G100074 Development of Absolute Displacement Sensor for Measuring Long period and Large Amplitude

An analytical discussion of that case of motion in the restricted problem, in which the mean motions of the infinitesimal, and smaller-massed, bodies about the larger one are nearly in the ratio of two small integers displays the existence of a series of periodic solutions which, for commensurabilities of the typep+ 1:p, includes solutions of Poincaré'sdeuxième sortewhen the commensurability is very close, and of thepremière sortewhen it is less close. A linear treatment of the long-period variations of the elements, valid for motions in which the elements remain close to a particular periodic solution of this type, shows the continuity of near-commensurable motion with other motion, and some of the properties of long-period librations of small amplitude.To extend the investigation to other types of motion near commensurability, numerical integrations of the equations for the long-period variations of the elements were carried out for the 2:1 interior case (of which the planet 108 “Hecuba” is an example) to survey those motions in which the eccentricity takes values less than 0·1. An investigation of the effect of the large amplitude perturbations near commensurability on a distribution of minor planets, which is originally uniform over mean motion, shows a “draining off” effect from the vicinity of exact commensurability of a magnitude large enough to account for the observed gap in the distribution at the 2:1 commensurability.

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Exploring the robustness of Keplerian signals to the removal of active and telluric features

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa3180 ◽

2020 ◽

Vol 500 (1) ◽

pp. 548-557

Author(s):

M Lisogorskyi ◽

H R A Jones ◽

F Feng ◽

R P Butler ◽

S Vogt

Keyword(s):

Monte Carlo ◽

High Resolution ◽

Monte Carlo Simulations ◽

Large Amplitude ◽

Absorption Cell ◽

Stellar Rotation ◽

Long Period ◽

Active Line ◽

Low Amplitude ◽

Rotation Signal

ABSTRACT We examine the influence of activity- and telluric-induced radial velocity (RV) signals on high-resolution spectra taken with an iodine absorption cell. We exclude 2-$\mathring{\rm A}$ spectral chunks containing active and telluric lines based on the well-characterized K1V star α Centauri B and illustrate the method on Epsilon Eridani – an active K2V star with a long-period, low-amplitude planetary signal. After removal of the activity- and telluric-sensitive parts of the spectrum from the RV calculation, the significance of the planetary signal is increased and the stellar rotation signal disappears. In order to assess the robustness of the procedure, we perform Monte Carlo simulations based on removing random chunks of the spectrum. Simulations confirm that the removal of lines impacted by activity and tellurics provides a method for checking the robustness of a given Keplerian signal. We also test the approach on HD 40979, which is an active F8V star with a large-amplitude planetary signal. Our Monte Carlo simulations reveal that the significance of the Keplerian signal in the F star is much more sensitive to wavelength. Unlike the K star, the removal of active lines from the F star greatly reduces the RV precision. In this case, our removal of a K star active line from an F star does not a provide a simple useful diagnostic because it has far less RV information and heavily relies on the strong active lines.

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