Shortly after the discovery of the first exoplanets, host star metallicity was suggested to have a role in the formation of planetary systems⁴. Indeed, the well-established tendency for hot Jupiters to be more frequently found orbiting metal-rich stars has been confirmed by a number of studies^5,6. Although it has recently been shown that small planets form for a wide range of host star metallicities^7-11, it is clear that the metallicities of stars with small planets are on average lower than those of gas giants. This suggests that subtle differences may exist in the metallicities of the host stars of small exoplanets, and this, in turn, may be linked to distinct physical properties of the underlying planet populations. However, effectively probing this regime requires a large sample of homogeneously derived metallicities for stars with small planets. Therefore, using our stellar parameters classification (SPC) tool⁷, we analyse more than 2,000 high-resolution spectra of Kepler Objects of Interest¹² (KOIs) gathered by the Kepler Follow-up Program, yielding precise stellar parameters (provided as a table in machine-readable form), including metallicities, of 405 stars orbited by 600 exoplanet candidates.

Our sample of spectroscopic metallicities of stars hosting small planets is a factor of two larger than any previous sample⁷, allowing us to probe in greater detail for significant differences in the metallicities of stars hosting planets of different sizes. At various radii, we divide the sample into two bins of stars hosting small and large planets, and per-form a two-sample Kolmogorov–Smirnov test to determine whether the metallicities of the two distributions of host stars are not drawn randomly from the same parent population. We find two significant features in the Kolmogorov–Smirnov test diagram, one at 1.7R_⊕ (Earth radii) with a significance of 4.5σ and one at 3.9R_⊕ with a significance of 4.6σ, suggesting transitions between three exoplanet size regimes (Fig. 1). The average metallicity of the host stars increases with planet size, yielding average metallicities of −0.02 ± 0.02, 0.05 ± 0.01 and 0.18 ± 0.02 dex in the respective regimes. To assess the uncertainty in radius at which these transitions occur, we perform a Monte Carlo simulation by drawing 10⁶ sets of data, where the host star metallicities and planetary radii are randomly perturbed within the uncertainties (the uncertainty in the planetary radius is assumed to be dominated by the uncertainty in the radius of the host star). We find the two features to be at${1.55}_{-0.84}^{+0.88}{R}_{\oplus }\left({4.2}_{-0.4}^{+0.5}\sigma \right)$ and${3.52}_{-0.28}^{+0.74}{R}_{\oplus }\left({4.7}_{-0.4}^{+0.6}\sigma \right)$, consistent with the original data.

Small planets with short periods could undergo significant evaporation of their atmospheres¹³. These planets will therefore not obey the radius-metallicity relation we are studying, because any accumulated gas would have evaporated. Therefore, we remove small (R_P <3R_⊕, whereR_P is the exoplanet radius), highly irradiated planets (stellar flux,F_v >5 × 10⁵ J s⁻¹ m⁻²) from the sample, leaving 463 planets orbiting 324 stars, which increases the significance of the feature at 1.7R_⊕ from 3.5σ to the reported 4.5σ. For comparison, the rocky planet Kepler-10b, with an 0.8-d period¹⁴, receives a flux ofF_v ≈ 48 × 10⁵ J s⁻¹ m⁻², whereas Kepler-11c¹⁵, whose density suggests it is gaseous, receivesF_v ≈ 1.3 × 10⁵ J s⁻¹ m⁻².

Recent studies suggest that the masses and radii of small planets (1.5R_⊕-4R_⊕) follow a linear relationship, implying that planet density decreases with increasing planet radius². However, this relationship must change significantly for larger planets (>4R_⊕) to explain the large mass of gas giant planets such as Jupiter². Our data indicate a statistically significant increase in metallicity at a comparable planetary radius,R_P = 3.9R_⊕. This observation is in agreement with the well-established correlation between a star’s metallicity and its likelihood to host hot Jupiters^5,6, confirming that the formation regime for larger planets (>3.9R_⊕) requires exceptionally high metallicity environments⁷. We therefore interpret the regime of larger planets (R_P >3.9R_⊕) to consist of ice and gas giant planets formed beyond the ‘snow line’ at around ~3 AU (1 AU is the average Sun–Earth distance), where the availability of solids is a factor of four higher because volatile elements are able to condense and form solids at cooler temperatures¹⁶. The high concentration of heavy elements in the protoplanetary disk, resulting from the higher metallicity and the condensation of volatiles, and the planet’s large distance to the host star allow these planets to grow rapidly and amass a gaseous atmosphere before the gas in the proto-planetary disk dissipates. These planets then migrate to their present positions much closer to their host stars¹⁷, yielding the hot Jupiters seen orbiting stars with high metallicities.

To explore the implications of the feature at 1.7R_⊕ in the metallicity–radius plane (Fig. 1), we compare our results with recent work attempting to determine the radius at which the transition from gaseous to rocky planets occurs. Dynamical masses derived from precise radial velocities of transiting exoplanets indicate that planets withR_P >2R_⊕ have densities that imply increasing amounts by volume of light material, whereas planets withR_P >1.5R_⊕ have densities systematically greater than that of Earth². Moreover, an analysis of data for a larger sample of planets (including masses derived from transit timing variations), has shown that planets withR_P <1.5R_⊕ probably are of rocky composition³. Finally, it has been suggested thatR_P ≈ 1.75R_⊕ is a physically motivated transition point between rocky and gaseous planets, based on reported masses and radii combined with thermal evolutionary atmosphere models¹⁸. The statistically significant peak in the metallicity–radius plane at 1.7R_⊕ agrees with these findings, suggesting that the compositions of small exoplanets (R_P <3.9R_⊕) in close proximity to their host stars are also regulated by the number density of solids in the protoplanetary disk. Thus, we interpret the two regimes of smaller planets identified by the host star metallicities as reflecting the transition between rocky terrestrial exoplanets that have not amassed a gaseous atmosphere (R_P <1.7R_⊕) and planets with rocky cores that have accumulated an envelope of hydrogen, helium and other volatiles, which we denote gas dwarfs (1.7R_⊕ <R_P <3.9R_⊕).

The formation mechanism of the terrestrial and gas dwarf exoplanet regimes in short orbital periods is not fully understood. In one model, these small exoplanets are believed to formin situ with little post-assembly migration^19,20. Although thein situ accretion model seems to be successful in reproducing the observed distribution of the ‘hot Neptune’ and super-Earth systems, including their orbital spacing²¹, it requires unusually large amounts of solids in the innermost protoplanetary disk. A competing model invokes accretion during the inward migration of a population of planetary embryos formed at a range of orbital distances beyond the snow line^22,23. On this view, Mars- and Earth-size embryos migrate inwards owing to tidal interaction with the disk²⁴, and accumulate at the inner edge of the protoplanetary disk, where they complete their assembly²⁵. Irrespective of the formation mechanism, however, the observed peak in the metallicity–radius plane at 1.7R_⊕ suggests that the final mass and composition of a small exoplanet is controlled by the amount of solid material available in the protoplanetary disk. A higher-metallicity environment promotes a more rapid and effective accretion process, thereby allowing the cores to amass a gaseous envelope before dissipation of the gas. In contrast, lower-metallicity environments may result in the assembly of rocky cores of several Earth masses on timescales greater than that inferred for gas dispersal in protoplanetary disks¹⁹ (<10 Myr), yielding cores without gaseous hydrogen–helium atmospheres.

A prediction from gas accretion on short orbital periods is that the critical mass at which a core can accrete an atmosphere isM_cr≈2.6M (ν/0.3)^1/2(P_orb 1 d)^5/12, where ν=M_atm/M_cr is the fractional mass comprised by the atmosphere²⁶. In this model, the planetary mass and, thus, radius indicating the transition from rocky to gaseous planets should increase with orbital period. However, the exact opposite dependence, namely a decrease in core mass with increased orbital period, has also been suggested²⁷. To investigate whether the radius of transition from rocky to gaseous planets found in our data shows a dependence on orbital period, we segregate the sample by period into four bins with approximately equal numbers of planets. We repeat the previously described Kolmogorov–Smirnov test for the planets in each of the period bins: we remove the larger planets (R_P >3.9R_⊕) and perform a Monte Carlo simulation by drawing 10⁶ sets of data, where the host star metallicities and planetary radii are randomly perturbed within the uncertainties. The red line inFig. 2 is a power-law fit to the transition radius, R_cr, inferred from our data (R_cr=1.06R_⊕(P_orb/1 day)^0.17. Although additional data are required to confirm this relationship, the fit is apparently consistent with a critical core mass that increases with orbital period and an atmospheric fraction of 5% (ref.26; blue dashed line inFig.2). If correct, this predicts the existence of more massive rocky exoplanets at longer orbital periods.

Although our analysis of a statistically significant number of planets and their host star metallicities allows us to distinguish between three distinct exoplanet regimes, we emphasize that a multitude of factors can affect the outcome of planet formation. Therefore, the transition radii inferred from our analysis probably represent gradual transitions between the different planet regimes and so may not apply to all planetary systems. However, the agreement between the transition radii inferred here and those deduced from dynamical mass measurements of transiting planets^2,3 implies that host star metallicity—and, by extension, the solids inventory of a protoplanetary disk—is one of the driving factors determining the outcome of planet formation.