The µ Herculis system solved after nearly three centuries

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Volume 709 (May 2026)

A&A, 709 (2026) A145

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Table 4

Joint solution.

Parameter	Unit	Joint solution	$σ_{M_{1}}$ $Mathematical equation: ${\sigma _{{M_1}}}$$ [%]
Astrometry

ϖ_CM	mas	120.069 ± 0.089	12.1
$μ_{α^{}, CM}$ $Mathematical equation: ${\mu _{{\alpha ^},{\rm{CM}}}}$$	mas yr⁻¹	−324.13 ± 0.25	<0.1
µ_δ,CM	mas yr⁻¹	−747.74 ± 0.22	<0.1
$μ_{δ, CM}$ $Mathematical equation: ${\mu _{\delta ,{\rm{CM}}}}$$	mas	550.26 ± 8.60	<0.1
∆δ_A	mas	−420.19 ± 7.55	<0.1

Orbits

P_A	yr	78.987 ± 0.288	50.9
τ_A	BJD	2460156.6 ± 7.3	<0.1
e_A		0.379 ± 0.001	<0.1
a_A	au	20.418 ± 0.050	26.6
a_1,A	au	3.427 ± 0.015	10.2
i_A	deg	62.39 ± 0.07	<0.1
ω_A	deg	50.303 ± 0.224	<0.1
Ω_A	deg	267.50 ± 0.06	<0.1
P_BC	yr	43.141 ± 0.008	<0.1
τ_BC	BJD	2454637.0 ± 20.8	<0.1
e_BC		0.179 ± 0.001	<0.1
a_BC	au	11.705 ± 0.031	<0.1
a_1,BC	au	5.664 ± 0.052	<0.1
i_BC	deg	66.10 ± 0.09	<0.1
ω_BC	deg	173.430 ± 0.510	<0.1
Ω_BC	deg	60.48 ± 0.14	<0.1
P_A,BC	yr	${12905.46}_{- 608.68}^{+ 421.70}$ $Mathematical equation: $12905.46_{ - 608.68}^{ + 421.70}$$	<0.1
τ_A,BC	BJD	${4690500.10}_{- 110823.59}^{+ 77254.66}$ $Mathematical equation: $4690500.10_{ - 110823.59}^{ + 77254.66}$$	<0.1
e_A,BC		0.879 ± 0.004	<0.1
a_A,BC	au	$1132_{- 33}^{+ 25}$ $Mathematical equation: $1132_{ - 33}^{ + 25}$$	<0.1
i_A,BC	deg	79.58 ± 0.21	<0.1
ω_A,BC	deg	290.6 ± 0.8	<0.1
Ω_A,BC	deg	238.05 ± 0.34	<0.1

Other

f_B/ f_C		0.50 ± 0.10	<0.1
σ_HIRES	m s⁻¹	3.28 ± 0.34	<0.1
γ_HIRES	m s⁻¹	−16237.44 ± 3.26	<0.1
σ_Hamilton	m s⁻¹	8.28 ± 0.56	<0.1
γ_Hamilton	m s⁻¹	−16248.88 ± 3.16	<0.1
$σ_{{SONG}_{old}}$ $Mathematical equation: ${\sigma _{{\rm{SON}}{{\rm{G}}_{{\rm{old}}}}}}$$	m s⁻¹	2.44 ± 0.39	<0.1
$γ_{{SONG}_{old}}$ $Mathematical equation: ${\gamma _{{\rm{SON}}{{\rm{G}}_{{\rm{old}}}}}}$$	m s⁻¹	−16238.87 ± 3.56	<0.1
$σ_{{SONG}_{new}}$ $Mathematical equation: ${\sigma _{{\rm{SON}}{{\rm{G}}_{{\rm{new}}}}}}$$	m s⁻¹	3.35 ± 0.14	<0.1
$γ_{{SONG}_{new}}$ $Mathematical equation: ${\gamma _{{\rm{SON}}{{\rm{G}}_{{\rm{new}}}}}}$$	m s⁻¹	−16251.49 ± 3.30	<0.1
σ_APF	m s⁻¹	3.54 ± 0.11	<0.1
γ_APF	m s⁻¹	−16258.87 ± 3.32	<0.1
σ_CORAVEL	m s⁻¹	${0.00}_{- 0.00}^{+ 0.00}$ $Mathematical equation: $0.00_{ - 0.00}^{ + 0.00}$$	<0.1
γ_CORAVEL	m s⁻¹	−16373.63 ± 51.90	<0.1

Derived

M_Aa	M_⊙	1.134 ± 0.007	–
M_Ab	M_⊙	0.2286 ± 0.0006	–
M_C	M_⊙	0.445 ± 0.005	–
M_B	M_⊙	0.417 ± 0.005	–
Φ_A/A−BC	deg	32.59 ± 0.24	–
Φ_BC/A−BC	deg	145.58 ± 0.24	–
Φ_A/BC	deg	122.31 ± 0.11	–
r_p	au	137.42 ± 3.15	–

Notes. Median and 68% credible intervals on all parameters of our joint solution. The column $σ_{M_{1}}$ $Mathematical equation: ${\sigma _{{M_1}}}$$ describes the error budget of each parameter to the mass of µ Her Aa.

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