Confirmation of the hot super-Neptune TOI-672 b with NIRPS and HARPS - Insights into the Neptunian desert around M dwarfs

Open Access

Table D.1

Prior distributions used in our joint fit model and the resulting fit values.

Parameter		(Unit)	Prior distribution	Fit value
Planet

Period	P	(days)	U(3.6236, 3.6436)	3.633581 ± 0.000001
Reference time of midtransit	t₀	(BJD_TDB-2457000)	U(1546.4700, 1546.4900)	1546.4796 ± 0.0003
Log of the radius	log(R_p)	(R_⊙)	U(-3.99, -1.99)^*	$- {3.02}_{- 0.05}^{+ 0.04}$ $Mathematical equation: $-3.02^{+0.04}_{-0.05}$$
Radius	R_p	(R_⊕)	– (derived)	${5.31}_{- 0.26}^{+ 0.24}$ $Mathematical equation: $5.31^{+0.24}_{-0.26}$$
Eccentricity	e		0 (fixed)	−
Argument of periastron	ω	(°)	0 (fixed)	−

Host star

Radius	R_*	(R_⊙)	*N_B*(0.54, 0.02, 0.0, 3.0)	0.54 ± 0.03
Mass	M_*	(M_⊙)	*N_B*(0.54, 0.01, 0.0, 3.0)	0.54 ± 0.03

Photometry

TESS
Offset			N(0.0, 1.0)	0.00005 ± 0.00010
Log of the jitter	log (J_TESS)		N(-11.58^†, 10.0)	−11.805 ± 0.006
Log of the maximum power	log (S₀ω⁴₀)		N(-11.58^†, 10.0)	−10.4 ± 0.3
Log of the undamped angular frequency	log (ω₀)		N(0.0, 10.0)	1.1 ± 0.1

ExTrA
Offset			N(0.0, 1.0)	${0.0005}_{- 0.0242}^{+ 0.0246}$ $Mathematical equation: $0.0005^{+0.0246}_{-0.0242}$$
Log of the amplitude scale	log (σ)		U(log (0.01), log (0.1))	$- {3.8}_{- 0.6}^{+ 0.7}$ $Mathematical equation: $-3.8^{+0.7}_{-0.6}$$
Log of the length scale	log (ρ)		U(log (0.3), log (3.0))	${0.4}_{- 0.7}^{+ 0.5}$ $Mathematical equation: $0.4^{+0.5}_{-0.7}$$

RVs

Log of the radial velocity semi-amplitude	log (K)		U(0.0,10.0)	3.47 ± 0.08
Radial velocity semi-amplitude	K	(ms⁻¹)	– (derived)	${32.0}_{- 2.5}^{+ 2.6}$ $Mathematical equation: $32.0^{+2.6}_{-2.5}$$

NIRPS
Offset		(ms⁻¹)	U(-4650.0,-4550.0)	$- {4604.3}_{- 2.8}^{+ 2.9}$ $Mathematical equation: $-4604.3^{+2.9}_{-2.8}$$
Log of the jitter	log (J_NIRPS)	(ms⁻¹)	N(2.90^‡, 5.0)	${1.14}_{- 4.05}^{+ 1.06}$ $Mathematical equation: $1.14^{+1.06}_{-4.05}$$
Jitter	J_NIRPS	(ms⁻¹)	– (derived)	${1.77}_{- 1.54}^{+ 1.24}$ $Mathematical equation: $1.77^{+1.24}_{-1.54}$$
Amplitude	η_NIRPS	(ms⁻¹)	HC(5.0)$	${7.5}_{- 4.7}^{+ 3.2}$ $Mathematical equation: $7.5^{+3.2}_{-4.7}$$
Recurrence timescale	θ_NIRPS	(days)	U(10.0,40.0)	${23.4}_{- 9.6}^{+ 11.0}$ $Mathematical equation: $23.4^{+11.0}_{-9.6}$$
Growth and decay timescale	λ_NIRPS	(days)	U(log (10.0), log (4000.0))	${165.9}_{- 143.6}^{+ 1261.4}$ $Mathematical equation: $165.9^{+1261.4}_{-143.6}$$
Smoothing parameter	γ_NIRPS		*N_T*(0.2, 5.0, 0.0, 1.0)	${0.32}_{- 0.2}^{+ 0.32}$ $Mathematical equation: $0.32^{+0.32}_{-0.2}$$

HARPS
Offset		(ms⁻¹)	U(-4700.0,-4600.0)	−4653.5 ± 2.9
Log of the jitter	log (J_HARPS)	(ms⁻¹)	N(1.52^‡, 5.0)	2.4 ± 0.2
Jitter	J_HARPS	(ms⁻¹)	– (derived)	${3.3}_{- 0.3}^{+ 0.4}$ $Mathematical equation: $3.3^{+0.4}_{-0.3}$$

The joint fit model is fully described in Section 4. The priors are created using distributions in PyMC, with the relevant inputs to each distribution described below. The fit values are given as the median values of the samples, and the uncertainties as the 16th and 84th percentiles. Further (derived) system parameters can be found in Table 3.

Distributions:

N(μ,σ): a normal distribution with a mean μ and a standard deviation a;

N_B(μ, σ, a, b): a bounded normal distribution with a mean μ, a standard deviation σ, a lower bound a, and an upper bound b (bounds optional);

N_T(μ, σ, a, b): a truncated normal distribution with a mean μ, a standard deviation σ, a lower bound a, and an upper bound b (bounds optional);

U(a, b): a uniform distribution with a lower bound a, and an upper bound b;

HC(a): a Half-Cauchy distribution with scale factor a.

Prior values:

^*equivalent to 0.5(log (D)) + log (R_*) ± 1 where D is the transit depth (ppm multiplied by 10⁻⁶) and R_* is the mean of the prior on the stellar radius (R_e), and −1 computes the lower bound while +1 computes the upper bound;

^†equivalent to the log of the variance of the TESS flux;

^‡equivalent to 2 multiplied by the log of the minimum error on the NIRPS or HARPS RV data, respectively.

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