Two neighbours of the ultra-short-period Earth-sized planet K2-157 b in the warm Neptunian savanna

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Volume 699 (July 2025)

A&A, 699 (2025) A344

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Table B.5

Parameters of K2-157 b, K2-157 c, and K2-157 d based on the joint fit analysis described in Sect. 4.4.

Parameter	Priors	Posteriors

Orbital and physical parameters of K2-157 b
Orbital period, P_orb,b (days)	𝒰(0.3, 0.4)	${0.3652575}_{- 0.0000088}^{+ 0.0000078}$ $0.3652575_{ - 0.0000088}^{ + 0.0000078}$
Time of mid-transit, T_0,b (JD)	𝒰(2457582.6, 2457583.0)	${2457582.8220}_{- 0.0032}^{+ 0.0041}$ $2457582.8220_{ - 0.0032}^{ + 0.0041}$
Orbital inclination, i_b (degrees)	𝒰(50, 150)	${89.2}_{- 9.1}^{+ 9.3}$ $89.2_{ - 9.1}^{ + 9.3}$
Scaled planet radius, R_p,b/R_★	𝒰(0.00, 0.05)	0.00996 ± 0.00094
RV semi-amplitude, K_b (ms^–1)	𝒰(0, 20)	${1.10}_{- 0.41}^{+ 0.39}$ $1.10_{ - 0.41}^{ + 0.39}$
Planet radius, R_p,b (R_⊕)	(derived)	0.935 ± 0.090
Planet radius, R_p,b (R_J)	(derived)	0.0834 ± 0.0081
Planet mass, M_p,b(M_⊕)	(derived)	${1.14}_{- 0.42}^{+ 0.41}$ $1.14_{ - 0.42}^{ + 0.41}$
Planet mass, M_p,b(M_J)	(derived)	0.0036 ± 0.0013
Planet density, ρ_p,b (g cm^–3)	(derived)	7.7 ± 3.6
Transit depth, Δ_b (ppm)	(derived)	99 ± 19
Transit duration, T_14,b (hours)	(derived)	1.161 ± 0.032
Relative orbital separation, a_b/R_★	(derived)	2.405 ± 0.059
Orbit semi-major axis, a_b (au)	(derived)	0.00962 ± 0.00010
Planet surface gravity, g_b (ms^–2)	(derived)	12.8 ± 5.3
Impact parameter, b_b	(derived)	0.03 ± 0.38
Incident flux, F_inc,b (F_⊕)	(derived)	(6.66 ± 0.20) × 10³
Equilibrium temperature [A=0], T_eq,b (K)	(derived)	2432 ± 42

Orbital and physical parameters of K2-157 c

Orbital period, P_orb,c (days)	𝒰(0, 400)	${25.942}_{- 0.044}^{+ 0.045}$ $25.942_{ - 0.044}^{ + 0.045}$
Time of mid-transit, T_0,c (JD)	𝒰(2458533, 2458933)	2458557.02 ± 0.30
RV semi-amplitude, K_c (ms^–1)	𝒰(0, 20)	7.17 ± 0.42
Minimum mass, M_p,c sin i (M_⊕)	(derived)	30.8 ± 1.9
Minimum mass, M_p,c sin i (M_J)	(derived)	0.0967 ± 0.0060
Relative orbital separation, a_c/R_★	(derived)	41.2 ± 1.0
Orbit semi-major axis, a_c (au)	(derived)	0.1650 ± 0.0018
Incident flux, F_inc,c (F_⊕)	(derived)	22.65 ± 0.68
Equilibrium temperature [A=0], T_eq,c (K)	(derived)	587 ± 10

Orbital and physical parameters of K2-157 d

Orbital period, P_orb,d (days)	𝒰(0, 400)	${66.50}_{- 0.59}^{+ 0.71}$ $66.50_{ - 0.59}^{ + 0.71}$
Time of mid-transit, T_0,d (JD)	𝒰(2458533, 2458933)	${2458589.3}_{- 2.0}^{+ 1.7}$ $2458589.3_{ - 2.0}^{ + 1.7}$
RV semi-amplitude, K_d (ms^–1)	𝒰(0, 20)	${3.96}_{- 0.41}^{+ 0.42}$ $3.96_{ - 0.41}^{ + 0.42}$
Minimum mass, M_p,d sin i (M_⊕)	(derived)	23.3 ± 2.5
Minimum mass, M_p,d sin i (M_J)	(derived)	0.0732 ± 0.0077
Relative orbital separation, a_d/R_★	(derived)	77.3 ± 2.0
Orbit semi-major axis, a_d (au)	(derived)	0.3090 ± 0.0038
Incident flux, F_inc,d (F_⊕)	(derived)	6.46 ± 0.21
Equilibrium temperature [A=0], T_eq,d (K)	(derived)	429.1 ± 7.5

RV quadratic trend

Systemic velocity, v_sys (ms^–1)	𝒰(43430, 43460)	${43448.11}_{- 0.66}^{+ 0.64}$ $43448.11_{ - 0.66}^{ + 0.64}$
Linear term, γ (ms^–1 day^–1)	𝒰(–0.1, 0.1)	$- {0.0491}_{- 0.0051}^{+ 0.0052}$ $- 0.0491_{ - 0.0051}^{ + 0.0052}$
Quadratic term, δ (ms^–1 day^–2)	𝒰(–0.01, 0.01)	${6.20}_{- 0.91}^{+ 0.92} \times 10^{- 5}$ $6.20_{ - 0.91}^{ + 0.92} \times {10^{ - 5}}$

Instrument-dependent parameters

K2 LC level C10, F_0,C10	𝒰(–0.1, 0.1)	$- {0.000042}_{- 0.000233}^{+ 0.000216}$ $- 0.000042_{ - 0.000233}^{ + 0.000216}$
K2LC jitter C10, σ_K2,C10	𝒰(0,0.005)	${4.6}_{- 3.2}^{+ 4.8} \times 10^{- 6}$ $4.6_{ - 3.2}^{ + 4.8} \times {10^{ - 6}}$
RV jitter, σ_jit	𝒰(0, 10)	${1.06}_{- 0.43}^{+ 0.38}$ $1.06_{ - 0.43}^{ + 0.38}$

Limb-darkening coefficients

Limb-darkening coefficient, q_1,Kepler	𝒰(0, 1)	${0.62}_{- 0.34}^{+ 0.26}$ $0.62_{ - 0.34}^{ + 0.26}$
Limb-darkening coefficient, q_2,Kepler	𝒰(0, 1)	${0.45}_{- 0.30}^{+ 0.33}$ $0.45_{ - 0.30}^{ + 0.33}$

GP hyperparameters

η_σ	𝒰(0, 0.5)	${0.00048}_{- 0.00015}^{+ 0.00031}$ $0.00048_{ - 0.00015}^{ + 0.00031}$
η_ρ (days)	𝒰(0, 30)	${6.3}_{- 1.8}^{+ 3.1}$ $6.3_{ - 1.8}^{ + 3.1}$

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