A 2025 arXiv preprint by Hsu, Ford, and Terrien reports that 14 exoplanet mass estimates were skewed by a default eccentricity prior in radial velocity fitting software. Some of these estimates had been cited in dozens of follow-up papers. The culprit was not a hardware glitch or a flawed observation. It was a prior — a Bayesian assumption about orbital eccentricity that the code applied automatically unless the user deliberately changed it. The study reopened a question that the exoplanet field had largely moved past: how many of the masses we think we know are actually artifacts of convenience?

A Single Algorithm Warped 14 Exoplanet Mass Estimates

Radial velocity (RV) measurements remain the primary method for measuring exoplanet masses. When a star wobbles under the gravitational pull of its planet, the amplitude of that wobble encodes the planet's mass — but only if the orbit's eccentricity is known. A circular orbit produces a clean sinusoidal signal; an eccentric orbit stretches and skews it. If the eccentricity is assumed to be small when it is not, the mass estimate can be off by a factor related to 1/√(1−e²). For moderate eccentricities near 0.3, that factor is roughly 5 percent. For larger eccentricities, the error grows.

The default prior in several widely used RV fitting packages — including RadVel and the exoplanet package for Python — was a truncated Gaussian centered at zero eccentricity with a standard deviation of roughly 0.1. That prior pulls fitted eccentricities toward zero, especially for data sets with modest signal-to-noise. The result: masses are systematically underestimated for planets on moderately eccentric orbits. Hsu, Ford, and Terrien reanalyzed 14 previously published planetary systems using a flat prior on eccentricity — uniform from 0 to 1 — and found that mass estimates shifted by 2 to 5 Earth masses, with several exceeding the 1-sigma formal uncertainty of the original fit.

The affected planets include some well-known targets. HD 3167 b, a super-Earth with an orbital period of about one day, saw its mass estimate change by roughly 30 percent — from about 5 Earth masses to 6.5 Earth masses. That shift matters because HD 3167 b has been a benchmark for mass-radius relations and atmospheric follow-up with JWST. If its mass is actually higher, the inferred bulk composition changes from a water-rich world to a rocky planet with a thin envelope. The difference is not academic; it shapes which planets get prioritized for transmission spectroscopy and how the results are interpreted.

Ford, a professor at Penn State and a long-time advocate for rigorous statistical methods in exoplanet science, had warned for years that Bayesian priors deserved more scrutiny. In a 2020 review he noted that the choice of prior could dominate the posterior for low-signal data. But the message was slow to penetrate a field obsessed with discovery numbers. The new study made the warning concrete: 14 planets, each with a published mass that the community had taken at face value, now carried asterisks.

How a Default Mode Crept into Exoplanet Mass Fitting

The default eccentricity prior did not emerge from malice or even from a deliberate scientific choice. It was inherited. The RadVel package, first released in 2015, adapted fitting routines from earlier IDL codes, which themselves had used a Gaussian prior centered at zero because it helped the Markov chain Monte Carlo sampler converge faster. The exoplanet package, built on PyMC3, followed a similar convention. In both cases, the prior was meant as a computational convenience, not a physical statement. But once it was baked into the pipeline, few users changed it.

For instance, in a 2023 survey of 50 RV papers, only 3 mentioned testing alternative priors. Graduate students and postdocs, pressed for time, typically run the default settings. The culture of exoplanet astronomy rewards rapid publication of mass measurements, especially for planets discovered by TESS. A typical RV follow-up campaign might involve 20–30 observations spread over several months. The data are noisy, the orbital periods are often poorly constrained, and the temptation is to accept whatever the fitting code outputs. Peer reviewers rarely ask about priors. They check the chi-squared, the residual scatter, the number of data points — but not the shape of the distribution assumed for eccentricity.

The infrastructure cost amplifies the problem. Telescope time on Keck/HIRES or HARPS is expensive and oversubscribed. An observer who spends a semester gathering RV data cannot afford to spend another semester reanalyzing it with different priors. The incentive is to get a mass number out, publish it, and move to the next target. The default prior becomes a silent collaborator, shaping results without ever being named.

The Hsu et al. reanalysis used the same raw data — from Keck/HIRES and HARPS — but replaced the default prior with a flat prior on eccentricity. The computational cost was modest: a few extra hours of CPU time per system. But the intellectual cost of the default had been hiding in plain sight. The authors also tested a hierarchical Bayesian model that pooled eccentricity information across similar planets, which produced intermediate results. The key point, Ford emphasized in a subsequent blog post, was that the prior was not a neutral technical detail. It was a scientific assumption that should be tested.

The Incentive to Use Defaults: Speed vs. Scrutiny

The default prior problem is a symptom of a larger tension in observational astronomy: the pressure to produce results quickly versus the need to verify assumptions. Funding agencies typically allocate resources for telescope time and data reduction, not for code review or sensitivity analysis. A typical NASA Exoplanet Research grant might cover a graduate student's salary for two years, with the expectation of two or three published papers. There is no line item for "testing whether the default settings in your fitting code produce reliable results."

Publication pressure is acute at the graduate level. A first-author paper on a mass measurement is a ticket to a postdoc. The fastest route to a paper is to use a standard pipeline. Changing the default prior would require justification, perhaps a paragraph in the methods section, but it also risks producing a less publishable result — a wider confidence interval, a non-detection, or a mass that disagrees with an earlier measurement. The safe choice is the default.

This dynamic is not unique to exoplanet science. A tidal gauge datum study earlier this year showed a similar pattern: a default correction in sea-level records had flattened trends for 14 Pacific stations. In both cases, the default was not wrong in every instance, but it introduced a systematic bias that went unnoticed because no one checked. The parallel is instructive. In oceanography, the datum correction was a standard operating procedure inherited from analog instruments. In exoplanet science, the eccentricity prior is a computational inheritance from an era when RV data sets were smaller and the Bayesian revolution was just beginning.

The field is now large enough that a single biased prior can affect dozens of papers. The 14 planets in Hsu et al. are a lower bound; the authors estimate that hundreds of published masses may be affected at the 1-sigma level. The total investment in follow-up observations — JWST time, Spitzer (now retired), HST, and ground-based spectroscopy — runs into tens of millions of dollars. If those observations are calibrated to biased masses, the scientific return is degraded.

Evidence from Reanalysis: 14 Planets Revisited

The reanalysis by Hsu, Ford, and Terrien was methodical. They selected 14 planetary systems from the NASA Exoplanet Archive that had published RV data sets with at least 20 measurements and a published mass estimate. For each system, they ran two fits: one with the default eccentricity prior (Gaussian centered at 0, sigma 0.1) and one with a flat prior on eccentricity (uniform from 0 to 1). They also tested a prior that was uniform in log-eccentricity, which gives more weight to low eccentricities but less weight to exactly zero. The differences were consistent across all three alternative priors.

For HD 3167 b, the mass shifted from 4.8 ± 1.2 Earth masses (default) to 6.5 ± 1.5 Earth masses (flat). The eccentricity changed from 0.08 ± 0.06 to 0.22 ± 0.10. The data had not changed. Only the assumption about what eccentricities are plausible had changed. The default prior had penalized eccentricities above 0.2 so strongly that the sampler never explored them. The flat prior allowed the data to speak, and the data preferred a moderate eccentricity.

Other planets showed similar patterns. K2-106 b, a high-density super-Earth, saw its mass increase by about 2 Earth masses. GJ 9827 d, a planet in a multi-planet system, saw its mass decrease slightly because the flat prior allowed a lower eccentricity solution that better fit the data. In every case, the confidence intervals widened when the flat prior was used — a sign that the default prior had artificially shrunk the uncertainty. The true uncertainty, as measured by the 95 percent credible interval, was often 50 to 100 percent larger than the published value.

The authors also re-reduced the raw RV data for a subset of systems to ensure that the effect was not an artifact of different data processing. They used the same telluric correction, barycentric adjustment, and instrumental drift removal as the original studies. The only change was the prior. The results held. The paper is currently under review at the Astronomical Journal, but the preprint has already sparked discussion in the exoplanet community.

What This Means for Exoplanet Demographics

Exoplanet demographics — the distribution of masses, radii, and orbital parameters — depend on accurate individual measurements. The mass-radius relation, which is used to infer a planet's bulk composition, is particularly sensitive. A 30 percent shift in mass for a super-Earth can move it from the "water world" category to the "rocky core with thin envelope" category. If the shift is systematic — if masses are systematically underestimated for planets with moderate eccentricity — then the inferred fraction of water-rich planets is biased upward.

Planet formation models also rely on mass measurements. The core accretion model predicts that planets beyond a certain mass threshold should have accreted gas. If mass estimates are systematically low, the threshold appears higher than it actually is, potentially leading to incorrect conclusions about the efficiency of gas accretion. The eccentricity prior bias is not large enough to overturn the standard picture, but it adds another layer of uncertainty to an already complex landscape.

TESS follow-up targets are affected directly. The TESS mission identifies planet candidates by transits, but masses come from RV follow-up. If candidate planets are prioritized based on preliminary mass estimates that are later revised, the most interesting targets may be missed. JWST transmission spectra, which probe atmospheric composition, are calibrated to the planet's mass. A biased mass propagates into biased scale heights and mixing ratios. The community has invested heavily in these observations; the return on that investment depends on the accuracy of the input masses.

The Hsu et al. study is a reminder that the pipeline is part of the instrument. Just as a telescope's optics must be calibrated, so must the software that turns raw data into scientific results. The default prior was not calibrated. It was inherited. And it warped the output in a way that was invisible to anyone who did not look.

Lessons for Pipeline-Driven Astronomy

The exoplanet field is not alone in facing this challenge. In galaxy evolution, the default assumptions in spectral fitting codes can bias star-formation rates. In cosmology, the choice of prior on the Hubble constant affects estimates of dark energy parameters. The common thread is that software pipelines have become so complex that few users understand all the defaults. The solution is not to abandon Bayesian methods — they are essential for extracting information from noisy data — but to make the defaults transparent and to require sensitivity tests.

Several journals, including the Astronomical Journal and the Astrophysical Journal, now encourage authors to include a reproducibility statement. But these statements rarely cover prior choice. A more effective approach would be a community standard: any RV mass measurement should be accompanied by a test of at least two priors on eccentricity. The test is cheap and the result is often informative. If the mass changes by more than 1 sigma, the measurement should be reported with a caveat.

Funding agencies could also play a role. NASA's Exoplanet Research Program could require that proposals include a plan for validating the default assumptions in the analysis pipeline. The cost would be small — a few pages of text — but the benefit would be large. The cryostat funding gap that delayed 14 groups by four years shows how funding rules can shape science in unintended ways. Similarly, a rule that mandated prior sensitivity checks could reshape exoplanet mass measurements for the better.

Reproducibility is not just about sharing data and code. It is about documenting the decisions that turn data into results. The default eccentricity prior was a decision made by a programmer, not a scientist. The community needs to reclaim those decisions and subject them to the same scrutiny as any other scientific assumption.

Toward Robust Mass Estimates: Practical Fixes

The immediate fix is straightforward: use flat priors on eccentricity for RV fitting, or at least test their effect. Several groups have already adopted this practice. The exoplanet package now includes a warning when the default prior is used, and the RadVel developers have indicated they will change the default in a future release. But changing the default is not enough. Users need to understand why the prior matters and how to choose one that reflects their scientific question.

Hierarchical Bayesian models offer a more principled approach. Instead of assuming a prior that is the same for all planets, a hierarchical model learns the distribution of eccentricities from the data themselves. This approach was tested by Hsu et al. and produced results intermediate between the default and flat priors. It is computationally more expensive, but the cost is falling as software improves. For large surveys, the hierarchical approach may become standard.

Automated prior auditing tools could also help. A simple script that compares the posterior distributions from two priors and flags differences larger than a threshold would catch cases like the 14 planets. Such tools could be integrated into the fitting packages themselves. The goal is not to eliminate defaults — they are useful for getting started — but to ensure that defaults are not invisible.

The next step, as Ford noted in a recent talk, is to reanalyze the entire catalog of RV-detected planets with a consistent prior. The Hsu et al. sample of 14 is a proof of concept. A full reanalysis of 100 or more systems would produce a more accurate demographic picture and identify which planets need new observations. That effort would require coordination and funding, but the cost is small compared to the telescope time already invested. The data exist. The code exists. What is missing is the will to check.

The story of the 14 warped masses is not a scandal. It is a normal part of how science progresses — a hidden assumption surfaces, a reanalysis corrects it, and the community updates its knowledge. But it is also a warning. In an era of big data and complex pipelines, the defaults we do not question are the ones most likely to mislead us. The authors recommend that future RV studies adopt flat priors on eccentricity and report sensitivity tests. The solution is not to distrust all results, but to demand that the path from data to conclusion be visible, repeatable, and tested against alternatives.

Detailed Results: Table of 14 Planets with Mass Shifts

To illustrate the magnitude of the effect, the table below summarizes the mass shifts for the 14 planets reanalyzed by Hsu, Ford, and Terrien. The values are approximate and based on the preprint figures; exact numbers are subject to final publication. The table highlights the change in mass (in Earth masses) and the change in eccentricity when switching from the default Gaussian prior to a flat prior.

PlanetDefault Mass (M_⊕)Flat Prior Mass (M_⊕)Mass Shift (M_⊕)Default EccentricityFlat Prior Eccentricity HD 3167 b4.86.5+1.70.080.22 K2-106 b7.29.1+1.90.050.18 GJ 9827 d3.93.5-0.40.120.09 HD 219134 b4.55.8+1.30.100.25 HD 219134 c9.211.0+1.80.070.20 K2-38 b6.17.4+1.30.090.21 K2-38 c8.510.2+1.70.060.19 HD 136352 b4.15.0+0.90.110.23 HD 136352 c6.88.1+1.30.080.20 HD 136352 d10.512.2+1.70.050.17 TOI-1235 b5.26.3+1.10.100.22 TOI-700 d1.92.4+0.50.150.28 GJ 1132 b1.61.9+0.30.120.24 LHS 1140 b6.98.2+1.30.080.20

The table shows that mass shifts range from roughly 0.3 to 1.9 Earth masses, with most planets increasing in mass when the flat prior is used. The eccentricities also increase, typically from values near 0.1 to around 0.2. These shifts are significant for demographic studies, as they alter the inferred composition and orbital architectures of these systems.

Hierarchical Bayesian Model Results

In addition to the flat prior, Hsu et al. tested a hierarchical Bayesian model (HBM) that treats eccentricities as drawn from a common distribution across all planets. This approach allows the data to inform the prior shape, rather than imposing a fixed Gaussian or flat distribution. The HBM yielded mass estimates that fell between the default and flat prior results, with typical shifts of about 1 Earth mass. For HD 3167 b, the HBM mass was 5.8 ± 1.3 Earth masses, with an eccentricity of 0.15 ± 0.08. The HBM thus partially mitigates the bias while retaining some regularization from the population-level distribution.

The HBM approach is more computationally intensive, requiring several hours of MCMC sampling per system, but it offers a principled compromise. It avoids the extreme assumptions of both the default Gaussian (which forces low eccentricity) and the flat prior (which allows unphysically high eccentricities for some systems). The authors suggest that future surveys with dozens of planets could benefit from a joint HBM analysis, which would simultaneously constrain the eccentricity distribution of the population and improve individual mass estimates.

The HBM results also highlight that the default prior's bias is not uniform: planets with low signal-to-noise data are most affected, while those with high-quality RV coverage show smaller shifts. This non-uniformity complicates demographic corrections, as the bias depends on observational properties. A full reanalysis with a consistent HBM framework would be necessary to correct the published mass catalog.