A planetary ‘ridge’ may depend on how orbital periods are counted

What is the Neptunian ridge?

Astronomers map planetary populations by comparing planet sizes and orbital periods—the time needed to complete an orbit. One reported feature, the Neptunian ridge, contains planets roughly five to eight times Earth's radius on orbits lasting about three to six days. It lies between a relatively depleted region called the Neptunian desert and a longer-period region nicknamed the savanna.

Earlier analyses of Kepler and TESS results reported roughly twice the occurrence density in the ridge as in the neighbouring savanna. In an arXiv preprint, Kaiming Cui and David J. Armstrong argue that this contrast does not, by itself, establish a distinct concentration of planets. Their study combines a mathematical comparison, a simulated population and a reanalysis of TESS occurrence rates—not a new observing experiment.

Two different statistical rulers

The distinction is between counting planets per unit orbital period and counting them per unit logarithm of period. The first compares equal numbers of days; the second compares equal factors in period, such as successive doublings.

These measure different densities. A population with equal occurrence in successive period doublings is flat on the logarithmic measure, but its density per day decreases as periods grow. Mathematically, the logarithmic density equals the linear-period density multiplied by orbital period.

Consider the comparison intervals used in a recent ridge analysis: approximately 2.83–5.66 days for the ridge and 5.66–11.31 days for the savanna. Both span a doubling, but the savanna interval covers twice as many days. If they contain equal integrated occurrence, dividing each by its width in days makes the ridge look twice as dense. Dividing by their equal logarithmic widths gives equal densities.

No planets have been added or removed. Nor is this merely changing the appearance of an axis: the denominator defining density has changed. The authors favour logarithmic period, standard in planet-occurrence studies, and stress that any claimed excess needs an explicit variable and an appropriate smooth reference population.

A ridge without an added population

To illustrate the effect, the researchers generated 10,000 simulated planets, distributed uniformly in logarithmic period and logarithmic radius. Periods ranged from 0.5 to 50 days and radii from one to 16 Earth radii. They then retained only one per cent of planets falling inside adopted desert boundaries.

Outside that imposed desert, the underlying logarithmic distribution had no ridge. Nevertheless, measuring density per day produced a peak near the desert edge in relevant size ranges, followed by a decline. The simulation demonstrates that a ridge-like profile can arise without inserting an additional concentration. It does not establish that real planets follow this deliberately simplified population.

Converting previously published Kepler and TESS ridge-to-savanna contrasts gave a similar result. Ratios of about 1.6–2.2 per unit period became about 0.8–1.2 per unit logarithmic period, all compatible with equal densities within their reported uncertainties.

What the TESS reanalysis finds

The authors also remeasured occurrence for planets with radii of 5.5–8.5 Earth radii around F-, G- and K-type main-sequence stars, using their existing TESS-SPOC detection pipeline and hierarchical Bayesian framework.

Their logarithmic ridge-to-savanna ratio was 0.91, with quoted uncertainties of minus 0.16 and plus 0.21. A ratio of one means equal mean densities. Only 33 per cent of the posterior samples—the distribution of estimates produced by their statistical analysis—favoured an excess.

The occurrence profile instead rose steeply out of the desert and then became approximately flat. A model allowing an extra bump was marginally preferred over a smooth broken power law, but its estimated maximum lay just beyond the adopted ridge boundary, with substantial uncertainty. That comparison therefore did not establish the claimed ridge.

What remains unresolved

The conclusion is not that this orbital region lacks interesting physics, or that every possible excess has been excluded. Current uncertainties still allow structure that larger samples might resolve. The preprint challenges the interpretation of the reported twofold contrast: a peak relative to one statistical baseline need not be a peak relative to another.

This briefing uses the supplied paper-text extraction; figures were omitted and equations or tables may have extraction damage. The work is a preprint, and its interpretation should be treated as a research claim rather than a settled result.