Stellar Cartography

Astrometry As A Tool For Discovering And Weighing Faint Companions To Nearby Stars

By Keith Cowing
Status Report
June 21, 2024
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Astrometry As A Tool For Discovering And Weighing Faint Companions To Nearby Stars
Illustration of the positions and proper motions that Hipparcos and Gaia would measure for the same hypothetical orbit but with six different periods. The orbits shown have had parallactic and proper motion removed (c.f. Figure 1). The small colored ellipses show the quasi-one-dimensional position measurements made by Hipparcos and Gaia, the diamonds show the best-fit positions at Jyr 1991.25 and 2016.0 from fitting straight lines to the blue and orange points, respectively, and the arrows show the best-fit proper motions. The portions of the orbit covered by Hipparcos and Gaia are indicated by shading on the orbit, and a black arrow indicates the (counterclockwise) direction of orbital motion. Differences between the Hipparcos proper motion, the Gaia proper motion, and the scaled difference between the Hipparcos and Gaia positions can constrain orbital motion. At short periods (top middle and especially top left), the positions and proper motions can bear little resemblance to the instantaneous position and proper motion at the average epoch of observation, while at long periods (lower right) this distinction becomes insignificant. For all periods shown other than 50 years the star completes more than one full orbit between the Hipparcos and Gaia central epochs. — astro-ph.IM

This tutorial covers the use of absolute astrometry, in particular from the combination of the Hipparcos and Gaia missions, to identify faint companions to nearby stars and to measure the masses and orbits of those companions.

Absolute astrometry has been used with increasing success to discover new planets and brown dwarfs and to measure masses and orbits for systems with periods as long as centuries. This tutorial summarizes the nature of the underlying astrometric data, the approach typically used to fit orbits, and the assumptions about that data implicit throughout the process.

It attempts to provide intuition for the sensitivity of astrometry as a function of stellar and companion properties and how the available constraints depend on the character and quantity of data available. This tutorial is written for someone with some background in astronomy but with no more than a minimal acquaintance with astrometry or orbit fitting.

Left: projected separation consistent with an assumed 13Οƒ significant proper motion difference in the HipparcosGaia Catalog of Accelerations (Brandt 2021) assuming no additional data (top), a ten-year radial velocity trend (middle), and most of a radial velocity orbit (bottom). Right: the radial velocity measurements adopted, color-coded by different assumed instruments, together with random orbits from the MCMC orbit fitting code orvara. The actual radial velocity points were those published for HIP 58289 (Trifonov et al. 2020) for the trend and HD 92987 (Rickman et al. 2019) for the orbit. — astro-ph.IM

Timothy D. Brandt

Comments: 17 pages, 5 figures, PASP accepted. Tutorial intended primarily as an introduction and reference for non-experts
Subjects: Instrumentation and Methods for Astrophysics (astro-ph.IM); Earth and Planetary Astrophysics (astro-ph.EP); Solar and Stellar Astrophysics (astro-ph.SR)
Cite as: arXiv:2406.11593 [astro-ph.IM] (or arXiv:2406.11593v1 [astro-ph.IM] for this version)
Submission history
From: Timothy Brandt
[v1] Mon, 17 Jun 2024 14:41:49 UTC (672 KB)


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