The star HIP 41378 potentially misaligned with its cohort of long-period planets

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Table C.2

Posteriors with median and 68% highest density intervals.

Parameter	Model with α = 0	Model with α = 0.2	Model with α between 0 and 1
MCMC Inputs:
Transits:
R_*	1.299 ± 0.002	1.299 ± 0.002	1.297 ± 0.002
u₁	0.42 ± 0.01	0.42 ± 0.01	0.41 ± 0.01
u₂	${0.09}_{- 0.03}^{+ 0.02}$ $0.09_{ - 0.03}^{ + 0.02}$	0.09 ± 0.03	0.11 ± 0.02
R_p / R_*	0.0666 ± 0.0001	0.0666 ± 0.0001	0.0665 ± 0.0001
B	0.18 ± 0.01	0.18 ± 0.01	${0.16}_{- 0.02}^{+ 0.01}$ $0.16_{ - 0.02}^{ + 0.01}$
T₀	58271.0738 ± 0.0001	57186.9146 ± 0.0002	57186.9144 ± 0.0002
T_0,RM	59897.0199 ± 0.0009	59897.0199 ± 0.0009	59897.0196 ± 0.0009
P_f	${542.0797}_{- 0.0002}^{+ 0.0001}$ $542.0797_{ - 0.0002}^{ + 0.0001}$	${542.0797}_{- 0.0002}^{+ 0.0001}$ $542.0797_{ - 0.0002}^{ + 0.0001}$	${542.0797}_{- 0.0002}^{+ 0.0001}$ $542.0797_{ - 0.0002}^{ + 0.0001}$
γ_C18	${1.000003}_{- 0.000003}^{+ 0.000004}$ $1.000003_{ - 0.000003}^{ + 0.000004}$	${1.000003}_{- 0.000003}^{+ 0.000004}$ $1.000003_{ - 0.000003}^{ + 0.000004}$	${1.000003}_{- 0.000003}^{+ 0.000004}$ $1.000003_{ - 0.000003}^{ + 0.000004}$
RM effect
P_rot	7.8 ± 1.0	8.4 ± 1.0	${8.1}_{- 0.9}^{+ 0.6}$ $8.1_{ - 0.9}^{ + 0.6}$
Λ	21 ± 8	$30_{- 8}^{+ 7}$ $30_{ - 8}^{ + 7}$	38 ± 3
cos (i_*)	0.74 ± 0.08	${0.68}_{- 0.10}^{+ 0.08}$ $0.68_{ - 0.10}^{ + 0.08}$	0.45 ± 0.06
Α	–		${0.93}_{- 0.1}^{+ 0.05}$ $0.93_{ - 0.1}^{ + 0.05}$
cos(θ)	–	${0.8}_{- 0.4}^{+ 0.2}$ $0.8_{ - 0.4}^{ + 0.2}$	${0.94}_{- 0.06}^{+ 0.04}$ $0.94_{ - 0.06}^{ + 0.04}$
γ_{HARPS –N}	–11 ± 1	–11 ± 1	–11 ± 1
γ_{ES PRES S O}	–16 ± 1	–15 ± 1	–16 ± 1
γ_CARMENES	–8 ± –2	$- 8_{- 2}^{+ 1}$ $- 8_{ - 2}^{ + 1}$	–8 ± –2
γ_NEID	–5 ± 1	–5 ± 1	–7 ± 1
γ_HIRES	$- {1.3}_{- 1.3}^{+ 1.1}$ $- 1.3_{ - 1.3}^{ + 1.1}$	${0.8}_{- 1.4}^{+ 1.1}$ $0.8_{ - 1.4}^{ + 1.1}$	${0.2}_{- 1.1}^{+ 1.2}$ $0.2_{ - 1.1}^{ + 1.2}$
γ_EXPRESS	–3 ± 1	–4 ± 1	–5 ± 1
γ_MERCATOR	–4 ± 5	$- 4_{- 5}^{+ 4}$ $- 4_{ - 5}^{ + 4}$	$- 4_{- 5}^{+ 4}$ $- 4_{ - 5}^{ + 4}$
γ_PARAS	$3_{- 8}^{+ 9}$ $3_{ - 8}^{ + 9}$	$3_{- 10}^{+ 8}$ $3_{ - 10}^{ + 8}$	3 ± 9
σ_{HARPS –N}	${1.13}_{- 1.03}^{+ 0.47}$ $1.13_{ - 1.03}^{ + 0.47}$	${1.22}_{- 1.03}^{+ 0.56}$ $1.22_{ - 1.03}^{ + 0.56}$	${1.07}_{- 1.00}^{+ 0.41}$ $1.07_{ - 1.00}^{ + 0.41}$
σ_{ES PRES S O}	${1.7}_{- 0.4}^{+ 0.5}$ $1.7_{ - 0.4}^{ + 0.5}$	${1.7}_{- 0.5}^{+ 0.4}$ $1.7_{ - 0.5}^{ + 0.4}$	${1.18}_{- 0.5}^{+ 0.6}$ $1.18_{ - 0.5}^{ + 0.6}$
σ_CARMENES	${3.8}_{- 1.1}^{+ 1.4}$ $3.8_{ - 1.1}^{ + 1.4}$	${3.9}_{- 1.2}^{+ 1.3}$ $3.9_{ - 1.2}^{ + 1.3}$	${3.6}_{- 1.4}^{+ 1.3}$ $3.6_{ - 1.4}^{ + 1.3}$
σ_NEID	${0.6}_{- 0.6}^{+ 0.3}$ $0.6_{ - 0.6}^{ + 0.3}$	${0.6}_{- 0.6}^{+ 0.3}$ $0.6_{ - 0.6}^{ + 0.3}$	${0.5}_{- 0.5}^{+ 0.2}$ $0.5_{ - 0.5}^{ + 0.2}$
σ_HIRES	3.2 ± 0.4	3.2 ± 0.4	2.9 ± 0.4
σ_EXPRESS	${2.7}_{- 0.9}^{+ 0.8}$ $2.7_{ - 0.9}^{ + 0.8}$	${2.8}_{- 0.8}^{+ 0.9}$ $2.8_{ - 0.8}^{ + 0.9}$	3.2 ± 0.9
σ_MERCATOR	21 ± 2	21 ± 2	21 ± 2
σ_PARAS	$4_{- 4}^{+ 1}$ $4_{ - 4}^{ + 1}$	$4_{- 4}^{+ 1}$ $4_{ - 4}^{ + 1}$	$4_{- 4}^{+ 2}$ $4_{ - 4}^{ + 2}$
a₀	$- {0.0002}_{- 0.0089}^{+ 0.0111}$ $- 0.0002_{ - 0.0089}^{ + 0.0111}$	$- {0.0002}_{- 0.0093}^{+ 0.0105}$ $- 0.0002_{ - 0.0093}^{ + 0.0105}$	${0.0004}_{- 0.0095}^{+ 0.0101}$ $0.0004_{ - 0.0095}^{ + 0.0101}$
a₁	–0.01 ± 0.09	$- {0.009}_{- 0.108}^{+ 0.091}$ $- 0.009_{ - 0.108}^{ + 0.091}$	$- {0.02}_{- 0.09}^{+ 0.10}$ $- 0.02_{ - 0.09}^{ + 0.10}$
a₂	0.02 ± 1.00	${0.02}_{- 0.91}^{+ 1.10}$ $0.02_{ - 0.91}^{ + 1.10}$	${0.01}_{- 0.93}^{+ 1.00}$ $0.01_{ - 0.93}^{ + 1.00}$
Derived Parameters:
a/R_*	${230.04}_{- 0.34}^{+ 0.39}$ $230.04_{ - 0.34}^{ + 0.39}$	${230.12}_{- 0.37}^{+ 0.35}$ $230.12_{ - 0.37}^{ + 0.35}$	${230.62}_{- 0.39}^{+ 0.38}$ $230.62_{ - 0.39}^{ + 0.38}$
I	89.953 ± 0.003	89.954 ± 0.003	89.958 ± 0.003
i_*	$42_{- 7}^{+ 6}$ $42_{ - 7}^{ + 6}$	47 ± 7	66 ± 5
υ_eq sin(i_*)	5.6 ± 0.3	${6.3}_{- 0.4}^{+ 0.5}$ $6.3_{ - 0.4}^{ + 0.5}$	${8.6}_{- 0.8}^{+ 0.9}$ $8.6_{ - 0.8}^{ + 0.9}$
υ_eq	${8.4}_{- 0.8}^{+ 1.4}$ $8.4_{ - 0.8}^{ + 1.4}$	${8.6}_{- 0.8}^{+ 1.1}$ $8.6_{ - 0.8}^{ + 1.1}$	${9.4}_{- 0.9}^{+ 1.2}$ $9.4_{ - 0.9}^{ + 1.2}$
Ψ	52 ± 6	51 ± 5	45 ± 3
Θ	–	$38_{- 20}^{+ 27}$ $38_{ - 20}^{ + 27}$	20 ± 9

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