Three Hot-Jupiters on the upper edge of the mass-radius distribution: WASP-177, WASP-181 and WASP-183

TL;DR

This paper reports the discovery of three transiting exoplanets, including two hot-Jupiters and one hot-Saturn, that are near the upper edge of the mass-radius distribution, providing insights into their orbital alignment characteristics.

Contribution

The study presents the discovery and characterization of three new transiting planets near the upper mass-radius boundary, highlighting their orbital properties and host star types.

Findings

All three planets are close to the upper bound of the mass-radius space.

The planets have scaled semi-major axes between 9.6 and 12.1.

Their orbits are in the transition between aligned and misaligned systems.

Abstract

We present the discovery of 3 transiting planets from the WASP survey, two hot-Jupiters: WASP-177b (~0.5 M_Jup, ~1.6 R_Jup) in a 3.07-d orbit of a V = 12.6 K2 star, WASP-183b (~0.5 M_Jup, ~1.5 R_Jup) in a 4.11-d orbit of a V = 12.8 G9/K0 star; and one hot-Saturn planet WASP-181b (~0.3 M_Jup, ~1.2 R_Jup) in a 4.52-d orbit of a V = 12.9 G2 star. Each planet is close to the upper bound of mass-radius space and has a scaled semi-major axis, a/R_star, between 9.6 and 12.1. These lie in the transition between systems that tend to be in orbits that are well aligned with their host-star's spin and those that show a higher dispersion.

Figures

Tables

Table 1. Table 1: Observations of WASP-177, WASP-181 and WASP-183.

Date	Source	N.Obs.
		Filter
WASP-177
2008 Jul–2010 Oct	WASP (North)	16 169
2008 Jun–2009 Oct	WASP (South)	10 825
2016 Aug–2018 Sep	CORALIE	26
2017 Jul 25	TRAPPIST-North	I+z
2017 Oct 19	EulerCam	B
2018 Jul 13	EulerCam	V
2018 Aug 13	TRAPPIST-North222Meridian flip at BJD 2458344.5639.	I+z
WASP-181
2008 Sep–2010 Dec	WASP (North)	12 938
2008 Jul–2009 Aug	WASP (South)	9 059
2016 Jan–2017 Dec	CORALIE	31
2018 Oct–2019 Jan	HARPS	7
2016 Dec 06	TRAPPIST-South	I+z
2017 Jul 29	TRAPPIST-North	I+z
2017 Sep 03	EulerCam	Ic
WASP-183
2008 Feb–2011 Mar	WASP (North)	13 733
2009 Jan–2010 May	WASP (South)	10 789
2015 May–2018 Jul	CORALIE	16
2018 Mar	HARPS	4
2018 Feb 24	TRAPPIST-North	I+z

Table 2. Table 2: Periodogram analysis for WASP lightcurves of WASP-177.

WASP	Dates	Period	Amp	FAP	Notes
Inst.	JD-2450000	$P_{\mathrm{rot}}$ (d)	(mag.)
North	4656-4767	7.569	0.005	0.0017	P/2
North	5026-5131	7.528	0.006	<0.0001	P/2
North	5387-5498	14.860	0.004	<0.0001
South	4622-4764	14.330	0.005	0.0007
South	4984-5129	7.456	0.006	<0.0001	P/2

Table 3. Table 3: System parameters

Parameter	Symbol (Unit)	WASP-177	WASP-181	WASP-183
1SWASP ID	$-$	J221911.19-015004.7	J014710.37+030759.0	J105509.36-004413.7
Right ascension	(h:m:s)	22:19:11.19	01:47:10.37	10:55:09.36
Declination	(°:’:”)	-01:50:04.7	+03:07:59.0	-00:44:13.7
V magnitude	$-$	12.58	12.91	12.76
Spectral type333Spectral type estimated by comparison of $T_{\mathrm{eff}}$ to the table in Gray (2008).	$-$	K2	G2	G9/K0
Stellar effective temperature	$T_{\mathrm{eff}}$ ($K$)	$5017\pm 70$	$5839\pm 70$	$5313\pm 72$
Stellar surface gravity	$\log \left(g\right)$ (cgs)	$4.49\pm 0.07$	$4.38\pm 0.08$	$4.25\pm 0.09$
Stellar metallicity	[Fe/H] (dex)	$0.25\pm 0.04$	$0.09\pm 0.04$	$-0.31\pm 0.04$
Projected equatorial spin velocity	$V_{\ast }\sin I_{\ast }$ ($km/s$)	$1.8\pm 1.0$	$3.3\pm 0.9$	$1.0\pm 1.0$
Stellar macro-turbulent velocity444Derived via the method of Doyle et al. (2014).	$V_{\mathrm{mac}}$ ($km/s$)	$2.7$	$3.3$	$2.8$
Stellar age	(Gyr)	$9.7\pm 3.9$	$2.5\pm 1.7$	$14.9\pm 1.7$
Distance555From Gaia DR2 Gaia Collaboration et al. (2016, 2018); Luri et al. (2018).	(pc)	$178\pm 2$	$443\pm 8$	$328\pm 4$
Period	$P$ (d)	$3.071722\pm 0.000001$	$4.5195064\pm 0.0000034$	$4.1117771\pm 0.0000051$
Transit Epoch	$T_0-2450000$	$7994.37140\pm 0.00028$	$7747.66681\pm 0.00035$	$7796.1845\pm 0.0024$
Transit Duration	$T_{14}$ (d)	$0.0672\pm 0.0013$	$0.1277\pm 0.0015$	$0.084\pm 0.005$
Scaled Semi-major Axis	$a/R_s$	${9.61}_{-0.53}^{+0.42}$	$12.09\pm 0.54$	$11.44\pm 0.54$
Transit Depth	${\left(R_p/R_s\right)}^2$	${0.0185}_{-0.0014}^{+0.0035}$	$0.01590\pm 0.00038$	${0.0226}_{-0.0036}^{+0.0060}$
Impact Parameter	$b$	${0.980}_{-0.060}^{+0.092}$	${0.34}_{-0.15}^{+0.10}$	${0.916}_{-0.091}^{+0.163}$
Orbital Inclination	$i$ (°)	${84.14}_{-0.83}^{+0.66}$	${88.38}_{-0.59}^{+0.76}$	${85.37}_{-0.88}^{+0.61}$
Systemic Velocity	$\gamma$ $\left({\mathrm{kms}}^{-1}\right)$	$-7.1434\pm 0.0041$	$-8.5489\pm 0.0072$	$68.709\pm 0.012$
Semi-amplitude	$K_1\left({\mathrm{ms}}^{-1}\right)$	$77.3\pm 5.2$	$35.7\pm 3.9$	$74.8\pm 6.6$
Semi-major Axis	$a$ (au)	$0.03957\pm 0.00058$	$0.05427\pm 0.00069$	$0.04632\pm 0.00075$
Stellar Mass	$M_s$ $\left(M_{\odot }\right)$	$0.876\pm 0.038$	$1.04\pm 0.04$	$0.784\pm 0.038$
Stellar Radius	$R_s$ $\left(R_{\odot }\right)$	$0.885\pm 0.046$	$0.965\pm 0.043$	$0.871\pm 0.038$
Stellar Density	${\rho }_s$ (${\rho }_{\odot }$)	${1.26}_{-0.15}^{+0.23}$	$1.16\pm 0.15$	$1.19\pm 0.17$
Stellar Surface Gravity	$\log \left(g_s\right)$ (cgs)	${4.486}_{-0.037}^{+0.049}$	$4.487\pm 0.039$	$4.452\pm 0.043$
Limb-darkening Temperature	$T_{L-D}$ (K)	$5012\pm 69$	$5835\pm 70$	$5313\pm 72$
Stellar Metallicity	$\left[\text{Fe/H}\right]$	$0\pm 0$	$0\pm 0$	$0\pm 0$
Planet Mass	$M_p$ $\left(M_{\text{Jup}}\right)$	$0.508\pm 0.038$	$0.299\pm 0.034$	$0.502\pm 0.047$
Planet Radius	$R_p$ $\left(R_{\text{Jup}}\right)$	${1.58}_{-0.36}^{+0.66}$	${1.184}_{-0.059}^{+0.071}$	${1.47}_{-0.33}^{+0.94}$
Planet Density	${\rho }_p$ (${\rho }_{\text{Jup}})$	${0.130}_{-0.085}^{+0.153}$	$0.179\pm 0.033$	${0.16}_{-0.12}^{+0.18}$
Planet Surface	$\log \left(g_p\right)$ (cgs)	${2.67}_{-0.31}^{+0.22}$	$2.686\pm 0.065$	${2.72}_{-0.43}^{+0.22}$
Planet Equilibrium Temperature666Assuming 0 albedo and complete redistribution of heat.	$T_{eq}\left(K\right)$	$1142\pm 32$	${1186}_{-26}^{+32}$	$1111\pm 30$

Table 4. Table 4: Comparison of stellar radii output by the MCMC analysis with radii derived from Gaia DR2.

Radius source	WASP-177	WASP-181	WASP-183
MCMC	$0.885\pm 0.046$	$0.965\pm 0.043$	$0.871\pm 0.038$
Gaia parallax	$0.80\pm 0.04$	$0.97\pm 0.06$	$0.87\pm 0.04$
+ IRFM (Corrected)
Gaia parallax	$0.81\pm 0.04$	$1.01\pm 0.05$	$0.89\pm 0.04$
+ IRFM (Uncorrected)
Reddening	0.072	0.023	0.04

Table 5. Table 5: Convective zone masses and estimated time-scales for realignment of systems in this paper.

Star	$M_{\mathrm{cz}}$777Dervied from Pinsonneault et al. (2001).	$\tau$
	($M_{\odot }$)	(Gyr)
WASP-177	${10}^{-1.3}$	120
WASP-181	${10}^{-1.7}$	7500
WASP-183	${10}^{-1.4}$	200

Table 6. Table 6: Data from WASP

BJD -2450000	Diff.	Mag.	Target
	magnitude	error
5026.54902768	-0.00254900	0.01949100	WASP-177
5026.54946749	0.02243000	0.01957700	WASP-177
5026.55550916	-0.00315500	0.01926500	WASP-177
5026.55596055	-0.00210900	0.01891800	WASP-177
5026.56091425	0.02301800	0.01892700	WASP-177
5026.56135407	-0.01070600	0.01829000	WASP-177
5026.56629620	-0.01820900	0.01836500	WASP-177
5026.56673601	-0.03087100	0.01769000	WASP-177
5026.57268508	-0.02453400	0.01780000	WASP-177
5026.57312490	-0.00700800	0.01818600	WASP-177

Table 7. Table 7: Data from Trappist

BJD -2450000	Dif. Mag.	Mag. error	Filter	Target
7960.51599185	-0.00760377	-0.00345472	I+z	WASP-177
7960.51636185	-0.00029799	-0.00344426	I+z	WASP-177
7960.51664185	0.00210904	-0.00344268	I+z	WASP-177
7960.51691185	-0.00560489	-0.00344076	I+z	WASP-177
7960.51718185	-0.00165321	-0.00342985	I+z	WASP-177
7960.51754185	-0.00448940	-0.00342637	I+z	WASP-177
7960.51782185	-0.00682232	-0.00342797	I+z	WASP-177
7960.51809185	0.00938183	-0.00343320	I+z	WASP-177
7960.51836185	-0.00237813	-0.00343161	I+z	WASP-177
7960.51863185	-0.00132194	-0.00342244	I+z	WASP-177

Table 8. Table 8: RV data

JD -2450000	RV	RV error	Instrument	Target
	(km/s)	(km/s)
7626.633110	-7.19243	0.01963	CORALIE	WASP-177
7629.687997	-7.21044	0.03748	CORALIE	WASP-177
7689.581199	-7.05873	0.01634	CORALIE	WASP-177
7695.567558	-7.10068	0.01812	CORALIE	WASP-177
7933.845373	-7.16482	0.02686	CORALIE	WASP-177
7937.771917	-7.12978	0.02180	CORALIE	WASP-177
7952.880188	-7.14280	0.02144	CORALIE	WASP-177
7954.787481	-7.19749	0.01473	CORALIE	WASP-177
7961.703754	-7.19347	0.02763	CORALIE	WASP-177
8047.604223	-7.20369	0.01660	CORALIE	WASP-177

Table 9. Table 9: Data from Euler

BJD - 2450000	Dif. Mag.	Mag.	X-pos	Y-pos	Airmass	FWHM	Sky Bkg.	Exp. time	Filter	Object
		error	(pix)	(pix)		(pix)		(s)	(days)
8046.53876846	0.00034578	0.00359381	1070.950	571.822	1.1298	9.369	0.869	110	B	WASP-177
8046.54029585	0.00037222	0.00358208	1086.396	562.842	1.1289	7.076	0.903	110	B	WASP-177
8046.54281198	-0.8042	0.00213508	1085.203	562.140	1.1279	7.496	2.5836	300	B	WASP-177
8046.54652188	-0.00024034	0.00213411	1086.544	558.005	1.1267	7.632	2.4149	300	B	WASP-177
8046.55014519	0.00031779	0.00213539	1086.429	558.463	1.1262	7.980	2.3836	300	B	WASP-177
8046.55443872	0.00313122	0.00184258	1085.948	555.787	1.1264	7.832	3.2365	400	B	WASP-177
8046.55920903	0.00363211	0.00184463	1084.985	556.119	1.1274	7.832	3.4133	400	B	WASP-177
8046.56407976	0.00279818	0.00185139	1087.955	557.254	1.1296	7.928	3.4343	400	B	WASP-177
8046.56884813	0.00639643	0.00186126	1087.783	558.089	1.1326	9.099	3.9564	400	B	WASP-177
8046.57371742	0.00938502	0.00185610	1089.022	557.002	1.1369	7.880	3.5795	400	B	WASP-177

Equations

$$H=\frac{k{T}_{\mathrm{eq}}}{g\mu }$$

Full text

††pubyear: 2018††pagerange: Three Hot-Jupiters on the upper edge of the mass-radius distribution: WASP-177, WASP-181 and WASP-183–A

1 Introduction

Since the beginning of the project the Wide Angle Search for Planets (WASP; Pollacco et al. 2006) survey has discovered nearly 190 transiting, close-in, giant exoplanets. As they transit their host stars their bulk properties, mass and radius, can be determined relatively easily. Their transits allow for deeper characterisation that has led to the discovery of multiple chemical and molecular species in their atmospheres (Birkby et al., 2013; de Kok et al., 2013; Wyttenbach et al., 2017; Hoeijmakers et al., 2018) and the observation of planetary winds (Brogi et al., 2016).

Close-in exoplanets can also provide information on the formation and migration mechanisms of solar systems. It is expected that hot-Jupiter exoplanets initially form much further from their stars than where we detect them today. Therefore some mechanism must cause this migration. There are two proposed pathways, high eccentricity migration or disk migration. In the former some mechanism e.g. Kozai cycles (Wu & Murray, 2003; Armitage, 2013) or planet-planet scattering (Rasio & Ford, 1996; Weidenschilling & Marzari, 1996), forces the cold Jupiter into a highly eccentric orbit which then is tidally circularised via interaction with the star. During this kind of migration it is possible for the planet orbital axis to become mis-aligned with the stellar spin axis (Fabrycky & Tremaine, 2007). In the latter mechanism the planet loses angular momentum via interaction with the stellar disk during formation and migrates inward (Goldreich & Tremaine, 1980). This is expected to preserve the initial spin-orbit alignment (Marzari & Nelson, 2009), though work is being done to investigate the production of mis-aligned planets due to inclined protoplanetary discs (Xiang-Gruess & Kroupa, 2017).

The alignment between the stellar rotation axis and planet orbit can be investigated with the Rossiter-McLaughlin (RM) technique (Rossiter 1924; McLaughlin 1924; Triaud et al. 2010, etc.). These observations have shown a general trend for systems orbiting cool stars (with $T_{\rm eff}<6250$K; Albrecht et al. 2012; Anderson et al. 2015b) to be more well aligned than systems orbiting hotter stars. Tides are also expected to play a role. In cool star systems, those with smaller scaled semi-major axes, $a/R_{*}$, tend to be more often well aligned than those with larger $a/R_{*}$. Though this picture is far from clear as there seems to be evidence for the hot/cool alignment disparity holding even for systems with large separations or low mass planets meaning tidal effects should be minimal (Mazeh et al. 2015) casting tidal realignment into doubt (see also the discussion of Dai & Winn 2017).

In this paper we present the discovery of three systems at the upper edge of the mass-radius envelop of hot-giants that could be useful probes of tidal re-alignment.

2 Observations

Each of these planets was initially flagged as a candidate in data taken with both WASP arrays located at Roque de los Muchachos Observatory on La Palma and at the South African Astronomical Observatory (SAAO). The data were searched for periodic signals using a BLS method as per Collier Cameron et al. (2006, 2007). The survey itself is described in more detail by Pollacco et al. (2006).

In order to confirm the planetary nature of the signals radial velocity (RV) data were obtained with the CORALIE spectrograph on the 1.2-m Swiss telescope at La Silla, Chile (Queloz et al., 2000). Additional photometry was acquired using EulerCam (Lendl et al. 2012, also on the 1.2-m Swiss) and the two 0.6-m TRAPPIST telescopes (Gillon et al., 2011; Jehin et al., 2011), based at La Silla and Oukaimeden Observatory in Morocco (Gillon et al., 2017; Barkaoui et al., 2018).

Due to the low masses of WASP-181 b and WASP-183 b, we also acquired HARPS data111These observations were made as part of the programs Anderson:0100.C-0847(A) and Nielsen:0102.C-0414(A).. These observations are summarised in Table 1. The TRAPPIST data from 2018-08-13 contain a meridian flip at BJD = 2458344.5639. During analysis the data were partitioned at this point and modeled as two datasets.

Figures LABEL:fig:W177-phot, 1 and 2 show the phase folded discovery and follow-up data. The RVs exhibit signals in phase with those found in the transit data and are consistent with companion objects of planetary mass. We checked for correlation between the RV variation and the bisector spans, see Fig.3. We find no strong correlation and so further exclude the possibility that these objects are transit mimics.

3 Analysis

3.1 Stellar Parameters

To obtain the stellar parameters effective temperature, $T_{\rm eff}$, metallicity, [Fe/H], and surface gravity, $\log g$, we followed the method of Giles et al. (2018a, b) using iSpec (Blanco-Cuaresma et al., 2014b). To do this we corrected each spectrum for the computed RV shift, cleaned them of cosmic ray strikes and convolved them to a spectral resolution, $R$, of $47\,000$. Then, ignoring areas typically affected by telluric lines we used the synthetic spectral fitting technique to derive the stellar parameters. Via iSpec we used SPECTRUM (Gray & Corbally, 1994) as the radiative transfer code with atomic data from VALD (Kupka et al., 2011), a line selection based on a $R\sim 47\,000$ solar spectrum (Blanco-Cuaresma et al., 2016, 2017) and the MARCS model atmospheres Gustafsson et al. (2008) in the wavelength range 480- to 680-nm. We increased the uncertainties in these parameters by adding the dispersion found by analysing the Gaia benchmark stars with iSpec as per Blanco-Cuaresma et al. (2014a); Jofré et al. (2014); Heiter et al. (2015).

We determined the stellar density from and initial fit to the lightcurves and then used it along with the $T_{\rm eff}$ and metallicity to determine stellar masses, for later use in the joint analysis, and the stellar ages with the Bayesian stellar evolution code BAGEMASS (Maxted et al., 2015). The resulting parameters are presented in the top part of Table 3 and the corresponding isochrons/evolutionary tracks are shown in Fig 4.

BAGEMASS uses an MCMC with a densely sampled grid of stellar models to compute stellar masses and ages. There are three usable grids with differing mixing length parameters, $\alpha_{\rm MLT}$, and helium enhancement. The default values of these are $\alpha_{\rm MLT}=1.78$ and no He-enhancement. We used the BAGEMASS default parameters to model WASP-177 and WASP-181 but found that they did not fit WASP-183 very well. This is likely because WASP-183 is among the $\sim 3\%$ of the K-dwarf population that are larger than models would predict (Spada et al., 2013). To account for this we follow the method of Maxted et al. (2015) in the case of Qatar-2 and use a the grid provided by BAGEMASS with $\alpha_{\rm MLT}=1.5$. This results in a much improved fit to the observed density and temperature. We find that the resulting mass estimate is unaffected.

3.2 System parameters

To determine the system parameters we modeled the discovery and follow-up data together using the most recent version of the Markov-Chain Monte Carlo (MCMC) code described in detail in Collier Cameron et al. (2007) and Anderson et al. (2015a). We modeled the transit lightcurves using the models of Mandel & Agol (2002) with the 4 parameter limb darkening law of Claret (2000, 2004).

In brief, the models were initialised using the period, $P$, epoch, $T_{0}$, transit depth, $(R_{p}/R_{s})^{2}$, transit duration, $T_{14}$, and impact parameter, $b$, output by the BLS search of each discovery lightcurve. The spectroscopic stellar effective temperature, $T_{\rm eff}$, and metallicity, [Fe/H], were used initially to estimate the stellar mass using the updated Torres mass calibration by Southworth (2011). To explore the effect of limb-darkening we extracted tables of limb- darkening parameters in each photometric band used for each star. They were extracted for a range of effective temperatures while keeping the stellar metallicity and surface gravity constant. The values used were perturbed during the MCMC via $T_{\rm L-D}$, the ‘limb-darkening temperature’, which has a mean and standard deviation corresponding to the spectroscopic $T_{\rm eff}$ and its uncertainty.

At each step of the MCMC each of these values are perturbed and the models are re-fit. These new proposed parameters are then accepted if the $\chi^{2}$ of the fit is better or accepted with a probability proportional to $\exp(-\Delta\chi^{2})$ if the $\chi^{2}$ of the fit is worse.

In the final MCMCs, in place of using the Torres relation to determine a mass, we provided the value given by BAGEMASS. The code then drew values at each step from a Gaussian with a mean and standard deviation given by the value and its uncertainty respectively. Due to the lack of good quality follow-up photometry we imposed a similar prior on the radius of the star WASP-183 using the Gaia parallax. Lacking a complete, good quality follow-up lightcurve can lead to a poor determination of, $\Delta F$, $T_{14}$ and $b$ which we use to calculate the $R_{*}/a$. This in turn results in a poorer determination of $R_{*}$, $R_{p}$ and other parameters that depend upon them.

In this way we also explored models allowing for eccentric orbits and the potential for linear drifts in the RVs. There was no strong evidence supporting either scenario so we present the system solutions corresponding to circular orbits (Anderson et al., 2012) with no trends due to unseen companions. The parameters derived by these fits can be found in the lower part of Table 3.

3.3 Rotational modulation

We checked the WASP lightcurves of the three stars for rotational modulation that could be caused by star spots using the method described by Maxted et al. (2011). The transits were fit with a simple model and removed. We performed the search over 16384 frequencies ranging from 0 to 1 cycles/day. Due to the limited lifetime and variable distribution of star spots this modulation is not expected to be coherent over long periods of time. As such, we modeled each season of data from each camera individually. WASP-181 and WASP-183 show no significant modulation, with an upper limit on the amplitude of 2- and 3-mmag respectively.

However, WASP-177 was found to exhibit modulation consistent with a rotational period, $P_{\rm rot}=14.86\pm 0.14$ days and amplitude of $5\pm 1$ mmag. The results of this analysis for each camera and season of data is shown in Table 2. Fig. 5 shows the periodograms of the fits and the discovery lightcurves phase-folded on the corresponding period of modulation. Three of the datasets exhibit $P_{\rm rot}\sim 7$-days while the other two exhibit $P_{\rm rot}\sim 14$-days. We interpret the $\sim 7$-day signals as a harmonic of the longer $\sim 14$-day signal as it is more easy for multiple active regions to produce a $\sim 7$-day signal when the true period is $\sim 14$-days than vice versa. Using this rotational period and our value for the stellar radius we find a stellar rotational velocity of, $v_{*}=2.9\pm 0.2$ km/s. When compared to the projected equatorial spin velocity we find a stellar inclination to our line of sight of $38\pm 25\degr$ which suggests that WASP-177 b could be quite mis-aligned.

4 Discussion

Our joint analysis shows that in this ensemble we have two large sub-Jupiter mass planets: WASP-177 b ($\sim$0.5 MJup, $\sim$1.6 RJup) and WASP-183 b ($\sim$0.5 MJup, $\sim$1.5 RJup) orbiting old stars. The third planet, WASP-181 b, is a large Saturn mass planet ($\sim$0.3 MJup, $\sim$1.2 RJup) . According to the analysis with BAGEMASS, WASP-177 and WASP-183 are both at the latter end of the main sequence explaining their slightly larger radii for stars of their spectral class; a $9.7\pm 3.9$ Gyr K2 and $14.9\pm 1.7$ Gyr G9/K0 respectively. WASP-183 is particularly noteworthy as its advanced age makes it one of the oldest stars known to host a transiting planet (see Fig. 6). Though, WASP-183 appears to be subject to the K-dwarf radius anomaly, making this determination less clear. Meanwhile, WASP-181 is a relatively young, standard example of a G2 star.

We compared the stellar radii derived from our MCMC to those we can calculate using the Gaia DR2 parallaxes (Luri et al., 2018; Gaia Collaboration et al., 2018), with the correction from Stassun & Torres (2018), and stellar angular radii from the infra-red flux fitting method (IRFM) these radii, with reddening accounted for by the use of dust maps (Schlafly & Finkbeiner, 2011). We find good agreement and present a summary in table 4.

All three planets occupy the upper edge of the mass-radius distribution, seen in Fig 7. WASP-181 b is amongst the group of the largest planets for an object of its mass. While its mass is not as well determined as the other two, further HARPS observations will help to refine this. WASP-177 b and WASP-183 b do lie above the bulk of the distribution, especially when compared to other objects with mass determinations of 10% precision or better. However, it is difficult to say how exceptional they are as a precise radius determination has proven difficult for them both. The transit of WASP-177 b is grazing and the transit of WASP-183 b, in addition to being grazing, lacks a full high precision follow-up lightcurve to refine the transit shape. We anticipate that TESS observations could soon solve the latter problem;the long cadence data would capture roughly 24 in transit points with a predicted precision from the ticgen tool of better than 1000 ppm in each 30-minute observation.

We used the the values derived for planet equilibrium temperature, $T_{\rm eq}$, and surface gravity, $g$, along with Boltzmann’s constant, $k$, and the atmospheric mean molecular mass, $\mu$, to estimate the scale heights, $H$, of these planets as:

[TABLE]

assuming an isothermal, hydrogen dominated atmosphere. The resulting scale heights were; $790\pm 320$ km, $770\pm 200$ km, $696\pm 464$ km for WASP-177 b, WASP-181 b and WASP-183 b respectively. These translate to transit depth variations of just under 300 ppm for WASP-177 and WASP-181 and $\sim 300$ ppm for WASP-183. If we account for the K-band flux and scale in the same way as Anderson et al. (2017), we get atmospheric signals of; 70, 41 and 60. In reality, we can expect this metric to be an over estimate of detectability for WASP-177 b and WASP-183 b as the grazing nature of their transits reduces the impact of the atmospheric signal further. For comparison we used the same metric on other planets with atmospheric detections: water has been detected in the atmospheres of both WASP-12 b (Kreidberg et al. 2015; signal $\sim 93$) and WASP-43 b (Kreidberg et al. 2014; signal $\sim 74$); titanium oxide has been detected in the atmosphere of WASP-19 b (Sedaghati et al. 2017; signal $\sim 83$); sodium and potassium have both been detected in the atmosphere of WASP-103 b (Lendl et al. 2017; signal $\sim 37$). While not ideal targets, this suggests such detections may be possible.

Investigation into any eccentricity or long-period massive companions in these systems has not yielded anything convincing. All of the orbits are circular, with the $2\sigma$ upper limits quoted in Table 3. As for long term trends, WASP-177 shows the possibility of a very low significance ($\sim 1.5\sigma$) drift with $\delta\gamma/\delta t$ of $(-2.4\pm 1.6)\times 10^{-5}$ km/s/d. Neither WASP-181 nor WASP-183 show significant drifts with $\delta\gamma/\delta t$ of $(1.2\pm 4.0)\times 10^{-5}$ km/s/d and $(-1.9\pm 5.1)\times 10^{-5}$ km/s/d respectively.

Finally, these systems do present interesting targets for the investigation of the observed spin-orbit mis-alignment distribution (Albrecht et al. 2012; Anderson et al. 2015b). All of the stellar hosts fall into the "cool" regime of Albrecht et al. (2012) and despite their short periods have scaled semi-major axes, $a/R_{*}$, above 8. They are therefore above the empirical boundary noted by Dai & Winn (2017) as the transition region where systems with cooler stars show more tendency to be mis-aligned. Since the study in 2017 the number of systems with obliquity measurements has increased. Most of the cool-star systems with $a/R_{*}$ above 8 are well aligned, see Fig 8.

We estimated the alignment time-scale for each system using Eq.4 of Albrecht et al. (2012) as was done for WASP-117 (Lendl et al., 2014). These time-scales, along with the mass of the convective zone, $M_{\rm cz}$, are shown in Tab 5. In each case, the time-scale for realignment is much longer than the ages of the systems. Therefore, we would expect the initial state of alignment of the systems to have been preserved. We have estimated the inclination of WASP-177 to be $38\pm 25\degr$ and so may expect it to join only 12 systems with $a/R_{*}$ < 15 that show mis-alignment this makes it a potentially important diagnostic in determining the factors that cause or preserve mis-alignment.

We calculate that the amplitude of the RM effect will be greatest for WASP-181 at $\sim 50$ ms*-1*. The effect should also be detectable for WASP-177 and WASP-183 despite their more grazing transits, with an amplitude of $\sim 10$ ms*-1*.

5 Conclusions

We have presented the discovery of 3 transiting exoplanets from the WASP survey; WASP-177 b ($\sim$0.5 MJup, $\sim$1.6 RJup), WASP-181 b ($\sim$0.3 MJup, $\sim$1.2 RJup), and WASP-183 b ($\sim$0.5 MJup, $\sim$1.5 RJup). They all occupy the upper region of the mass-radius distribution for hot gas-giant planets but do not present exceptional targets for transmission spectroscopy. However, regarding the investigation of system spin-orbit alignment they do occupy an under investigated range of $a/R_{*}$ and so could act as good probes of tidal realignment time-scales.

Acknowledgements

We thank the Swiss National Science Foundation (SNSF) and the Geneva University for their continuous support to our planet search programs. This work has been in particular carried out in the frame of the National Centre for Competence in Research ‘PlanetS’ supported by the Swiss National Science Foundation (SNSF). WASP-South is hosted by the South African Astronomical Observatory 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. TRAPPIST is funded by the Belgian Fund for Scientific Research (Fond National de la Recherche Scientifique, FNRS) under the grant FRFC 2.5.594.09.F, with the participation of the Swiss National Science Fundation (SNF). MG is a F.R.S.-FNRS Senior Research Associate. The research leading to these results has received funding from the European Research Council under the FP/2007-2013 ERC Grant Agreement 336480, from the ARC grant for Concerted Research Actions financed by the Wallonia-Brussels Federation, from the Balzan Foundation, and a grant from the Erasmus+ International Credit Mobility programme (K Barkaoui). We thank our anonymous reviewer for their comments which helped improve the clarity of the paper.

Appendix A Online Data