Planets similar in size are often dissimilar in interior

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Table 1

Pearson’s R and p−value for the radii (r), masses (m), densities (ρ), and period ratios (pr) of adjacent planets

Main sample correlation

	N_p, N_s, N_pl	p-value	R	CI	p_err	$\tilde{X} (R)$ $\mathop X\limits^ (R)$	CI_err	$\bar{R_{sim}}$ $\overline {{R_{{\rm{sim}}}}}$
$\sum^{} \frac{(σ_{r \pm})}{r} \leq 2$ ${\mathop \sum \nolimits^ ^}{{\left( {{\sigma _{r \pm }}} \right)} \over r} \le 2$	269, 145, 414	9.7 × 10⁻²⁰	0.516	[0.423; 0.599]	1.28 × 10⁻¹⁹	0.511	[0.417; 0.595]	−
$\sum^{} \frac{(σ_{m \pm})}{m} \leq 2$ ${\mathop \sum \nolimits^ ^}{{\left( {{\sigma _{m \pm }}} \right)} \over m} \le 2$	184, 122, 306	0.92	−0.007	[−0.152; 0.138]	0.538	−0.007	[−0.152; 0.138]	0.095 ± 0.130
$\sum^{} \frac{(σ_{ρ \pm})}{ρ} \leq 2$ ${\mathop \sum \nolimits^ ^}{{\left( {{\sigma _{\rho \pm }}} \right)} \over \rho } \le 2$	167, 115, 282	0.0005	0.265	[0.118; 0.401]	0.0004	0.251	[0.109; 0.393]	0.225 ± 0.108
$\sum^{} \frac{(σ_{pr \pm})}{pr} \leq 2$ ${\mathop \sum \nolimits^ ^}{{\left( {{\sigma _{{\rm{pr}} \pm }}} \right)} \over {{\rm{pr}}}} \le 2$	167, 93, 353	0.83	−0.0166	[−0.168; 0.136]	0.584	−0.017	[−0.168; 0.136]	−

Error precision test

$\sum^{} \frac{(σ_{r \pm})}{r} \leq 0.5$ ${\mathop \sum \nolimits^ ^}{{\left( {{\sigma _{r \pm }}} \right)} \over r} \le 0.5$	263, 141, 404	1.2 × 10⁻¹⁵	0.467	[0.367; 0.556]	1.1 × 10⁻¹⁵	0.463	[0.362; 0.553]	−
$\sum^{} \frac{(σ_{m \pm})}{m} \leq 0.5$ ${\mathop \sum \nolimits^ ^}{{\left( {{\sigma _{m \pm }}} \right)} \over m} \le 0.5$	70, 52, 123	0.83	−0.027	[−0.260; 0.210]	0.581	−0.025	[−0.258; 0.211]	0.048 ± 0.133
$\sum^{} \frac{(σ_{ρ \pm})}{ρ} \leq 0.5$ ${\mathop \sum \nolimits^ ^}{{\left( {{\sigma _{\rho \pm }}} \right)} \over \rho } \le 0.5$	44, 33, 77	1.4 × 10⁻⁶	0.654	[0.443; 0.796]	1.2 × 10⁻⁶	0.644	[0.430; 0.790]	0.385 ± 0.163
$\sum^{} \frac{(σ_{pr \pm})}{pr} \leq 0.5$ ${\mathop \sum \nolimits^ ^}{{\left( {{\sigma _{{\rm{pr}} \pm }}} \right)} \over {{\rm{pr}}}} \le 0.5$	165, 92, 349	0.99	−0.001	[−0.154; 0.152]	0.99	−0.001	[−0.154; 0.152]	−
$\sum^{} \frac{(σ_{r \pm})}{r} \leq 0.32$ ${\mathop \sum \nolimits^ ^}{{\left( {{\sigma _{r \pm }}} \right)} \over r} \le 0.32$	239, 136, 378	4.4 × 10⁻¹⁵	0.479	[0.374; 0.571]	3.7 × 10⁻¹⁵	0.475	[0.371; 0.568]	−
$\sum^{} \frac{(σ_{m \pm})}{m} \leq 1$ ${\mathop \sum \nolimits^ ^}{{\left( {{\sigma _{m \pm }}} \right)} \over m} \le 1$	136, 92, 229	0.98	0.002	[−0.167; 0.170]	0.496	0.001	[−0.168; 0.169]	0.089 ± 0.134

Kepler planets subsample correlation

$\sum \frac{(σ_{r \pm})}{r} \leq 2$ $\mathop \sum \nolimits^ {{\left( {{\sigma _{r \pm }}} \right)} \over r} \le 2$	229, 120, 349	2.1 × 10⁻¹⁵	0.493	[0.388; 0.585]	2.7 × 10⁻¹⁵	0.486	[0.381; 0.580]	−
$\sum \frac{(σ_{m \pm})}{m} \leq 2$ $\mathop \sum \nolimits^ {{\left( {{\sigma _{m \pm }}} \right)} \over m} \le 2$	145, 97, 242	0.75	−0.026	[−0.189; 0.137]	0.623	−0.027	[−0.189; 0.137]	0.083 ± 0.131
$\sum \frac{(σ_{ρ \pm})}{ρ} \leq 2$ $\mathop \sum \nolimits^ {{\left( {{\sigma _{\rho \pm }}} \right)} \over \rho } \le 2$	145, 91, 220	0.004	0.253	[0.084; 0.408]	0.002	0.239	[0.076; 0.401]	0.230 ± 0.116
$\sum \frac{(σ_{pr \pm})}{pr} \leq 2$ $\mathop \sum \nolimits^ {{\left( {{\sigma _{{\rm{pr}} \pm }}} \right)} \over {{\rm{pr}}}} \le 2$	143, 80, 303	0.98	−0.002	[−0.166; 0.162]	0.51	−0.006	[−0.166; 0.162]	−

Radii from Gaia DR3 correlation

	N_P, N_s, N_pl	p_flame	R_flame	CI_flame	p_gspphot	R_gspphot	CI_gspphot
$\sum^{} \frac{(σ_{r \pm})}{r} \leq 2$ ${\mathop \sum \nolimits^ ^}{{\left( {{\sigma _{r \pm }}} \right)} \over r} \le 2$	227, 126, 353	5.9 × 10⁻¹³	0.454	[0.344; 0.552]	1.4 × 10⁻¹²	0.447	[0.337; 0.546]
$\sum^{} \frac{(σ_{r \pm})}{r} \leq 0.5$ ${\mathop \sum \nolimits^ ^}{{\left( {{\sigma _{r \pm }}} \right)} \over r} \le 0.5$	223, 124, 347	2.7 × 10⁻¹¹	0.427	[0.313; 0.529]	6.0 × 10⁻¹¹	0.420	[0.306; 0.523]

HCR, HCM, HCD, HCP subsamples

	N_P, N_s, N_pl	p-value	R	CI	p_err-value	$\tilde{X} (R)$ $\mathop X\limits^ (R)$
$\sum^{} \frac{(σ_{r \pm})}{r} \leq 2$ ${\mathop \sum \nolimits^ ^}{{\left( {{\sigma _{r \pm }}} \right)} \over r} \le 2$	149, 97, 254	5.7 × 10⁻⁸²	0.958	[0.943; 0.970]	5.86 × 10⁻⁷⁰	0.943	[0.920; 0.958]
$\sum^{} \frac{(σ_{m \pm})}{m} \leq 2$ ${\mathop \sum \nolimits^ ^}{{\left( {{\sigma _{m \pm }}} \right)} \over m} \le 2$	67, 61, 130	1.7 × 10⁻³⁷	0.959	[0.935 0.975]	1.2 × 10⁻²⁴	0.905	[0.840; 0.938]
$\sum^{} \frac{(σ_{ρ \pm})}{ρ} \leq 2$ ${\mathop \sum \nolimits^ ^}{{\left( {{\sigma _{\rho \pm }}} \right)} \over \rho } \le 2$	69, 59, 129	2.6 × 10⁻³⁸	0.959	[0.954; 0.984]	4.5 × 10⁻⁷	0.904	[0.821; 0.933]
$\sum^{} \frac{(σ_{pr})}{pr} \leq 2$ ${\mathop \sum \nolimits^ ^}{{\left( {{\sigma _{{\rm{pr}}}}} \right)} \over {{\rm{pr}}}} \le 2$	43, 34, 112	1.2 × 10⁻²¹	0.956	[0.920; 0.976]	4.0 × 10⁻¹⁴	0.966	[0.920; 0.986]

HCR subsample correlation

	N_P, N_s, N_pl	p-value	R	CI	P_err	$\tilde{X} (R)$ $\mathop X\limits^ (R)$	CI_err	p_sim	$\bar{R_{sim}}$ $\overline {{R_{{\rm{sim}}}}}$
$\sum^{} \frac{(σ_{m \pm})}{m} \leq 2$ ${\mathop \sum \nolimits^ ^}{{\left( {{\sigma _{m \pm }}} \right)} \over m} \le 2$	91, 74, 168	0.0016	0.326	[0.130; 0.499]	0.0007	0.333	[0.135; 0.503]	0.16	0.355 ± 0.267
$\sum^{} \frac{(σ_{ρ \pm})}{ρ} \leq 2$ ${\mathop \sum \nolimits^ ^}{{\left( {{\sigma _{\rho \pm }}} \right)} \over \rho } \le 2$	84, 67, 154	0.00001	0.463	[0.275; 0.616]	3.3 × 10⁻⁵	0.415	[0.228; 0.583]	0.012	0.443 ± 0.142

Stellar HCM and HCD subsamples (N_P = 40)					Bootstrap test (N_P = 40)

Subsample type	N_s, N_pl	p-value	R	CI		p_bts	$\tilde{X} {(R)}_{bts}$ $\mathop X\limits^ {(R)_{{\rm{bts}}}}$	CI_bts

m T_eff [2566; 4398] K	24, 64	5.6 × 10⁻¹⁵	0.896	[0.811; 0.944]	$\sum^{} \frac{(σ_{r +})}{r} \leq 2$ ${\mathop \sum \nolimits^ ^}{{\left( {{\sigma _{r + }}} \right)} \over r} \le 2$	1.7 × 10⁻²²	0.545	[0.455; 0.624]
p [−0.21;−0.01] [Fe/H]	31, 71	3.99 × 10⁻¹⁴	0.884	[0.790; 0.937]	$\sum^{} \frac{(σ_{m \pm})}{m} \leq 2$ ${\mathop \sum \nolimits^ ^}{{\left( {{\sigma _{m \pm }}} \right)} \over m} \le 2$	0.5	0.002	[−0.143; 0.146]
p [6.03; 12.3] Gyr	24, 64	3.7 × 10⁻¹²	0.850	[0.733 0.919]	$\sum^{} \frac{(σ_{ρ_{\pm}})}{ρ} \leq 2$ ${\mathop \sum \nolimits^ ^}{{\left( {{\sigma _{{\rho _ \pm }}}} \right)} \over \rho } \le 2$	4.5 × 10⁻⁷	0.362	[0.223; 0.487]
					$\sum^{} \frac{(σ_{pr \pm})}{p r} \leq 2$ ${\mathop \sum \nolimits^ ^}{{\left( {{\sigma _{{\rm{pr}} \pm }}} \right)} \over {pr}} \le 2$	0.21	0.066	[−0.097; 0.226]

Notes. N_P, N_s, N_pl stand for the number of pairs/triples, the total number of systems, and the total number of planets in the subsample, respectively. $\tilde{X} (R)$ $\mathop X\limits^ (R)$ and $\bar{R_{sim}}$ $\overline {{R_{{\rm{sim}}}}}$ stand for median and mean R-value, respectively, p is the p-value, and CI is the confidence interval stated for α = 0.05. Prefix err stands for the results of the error-accommodation test for uncertainties. Prefix sim stands for results after 10⁵ simulations of mass and density populations from the non-parametric MRR (Ning et al. 2018) giving the observed radii. Prefix bts stands for results after the bootstrap test was performed on the entire sample.

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