Stability of a cluster-disrupted mean-motion resonance (chain) in HR 8799 and PDS 70

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Table 1

λ, ln f_s, and 5 σf_s CI of planetary systems at certain current ages.

Planetary system (age)	Configuration	λ(Myr⁻¹)^a	$ln f_{s}^{b}$ $\ln f_{s}^{b}$	f_s(5σ CI)^c
HR 8799 (20 Myr)	Resonant, perturbed	0.17 ± 0.16	−3.4 ± 3.3	(2.4 · 10⁻⁹, 1]
	Non-resonant, isolated	2.29 ± 0.32	−46 ± 6.5	(1.2 · 10⁻³⁴, 1.3 · 10⁻⁶)
	Non-resonant, perturbed	2.31 ± 0.33	−46 ± 6.6	(3.7 · 10⁻³⁵, 2.4 · 10⁻⁶)

HR 8799 (50 Myr)	Resonant, perturbed	0.17 ± 0.16	−8.6 ± 8.2	(2.7 · 10⁻²², 1]
	Non-resonant, isolated	2.29 ± 0.32	−114 ± 16	(1.7 · 10⁻⁸⁵, 2.1 · 10⁻¹⁵)
	Non-resonant, perturbed	2.31 ± 0.33	−115 ± 17	(8.1 · 10⁻⁸⁷, 8.7 · 10⁻¹⁵)

PDS 70 (5.4 ± 1.0 Myr)	Resonant, perturbed	0.52 ± 0.32	−2.8 ± 1.8	(7.1 · 10⁻⁶, 1]
	Non-resonant, isolated	0.55 ± 0.11	−2.9 ± 0.8	(1.0 · 10⁻³, 1]
	Non-resonant, perturbed	0.67 ± 0.13	−3.6 ± 1.0	(2.2 · 10⁻⁴, 1]

Notes. ^(a)The exponential distribution parameter. ^(b)The natural logarithm of the expected fraction of surviving planetary systems at the current age. ^(c)The 5σ confidence interval of the expected fraction of surviving planetary systems at the current age f_s (bounded by [0, 1]).

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