Two CARMENES reductions support an eccentric GJ 4276 orbit over a circular 2:1 pair under independent Gaussian noise
We test whether CARMENES Data Release 1 (DR1) changes the orbit comparison for GJ 4276. We match all 100 discovery observations to DR1. We assume independent Gaussian errors and fit extra variance. One eccentric orbit fits better than two circular, non-interacting orbits with exactly 2:1 periods. The maximum log-likelihood difference changes from 4.618 to 4.709. It stays positive after every single-observation deletion and in six sensitivity checks. Changes in velocities and error bars have partly opposing effects. Use of velocities before the nightly zero-point correction reverses the preference. We simulate both fitted models with one signed likelihood statistic. In an extended run for each reduction, 4 of 2048 circular-pair simulations reach the observed statistic. The plus-one tail estimate is 0.00244. Its simulation-only 95% interval is 0.00053 to 0.00499. The statistic has opposite signs for the two simulated populations in Figure 6 of the inspected 2019 arXiv report. DR1 adds no later observations for this star. Both reductions use the same spectra. The simulation tail is conditional on fitted templates and independent Gaussian noise. It does not give a planet-count probability or test interacting eccentric pairs. The package contains code, exact input hashes and addresses, derived data, simulated statistics, numerical checks, figures, and reproduction instructions.
GJ 4276 · CARMENES · radial velocity · eccentric orbit · model comparison · data reduction · parametric simulation
References
6- usesdoi:10.1051/0004-6361/201834569
We use the 100 discovery velocities from CDS J/A+A/622/A153 and test the reported eccentric orbit and circular pair. Our fitted likelihood difference is close to the reported value.
- challengesdoi:10.48550/arXiv.1901.02367
Figure 6 and the text in the inspected version 1 use opposite likelihood differences for the two truth populations. We test both fitted models with one signed statistic. This statement is limited to the arXiv version; the final publisher figure and original code were not inspected.
- usesdoi:10.1051/0004-6361/202244879
We use CARMENES DR1 velocities, errors, flags, and activity columns for J22252+594 and audit the change from the discovery data.
- doi:10.1088/0004-637X/709/1/168
This work explains the harmonic ambiguity between an eccentric orbit and a circular pair.
- doi:10.1093/mnras/stz2584
This work studies interacting two-planet solutions for GJ 4276. Those solutions are outside our tested model family.
- doi:10.48550/arXiv.2610.07181
Nixon et al. (2026), version 1, also favor the eccentric orbit with a predictive leave-one-out score on the original data. Our new scope is the paired DR1 audit and one-sign simulation test. Our deletion fits are training-likelihood influence checks.
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