Closeby Habitable Exoplanet Survey (CHES). V. Planetary Parameters Derived from Angular Separation Variations

Abstract

The Closeby Habitable Exoplanet Survey (CHES) aims to achieve microarcsecond-level astrometry of about one hundred nearby FGK-type stars within 10 parsecs to detect Earth-like planets. Such precision exceeds the capability of absolute astrometry relying on Gaia catalogs, whose positional accuracy degrades over time due to error propagation from stellar motion and epoch offsets, limiting their use in microarcsecond-level detection. Traditional relative astrometry depends on positional components along right ascension and declination, requiring precise knowledge of field rotation and satellite attitude, which introduces additional errors. To address this, we propose a new relative measurement model based solely on variations in the length of angular separation between the target and reference stars, independent of direction. The model incorporates effects such as proper motion, parallax, radial velocity, light aberration, gravitational lensing, and planetary perturbations, enabling reconstruction of planetary orbits and masses. This approach enhances measurement stability and precision, providing a framework that is not entirely dependent on the Gaia catalog and suitable for CHES and other future high-accuracy astrometric missions.

Figures (7)

• Figure 1: Simulated observation of HD 88230 GaiaCollaboration2023, showing all stars brighter than magnitude 16 within a $0.44^{\circ} \times 0.44^{\circ}$ field of view. The image was downsampled from an array of 9 $\times$ 9 CMOS detectors, each with 4096 $\times$ 4096 pixels, to a final resolution of 2000 $\times$ 2000 pixels. The simulation is based on the technical specifications of the CHES optical telescope payload Ji2024.
• Figure 2: The angular separation variation caused by proper motion. $S_1, S_2$ represent two stars, $\mathbf{u_1}, \mathbf{u_2}$ denote their respective proper motion directions, and $l$ is the angular separation between the two stars. As the stars move along their proper motion directions, the angular separation $l$ changes accordingly.
• Figure 3: Parallax is added to the angular separation variation caused by proper motion. Left panel: $l_{\rm pm}$ denotes the angular separation considering only proper motion; parallax shifts the stellar positions toward the Sun by distances $r_1$ and $r_2$, resulting in a new separation $l_{\rm pm+plx}$. Right panel: Geometry of the relevant angles in the model, defined using the stars' ecliptic longitude and latitude.
• Figure 4: The star $S_2$, influenced by gravitational perturbations from its planet, shifts its position to point $S_{22}$. Its projection in the angular separation direction is represented as point $Q_1$ in the diagram. $S_1Q_2$ illustrates the actual length of $S_1S_{22}$ in the angular separation direction.
• Figure 5: Fitting of exoplanets. (a) The target star is HD 88230, with a hypothetical Earth-like planet placed at a distance of 1 AU from the star. (b) The target star is again HD 88230, with a hypothetical warm Jupiter placed at a distance of 0.1 AU. (c) The target star is HD 147513, which is known to host the detected Jovian planet HD 147513 b. The angular distance measurement accuracy is $1~\mu \rm as$. The black points represent the simulated planetary parameters, while the red points show the residuals after removing proper motion and parallax through fitting. The blue points depict the stellar motion orbit induced by planetary perturbations, derived from a Keplerian fit to the residuals.