Planetary edge trends - I. The inner edge – stellar mass correlation

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Volume 699 (July 2025)

A&A, 699 (2025) A333

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Table 2

Power-law index of the result and model.

Dataset and Mechanism		Index (γ₁ )¹	Reference
Observational Result	Previous Work	0.38 – 0.9	Plavchan & Bilinski (2013)
	Previous Work	1/3 ~ 0.33	Mulders et al. (2015)

	all multiple systems	${0.81}_{- 0.08}^{+ 0.09} ({0.63}_{- 0.04}^{+ 0.04})$ $0.81_{-0.08}^{+0.09} (0.63_{-0.04}^{+0.04})$	This Work
	R_p < R_gap (super-Earths)	${0.57}_{- 0.11}^{+ 0.10} ({0.54}_{- 0.05}^{+ 0.05})$ $0.57_{-0.11}^{+0.10} (0.54_{-0.05}^{+0.05})$
	R_p ≥ R_gap (sub-Neptunes)	${0.67}_{- 0.18}^{+ 0.17} ({0.38}_{- 0.09}^{+ 0.09})$ $$0.67_{-0.18}^{+0.17} (0.38_{-0.09}^{+0.09})$
	mixed multiple systems	${1.12}_{- 0.07}^{+ 0.08} ({0.95}_{- 0.05}^{+ 0.05})$ $1.12_{-0.07}^{+0.08} (0.95_{-0.05}^{+0.05})$

Theoretical Model	Sublimation (active, α = 2)³	11/9 ∼ 1.22	Liu et al. (2019)
	Sublimation (passive, k = 2)⁴	1.0	Dullemond et al. (2001)
	Sublimation (active, α = 1)³	7/9 ∼ 0.78	Liu et al. (2019)
	Stellar Tides	9/13 ∼ 0.69	Jackson et al. (2009)
	Sublimation (passive, k = 1)⁴	0.5	Dullemond et al. (2001)
	Co-rotation Radius	1/3 ∼ 0.33	Mulders et al. (2015)
	Planetary Tides	3/13 ∼ 0.23	Jackson et al. (2009)

Notes. ¹The index represents the power-law relationship between the inner edge and stellar mass (γ₁ ). ²To compare with the degree of metallicity correction presented in the observational results of this work, it is expressed here in the form: “γ₁ in Eq. (8) (γ₁ in Eq. (3))”. ³In the theoretical model of active dust sublimation, α represents the power-law index of the mass accretion rate scaling with stellar mass. ⁴In the theoretical model of passive dust sublimation, k represents the power-law index of the luminosity-mass dependence.

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