A fixed Gaussian HARPS model gives a nominal 95% amplitude bound below 0.90 m/s at 197.8 days for HD 40307 orbits with eccentricity up to 0.60
We tested whether an eccentric orbit can explain the weak nominal-period signal of candidate HD 40307 g. We used 253 public HARPS night means. The fixed mean model has four other signal periods, two instrument offsets, a cubic time trend, and a stellar activity term. The errors are independent Gaussian variables with a fixed 1 m/s term added in quadrature. At exactly 197.8 days, the largest two-coefficient nominal 95% ellipse amplitude is bounded by 0.892248 m/s. An analytic matrix perturbation allowance covers all phases, all pericentre angles, and every eccentricity from 0 to 0.60 between 347,040 grid centers. The rounded-up bound is 0.90 m/s, below the reported 0.95 m/s value. A separate 3,744-shape grid at this period has a largest ellipse bound of 0.691650 m/s. This conclusion has two main limits. A separate grid over 188.8 to 203.5 days allows a 0.95 m/s orbit at 203.5 days and eccentricity 0.60. An added 2 m/s noise term also raises the nominal-period sampled bound above 0.95 m/s. Earlier work estimated the four other periods from these same data. The 95% label is a fixed-design calculation and does not include that selection uncertainty or establish a true stellar noise model. This result does not exclude the planet in general. The package preserves code, input rows, source hashes, all shape results, figures, mathematical derivations, and numerical audits.
HD 40307 · HARPS · radial velocity · eccentric orbits · amplitude bounds · fixed Gaussian model · reproducible astronomy
References
7- Six fixed noise models give conditional 95% CARMENES amplitude bounds of 0.720–1.444 m/s for Barnard's star at eccentricity 0.306 on a finite 58.59–58.88-day orbit grid sci:sha256:b12513edcdb07eec8743e1f817d48399bb036020afa45592ade925a668fba6ec
This prior study used two-coefficient Gaussian ellipses and their union for finite eccentric-orbit grids. That confidence construction is prior work. Our HD 40307 calculation adds an analytic allowance between eccentricity and phase samples at one fixed period, with an audited support-function bracket for sampled ellipses. We do not reuse this prior package code or data.
- usesAdded 0.95 m/s circular signals at 197.8 days pass a 99% search threshold in over 99% of block residual trials at 24 phases on 253 HD 40307 nights sci:sha256:d40e8e6f40bdb590458dfb19464f866f474425cd676fdbd97d555bccd11b1a31
We reuse its input data records, MIT night-mean preparation code, primary mean model, and four fitted signal periods. Its circular injection result defines the gap tested here. We add eccentric-orbit confidence sets and a bound for continuous eccentricity and phase.
- usesdoi:10.26093/cds/vizier.36830125
This corrected HARPS-RVBank table supplies the primary public velocity, error, activity, quality, and zero-point data for target GJ2046 (HD 40307).
- usesdoi:10.1051/0004-6361/202348263
This paper describes HARPS-RVBank version 02 and the source data.
- usesdoi:10.1051/0004-6361/201220268
Table 4 gives the reported candidate period, amplitude, and eccentricity limits that define the tested scope.
- doi:10.1051/0004-6361/201526729
This earlier HARPS analysis found no conclusive evidence for candidate g and motivates a limited statement about the new calculation.
- doi:10.1111/j.1365-2966.2004.08275.x
This prior study treated the general effect of eccentricity on radial-velocity sensitivity. We make a target-specific contribution and do not claim that general effect as new.
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