On the co-orbital motion in the planar restricted three-body problem: the quasi-satellite motion revisited

In the framework of the planar and circular restricted three-body problem, we consider an asteroid that orbits the Sun in quasi-satellite motion with a planet. A quasi-satellite trajectory is a heliocentric orbit in co-orbital resonance with the planet, characterized by a nonzero eccentricity and a resonant angle that librates around zero. Likewise, in the rotating frame with the planet, it describes the same trajectory as the one of a retrograde satellite even though the planet acts as a perturbator. In the last few years, the discoveries of asteroids in this type of motion made the term “quasi-satellite” more and more present in the literature. However, some authors rather use the term “retrograde satellite” when referring to this kind of motion in the studies of the restricted problem in the rotating frame. In this paper, we intend to clarify the terminology to use, in order to bridge the gap between the perturbative co-orbital point of view and the more general approach in the rotating frame. Through a numerical exploration of the co-orbital phase space, we describe the quasi-satellite domain and highlight that it is not reachable by low eccentricities by averaging process. We will show that the quasi-satellite domain is effectively included in the domain of the retrograde satellites and neatly defined in terms of frequencies. Eventually, we highlight a remarkable high eccentric quasi-satellite orbit corresponding to a frozen ellipse in the heliocentric frame. We extend this result to the eccentric case (planet on an eccentric motion) and show that two families of frozen ellipses originate from this remarkable orbit.     

Tides in a body librating about a spin–orbit resonance: generalisation of the Darwin–Kaula theory

The Darwin-Kaula theory of bodily tides is intended for celestial bodies rotating without libration. We demonstrate that this theory, in its customary form, is inapplicable to a librating body. Specifically, in the presence of libration in longitude, the actual spectrum of Fourier tidal modes differs from the conventional spectrum rendered by the Darwin–Kaula theory for a nonlibrating celestial object. This necessitates derivation of formulae for the tidal torque and the tidal heating rate, that are applicable under libration. We derive the tidal spectrum for longitudinal forced libration with one and two main frequencies, generalisation to more main frequencies being straightforward. (By main frequencies we understand those emerging due to the triaxiality of the librating body.) Separately, we consider a case of free libration at one frequency (once again, generalisation to more frequencies being straightforward). We also calculate the tidal torque. This torque provides correction to the triaxiality-caused physical libration. Our theory is not self-consistent: we assume that the tidal torque is much smaller than the permanent-triaxiality-caused torque, so the additional libration due to tides is much weaker than the main libration due to the permanent triaxiality. Finally, we calculate the tidal dissipation rate in a body experiencing forced libration at the main mode, or free libration at one frequency, or superimposed forced and free librations.     

Non-resonant secular dynamics of trans-Neptunian objects perturbed by a distant super-Earth

We use a secular model to describe the non-resonant dynamics of trans-Neptunian objects in the presence of an external ten-Earth-mass perturber. The secular dynamics is analogous to an “eccentric Kozai mechanism” but with both an inner component (the four giant planets) and an outer one (the eccentric distant perturber). By the means of Poincaré sections, the cases of a non-inclined or inclined outer planet are successively studied, making the connection with previous works. In the inclined case, the problem is reduced to two degrees of freedom by assuming a non-precessing argument of perihelion for the perturbing body. The size of the perturbation is typically ruled by the semi-major axis of the small body: we show that the classic integrable picture is still valid below about 70 AU, but it is progressively destroyed when we get closer to the external perturber. In particular, for \(a>150\) AU, large-amplitude orbital flips become possible, and for \(a>200\) AU, the Kozai libration islands at \(\omega =\pi /2\) and \(3\pi /2\) are totally submerged by the chaotic sea. Numerous resonance relations are highlighted. The most large and persistent ones are associated with apsidal alignments or anti-alignments with the orbit of the distant perturber.     

Performance results of HESP physical model

As a continuation to the published work on model based calibration technique with HESP(Hanle Echelle Spectrograph) as a case study, in this paper we present the performance results of the technique. We also describe how the open parameters were chosen in the model for optimization, the glass data accuracy and handling the discrepancies. It is observed through simulations that the discrepancies in glass data can be identified but not quantifiable. So having an accurate glass data is important which is possible to obtain from the glass manufacturers. The model’s performance in various aspects is presented using the ThAr calibration frames from HESP during its pre-shipment tests. Accuracy of model predictions and its wave length calibration comparison with conventional empirical fitting, the behaviour of open parameters in optimization, model’s ability to track instrumental drifts in the spectrum and the double fibres performance were discussed. It is observed that the optimized model is able to predict to a high accuracy the drifts in the spectrum from environmental fluctuations. It is also observed that the pattern in the spectral drifts across the 2D spectrum which vary from image to image is predictable with the optimized model. We will also discuss the possible science cases where the model can contribute.     

Bandpass calibration of a wideband spectrometer using coherent pulse injection

We present a relatively simple time domain method for determining the bandpass response of a system by injecting a nanosecond pulse and capturing the system voltage output. A pulse of sub-nanosecond duration contains all frequency components with nearly constant amplitude up to 1 GHz. Hence, this method can accurately determine the system bandpass response to a broadband signal. In a novel variation on this impulse response method, a train of pulses is coherently accumulated providing precision calibration with a simple system. The basic concept is demonstrated using a pulse generator-accumulator setup realised in a Bedlam board which is a high speed digital signal processing unit. The same system was used at the Parkes radio telescope between 2–13 October 2013 and we demonstrate its powerful diagnostic capability. We also present some initial test data from this experiment.     

On the extension of the sensitive area of an extensive air shower surface array

A large distance between true and reconstructed core locations of an extensive air shower (EAS) may result in great systematic mis-estimation of EAS parameters. The reconstruction of those EASs whose core locations are outside the boundary of a surface array (outside EAS (OEAS)) results in a large distance of the reconstructed core location from the true one, especially when the true core is far outside the array. Although it may not be mentioned, the rejection of OEASs is a necessary and important step in the reconstruction procedure of an EAS. In this paper, an existing technique is optimized for the rejection of OEASs. The simultaneous use of this technique and a recently developed approach for reconstructing the core location of an EAS can significantly increase the sensitive area of a surface array.     

Calibration of the ART-XC mirror modules at MSFC

The Astronomical Röntgen Telescope X-ray Concentrator (ART-XC) is a hard X-ray telescope with energy response up to 30 keV, to be launched on board the Spectrum Röntgen Gamma (SRG) spacecraft in 2018. ART-XC consists of seven identical co-aligned mirror modules. Each mirror assembly is coupled with a CdTe double-sided strip (DSS) focal-plane detector. Eight X-ray mirror modules (seven flight and one spare units) for ART-XC were developed and fabricated at the Marshall Space Flight Center (MSFC), NASA, USA. We present results of testing procedures performed with an X-ray beam facility at MSFC to calibrate the point spread function (PSF) of the mirror modules. The shape of the PSF was measured with a high-resolution CCD camera installed in the focal plane with defocusing of 7 mm, as required by the ART-XC design. For each module, we performed a parametrization of the PSF at various angular distances Θ. We used a King function to approximate the radial profile of the near on-axis PSF (Θ < 9 arcmin) and an ellipse fitting procedure to describe the morphology of the far off-axis angular response (9 < Θ < 24 arcmin). We found a good agreement between the seven ART-XC flight mirror modules at the level of 10%. The on-axis angular resolution of the ART-XC optics varies between 27 and 33 arcsec (half-power diameter), except for the spare module.     

Spectral Trends of Solar Bursts at Sub-THz Frequencies

Previous sub-THz studies were derived from single-event observations. We here analyze for the first time spectral trends for a larger collection of sub-THz bursts. The collection consists of a set of 16 moderate to small impulsive solar radio bursts observed at 0.2 and 0.4 THz by the Solar Submillimeter-wave Telescope (SST) in 2012?–?2014 at El Leoncito, in the Argentinean Andes. The peak burst spectra included data from new solar patrol radio telescopes (45 and 90 GHz), and were completed with microwave data obtained by the Radio Solar Telescope Network, when available. We critically evaluate errors and uncertainties in sub-THz flux estimates caused by calibration techniques and the corrections for atmospheric transmission, and introduce a new method to obtain a uniform flux scale criterion for all events. The sub-THz bursts were searched during reported GOES soft X-ray events of class C or larger, for periods common to SST observations. Seven out of 16 events exhibit spectral maxima in the range 5?–?40 GHz with fluxes decaying at sub-THz frequencies (three of them associated to GOES class X, and four to class M). Nine out of 16 events exhibited the sub-THz spectral component. In five of these events, the sub-THz emission fluxes increased with a separate frequency from that of the microwave spectral component (two classified as X and three as M), and four events have only been detected at sub-THz frequencies (three classified as M and one as C). The results suggest that the THz component might be present throughout, with the minimum turnover frequency increasing as a function of the energy of the emitting electrons. The peculiar nature of many sub-THz burst events requires further investigations of bursts that are examined from SST observations alone to better understand these phenomena.     

Bayesian Methods for Reconstructing Sunspot Numbers Before and During the Maunder Minimum

The Maunder Minimum (MM) was an extended period of reduced solar activity in terms of yearly sunspot numbers (SSN) during 1610?–?1715. The reality of this “grand minimum” is generally accepted in the scientific community, but the statistics of the SSN record suggest a need for data reconstruction. The MM data show a nonstandard distribution compared with the entire SSN signal (1610?–?2014). The pattern does not satisfy the weakly stationary solar dynamo approximation, which characterizes many natural events spanning centuries or even millennia, including the Sun and the stars. Over the entire observation period (1610?–?2014), the reported SSN exhibits statistically significant regime switches, departures from autoregressive stationarity, and growing trends. Reconstruction of the SSN during the pre-MM and MM periods is performed using five novel statistical procedures in support of signal analysis. A Bayesian–Monte Carlo backcast technique is found to be most reliable and produces an SSN signal that meets the weak-stationarity requirement. The computed MM signal for this reconstruction does not show a “grand” minimum or even a “semi-grand” minimum.     

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).