and Support Vector Machines algorithms have become popular over the last few years and they are widely used for different stellar classification problems. In this article, we explore an alternative supervised classification method scarcely exploited in astronomy, Logistic Regression, that has been applied successfully in other scientific areas, particularly biostatistics. We have applied this method in order to derive membership probabilities for potential T Tauri star candidates from ultraviolet-infrared colour-colour diagrams.     

The First Solar Seeing Profile Measurement with Two Apertures and Multiple Guide Regions

The sky brightness is a critical parameter for estimating the coronal observation conditions for a solar observatory. As part of a site-survey project in Western China, we measured the sky brightness continuously at the Lijiang Observatory in Yunnan province in 2011. A sky brightness monitor (SBM) was adopted to measure the sky brightness in a region extending from 4.5 to 7.0 apparent solar radii based on the experience of the Daniel K. Inouye Solar Telescope (DKIST) site survey. Every month, the data were collected manually for at least one week. We collected statistics of the sky brightness at four bandpasses located at 450, 530, 890, and 940 nm. The results indicate that aerosol scattering is of great importance for the diurnal variation of the sky brightness. For most of the year, the sky brightness remains under 20 millionths per airmass before local Noon. On average, the sky brightness is less than 20 millionths, which accounts for 40.41% of the total observing time on a clear day. The best observation time is from 9:00 to 13:00 (Beijing time). The Lijiang Observatory is therefore suitable for coronagraphs investigating the structures and dynamics of the corona.     

Temporal and Periodic Variations of Sunspot Counts in Flaring and Non-Flaring Active Regions

We analyzed temporal and periodic variations of sunspot counts (SSCs) in flaring (C-, M-, or X-class flares), and non-flaring active regions (ARs) for nearly three solar cycles (1986 through 2016). Our main findings are as follows: i) temporal variations of monthly means of the daily total SSCs in flaring and non-flaring ARs behave differently during a solar cycle and the behavior varies from one cycle to another; during Solar Cycle 23 temporal SSC profiles of non-flaring ARs are wider than those of flaring ARs, while they are almost the same during Solar Cycle 22 and the current Cycle 24. The SSC profiles show a multi-peak structure and the second peak of flaring ARs dominates the current Cycle 24, while the difference between peaks is less pronounced during Solar Cycles 22 and 23. The first and second SSC peaks of non-flaring ARs have comparable magnitude in the current solar cycle, while the first peak is nearly absent in the case of the flaring ARs of the same cycle. ii) Periodic variations observed in the SSCs profiles of flaring and non-flaring ARs derived from the multi-taper method (MTM) spectrum and wavelet scalograms are quite different as well, and they vary from one solar cycle to another. The largest detected period in flaring ARs is \(113\pm 1.6~\mbox{days}\) while we detected much longer periodicities (\(327\pm 13\), \(312 \pm 11\), and \(256\pm 8~\mbox{days}\)) in the non-flaring AR profiles. No meaningful periodicities were detected in the MTM spectrum of flaring ARs exceeding \(55\pm 0.7~\mbox{days}\) during Solar Cycles 22 and 24, while a \(113\pm 1.3~\mbox{days}\) period was detected in flaring ARs of Solar Cycle 23. For the non-flaring ARs the largest detected period was only \(31\pm 0.2~\mbox{days}\) for Cycle 22 and \(72\pm 1.3~\mbox{days}\) for the current Cycle 24, while the largest measured period was \(327\pm 13~\mbox{days}\) during Solar Cycle 23.