Inner-to-Outer Planet Radii Ratios

Updated 23 August 2025

Inner-to-outer planet radii ratios are defined as the ratio of an inner planet's radius to its outer companion's, quantifying size ordering in exoplanet systems.
Empirical findings reveal that inner planets are generally smaller, with ratios peaking near unity in 'peas-in-a-pod' systems and varying with planet mass and host star metallicity.
Statistical analyses and regression models demonstrate that these ratios capture key effects of irradiation, atmospheric loss, and disk properties on planetary formation and evolution.

The inner-to-outer planet radii ratio is a central observable in exoplanet science, quantifying how the sizes of neighboring planets (ordered by increasing orbital period or semi-major axis) compare within the same system. This metric illuminates formation and evolutionary processes shaping planetary architectures. Across multiple regimes, empirical studies reveal that the relative radii of inner and outer planets encode information about planet migration, atmospheric loss, disk metallicity, resonance capture, and post-formation dynamical history.

1. Definition and Quantitative Measures

The inner-to-outer planet radii ratio, denoted as $\mathcal{R} = R_{\rm in} / R_{\rm out}$ , captures the relative size of the inner planet compared to its outer companion in a given pair. Aggregating these ratios over all pairs in multi-planet systems enables statistical characterization of size ordering patterns. Typical analysis includes:

Metric/Statistic	Definition/Value	Context
$\mathcal{R}$	$R_{\rm in}/R_{\rm out}$	Primary observable for size order
Median/Mean ratio	e.g., median $\sim$ 1.14	Peaked near unity in "peas-in-a-pod" systems (Weiss et al., 2017)
Dispersion $D_r$	$D_r \approx 0.32$	Intrinsic radius uniformity (Mamonova et al., 5 Jun 2025)

Precise measurement requires corrections for detection bias (e.g., via transit signal-to-noise scaling $(S/N) \propto P^{-1/3}$ (Ciardi et al., 2012)) and careful treatment of period/radius uncertainties.

2. Empirical Trends and Regime Dependence

Empirical studies consistently find that inner planets are typically smaller than their next outer neighbors, but the strength and nature of this ordering depend on planet size, host star metallicity, and system architecture:

Neptune-sized and larger: For pairs with at least one planet $\gtrsim 3R_\oplus$ , $\sim68\pm6\%$ have $R_{\rm in} < R_{\rm out}$ , indicating systematic size growth with distance (Ciardi et al., 2012).
Sub-Neptune and Super-Earths: Uniformity in size is markedly strong within pure super-Earth or pure sub-Neptune categories, with $R_{\rm SN} \approx 1.7 R_{\rm SE}$ when both types are present in the same system (Millholland et al., 2021). The radius ratio within the same category is sharply peaked near unity, following $\mathcal{N}(\mu=1,\sigma=0.3)$ .
Radius Gap Planets: Planets near the "radius gap" ( $\sim1.8R_\oplus$ ) do not resemble their neighbors; there is a $3-4\sigma$ deficit of pairs with $\mathcal{R}\approx1$ and a prominent reversal in size ordering (Chance et al., 3 Oct 2024).
High-Multiplicity Systems: The "peas in a pod" pattern breaks down beyond periods $\sim$ 100–300 days, with a $\sim7\sigma$ deficit of outer planets matching the radii and period ratios of inner planets (Millholland et al., 2022).
Resonant vs. Non-Resonant: No significant difference found between resonant and non-resonant planet pairs in radius ratios (Lozovsky et al., 18 Aug 2025).

These trends suggest a strong link between planet formation environment, migration, and evolutionary modification.

3. Physical Drivers: Irradiation, Metallicty, and Mass Effects

The drivers of radii ratios operate differently across mass and regime:

Stellar Irradiation: Higher equilibrium temperature ( $T_{\rm eq}$ ) "puffs up" planets due to heating, yet in close-in orbits enhanced atmospheric loss can offset this, making inner planets smaller overall (Enoch et al., 2012).
Host Star Metallicity / Heavy Element Content: Increased [Fe/H] leads to smaller radii via larger planetary cores. Mass–radius relations for Saturn-mass and high-mass planets show negative [Fe/H] coefficients (Enoch et al., 2012). The radii ratio trend is often more pronounced in high-metallicity systems (Lozovsky et al., 18 Aug 2025).
Planetary Mass Dependence: Mass effects are not monotonic; increased mass inflates Saturn-mass planets but contracts high-mass planets due to electron degeneracy pressure (Enoch et al., 2012).

Regression formulas quantify these dependencies:

Saturn-mass: $\log(R_p/R_J) = -0.077 + 0.450\log(M_p/M_J) - 0.314[\mathrm{Fe/H}] + 0.671\log(a/{\rm AU}) + 0.398\log(T_{\rm eq}/{\rm K})$
Jupiter-mass: $\log(R_p/R_J) = -2.217 + 0.856\log(T_{\rm eq}/{\rm K}) + 0.291\log(a/{\rm AU})$
High-mass: $\log(R_p/R_J) = -1.067 + 0.380\log(T_{\rm eq}/{\rm K}) - 0.093\log(M_p/M_J) - 0.057[\mathrm{Fe/H}] + 0.019\log(H_{\rm tidal}/10^{20})$

These models reproduce radii differences within $0.11R_J$ .

4. Formation and Migration Scenarios

Planet formation hypotheses predict size ordering through the interplay of disk accretion, migration, and dynamical evolution:

Core Accretion and Migration: Models predict smaller rocky planets (super-Earths) form closer in, while gas-rich planets form farther out and migrate inward, leading to larger outer planets (Ciardi et al., 2012, Chatterjee et al., 2013).
Pebble Accumulation and Inside-Out Growth: Pebble rings at disk pressure maxima allow sequential planet formation with only weak scaling ( $M_R \propto r^{1/5}$ ), explaining the similar radii among inner and outer planets (Chatterjee et al., 2013).
Resonant Chains and Chain Instability: Gas-driven migration creates chains of resonantly-locked planets; after gas dissipation, giant impacts break the chains, strip atmospheres, cause "radius valley" features, and enforce intra-system size uniformity (Izidoro et al., 2022).
Photoevaporation/Atmospheric Loss: Outer planets, being less irradiated, retain more envelope, resulting in slightly larger radii. Mild positive correlation between temperature difference and radii ratio supports photoevaporative sculpting (Weiss et al., 2017).

5. Dynamical Architecture and Evolutionary Modification

System architecture—including resonance locking and post-formation instabilities—affects radii ratios and the observed size-ordering:

Resonant Evolution in Circumbinary Disks: Convergent migration and resonant locking can yield a larger inner planet parked near the disk edge and a smaller outer planet in resonance. High outer/inner mass ratios destabilize this (Fitzmaurice et al., 2022).
Gap Planets and Collisional History: Systems with radius gap planets feature reversed size-ordering and an excess of near-resonant period ratios, suggestive of late giant impacts or dynamical scattering rather than simple evolutionary loss (Chance et al., 3 Oct 2024).
Multiplicity and Period Ratio Regularity: Regular period ratios and sizes in "peas-in-a-pod" systems reflect finely tuned formation or migration but may truncate in outer regions (Millholland et al., 2022).

6. Connection to Composition and Interior Structure

Despite pronounced uniformity in radii between inner and outer planets, composition and interior structure may be disparate:

Radius Uniformity vs. Density/Mass Dispersion: While radii correlations are moderate or strong (Pearson $R \approx 0.5$ ), mass and density correlations are weak or absent among neighboring planets (Mamonova et al., 5 Jun 2025). Dispersion in radii ( $D_r \approx 0.317$ ) is consistently less than in mass or density.
Compositional Decoupling: Systems with adjacent planets of similar radii can host planets on distinct mass–radius/composition tracks, meaning size is not a direct proxy for interior structure.
Impact of Stellar Properties: Uniformity in radii does not sensitively track host star metallicity, age, or temperature, while mass/density uniformity is promoted for low $T_{\rm eff}$ , low metallicity, and old stars (Mamonova et al., 5 Jun 2025).

7. Statistical Approaches and Observational Constraints

The reliability of observed inner-to-outer radii ratios is established through:

Monte Carlo Uncertainty Accommodation
Distribution Comparisons via Anderson–Darling, Fisher’s Exact Test
Poisson Likelihood for sub-sample significance (Chance et al., 3 Oct 2024)
Random draw ("bootstrap") tests on radius distributions (Weiss et al., 2017, Ciardi et al., 2012)

These approaches consistently show that the size-ordering pattern is astrophysical, not a bias artifact.

Inner-to-outer planet radii ratios present a robust but nuanced constraint on models of exoplanet system assembly, migration, and evolution. The canonical trend—smaller inner planets with systematic ordering by size—emerges from a spectrum of physical drivers: irradiation, metallicity, mass-dependent accretion, resonance capture, and dynamical modification including giant impacts. However, underlying compositional diversity remains even when radii are similar, highlighting the need for joint radius–mass–density measurements and precise dynamical characterization to disentangle the coupled formation and evolutionary pathways of exoplanetary systems.