The GAPS Programme at TNG - LIX. Characterisation study of the ∼300 Myr-old multi-planetary system orbiting the star BD+40 2790 (TOI-2076)

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Volume 690 (October 2024)

A&A, 690 (2024) A235

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Table B.1

Prior used to model RVs and spectroscopic activity diagnostics.

Parameter	Prior
GP hyper-parameters:
h_HARPS-N [ m s⁻¹]	𝒰(0,100)
h_CARMENES-VIS [m s⁻¹]	𝒰(0,100)
h_NEID [m s⁻¹]	𝒰(0,100)
ln λ [days]	𝒰(0,10)
w	𝒰(0,2)
θ [days]	𝒰(0,10)
Planet-related parameters:
K_b [m s⁻¹]	𝒰(0,20)
orbital period, P_b [days]	𝒩(10.35523,0.00001)
T_{conj, b} [BJD-2450000]	𝒩(8950.8289,0.0005)
K_c [m s⁻¹]	𝒰(0,20)
orbital period, P_c [days]	𝒩(21.01549,0.00003)
T_{conj, c} [BJD-2450000]	𝒩(8937.8283,0.0007)
K_d [m s⁻¹]	𝒰(0,20)
orbital period, P_d [days]	𝒩(35.125514,0.00007)
T_{conj, d} [BJD-2450000]	𝒩(8938.2965,0.001)
acceleration, $\dot{γ} [m s^{- 1} d^{- 1}]$ $\dot \gamma \left[ {{\rm{m}}\,{{\rm{s}}^{ - 1}}{d^{ - 1}}} \right]$	𝒰(−1,1)
activity diagnostic-related parameters:
semi-amplitude of a long-term activity signal (log ${R^{'}}_{HK}$ ${{{\rm{R'}}}_{{\rm{HK}}}}$ ) [dex]	𝒰(0,1)
semi-amplitude of a long-term activity signal (FWHM) [m/s]	𝒰(0,100)
period of a long-term activity signal (log ${R^{'}}_{HK}$ ${{{\rm{R'}}}_{{\rm{HK}}}}$ and FWHM) [days]	𝒰(0,2000)
Reference time of a long-term activity signal (log ${R^{'}}_{HK}$ ${{{\rm{R'}}}_{{\rm{HK}}}}$ and FWHM) [BJD-2450000]	𝒰(9000,11000)
$σ_{jit} log {R^{'}}_{HK} [dex]$ ${\sigma _{{\rm{jit}}}}\,{\rm{and}}\,{{{\rm{R'}}}_{{\rm{HK}}}}\,\left[ {{\rm{dex}}} \right]$	𝒰(0,0.1)
offset, $γ_{\log {R^{'}}_{HK}} [dex]$ ${\gamma _{\log \,{{{\rm{R'}}}_{{\rm{HK}}}}}}$	𝒰(−4.6,-4)
σ_{jit, FWHM} [m/s]	𝒰(0,50)
offset, γ_FWHM [m/s]	𝒰(8000,9500)
multi-dimensional GP-related parameters:
A_RV, B_RV [m/s]	𝒰(−100,100)
A_BIS, B_BIS [m/s]	𝒰(−100,100)
A_FWHM [m/s]	𝒰(−100,100)
$A_{\log {R^{'}}_{HK}} [dex]$ ${A_{\log \,{{{\rm{R'}}}_{{\rm{HK}}}}}}\left[ {{\rm{dex}}} \right]$	𝒰(−0.1,0.1)
Instrument-related parameters:
σ_{jit, HARPS-N} [m s⁻¹]	𝒰(0,50) (all RV extractions)
offset, γ_HARPS-N [m s⁻¹]	𝒰(−13000,−12500) (DRS)
offset, γ_HARPS-N [ms⁻¹]	𝒰(−100,100) (SERVAL)
offset, γ_HARPS-N [m s⁻¹]	𝒰(−12700,−12300) (LBL)
σ_{jit, CARMENES-VIS} [ m s⁻¹]	𝒰(0,50)
γ_CARMENES-VIS [ m s⁻¹]	𝒰(−100,100)
σ_{jit, NEID} [m s⁻¹]	𝒰(0,50)
γ_NEID [m s⁻¹]	𝒰(−12800,−12600)
TRADES specific parameters:
planet mass [M_⊙]	𝒰(0,0.0003) ^(a)
planet eccentricity	𝒩(0,0.1) ^(b)
argument of periastron [deg]	𝒰(0,360) ^(a)
mean anomaly [deg]	𝒰(0,360) ^(a)
stellar mass [M_⊙]	0.849 (fixed)
longitude of ascending node [deg]	180 (fixed)

^(a) Same prior adopted for all the transiting planets in the system.

^(b) Following the result of Van Eylen et al. (2019) for multi-planet systems. Only positive values were sampled. The same prior has been adopted for all three transiting planets in the system.

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