A decade of transit photometry for K2-19: Revised system architecture

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Volume 703 (November 2025)

A&A, 703 (2025) A167

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Table 5

Fourier and photodynamical mass estimates.

Parameter	Units	Median and 68.3% CI	MAP	v_R/v_S, A_S ⁽¹⁾	Petigura⁽²⁾	From Radii⁽³⁾
		Photodyn	Photodyn	Fourier	Photodyn
		10 yr	10 yr	10 yr	3.3 yr
m_b	M_⊕	30.8 ± 1.3	29.62	30.03	32.4 ± 1.7	39.6
m_c	M_⊕	11.12 ± 0.44	10.94	11.08	10.8 ± 0.6	18.0
Δm_b,c/m_b,c			−0.04, −0.02	−0.02, −0.004	+0.05, +0.03	+0.29, +0.62
ρ_b	g cm⁻³	0.59	0.57	0.58	0.52	0.76
ρ_c	g cm⁻³	1.05	1.03	1.04	0.86	1.69
$P_{S} ({\bar{P}}_{S})$ ${P_S}\,\left( {{{\bar P}_S}} \right)$	d			2711.2		(2751.9)
P_R	d			717.4
$A_{S}^{(b)}, A_{R}^{(b)}$ $A_S^{\left( b \right)},\,A_R^{\left( b \right)}$	min			53.4, (41.7)
$A_{S}^{(c)}, A_{R}^{(c)}$ $A_S^{\left( c \right)},\,A_R^{\left( c \right)}$	min			233.2, (148.3)
β_S, β_R	deg	$\begin{matrix} {[- 101.9]}_{- 1.4}^{+ .1.5} & {[- 42.7]}_{- 1.9}^{+ .2.2} \end{matrix}$ $\matrix{ {\left[ { - 101.9} \right]_{ - 1.4}^{ + .1.5}} & {\left[ { - 42.7} \right]_{ - 1.9}^{ + .2.2}} \cr }$	[−103.9], [−41.9]	(−103.5, −35.7)
λ_n	deg	${85.8}_{- 1.9}^{+ 1.7}$ $85.8_{ - 1.9}^{ + 1.7}$	82.8		37.5⁽⁴⁾
R		${[14.81]}_{- 0.26}^{+ 0.37}$ $\left[ {14.81} \right]_{ - 0.26}^{ + 0.37}$	[15.49]	13.28	[15.7]
∆σ		${[0.0029]}_{- 2. e - 5}^{+ 1. e - 5}$ $\left[ {0.0029} \right]_{ - 2.e - 5}^{ + 1.e - 5}$	[0.0029]	0.0030	[0.0029]
$e_{b}^{(+)} (e_{b})$ $e_b^{\left( + \right)}\left( {{e_b}} \right)$		${[0.015]}_{- 0.0002}^{+ 0.0002} ({0.043}_{- 0.024}^{+ 0.024})$ $\left[ {0.015} \right]_{ - 0.0002}^{ + 0.0002}\left( {0.043_{ - 0.024}^{ + 0.024}} \right)$	[0.015] (0.069)	0.015	$[0.015] ({0.20}_{- 0.03}^{+ 0.03})$ $\left[ {0.015} \right]\left( {0.20_{ - 0.03}^{ + 0.03}} \right)$
$e_{c}^{(+)} (e_{c})$ $e_c^{\left( + \right)}\left( {{e_c}} \right)$		${[0.044]}_{- 0.0004}^{+ 0.0005} ({0.067}_{- 0.017}^{+ 0.017})$ $\left[ {0.044} \right]_{ - 0.0004}^{ + 0.0005}\left( {0.067_{ - 0.017}^{ + 0.017}} \right)$	[0.045] (0.078)	0.043	$[0.047] ({0.21}_{- 0.03}^{+ 0.03})$ $\left[ {0.047} \right]\left( {0.21_{ - 0.03}^{ + 0.03}} \right)$

Notes. (1): ν_R/ν_S, A_S / Fourier A uses the frequency ratio and superamplitudes only to estimate masses; (2): Petigura / Photodyn uses system parameters from the photodynamical analysis of Petigura et al. (2020); (3): Estimates using mass-radius relation m_p/M_E = (R_p/0.56 R_E)^1/0.67 (Müller et al. 2024); (4): Petigura et al. (2020) value minus 180° to account for the fact that the authors assumed Ω_b(t_ref) = 0; [Square brackets] show the quantity calculated analytically from elements and masses using the formalism of Mardling (2025a); ∆m_b,c/m_b,c = relative difference in masses compared to median value; ${\bar{P}}_{S}$ ${\bar P_S}$ (defined from ephemeris periods such that ${\bar{P}}_{S}^{- 1} = n {\bar{P}}_{b}^{- 1} - (n + 1) {\bar{P}}_{c}^{- 1}$ $\bar P_S^{ - 1} = n\bar P_b^{ - 1} - \left( {n + 1} \right)\bar P_c^{ - 1}$ ) listed in the last column for comparison with the Fourier superperiod; Boldface entries: highlighted for comparison; Amplitudes and phases in brackets were not used directly in mass estimates. Last two rows: Entries in brackets are the median and 68.3% CI eccentricities for comparison with the fixed-point values $e_{b}^{(+)}$ $e_b^{\left( + \right)}$ and $e_{b}^{(+)}$ $e_b^{\left( + \right)}$ . The reference mean densities are ρ_Saturn = 0.69 g cm⁻³, ρ_Uranus = 1.15 g cm⁻³.

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