Discovery of Three New Transiting Hot Jupiters: WASP-161 b, WASP-163 b, and WASP-170 b

Inaugurated by the seminal discovery of 51 Peg b in 1995 (Mayor & Queloz 1995), the study of exoplanets has dramatically developed to become one of the most important fields of modern astronomy. Since 1995, most of the exoplanets have been detected by the transit technique (Charbonneau et al. 2000; Henry et al. 2000).

Among this large harvest, highly irradiated giant planets (a.k.a. hot Jupiters) transiting bright nearby stars have a particular scientific interest. These rare objects—<1% of solar-type stars (Winn & Fabrycky 2015)—undergo irradiation that is orders of magnitude larger than that of any solar system planet (Fortney et al. 2007), and are subject to intense gravitational and magnetic fields (Chang et al. 2010; Correia & Laskar 2010). Studying in detail their physical and chemical responses to such extreme conditions provides a unique opportunity to improve our knowledge on planetary structure, composition, and physics. The brightness of their host star combined with their eclipsing configuration makes such detailed characterization possible, notably to precisely measure their size, mass, and orbital parameters (Deming & Seager 2009; Winn 2010), but also to probe their atmospheric properties, for example, the P − T profiles, chemical composition, and albedos (Seager & Deming 2010; Crossfield 2015; Sing et al. 2016).

The WASP (Wide Angle Search for Planets) project (described in Pollacco et al. 2006; Collier Cameron et al. 2007) uses two robotic installations, one at La Palma (Spain) and one at Sutherland (South Africa), to scout the sky for gas giants transiting the solar-type stars. With more than 100 hot Jupiters discovered so far in front of bright nearby stars, WASP is a key contributor to the study of highly irradiated giant planets. In this paper, we report the discovery of three new gas giants, WASP-161 b, WASP-163 b, and WASP-170 b, transiting bright (V = 11.1, 12.5, and 12.8) solar-type (F6-, G8-, and G1-type) dwarf stars.

In Section 2, we present the observations used to discover WASP-161 b, WASP-163 b, and WASP-170 b, and to confirm their planetary natures and measure their parameters. In Section 2.2.1, we describe notably TRAPPIST-North, a 60 cm robotic telescope installed recently by the University of Liège at Oukaimeden observatory (Morocco), that played a significant role in the confirmation and characterization of the planets. Section 3.1 presents the determination of the atmospheric parameters of the host stars. In Section 3.2, we describe our global analysis of the data set for the three planetary systems that enabled us to determine their main physical and orbital parameters. We discuss briefly our results in Section 6.

2.1. WASP Photometry

WASP-161 and WASP-170 (see Table 1 for coordinates and magnitudes) were observed with WASP-South (Hellier et al. 2011, 2012) in 2011 and 2012, while WASP-163 was observed in 2010 and 2012. The WASP-South data reduction methods described by Collier Cameron et al. (2006) and selected (Collier Cameron et al. 2007) as valuable candidates showing possible transits of short-period (∼5.4, 1.6, and 2.3 days) planetary sized bodies (Figure 1).

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Table 1.  The Parameters of the WASP-161, WASP-163, and WASP-170 Planetary Systems (Values + 1σ Error Bars), As Deduced from Our Data Analysis Presented in Section 3

	General Star Information
	WASP-161	WASP-163	WASP-170
	2MASS08252108–1130035	2MASS17060901–1024467	2MASS09013992–2043133
	GaiaId 5751177091580191360	GaiaId 4334991786994866304	GaiaId 5656184406542140032
R.A. (J200)	08h25m2109	17h06m0898	09h01m3993
Decl. (J200)	−11°30'036	−10°24'470	−20°43'136
Vmag [UCAC4]	10.98	12.54	12.65
Jmag [2MASS]	10.09	10.67	11.13
Gmag [Gaia-DR1]	10.84	12.13	12.36
Parallax [mas] [Gaia-DR2]	2.8864 ± 0.0345	3.7981 ± 0.0525	3.2439 ± 0.0390
	Stellar parameters from spectroscopic analysis
Teff (K)	6400 ± 100	5500 ± 200	5600 ± 150
$\mathrm{log}{g}_{\star }$ [cgs]	4.5 ± 0.15	4.0 ± 0.3	4.0 ± 0.2
[Fe/H]	+0.16 ± 0.09	−0.34 ± 0.21	+0.22 ± 0.09
Spectral type	F6	G8	G1
$V\sin i$ [Km/s]	18 ± 0.8	<5	5.6 ± 1
$\mathrm{log}A({Li})$	No Lithium seen	<1.6	1.52 ± 0.09
	Parameters from MCMC analysis
MCMC Jump Parameters
(Rp/R⋆)2 [%]	0.45092 ± 0.00023	1.417 ± 0.067	1.382 ± 0.001
Impact parameter b [R⋆]	${0.14}_{-0.10}^{+0.15}$	${0.45}_{-0.06}^{+0.09}$	0.689 ± 0.021
Transit duration W [day]	0.2137 ± 0.0022	0.093 ± 0.001	0.085 ± 0.001
Midtransit T0 [HJD]	7416.5289 ± 0.0011	7918.4620 ± 0.0004	7802.3915 ± 0.0002
Orbital period P [day]	5.4060425 ± 0.0000048	1.6096884 ± 0.0000015	2.34478022 ± 0.0000036
RV K2 [m s−1d1/3]	405 ± 20	386.69 ± 16	340 ± 20
Effective temperature Teff [K]	6406 ± 100	5499 ± 200	5593 ± 150
Metallicity [Fe/H]	0.16 ± 0.09	−0.34 ± 0.21	0.21 ± 0.19
Deduced Stellar Parameters from MCMC
Mean density ρ⋆ [ρ⊙]	${0.282}_{-0.027}^{+0.013}$	${0.92}_{-0.10}^{+0.13}$	${1.121}_{-0.076}^{+0.093}$
Stellar surface gravity $\mathrm{log}{g}_{\star }$ [cgs]	${4.111}_{-0.033}^{+0.023}$	${4.411}_{-0.040}^{+0.042}$	4.466 ± 0.031
Stellar mass M⋆ [M⊙]	1.39 ± 0.14	0.97 ± 0.15	0.93 ± 0.15
Stellar radius R⋆ [R⊙]	${1.712}_{-0.072}^{+0.083}$	${1.015}_{-0.074}^{+0.071}$	${0.938}_{-0.061}^{+0.056}$
Luminosity L⋆ [L⊙]	${4.44}_{-0.48}^{+0.56}$	${0.84}_{-0.17}^{+0.20}$	0.77 ± 0.14
Deduced Planet Parameters from MCMC	WASP-161 b	WASP-163 b	WASP-170 b
RV K [ms−1]	230 ± 12	329 ± 14	255 ± 15
Planet/star radius ratio Rp/R⋆	0.0671 ± 0.0017	0.119 ± 0.003	0.1175 ± 0.0041
Impact parameter b [R⋆]	${0.14}_{-0.10}^{+0.15}$	${0.448}_{-0.094}^{+0.063}$	0.689 ± 0.021
Semimajor axis a/R⋆	${8.49}_{-0.28}^{+0.13}$	${5.62}_{-0.21}^{+0.26}$	${7.71}_{-0.18}^{+0.21}$
Orbital semimajor axis a [au]	0.0673 ± 0.0023	0.0266 ± 0.0014	0.0337 ± 0.0018
Inclination ip [deg]	${89.01}_{-1.0}^{+0.69}$	${85.42}_{-0.85}^{+1.10}$	84.87 ± 0.28
Density ρp [ρJup]	1.66 ± 0.22	${1.07}_{-0.17}^{+0.23}$	${1.21}_{-0.19}^{+0.24}$
Surface gravity $\mathrm{log}{g}_{p}$ [cgs]	${3.69}_{-0.42}^{+0.37}$	3.52 ± 0.05	3.54 ± 0.05
Mass Mp [MJup]	2.49 ± 0.21	1.87 ± 0.21	1.6 ± 0.2
Radius Rp [RJup]	${1.143}_{-0.058}^{+0.065}$	1.202 ± 0.097	1.096 ± 0.085
Roche limit aR [au]	${0.01101}_{-0.00068}^{+0.00075}$	0.011 ± 0.001	0.011 ± 0.001
a/aR	${6.12}_{-0.28}^{+0.25}$	${2.35}_{-0.13}^{+0.16}$	3.15 ± 0.19
Equilibrium temperature Teq [K]	${1557}_{-29}^{34}$	1638 ± 68	1422 ± 42
Irradiation [erg s−1 cm−2]	${1.35}_{-0.26}^{+0.34}\times {10}^{9}$	1.63 ± 0.45 × 109	${9.3}_{-2.5}^{+2.3}\times {10}^{8}$

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2.2. Follow-up Photometry

2.2.1. TRAPPIST-North

TRAPPIST-North is a new robotic telescope that is 60 cm in diameter and was installed in 2016 June at the Oukaimeden Observatory (Morocco). It was installed by the University of Liège (Belgium) and in collaboration with the Cadi Ayyad University of Marrakech (Morocco). TRAPPIST-North extends the TRAPPIST project to the northern hemisphere, and, like its southern twin TRAPPIST-South, aims to detect and characterize transiting exoplanets and to study comets and other small bodies (e.g., asteroids) in the solar system. The exoplanet program of TRAPPIST (75% of its observational time) is dedicated to several programs: participating in the SPECULOOS project that aims to explore the nearest ultracool dwarf stars for transiting terrestrial planets (Burdanov et al. 2017; Gillon et al. 2017; Delrez et al. 2018; Gillon 2018); the search for the transit of planets previously detected by radial velocity (Bonfils et al. 2011); the follow-up of transiting planets of high interest (e.g., Gillon et al. 2012); and the follow-up of transiting planet candidates identified by wide-field transit surveys like WASP (e.g., Delrez et al. 2014). TRAPPIST-North has an F/8 Ritchey–Chretien optical design and is protected by a 4.2 m diameter dome equipped with a weather station and independent rain and light sensors. The telescope is equipped with a thermoelectrically cooled 2048 × 2048 deep-depletion Andor IKONL BEX2 DD CCD camera that has a pixel scale of 060 that translates into an FOV of 198 × 198. It is coupled with a direct-drive mount of German equatorial design. For more technical details and performances of the TRAPPIST telescopes, see Jehin et al. (2011).

TRAPPIST-North observed two partial transits of WASP-161 b in the Sloan-z' filter (2017 December 20 and 2018 February 12), two partial transits and one full transit of WASP-163 b in the I + z filter (2017 April 24, May 2, and June 13), and three partial transits of WASP-170 b in the I + z (2017 April 19 and 2018 January 11) and V (2017 February 17) filters. The reduction and photometric analysis of the data were performed as described in Gillon et al. (2013). The resulting light curves are shown in Figures 2–4.

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2.2.2. TRAPPIST-South

We used the 60 cm robotic telescope TRAPPIST-South (TRansiting Planets and PlanetesImals Small Telescope; Gillon et al. 2011; Jehin et al. 2011) at La Silla (Chile) to observe a partial transit of WASP-161 b in the Sloan-z' filter on 2016 January 28, two partial transits of WASP-163 b in a broad I + z filter on 2014 September 6 and 2016 July 5, and two transits (one full + one partial) of WASP-170 b in I + z on 2015 December 25 and 2017 February 26. TRAPPIST-South is equipped with a thermoelectrically cooled 2 K × 2 K CCD with the pixel scale of 065 that translates into a 22' × 22' of FOV. Standard calibration of the images, fluxes extraction, and differential photometry were then performed as described in Gillon et al. (2013). The resulting light curves are shown in Figures 2–4.

2.2.3. EulerCam

We used the EulerCam camera (Lendl et al. 2012) on the 1.2 m Euler-Swiss telescope at La Silla Observatory in Chile to observe a transit of WASP-163 b on 2016 July 27 in the RG filter, and also a transit of WASP-170 b on 2016 December 20 in the broad NGTS filter (λ_NGTS = [500–900 nm]; Wheatley et al. 2018). The calibration and photometric reduction (aperture + differential photometry) of the images were performed as described by Lendl et al. (2012). The resulting light curves are shown in Figures 3 and 4.

2.2.4. NITES

We use 0.4 m NITES (Near-Infrared Transiting ExoplanetS Telescope, McCormac et al. 2014) robotic telescope at La Palma (Canary Islands) to observe two transits of WASP-163 b. The first transit was full and observed in R-band on 2016 June 27, while the second was only partial and observed in I-band on 2016 July 10. NITES is equipped with a 1024 × 1024 CCD camera that has a pixel scale of 066 that translates into an FOV of 113 × 113. The standard calibration of the science images, fluxes extraction, and differential photometry were then performed as described in Craig et al. (2015), Barbary (2016), Bertin & Arnouts (1996), and McCormac et al. (2013). The resulting light curves are shown in Figure 3.

2.2.5. SPECULOOS-South

We use 1 m robotic SSO-Europa telescope, one of the four telescopes of the SPECULOOS-South facility, (more details found in Delrez et al. 2018; Gillon 2018; Burdanov et al. 2017) to observe one full-transit of WASP-161 b on 2018 January 5 in the Sloan-z' filter. Each 1 m robotic telescope is equipped with a 2 K × 2 K CCD camera, with good sensitivity in the very-near-infrared up to 1 μm. The calibration and photometric reduction of the data were performed as described in Gillon et al. (2013). The resulting light curve is shown in Figure 2.

2.3. Follow-up Spectroscopy

3.1. Spectroscopic Analysis

3.2. RVs + Light-curves Analysis

We performed a global analysis of the RVs (Table 6) and transit light curves (Table 3) with the MCMC (Markov chain Monte Carlo) algorithm described by Gillon et al. (2012) to determine the parameters of each planetary system. While the CORALIE RVs were modeled with a classical Keplerian model (e.g., Murray & Correia 2010), the transit light curves were represented by the transit model of Mandel & Agol (2002), assuming a quadratic limb-darkening law, multiplied by a baseline model consisting of a polynomial function of one or several external parameters (time, background, airmass, etc.; see Table 3). The selection of the model used for each time-series was based on the minimization of the Bayesian Information Criterium (BIC, Schwarz 1978).

Table 3.  Parameters of Each Light Curve

Target	Night	Telescope	Filter	Np	Texp (s)	Baseline function	σ (%)	σ7.2 m(%)	βw	βr	CF
WASP-161	2016 Jan 28	TRAPPIST-S	Sloan-z'	938	10	p(t + xy + o)	0.37	0.051	1.29	1.08	1.39
WASP-161	2017 Dec 20	TRAPPIST-N	Sloan-z'	902	10	p(t + b)	0.43	0.072	1.14	1.05	1.20
WASP-161	2018 Jan 5	SPECULOOS	Sloan-z'	1235	10	p(xy)	0.44	0.087	1.22	1.44	1.72
WASP-161	2018 Feb 12	TRAPPIST-N	Sloan-z'	892	10	p(a)	0.46	0.054	1.14	1.20	1.37
WASP-163	2014 Sep 6	TRAPPIST-S	I + z	345	12	p(t)	0.33	0.006	1.06	1.00	1.06
WASP-163	2016 Jun 27	NITES	Johnson-R	443	30	p(t)	0.41	0.012	1.71	1.00	1.71
WASP-163	2016 Jun 27	EulerCam	RG	170	60	p(t + f + b)	0.11	0.005	1.20	1.10	1.31
WASP-163	2016 Jul 5	TRAPPIST-S	I + z	602	12	p(a + xy)	0.35	0.011	1.16	1.35	1.56
WASP-163	2016 Jul 10	NITES	Johnson-I	388	30	p(t)	0.58	0.012	1.55	1.18	1.83
WASP-163	2017 Apr 24	TRAPPIST-N	I + z	487	12	p(t + xy + o)	0.31	0.008	1.02	1.07	1.09
WASP-163	2017 May 2	TRAPPIST-N	I + z	213	12	p(b)	0.54	0.009	0.90	1.00	0.90
WASP-163	2017 Jun 13	TRAPPIST-N	I + z	557	14	p(t + f)	0.69	0.021	0.87	1.16	1.01
WASP-170	2015 Dec 25	TRAPPIST-S	I + z	359	15	p(f)	0.29	0.008	1.04	1.05	1.09
WASP-170	2016 Dec 20	EulerCam	NGTS	207	40	p(t)	0.11	0.005	1.49	1.13	1.68
WASP-170	2017 Feb 17	TRAPPIST-N	Johnson-V	239	20	p(t)	0.46	0.013	1.22	1.00	1.22
WASP-170	2017 Feb 26	TRAPPIST-S	I + z	545	15	p(t + a)	0.51	0.015	1.32	1.16	1.53
WASP-170	2017 Apr 19	TRAPPIST-N	I + z	186	15	p(a + xy)	0.41	0.008	0.99	1.00	0.99
WASP-170	2018 Jan 11	TRAPPIST-N	I + z	315	15	p(t)	0.26	0.007	0.75	1.11	0.83

Note. The table shows for each light curve the date, telescope, filter, number of data points, exposure time, selected baseline function, rms of the best-fit residuals, deduced values for β_w, β_r and CF = β_w × β_r. For the baseline function, p(^N), denotes, respectively, an N-order polynomial function of time ( = t), airmass ( = a), full width at half maximum ( = f), background ( = b), and x and y positions ( = xy). The symbol o denotes an offset fixed at the time of the meridian flip.

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TRAPPIST-North and TRAPPIST-South telescopes are equipped with German equatorial mounts that have to rotate 180° at meridian, resulting in different positions of the stars' images on the detector after the flip, translating into an offset of the fluxes in the light curves. For the corresponding light curves, a normalization offset at the time of the flip was thus added to the assumed model (Table 3).

Table 4.  Stellar Mass and Age Estimates from the Software BAGEMASS

Star	Mass [M⊙]	Age [Gyr]
WASP-161 A	1.42 ± 0.05 (1.40)	2.4 ± 0.4 (2.4)
WASP-163 A	0.87 ± 0.06 (0.78)	11.4 ± 3.5 (17.4)a
WASP-170 A	0.99 ± 0.07 (1.03)	4.8 ± 3.1 (2.9)

Note.

^aBest fit occurs at edge of model grid.

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For each system, the "jump" parameters of the Markov Chains, i.e., the parameters perturbed at each step of the chains, were the transit duration, depth, and impact parameter (W, dF, and b, respectively), the orbital period P, the midtransit time T₀, the parameters $\sqrt{e}\cos \omega$ and $\sqrt{e}\sin \omega$ (with ω the argument of periastron and e the orbital eccentricity), the parameter $K2=K\sqrt{1-{e}^{2}}{P}^{1/3}$ (with K is the RV semiamplitude), and the stellar metallicity [Fe/H] and effective temperature T_eff. In addition, for each filter, the combinations, c₁ = 2 × u₁ + u₂ and c₂ = u₁ − 2 × u₂ were also jump parameters, u₁ and u₂ being the linear and quadratic limb-darkening coefficients. Normal prior probability distribution functions (PDFs) based on the theoretical tables of Claret (2000) were assumed for u₁ and u₂ (Table 5). For T_eff and [Fe/H], Gaussian PDFs based on the values + errors derived from our spectral analysis (Table 1) were used. For the other jump parameters, uniform prior PDFs were assumed (e.g., e ≥ 0, b ≥ 0).

Table 5.  The Quadratic Limb-darkening (LD) Coefficients u₁ and u₂ Used in Our MCMC Analysis

LD Coefficient	WASP-161	WASP-163	WASP-170
u1,z'	0.184 ± 0.011	⋯	⋯
u2,z'	0.300 ± 0.005	⋯	⋯
u1,I+z	⋯	0.207 ± 0.012	0.2539 ± 0.0202
u2,I+z	⋯	0.297 ± 0.010	0.2788 ± 0.0152
u1,Johnson–I	⋯	0.331 ± 0.034	0.2727 ± 0.0321
u2,Johnson–I	⋯	0.251 ± 0.019	0.2805 ± 0.0158
u1,Johnson–R	⋯	0.420 ± 0.043	⋯
u2,Johnson–R	⋯	0.248 ± 0.027	⋯
u1,Johnson–V	⋯	⋯	0.437 ± 0.044
u2,Johnson–V	⋯	⋯	0.271 ± 0.025

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Each global analysis was composed of three Markov chains of 10⁵ steps whose convergence was checked using the statistical test presented by Gelman & Rubin (1992). The correlation of the noise present in the light curves was taken into account by rescaling the errors as described by Gillon et al. (2012). For the RVs, the quadratic difference between the mean error of the measurements and the standard deviation of the best-fit residuals were computed as 32.6 m s⁻¹, 54.1 m s⁻¹, and 42.8 m s⁻¹ for WASP-161, WASP-163, and WASP-170, respectively. These "jitter" noises were added quadratically to the errors.

At each step of the Markov chains, a value for the stellar density ρ_* was computed from dF, b, W, P, $\sqrt{e}\cos \omega$, and $\sqrt{e}\sin \omega$ (see, e.g., Winn 2010). This value of ρ_* was then used in combination with the values for T_eff and [Fe/H] to compute a value for the stellar mass M_* from the empirical calibration of Enoch et al. (2010). Two MCMC analyses were performed for each system, one assuming an eccentric orbit and one assuming a circular one. The Bayes factors, computed as $\exp (-{\rm{\Delta }}\mathrm{BIC}/2)$, were largely (>1000) in favor of a circular model for the three systems, and we thus adopted the circular solution for all of them. These solutions are presented in Table 1. The noncircular solutions enable us to estimate the 3σ upper limits on the orbital eccentricity as 0.43, 0.13, and 0.23 for, respectively, WASP-161 b, WASP-163 b, and WASP-170 b.

As a sanity check of our results, we also estimated the stellar radius R_⋆ from the star's parallax determined by Gaia (Gaia Collaboration et al. 2018), its effective temperature T_eff, and its bolometric magnitude M_bol, using the equations:

$$\begin{eqnarray}&&{M}_{v}={V}_{\mathrm{mag}}-5{\mathrm{log}}_{10}(d/10),\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&{M}_{\mathrm{bol}}={M}_{v}+\mathrm{BC},\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&{L}_{\star }/{L}_{\odot }={10}^{0.4(4.74-{M}_{\mathrm{bol}})},\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&{R}_{\star }={L}_{\star }/4\pi \sigma {T}_{\mathrm{eff}}^{4},\end{eqnarray} \tag{ 4 }$$

where M_v is the absolute visual magnitude, BC is the bolometric correction (Pecaut & Mamajek 2013), d is the distance in parsec, pc, L_⋆ is the star luminosity, and σ is the Stefan–Boltzmann constant. We estimated the error on R_⋆ by propagating the errors of all other parameters. We obtained 1.55 ± 0.08 R_⊙ for WASP-161, 0.86 ± 0.07 R_⊙ for WASP-163, and 0.91 ± 0.06 R_⊙ for WASP-170, in good agreement with our MCMC results shown in Table 1.¹²

The WASP-170 light curve from WASP-South shows a quasi-periodic modulation with an amplitude of about 0.6% and a period of about 7.8 days. We assume this is due to the star spots (i.e., the combination of the star rotation and the magnetic activity). The rotational modulation of each star was estimated by using the sine-wave fitting method described in Maxted et al. (2011). The star variability due to star spots is not expected to be coherent on long timescales as a consequence of the finite lifetime of the star spots and differential rotation in the photosphere, so we analyzed the WASP-170 data separately. We separately analyzed the WASP-170 data from each camera used, so that we could estimate the reliability of the results. The transit signal was removed from the data to calculate the periodograms by subtracting a simple transit model from the light curve. We calculated the periodograms over uniformly spaced frequencies from 0 to 1.5 cycles/day. The false alarm probability (FAP) is calculated by the boot-strap Monte Carlo as described in Maxted et al. (2011). The results are presented in Table 2, and the periodograms and light curves are shown in Figure 5. The rotation period value we obtain is P_rot = 7.75 ± 0.02 days from the clear signal near 7.8 days in five out of seven data sets. From the stellar radius estimated and the rotation period, the value of ${V}_{\mathrm{rot}}\sin I=6.1\pm 0.3$ km s⁻¹ is implied, assuming that the axes of the star and the planet orbital are approximately aligned, in good agreement with our spectroscopic analysis (vsini = 5.6 ± 1.0 km s⁻¹, see the Table 1). We modeled the rotational modulation in the light curves for each camera and season with the rotation period fixed at P_rot = 7.75 days using the least-squares fit of a sinusoidal function and its first harmonic. Similar analyses are performed for WASP-161 and WASP-163.

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We estimated the mass and age of the host stars using the software BAGEMASS¹³ based on the Bayesian method described in Maxted et al. (2015). The models used in the software BAGEMASS were calculated using the GARSTEC stellar evolution code as described in Weiss & Schlattl (2008). The deduced stellar masses and ages calculated are shown in Table 4. The inferred masses are in good agreement with the ones resulting from our global MCMC analysis (see Table 1).

WASP-161 b, WASP-163 b, and WASP-170 b are planets slightly larger (1.14 ± 0.06 R_Jup, 1.2 ± 0.1 R_Jup, and 1.10 ± 0.09 R_Jup) and more massive (2.5 ± 0.2 M_Jup, 1.9 ± 0.2 M_Jup, and 1.6 ± 0.2 M_Jup) than Jupiter. Given their masses and their large irradiations (Figure 6(a)), their radii are well reproduced by the models of Fortney et al. (2007), assuming a core mass of a few dozens of M_⊕ and ages larger than a few hundreds of megayears (Figure 6(b)).

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The empirical relationship derived by Weiss et al. (2013) for planets more massive than 150M_⊕, R_p/R_⊕ = 2.45 (M_p/M_⊕)^{−0.039±0.01} (F/erg s⁻¹ cm⁻²)^0.094 predicts radii of 1.16 ± 0.30 R_Jup, 1.20 ± 0.34 R_Jup, and 1.15 ± 0.31 R_Jup for WASP-161 b, 163 b, and 170 b, respectively, which are consistent with our measured radii. The three new planets whose discovery is described thus appear to be "standard" hot Jupiters that do not present a "radius anomaly" challenging standard models of irradiated gas giants.

The discovery of WASP-161 b, WASP-163 b, and WASP-170 b establishes the new robotic telescope TRAPPIST-North as a powerful northern facility for the photometric follow-up of transiting exoplanet candidates found by ground-based wide-field surveys like WASP, and soon by the space-based mission TESS (Ricker et al. 2016).

WASP-South is hosted by the SAAO and we are grateful for their ongoing support and assistance. Funding for WASP comes from consortium universities and from the UK's Science and Technology Facilities Council. The Euler-Swiss telescope is supported by the Swiss National Science Foundation. TRAPPIST-South is funded by the Belgian Fund for Scientic Research (FNRS) under the grant FRFC 2.5.594.09.F, with the participation of the Swiss National Science Foundation (SNF). M.G. is FNRS Research Associate, and E.J. is FNRS Senior Research Associate. L.D. acknowledges support from the Gruber Foundation Fellowship. The research leading to these results has received funding from the European Research Council under the FP/2007-2013 ERC Grant Agreement 336480, and from the ARC grant for Concerted Research Actions, financed by the Wallonia-Brussels Federation. This work was also partially supported by a grant from the Simons Foundation (ID 327127 to Didier Queloz), a grant from the Erasmus+ International Credit Mobility programme (K. Barkaoui), as well as by the MERAC foundation (P. I. Triaud).