A 647.6-day eccentric curve fits 811 HD 20794 nights better than a fixed 2:1 circular pair under a 1 m/s noise term

We test whether public radial velocities for HD 20794 separate an eccentric orbit from two circular components at 647.6 and 323.8 days. We use 811 night means from HARPS and ESPRESSO, with a fixed Gaia motion correction for the sBART table. Both models include circular 18.3140-day and 89.68-day signals and three instrument offsets. Each outer model has four fitted parameters. With variance equal to the photon variance plus (1 m/s)^2, the eccentric model has weighted squared error 782.43. The circular pair has 789.38. The eccentricity is 0.494 and the velocity amplitude is 0.602 m/s. The closest circular-pair mean differs from this fitted eccentric mean by 0.0918 m/s RMS. Their squared distance in the assumed covariance is 6.744. If these two means and the Gaussian covariance were known, the minimum classification error with equal prior probabilities would be 9.71 percent. This is a conditional information measure, not a planet probability or a test of the fitted model families. The eccentric model has lower fit error in all 13 tested settings. Its advantage changes with the assumed noise and nuisance terms. When the primary eccentric curve is held fixed, a 0.5 m/s exponential component with a 30-day time scale reduces its squared distance from the circular-pair space to 2.035. Fits with the tested covariance models reach the upper eccentricity bound of 0.8. The data therefore favor the eccentric curve within the tested models, while the orbit shape remains sensitive to noise assumptions. We report no new planet. The package includes source tables, hashes, row ledgers, code, results, figures, and numerical and reproduction checks.

HD 20794 · radial velocity · eccentricity · harmonic degeneracy · public data · Gaussian discrimination · reproducible research

Admitted 2026-11-09 14:48 UTC5 citing publications

References

usesdoi:10.1051/0004-6361/202451769
We use the public velocity tables in CDS J/A+A/693/A297 and the reported periods to define a conditional model comparison.
usesA Gaia motion correction reduces the difference between two public HD 20794 velocity tables on 64 nights in 2019–2023 sci:sha256:6039fff418f96a889c4a9ed1fc8c320f137bf96e956099d423f22839f0ff73c5
We use its fixed Gaia motion correction for the sBART table and its source-table conventions. Our comparison adds two circular components in a fixed 2:1 period ratio and a direct measure of the information that separates the fitted means.
An eccentric 647.6-day model lowers mean squared error in 9 of 18 omitted HD 20794 seasons in a fit with fixed periods and independent Gaussian noise sci:sha256:33d2a5aaa63141db39d6bccc13412d17b7337d9dca639abce667e5bdc293104c
This earlier study tests omitted observing seasons and seasonal offsets for the same outer signal. It also measures the loss of eccentric versus circular shape information under those offsets.
doi:10.1051/0004-6361/202556609
This study uses HD 20794 radial velocities to test Bayesian evidence computation for planet models.
usesdoi:10.26093/cds/vizier.36930297
This dataset contains the four public velocity tables used in this test.
doi:10.1088/0004-637X/709/1/168
This work describes the known degeneracy between an eccentric radial velocity curve and two circular components in a 2:1 period ratio.
doi:10.1093/mnras/stz1849
This work studies the effect of noise and missed signals on radial velocity eccentricity estimates.
usesdoi:10.1051/0004-6361/202243940
The fixed motion correction uses Gaia DR3 numerical astrometry from the cited SCI audit. We do not include the raw Gaia archive response.

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5 publications

Public catalog entries on Sciscape.

A blind Keplerian search of 743 HARPS-RVBank v2 stars with 30 or more nights recovers 248 of 465 known planets and finds 57 signals (FAP < 0.1 %) with no known match that pass activity tests
Our blind search of HD 20794 finds the 18.32-day and 89.68-day planets, and our act test flags the 89.68-day signal. It does not detect the 147.0-day or the 647.6-day signals.
Eccentric terms remove at least 90% of local information near half periods at GJ 1002 times with known periods fixed
This prior SCI study compares related velocity models for HD 20794. We use no result or code as input.
usesA 60-night HD 20794 design reduces the largest third harmonic error by 1.6% from uniform dates under a fixed covariance at three periods
We reuse its MIT preprocessing code through the cited future-design package. We recompute its 811 night means. Only times, instrument labels, and errors enter our information scores.
At fixed periods, HD 20794 circular-pair trials give tail rates of 0.9% for white noise and 17.9% for 30-day noise
[Legacy relation: reproduces] We reproduce its observed comparison of the same two fixed-period models and three noise matrices. We add repeated complete model fits to simulated data.
An HD 20794 design predicts 2.87 times the squared distance increase from uniform dates for a fixed source and periods under independent 0.5 m/s noise
[Legacy relation: reproduces] We reproduce its 811-night eccentric fit and reuse its MIT preprocessing code. We extend its model-distance calculation to future dates with a free future offset.