The likelihood of not detecting cavity-carving companions in transition discs – A statistical approach

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Table 1

Comparison between observational $a_{cav}^{obs}$ $a_{\text{cav}}^{\text{obs}}$ and theoretical a_cav for a few systems with known orbital properties of the companions.

Name	R_mm (au)	$a_{cav}^{obs}$ $a_{\text {cav}}^{\text {obs}}$ = 0.75 × R_mm (au)	e_bin	a_bin (au)	q	i_d (^∘)	a_cav (au)
PDS 70⁽¹⁾	74	55	0.04	34	0.007	0.	51
V892 Tau⁽²⁾	27	20	0.27	7.1	∼1	8	20
IRAS 04158+2805⁽³⁾	240	180	∼0.7	∼55	∼1	≲20	185
GG Tau^{(4, 5)}	220	165	0.2–0.4	50–60	0.77	10^∘–30^∘	160

Notes. We defined $a_{cav}^{obs}$ $a_{\text{cav}}^{\text{obs}}$ = ϵ R_mm, where ϵ = 0.75, R_mm is the observed radius of the centre of the dust ring at the edge of the cavity, and the theoretical a_cav was obtained from Eqs. (5) and (6) using the orbital parameters constrained from observations. ⁽¹⁾Wang et al. 2021 (the reported parameters refer to the dynamically stable solutions of the outer planet, PDS 70c). ⁽²⁾Long et al. 2021. ⁽³⁾ Ragusa et al. 2021. ⁽⁴⁾Keppler et al. 2020. ⁽⁵⁾Toci et al. 2024.

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