High-Precision Photometry by Telescope Defocussing – VIII. WASP-22, WASP-41, WASP-42 and WASP-55

MNRAS 457, 4205–4217 (2016) doi:10.1093/mnras/stw279 Advance Access publication 2016 February 8

High-precision photometry by telescope defocussing – VIII. WASP-22, WASP-41, WASP-42 and WASP-55

John Southworth,1‹ J. Tregloan-Reed,2 M. I. Andersen,3 S. Calchi Novati,4,5,6 S. Ciceri,7 J. P. Colque,8 G. D’Ago,6 M. Dominik,9† D. F. Evans,1 S.-H. Gu,10,11 A. Herrera-Cordova,8 T. C. Hinse,12 U. G. Jørgensen,13 D. Juncher,13 M. Kuffmeier,13 7,14 8 13 7,15 13,16

L. Mancini, N. Peixinho, A. Popovas, M. Rabus, J. Skottfelt, Downloaded from R. Tronsgaard,17 E. Unda-Sanzana,8 X.-B. Wang,10,11 O. Wertz,18 K. A. Alsubai,19 J. M. Andersen,13,20 V. Bozza,5,21 D. M. Bramich,19 M. Burgdorf,22 Y. Damerdji,18 C. Diehl,23,24 A. Elyiv,25,18,26 R. Figuera Jaimes,9,27 T. Haugbølle,13 M. Hundertmark,13 N. Kains,28 E. Kerins,29 H. Korhonen,3,13,30 C. Liebig,9 M. Mathiasen,13 M. T. Penny,31 http://mnras.oxfordjournals.org/ S. Rahvar,32 G. Scarpetta,5,6,21 R. W. Schmidt,23 C. Snodgrass,33 D. Starkey,9 J. Surdej,18 C. Vilela,1 C. von Essen17 and Y. Wang10 Afﬁliations are listed at the end of the paper

Accepted 2016 February 1. Received 2016 January 28; in original form 2015 December 16 at Qatar Foundation for Education, Science and Commun on April 23, 2016

ABSTRACT We present 13 high-precision and four additional light curves of four bright southern- hemisphere transiting planetary systems: WASP-22, WASP-41, WASP-42 and WASP-55. In the cases of WASP-42 and WASP-55, these are the first follow-up observations since their discovery papers. We present refined measurements of the physical properties and orbital ephemerides of all four systems. No indications of transit timing variations were seen. All four planets have radii inflated above those expected from theoretical models of gas-giant planets; WASP-55 b is the most discrepant with a mass of 0.63 MJup and a radius of 1.34 RJup. WASP-41 shows brightness anomalies during transit due to the planet occulting spots on the stellar surface. Two anomalies observed 3.1 d apart are very likely due to the same spot. We measure its change in position and determine a rotation period for the host star of 18.6 ± 1.5 d, in good agreement with a published measurement from spot-induced brightness modulation, and a sky-projected orbital obliquity of λ = 6 ± 11◦. We conclude with a compilation of obliquity measurements from spot-tracking analyses and a discussion of this technique in the study of the orbital configurations of hot Jupiters. Key words: stars: fundamental parameters – stars: individual: WASP-22, WASP-41, WASP- 42, WASP-55– planetary systems.

due to their large masses and radii, and have highly irradiated and 1 INTRODUCTION often rareﬁed atmospheres in which many physical phenomena are Of the over 1200 transiting extrasolar planets (TEPs) now known,1 observable. the short-period gas-giant planets are of particular interest. These Most of the transiting hot Jupiters have been discovered by ‘hot Jupiters’ are the easiest to ﬁnd due to their deep transits and high ground-based surveys studying bright stars. The brightness of the orbital frequency, are the most amenable to detailed characterization host stars is also extremely helpful in further characterization of these objects via transmission spectroscopy and orbital obliquity studies. We are therefore undertaking a project to study TEPs orbit- E-mail: [email protected] ing bright host stars visible from the Southern hemisphere. Here we †Royal Society University Research Fellow. present transit light curves of four targets discovered by the WASP 1 See Transiting Extrasolar Planet Catalogue (TEPCat; Southworth 2011): project (Pollacco et al. 2006) and measure their physical properties http://www.astro.keele.ac.uk/jkt/tepcat/ and orbital ephemerides to high precision.

C 2016 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society 4206 J. Southworth et al.

Table 1. Log of the observations presented in this work. Nobs is the number of observations, Texp is the exposure time, Tdead is the dead time between exposures, ‘Moon illum.’ is the fractional illumination of the Moon at the midpoint of the transit, given in italics if the Moon was down at that time, and Npoly is the order of the polynomial ﬁtted to the out-of-transit data. The aperture radii refer to the target aperture, inner sky and outer sky, respectively.

Target Tele- Date of Start time End time Nobs Texp Tdead Filter Airmass Moon Aperture Npoly Scatter scope ﬁrst obs (UT)(UT) (s) (s) illum. radii (px) (mmag)

WASP-22 84 cm 2011 12 01 00:21 05:56 353 45 12 none 1.38 → 1.00 → 1.19 0.365 17 65 100 2 1.680 WASP-22 84 cm 2012 01 23 00:54 04:53 228 45 10 none 1.02 → 1.02 → 2.46 0.002 15 38 60 2 1.646 WASP-22 Danish 2012 09 19 05:34 09:43 133 100 13 I 1.25 → 1.00 → 1.06 0.137 18 32 50 1 0.703 WASP-22 Danish 2013 09 25 03:10 09:08 172 100 25 I 2.21 → 1.00 → 1.05 0.680 18 25 55 1 0.913 WASP-22 Danish 2015 09 05 04:38 10:08 369 35–45 12 I 2.11 → 1.00 → 1.03 0.510 14 20 40 1 1.087 → →

WASP-41 84 cm 2011 02 07 06:39 09:44 182 50 16 R 1.07 1.00 1.07 0.161 25 50 100 2 2.942 Downloaded from WASP-41 84 cm 2012 01 21 06:15 09:40 102 90 7 none 1.33 → 1.01 → 1.01 0.045 27 54 108 2 1.729 WASP-41 Danish 2014 05 31 00:35 05:03 155 80–100 13 I 1.01 → 1.00 → 1.71 0.055 22 30 55 1 0.571 WASP-41 Danish 2015 05 10 22:51 03:28 148 100 13 I 1.37 → 1.00 → 1.05 0.548 22 28 50 2 0.596 WASP-41 Danish 2015 05 13 23:25 04:30 159 100 13 I 1.19 → 1.00 → 1.19 0.214 17 27 45 2 0.646 WASP-41 Danish 2015 05 17 00:14 05:30 166 100 13 I 1.06 → 1.00 → 1.50 0.015 22 28 50 1 0.646

WASP-42 Danish 2013 05 25 00:51 06:28 164 100 20 R 1.04 → 1.03 → 2.10 1.000 20 28 45 2 0.673 http://mnras.oxfordjournals.org/ WASP-42 Danish 2013 06 18 23:11 04:33 168 100 16 R 1.04 → 1.03 → 1.92 0.745 19 27 50 1 0.501 WASP-42 Danish 2013 06 28 23:00 03:43 143 100 15 R 1.04 → 1.03 → 1.82 0.623 22 30 55 1 0.924 WASP-55 Danish 2013 05 04 02:26 07:42 152 90–98 25 R 1.05 → 1.02 → 1.94 0.314 17 42 80 1 0.815 WASP-55 Danish 2014 06 18 22:56 03:26 206 50–110 11 I 1.10 → 1.02 → 1.35 0.583 13 42 80 1 1.144 WASP-55 Danish 2015 04 23 01:06 07:29 184 100 25 I 1.41 → 1.02 → 1.45 0.231 16 26 50 1 0.899

WASP-22 was discovered by Maxted et al. (2010), who found of 13.7 arcmin×13.7 arcmin at a plate scale of 0.39 arcsec pixel−1. it to be a low-density planet (mass 0.56 MJup, radius 1.12 RJup) We defocussed the telescope in order to improve the precision and at Qatar Foundation for Education, Science and Commun on April 23, 2016 orbiting a V = 11.7 solar-type star every 3.53 d. A linear trend in efficiency of our observations (Southworth et al. 2009). The CCD the radial velocities (RVs) was noticed and attributed to the presence was windowed during some observing sequences in order to shorten of a third body in the system, which could be an M-dwarf, white the readout time, and no binning was used. In most cases the night dwarf or second planet. The trend in the RVs has been confirmed was photometric; observations taken through thin cloud were care- by Knutson et al. (2014), who measured the change in the systemic fully checked and rejected if their reliability was questionable. The γ = . +2.8 −1 −1 velocity of the system to be ˙ 21 3−2.7 ms yr . Anderson data were taken through either a Bessell R or Bessell I filter. An et al. (2011) measured the projected orbital obliquity of the system observing log is given in Table 1 and the final light curves are plot- ◦ ◦ to be λ = 22 ± 16 via the Rossiter–McLaughlin effect. ted in Fig. 1. All observations were taken after the upgrade of the WASP-41 was announced by Maxted et al. (2011b)tobea telescope and CCD controller in 2011 (Southworth et al. 2014). hot Jupiter of mass 0.94 MJup, radius 1.06 RJup, and orbital period We reduced the data using the DEFOT pipeline (see Southworth 2 Porb = 3.05 d. Its host is a V = 11.6 G8 V star showing magnetic et al. 2014, and references therein), which in turn uses the IDL activity indicative of a young age, and rotational modulation on a implementation of the APER routine from DAOPHOT (Stetson 1987) 3 period of 18.41 ± 0.05 d. Neveu-VanMalle et al. (2016) obtained contained in the NASA ASTROLIB library. For each data set, the further spectroscopic RV measurements from which they measured apertures were placed by hand on a reference image. Shifts between λ = +10◦ = 29−14 and detected a third object in the system with Porb the individual images and the reference image were measured by 421 ± 2 d and a minimum mass of 3.18 ± 0.20 MJup. cross-correlation, and applied to the aperture positions. The radii of WASP-42 was discovered by Lendl et al. (2012) and is a low- the object aperture and sky annulus were chosen to minimize the density planet (mass 0.50 MJup, radius 1.12 RJup) orbiting a V = 12.6 scatter in the final light curve (see Table 1). The science images star of spectral type K1 V every 4.98 d. An orbital eccentricity of were not calibrated using bias or flat-field frames as these tend to e = 0.060 ± 0.0013 was found by these authors, which is small but have little effect on the final light curves beyond a slight increase in significant (Lucy & Sweeney 1971). No other study of the WASP-42 the scatter of the data points. system has been published. We observed two transits of WASP-22 and two transits of WASP- WASP-55 was one of a batch of new TEPs announced by Hellier 41 using the 84 cm telescope at Observatorio Cerro Armazones in et al. (2012) and is the lowest density of the four planets considered Antofagasta, Chile (currently decommissioned). Three transits were here, with a mass of 0.50 MJup and radius of 1.30 RJup. Its host is a observed using an SBIG ST-10 CCD camera, giving a field of view −1 G1 V star with a slightly sub-solar metallicity, and the Porb of the of 15.6 arcmin × 10.5 arcmin at a plate scale of 0.43 arcsec pixel , system is 4.47 d. No other study of the WASP-55 system has been and the first transit of WASP-41 was monitored using an SBIG STL published, but it was a target in Field 6 of the K2 mission (Howell CCD camera with a field of view of 29.3 arcmin×19.5 arcmin at et al. 2014) and these observations will soon be available. a plate scale of 0.57 arcsec pixel−1. We defocussed the telescope and windowed the CCDs, and observed unfiltered except for the first transit of WASP-41 which was seen through an R filter. Data 2 OBSERVATIONS AND DATA REDUCTION reduction was performed using a custom pipeline based on Starlink We observed a total of 13 transits with the DFOSC (Danish Faint Object Spectrograph and Camera) instrument installed on the 1.54 m 2 http://www.exelisvis.co.uk/ProductsServices/IDL.aspx Danish Telescope at ESO La Silla, Chile. DFOSC has a field of view 3 http://idlastro.gsfc.nasa.gov/

MNRAS 457, 4205–4217 (2016) WASP-22, WASP-41, WASP-42 and WASP-55 4207 Downloaded from http://mnras.oxfordjournals.org/

Figure 1. DFOSC light curves presented in this work, in the order they are given in Table 1. Times are given relative to the midpoint of each transit, and the at Qatar Foundation for Education, Science and Commun on April 23, 2016 filter used is indicated. Blue and red filled circles represent observations through the Bessell R and I filters, respectively.

taining the weighted flux sum of the best three to five comparison stars. A polynomial was also fitted to the observations outside transit and subtracted to rectify the final light curve to zero differential magnitude. In most cases a first-order polynomial was an adequate match to the slow brightness variations seen throughout the observing sequences, but in some cases a quadratic was required (see Table 1). The coefficients of the polynomial and the weights of the comparison stars were simultaneously optimized to minimize the scatter in the data points outside eclipse. Manual time checks were obtained for several frames and the FITS file timestamps were confirmed to be on the UTC system to within a few seconds. They were then converted to the BJD(TDB) time-scale (Eastman, Siverd & Gaudi 2010). The light curves are shown in Fig. 1, and the reduced data (Table 2) will be made available at the CDS.4 Finally, each of the light curves was fitted with the JKTEBOP code (see below) in order to determine the quality of fit and the times of midpoint of the transits. The errorbars for each data set were 2 2 rescaled to give a reduced χ of χν = 1.0 versus the fitted model, necessary as the uncertainties from the APER algorithm are often underestimated. Figure 2. 84 cm telescope light curves presented in this work, in the order they are given in Table 1. Times are given relative to the midpoint of each transit, and the filter used is indicated. Blue and green filled circles represent 3 LIGHT-CURVE ANALYSIS observations through the R filter and without filter, respectively. We modelled the light curves of the four targets using the Homoge- routines, including calibration with dark frames but not flat-fields. neous Studies methodology (see Southworth 2012 and references 5 The PHOTOM package (Eaton, Draper & Allen 1999) was used to therein), which utilises the JKTEBOP code (Southworth 2013,andref- perform aperture photometry, and the apertures were placed by erences therein). JKTEBOP represents the star and planet as spheres hand. A growth-curve analysis was performed for each data set in order to find the aperture size which gave the lowest scatter. The data are plotted in Fig. 2. 4 http://vizier.u-strasbg.fr/ 5 For all data sets, differential-magnitude light curves were gener- JKTEBOP is written in FORTRAN77 and the source code is available at ated for each target star versus an ensemble comparison star con- http://www.astro.keele.ac.uk/jkt/codes/jktebop.html

MNRAS 457, 4205–4217 (2016) 4208 J. Southworth et al.

Table 2. The first line of each of the light curves presented in this work. weighted mean of the four values from the solutions using the The full data set will be made available at the CDS. two-parameter LD laws. Its errorbar was taken to be the larger of the Monte Carlo or residual-permutation alternatives, with an extra Target Tele- Filter BJD(TDB) Diff. mag. Uncertainty contribution to account for variations between solutions with the − scope 2400000 different LD laws. Tables of results for each light curve can be WASP-22 84 cm none 55896.520223 −0.00291 0.001 68 found in the Supplementary Information. WASP-22 84 cm none 55949.539861 −0.01180 0.001 65 WASP-22 Danish I 56189.736334 −0.00015 0.000 74 3.1 WASP-22 WASP-22 Danish I 56560.637168 −0.00034 0.000 96 WASP-22 Danish I 57270.696685 −0.00032 0.001 05 The three DFOSC light curves of WASP-22 were fitted simultane- WASP-41 84 cm R 55599.780710 −0.00329 0.002 94 ously (Table 3 and Fig. 3). A circular orbit was assumed as Anderson − WASP-41 84 cm none 55947.763186 0.00187 0.001 73 et al. (2011) found e < 0.063 at the 3σ level, and Pont et al. (2011) WASP-41 Danish I 56808.529719 −0.00050 0.000 54 Downloaded from found e < 0.059 at the 95 per cent confidence level. The overall WASP-41 Danish I 57153.458491 0.00071 0.000 89 χ 2 = . WASP-41 Danish I 57156.481701 0.00025 0.000 68 quality of the fit is ν 1 01 (remember that the errorbars on each χ 2 = . WASP-41 Danish I 57159.515981 −0.00007 0.000 65 data set were already scaled to give ν 1 0) which shows that the WASP-42 Danish R 56437.541226 0.00099 0.000 61 three light curves give highly consistent transit shapes. WASP-42 Danish R 56462.470118 −0.00036 0.000 49 Anderson et al. (2011) included in their analysis three new transit

WASP-42 Danish R 56472.461607 0.00013 0.000 97 light curves of WASP-22, two from the TRAPPIST telescope (Jehin http://mnras.oxfordjournals.org/ WASP-55 Danish R 56416.608745 −0.00146 0.000 83 et al. 2011) and one from EulerCam on the Euler telescope (Lendl WASP-55 Danish I 56827.462644 −0.00027 0.001 05 et al. 2012). We modelled these in the same way as used for our own WASP-55 Danish I 57135.553466 0.00004 0.000 94 data. The follow-up light curve presented by Maxted et al. (2010)has only partial coverage of one transit so we did not consider it further for the calculation of eclipse shapes and as biaxial spheroids for in this work. The full results for WASP-22 are given in Table 3 proximity effects. and show an acceptable agreement between the different data sets. The fitted parameters in our analysis were the fractional radii For our final values we adopt the weighted means of the individual of the star and planet (rA and rb), the orbital inclination (i), limb measurements, calculated by multiplying the probability density functions of the measurements. The final values are consistent with, darkening (LD) coefficients, and a reference time of mid-transit. at Qatar Foundation for Education, Science and Commun on April 23, 2016 The fractional radii are the ratio between the true radii and the and an improvement on, previously published values. R r = A,b semimajor axis: A,b a , and were expressed as their sum and rb ratio, rA + rb and k = , as these quantities are less strongly rA 3.2 WASP-41 correlated. The orbital periods were fixed at the values found in Section 6. A polynomial of brightness versus time was applied to WASP-41 is a trickier system because there are anomalies due to each transit light curve, with a polynomial order as given in Table 1. starspot-crossing events in at least two of our high-precision light This is not needed to fit the data, as the polynomial has already been curves. In the current part of the analysis these were ignored, in order removed at the data reduction stage, but is necessary to include the to maintain homogeneity of approach, so were therefore basically uncertainties of polynomial fit in the errorbars of the photometric treated as red noise. A detailed analysis of the spot anomalies will parameters (see Southworth et al. 2014). be presented below. Our four DFOSC light curves of WASP-41 LD was incorporated into the photometric model using each of were fitted simultaneously (Table 3 and Fig. 4), for which the best χ 2 = . five LD laws (see Southworth 2008), with the linear coefficients fit returns ν 1 05 despite the presence of the spot anomalies. A either fixed at theoretically predicted values6 or included as fitted circular orbit was assumed as Neveu-VanMalle et al. (2016) found parameters. We did not calculate fits for both LD coefficients in the e < 0.026 at the 2σ confidence level. four two-parameter laws as they are strongly correlated (Carter et al. As with WASP-22, the discovery paper of WASP-41 included 2008; Southworth 2008). The non-linear coefficients were instead only one high-precision light curve, which does not cover the full perturbed by ±0.1 on a flat distribution during the error analysis transit. This data set was not analysed here due to the weak con- simulations, in order to account for uncertainties in the theoretical straints on system properties from light curves missing coverage of coefficients. the third and fourth contact points in the eclipse. However, Neveu- All four targets have been observed in the HITEP high-resolution VanMalle et al. (2016) presented eight new light curves of WASP- imaging campaign by Evans et al. (2015) using the Two Colour 41 obtained from three telescopes. The single complete transit from Imager (TCI) (Skottfelt et al. 2015) to perform Lucky Imaging. No the Danish Telescope, labelled ‘DFOSC R’ in Fig. 4, and the transit stars were found close enough to WASP-22, WASP-41 or WASP- from Faulkes Telescope South (FTS) were each modelled in isola- 42 to affect our photometry. However, one star was found at an tion. The five data sets from TRAPPIST were modelled together, angular distance of 4.345 ± 0.010 arcsec from WASP-55, and was with an extra polynomial to account for the meridian flip at JD accounted for in the JKTEBOP model (see below). 2456402.653 (Delrez, private communication). The final results are Error estimates for the fitted parameters were obtained in several shown in Table 3 and agree with, but improve on, published values. ways. We ran solutions using different LD laws, and also calculated errorbars using residual-permutation and Monte Carlo algorithms 3.3 WASP-42 (Southworth 2008). The final value for each parameter is the un- Of the four systems studied in this work, WASP-42 is the only one with an eccentric orbit. Lendl et al. (2012) found that 6 Theoretical LD coefficients were obtained by bilinear interpolation their measurement of a small eccentricity was significant at the to the host star’s Teff and log g using the JKTLD code available from: 99.5 per cent level. We accounted for this in the JKTEBOP modelling http://www.astro.keele.ac.uk/jkt/codes/jktld.html by constraining the eccentricity and argument of periastron to be

MNRAS 457, 4205–4217 (2016) WASP-22, WASP-41, WASP-42 and WASP-55 4209

Table 3. Parameters of the JKTEBOP ﬁts to the new and published light curves of the four planetary systems.

◦ System Source Filter rA + rb ki( ) rA rb . +0.0039 . +0.0013 . +1.0 . +0.0035 . +0.00048 WASP-22 DFOSC I 0 1284−0.0017 0 0996−0.0012 89 3−1.3 0 1168−0.0015 0 01163−0.00020 z . +0.0083 . +0.0015 . +2.1 . +0.0074 . +0.00084 WASP-22 TRAPPIST I+ 0 1327−0.0059 0 0951−0.0013 87 9−1.3 0 1212−0.0053 0 01152−0.00059 . +0.0121 . +0.0041 . +2.6 . +0.0109 . +0.00166 WASP-22 Euler r 0 1404−0.0090 0 0982−0.0049 87 1−1.7 0 1278−0.0078 0 01255−0.00112 . +0.0031 . +0.0012 . +1.0 . +0.0027 . +0.00039 Weighted mean 0 1310−0.0028 0 0978−0.0012 88 6−1.0 0 1193−0.0026 0 01172−0.00025 WASP-41 DFOSC I 0.1143 ± 0.0013 0.1362 ± 0.0008 89.07 ± 0.53 0.1006 ± 0.0011 0.01369 ± 0.00021 WASP-41 DFOSC R 0.1128 ± 0.0015 0.1369 ± 0.0013 89.62 ± 1.06 0.0992 ± 0.0013 0.01358 ± 0.00027 WASP-41 TRAPPIST I+z 0.1176 ± 0.0034 0.1378 ± 0.0019 88.26 ± 0.98 0.1034 ± 0.0028 0.01424 ± 0.00053 WASP-41 FTS z 0.1198 ± 0.0054 0.1366 ± 0.0018 87.63 ± 0.80 0.1054 ± 0.0047 0.01440 ± 0.00078 Downloaded from Weighted mean 0.1142 ± 0.0009 0.1365 ± 0.0006 88.70 ± 0.39 0.1004 ± 0.0008 0.01373 ± 0.00015 WASP-42 DFOSC R 0.0851 ± 0.0027 0.1296 ± 0.0009 87.91 ± 0.19 0.0753 ± 0.0024 0.00976 ± 0.00034 WASP-42 Euler r 0.0794 ± 0.0047 0.1275 ± 0.0047 88.72 ± 1.01 0.0704 ± 0.0040 0.00897 ± 0.00071 WASP-42 TRAPPIST I+z 0.0829 ± 0.0033 0.1284 ± 0.0016 88.23 ± 0.36 0.0735 ± 0.0028 0.00943 ± 0.00043 Weighted mean 0.0834 ± 0.0019 0.1293 ± 0.0008 88.00 ± 0.17 0.0739 ± 0.0017 0.00955 ± 0.00025

. +0.0030 . +0.0014 . +0.57 . +0.0026 . +0.00044 http://mnras.oxfordjournals.org/ WASP-55 DFOSC R 0 1025−0.0009 0 1253−0.0010 89 83−1.20 0 0911−0.0008 0 01141−0.00012 . +0.0024 . +0.0009 . +0.59 . +0.0021 . +0.00033 WASP-55 DFOSC I 0 1028−0.0008 0 1236−0.0008 89 73−0.93 0 0915−0.0007 0 01130−0.00012 . +0.0064 . +0.0024 . +0.98 . +0.0055 . +0.00085 WASP-55 Euler r 0 1102−0.0064 0 1274−0.0025 87 79−0.86 0 0978−0.0054 0 01246−0.00088 . +0.0018 . +0.0007 . +0.59 . +0.0015 . +0.00025 Weighted mean 0 1033−0.0010 0 1246−0.0007 89 05−0.59 0 0918−0.0009 0 01143−0.00013 at Qatar Foundation for Education, Science and Commun on April 23, 2016

Figure 3. The phased light curves of WASP-22 analysed in this work, compared to the JKTEBOP best fits. The residuals of the fits are plotted at the base of the figure, offset from unity. Labels give the source and passband for each data set. The polynomial baseline functions have been subtracted Figure 4. As Fig. 3, but for WASP-41. from the data before plotting. (Fig. 5). We also modelled the light curves from the Euler and e = 0.060 ± 0.013 and ω = 167 ± 26◦, respectively. There also TRAPPIST telescopes presented in Lendl et al. (2012), which cover appears to be a starspot crossing event just after the midpoint of the two and four transits respectively. The three light curves are in ex- χ 2 third and final transit, which is not surprising given the Teff of the cellent agreement, with values of ν between 0.30 and 0.57 for the 2 host star. We did not make any attempt to fit this anomaly because photometric parameters, where χν is calculated for the individual it has a low amplitude and no other spot anomalies were seen. values of a parameter versus to the weighted mean of the values. Our three light curves were all obtained within 34 d – the observ- ability of transits in this object has a strong seasonal dependence 3.4 WASP-55 because its orbital period is close to an integer number of days – and 2 were modelled together (Table 3). The combined fit has χν = 1.09, From high-resolution imaging Evans et al. (2015) found a faint star once again showing good agreement between our three light curves close to the WASP-55 system. The star is at an angular distance

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Figure 6. As Fig. 3, but for WASP-55. Figure 5. As Fig. 3, but for WASP-42. of 4.345 ± 0.010 arcsec and has a magnitude difference of 5.210 Table 4. Spectroscopic properties of the planet host stars used in the deter- mination of the physical properties of the systems. ± 0.018 in the rTCI band, which is similar to a combined Gunn at Qatar Foundation for Education, Science and Commun on April 23, 2016 i+z band. No observations were obtained in the v band, so the TCI Target T (K) Fe (dex) K (ms−1)Refs colour and therefore spectral type of the faint companion cannot eff H A be constrained. We conservatively find that between 50 per cent WASP-22 6153 ± 50 0.26 ± 0.05 70.9 ± 1.6 1,1,2 and 90 per cent of the total light from this object is contained in WASP-41 5546 ± 50 0.06 ± 0.05 138 ± 2 1,1,3 the aperture used for WASP-55 itself, giving a contaminating light WASP-42 5315 ± 79 0.29 ± 0.05 64.8 ± 1.7 1,1,4 fraction of 0.41 per cent to 0.74 per cent. We account for this in WASP-55 6070 ± 53 0.09 ± 0.05 70 ± 4 1,1,5 the JKTEBOP fits by setting the third light parameter to be L3 = References: (1) Mortier et al. (2013); (2) Knutson et al. (2014); (3) Neveu- 0.006 ± 0.003, where the errorbar has been increased to account VanMalle et al. (2016); (4) Lendl et al. (2012); (5) Hellier et al. (2012). for possible differences between the rTCI band used for the high- resolution images and the R and I bands used in this work. tabulated predictions from theoretical models (Claret 2004; Demar- We observed three transits of WASP-55, one with an R filter and que et al. 2004; Pietrinferni et al. 2004; VandenBerg, Bergbusch & two through an I filter. The two data sets were modelled separately Dowler 2006;Dotteretal.2008). but both with the third light constraint (Fig. 6). The results (Table 3) For each object we estimated the value of the velocity amplitude are in good agreement. The discovery paper (Hellier et al. 2012) of the planet, Kb and calculated the physical properties of the system presented TRAPPIST light curves of two transits and a Euler light using this and the measured quantities. We then iteratively adjusted RA curve of one transit. Both TRAPPIST data sets have only partial Kb to obtain the best agreement between the calculated a and the coverage of the transit so were not analysed here. The Euler light measured rA, and between the Teff and that predicted by the stellar Fe curve is of decent quality albeit showing significant red noise, and models for the observed H and calculated stellar mass (MA). This was modelled with JKTEBOP in the same way as for our own data. was done for a range of ages, allowing us to identify the overall best As with WASP-22, we obtain weighted means of the photometric fit and age of the system (see Southworth 2009). This process was parameters by multiplying together the probability density functions performed for each of the five sets of theoretical models, allowing us 2 of the individual measurements for each parameter. We find χν to quantify the effect of using theoretical predictions on our results. values less than 1.0 for all photometric parameters, indicating that The measured physical properties of the four systems are given the results for the different light curves are in good agreement. in Table 5. Statistical errors were calculated by propagating the uncertainties in all the input quantities to each of the output quantities. Systematic uncertainties were obtained by taking the maximum de- 4 PHYSICAL PROPERTIES viation between the final value and the five values from using the The results of the above photometric analysis were combined with different stellar models. Our results are in good agreement with lit- measured spectroscopic quantities in order to determine the phys- erature values for three of the four systems, but differ in that they are ical properties of the four planetary systems. For each object we based on more extensive observational data and explicitly account used the weighted mean of the measured values of rA, rb and i from for systematic errors due to the use of theoretical stellar models. Table 3. To these we added spectroscopic values for the host star’s In the case of WASP-22, our measured system properties differ Fe effective temperature, Teff, metallicity, H , and velocity amplitude, moderately from previous values (Maxted et al. 2010; Anderson KA, from the literature (see Table 4). These quantities alone are in- et al. 2011). Whilst there are some differences in the photometric sufficient to yield the physical properties of the stars or planets, so parameters from our data, which are of significantly higher quality the properties of the host stars were additionally constrained using than the existing TRAPPIST and Euler light curves, the main effect

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Table 5. Derived physical properties of the four systems. Where two sets of errorbars are given, the ﬁrst is the statistical uncertainty and the second is the systematic uncertainty.

Quantity Symbol WASP-22 WASP-41 WASP-42 WASP-55 . +0.073 +0.015 ± ± ± ± . +0.029 +0.022 Stellar mass (M) MA 1 249 −0.030 −0.014 0.987 0.021 0.026 0.951 0.037 0.051 1 162 −0.033 −0.021 . +0.030 +0.005 ± ± ± ± . +0.020 +0.007 Stellar radius (R) RA 1 255 −0.029 −0.005 0.886 0.009 0.008 0.892 0.021 0.016 1 102 −0.015 −0.007 . +0.027 +0.002 ± ± ± ± . +0.009 +0.003 Stellar surface gravity (c.g.s) log gA 4 338 −0.020 −0.002 4.538 0.008 0.004 4.515 0.022 0.008 4 419 −0.015 −0.003 ρ ρ . +0.043 ± ± . +0.026 Stellar density ( ) A 0 632−0.041 1.420 0.034 1.338 0.092 0 869−0.041 . +0.028 +0.005 ± ± ± ± . +0.037 +0.008 Planet mass (MJup) Mb 0 617 −0.017 −0.005 0.977 0.020 0.017 0.527 0.020 0.019 0 627 −0.038 −0.007 . +0.046 +0.005 ± ± ± ± . +0.031 +0.008 Planet radius (RJup) Rb 1 199 −0.027 −0.005 1.178 0.015 0.010 1.122 0.033 0.020 1 335 −0.020 −0.008 −2 . +0.53 ± ± . +0.54 Downloaded from Planet surface gravity (m s ) gb 10 63−0.71 17.45 0.46 10.38 0.61 8 73−0.62 ρ ρ . +0.024 +0.001 ± ± ± ± . +0.017 +0.001 Planet density ( Jup) b 0 334 −0.033 −0.001 0.558 0.020 0.005 0.349 0.029 0.006 0 247 −0.021 −0.002 T +20 ± ± +15 Equilibrium temperature (K) eq 1502−20 1242 12 1021 19 1300−13 . +0.0010 +0.0002 ± ± ± ± . +0.0005 +0.0004 Orbital semimajor axis (au) a 0 0489 −0.0004 −0.0002 0.0410 0.0003 0.0004 0.0561 0.0007 0.0010 0 0558 −0.0005 −0.0003 +0.6 +0.4 +1.1 +0.3 +3.0 +3.2 +0.8 +0.4 τ . . . . http://mnras.oxfordjournals.org/ Age (Gyr) 1 3 −1.7 −0.2 1 2 −0.0 −0.2 4 4 −2.4 −2.4 1 1 −0.6 −0.1

is due to our adoption of the higher and more precise Teff value obtained by Mortier et al. (2013) for the host star. For comparison, we calculated an alternative set of results using the lower value of Teff = 6020 ± 50 K found from the infrared ﬂux method by Maxted,Koen&Smalley(2011b). The mass and radius of the host star change to 1.194 M and 1.236 R, respectively, and those of the planet to 0.598 MJup and 1.181 RJup. These numbers are all smaller than our adopted values, but in all cases the change is within at Qatar Foundation for Education, Science and Commun on April 23, 2016 the errorbars.

5 SPOT MODELLING OF WASP-41 Figure 7. Visualizations of the surface of WASP-41 A at the times of the The third and fourth transits of WASP-41 show clear evidence of third (left) and fourth (right) transits we observed with DFOSC, produced starspot activity, manifested as short increases in brightness during by PRISM. The boundaries of the path of the planet are shown with black lines transit when the planet crosses areas which are of lower surface and the spots are shown with their measured locations, sizes and contrasts. brightness than the rest of the stellar photosphere (see Fig. 1). The spot crossing events hold information on the size and brightness of the spots, and potentially allow the motion of spots and therefore the rotation of the star to be tracked (Silva-Valio 2008; Nutzman, Fabrycky & Fortney 2011). It was for this reason that we observed three transits of WASP-41 over a six-day period in 2015. We modelled these two transit light curves using the PRISM and GEMC codes (Tregloan-Reed, Southworth & Tappert 2013; Tregloan- Reed et al. 2015). PRISM uses a pixellation approach to calculate the light curve of a planet transiting a spotted star, and GEMC is a hybrid between a Markov chain Monte Carlo and a genetic algorithm to find the best fit to a light curve of a single transit. GEMC isbasedonthe differential evolution Markov chain approach by Ter Braak (2006). The light curve from the night of 2015/05/13 shows clear evidence for one spot crossing – attempts to fit for a postulated second spot crossing did not lead to a determinate solution – and the light curve from the night of 2015/05/17 contains two spot crossing events. These two data sets were fitted individually in order to determine the locations, sizes and contrasts of the spots, where ‘contrast’ refers to the ratio of the brightness of the spot to that of the pristine stellar photosphere in the passband used to obtain the observations (Figs 7 and 8). In order to limit the strong correlation between the orbital inclination (or, equivalently, the impact parameter) of the planet and the ◦ latitude of the spot, we fixed i = 88.7 in the PRISM+GEMC fits. We Figure 8. Best fits from PRISM+GEMC for the third (upper) and fourth (lower) also fitted for the linear LD coefficient whilst fixing the quadratic transits we observed with DFOSC. coefficient to 0.3. Exploratory fits used a resolution of 15 pixels for

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Table 6. Properties of the spots occulted during two transits of WASP-41 A of orbital misalignment. WASP-41 is therefore another example of by WASP-41 b, obtained from modelling the light curves with PRISM+GEMC. an aligned system containing a transiting hot Jupiter and a cool star Longitude and latitude are deﬁned to be zero at the centre of the stellar disc. with a precisely measured projected orbital obliquity.

Light curve 2015/05/13 2015/05/17 2015/05/17 Spot number Spot 1 Spot 2 6 TRANSIT TIMING ANALYSIS ◦ − ± − ± ± Spot longitude ( ) 36.3 4.5 37.2 2.8 23.7 1.6 Each of the transit light curves available for the four systems were Spot latitude (◦) 15.3 ± 10.3 27.4 ± 6.6 8.3 ± 6.5 fitted with the JKTEBOP code in order to determine the time of mid- Spot size (◦) 10.4 ± 6.5 15.5 ± 3.5 14.3 ± 3.2 point of the transit. We did not apply this analysis to light curves Spot contrast 0.80 ± 0.14 0.82 ± 0.07 0.89 ± 0.06 lacking complete coverage of a transit, as these give noisy and pos- sibly biased values (e.g. Gibson et al. 2009). We also obtained the the radius of the planet, for speed, and for final fits we used 50 pixels WASP-South light curves, divided them into individual observing Downloaded from to obtain higher precision in the results (see Table 6). seasons, and fit each season separately to obtain a time of minimum We found that the latitudes of the spots are not very well de- close to the midpoint of the data. In the case of the WASP-South termined, as expected for the case where the transit cord of the data, which have a very high scatter compared to the follow-up planet passes close to the centre of the star. Even in the case of a light curves, we fixed the values of the photometric parameters to fixed spot contrast, a similar amplitude in flux for the spot crossing the best estimates obtained in Section 3 and thus fitted for only the event can be obtained for a small spot which is totally occulted by time of midpoint and the out-of-transit brightness of the system. All http://mnras.oxfordjournals.org/ the planet, or a larger spot positioned either above or below the measured transit times were moved to the TDB time-scale. transit cord which is partially eclipsed by the planet. Similarly, a We also included times of minimum for WASP-41 and WASP- partially eclipsed spot can have very little effect on the light-curve 55 from the Exoplanet Transit Database8 (Poddany,´ Brat´ & Pejcha shape if a modest increase in its size is compensated for by moving 2010), which provides data and transit times from amateur observers its latitude further away from the transit cord, and vice versa. As affiliated with TRESCA.9 We assumed that the times were on the there is also a known degeneracy between spot contrast and size UTC time-scale and converted them to TDB. (e.g. Tregloan-Reed et al. 2013), but only for those parts of the spot For each object we fitted the times of mid-transit with straight which are occulted by the planet, it is clear that the parameter space lines to determine a new linear orbital ephemeris. Table 7 gives all for spot-modelling is inherently complex and degenerate. transit times plus their residuals versus the fitted ephemeris. In cases at Qatar Foundation for Education, Science and Commun on April 23, 2016 2 However, the spot longitudes are very well determined by our data where the χν was greater than 1.0 we scaled the uncertainties to 2 (see Table 6) because they govern the times at which spot crossings give χν = 1.0. E gives the cycle count versus the reference epoch, are detected. We now assert that the spot observed on 2015/05/13 and the bracketed numbers show the uncertainty in the final digit of is the same as the second spot observed on 2015/05/17. In this case the preceding number. the change in the longitude and latitude of the spot (both defined to The new ephemeris for WASP-22 is based on eight timing mea- be zero at the centre of the stellar disc) are 60.0 ± 4.8◦ and −7 ± surements and is 12◦, respectively, and the time difference between the midpoints of T = . + . × E the two spot crossings is 3.097 ± 0.005 d. If the spot moved directly 0 BJD(TDB) 2 455 532 727 76(22) 3 532 730 64(70) from the first to the second location, this gives a rotation period of 2 where the fit has χν = 1.46. The timebase of the ephemeris was ± ◦ 7 18.6 1.5 d at a latitude of approximately 12 , in good agreement chosen to be close to the weighted mean of the data and coincides ± with the value of 18.41 0.05 d measured from the spot-induced with the transit observed simultaneously by the TRAPPIST and brightness modulation of WASP-41 A by Maxted et al. (2011b). Euler telescopes. The most discrepant timing is the measurement v = ± This equates to a projected rotational velocity of sin i 2.4 from TRAPPIST data at cycle −4, which differs by 2.4σ from the −1 0.2 km s , again in good agreement with the measurements from timing predicted by the ephemeris. This is not sufficient grounds to Maxted et al. (2011b) and Neveu-VanMalle et al. (2016). We also reject the data point, so we did not√ do so. Instead, the errorbar for note that the measured radii and contrasts of the two spot events the ephemeris were multiplied by 1.46 to account for the excess agree to within the (relatively large) errorbars. 2 χν . The assumption that we have detected the same spot twice in For WASP-41 we have 19 timings and obtain the ephemeris: two different positions on the stellar surface leads directly to a T = . + . × E detection of a change of latitude and therefore a measurement of 0 BJD(TDB) 2 455 996 67927(10) 3 052 401 54(41) the sky-projected orbital obliquity of the system of λ = 6 ± 11◦. with χ 2 = 2.67. This is the largest χ 2 among the four objects in Neveu-VanMalle et al. (2016) used spectroscopy during a transit of ν ν this work, and occurs for the system with the most active host star. WASP-41 to measure λ = 29+10◦ with, and λ = 48 ± 29◦ without, −14 The errorbars of the ephemeris have been inflated to account for the a Bayesian prior on the projected rotational velocity. Our revised excess χ 2. The times of midpoint of the final two DFOSC transits value is consistent with both to within 1.3σ , removes the ambiguity ν were obtained using PRISM+GEMC, which agree with the midpoints due to choice of methodology, and also banishes the previous hints obtained using JKTEBOP to within 0.000 15 d. This is in line with expectations for the effects of starspots (Barros et al. 2013;Oshagh et al. 2013; Ioannidis, Huber & Schmitt 2016). 7 Alternative assumptions all yield much shorter rotation periods. For example, if the spot moves from the first to the second location but in a retrograde direction it has to travel 300◦ and the rotation period is 3.7 ± 0.3 d. If the rotation is instead prograde but the star rotates once plus the 60◦ difference 8 The Exoplanet Transit Database (ETD) can be found at: in longitude, then the rotation period is 2.4 ± 0.2 d. All other possibilities http://var2.astro.cz/ETD/credit.php require additional rotations of the star between the two detections of the 9 The TRansiting ExoplanetS and CAndidates (TRESCA) website can be spot, and thus yield ever-shorter rotation periods. found at: http://var2.astro.cz/EN/tresca/index.php

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Table 7. Times of minimum light and their residuals versus the ephemerides derived in this work.

Target Time of minimum Uncertainty Cycle Residual Reference (BJD/TDB) (d) number (d)

WASP-22 2454041.91397 0.00122 −422.0 −0.001 46 This work (WASP-South 2006) WASP-22 2454409.31798 0.00078 −318.0 −0.001 43 This work (WASP-South 2007) WASP-22 2455518.59851 0.00059 −4.0 0.001 67 This work (TRAPPIST) WASP-22 2455532.72730 0.00038 0.0 −0.000 46 This work (Euler) WASP-22 2455532.72761 0.00053 0.0 −0.000 15 This work (TRAPPIST) WASP-22 2455896.60029 0.00081 103.0 0.001 28 This work (84 cm) WASP-22 2456189.81595 0.00022 186.0 0.000 29 This work (Danish) WASP-22 2456560.75224 0.00029 291.0 −0.000 14 This work (Danish)

WASP-22 2457270.83104 0.00022 492.0 −0.000 20 This work (Danish) Downloaded from WASP-41 2454201.86515 0.00180 −588.0 −0.002 01 This work (WASP-South 2007) WASP-41 2454549.83845 0.00100 −474.0 −0.002 48 This work (WASP-South 2008) WASP-41 2455642.60026 0.00027 −116.0 −0.000 43 This work (TRAPPIST) WASP-41 2455654.81018 0.00020 −112.0 −0.000 12 This work (TRAPPIST) WASP-41 2455663.96815 0.00024 −109.0 0.000 65 This work (FTS) http://mnras.oxfordjournals.org/ WASP-41 2455694.49015 0.00091 −99.0 −0.001 37 This work (TRAPPIST) WASP-41 2455725.01389 0.00045 −89.0 −0.001 64 Tan (ETD) WASP-41 2455947.84052 0.00021 −16.0 −0.000 32 This work (84 cm) WASP-41 2455996.67838 0.00032 0.0 −0.000 89 This work (TRAPPIST) WASP-41 2456402.65000 0.00021 133.0 0.001 32 This work (TRAPPIST) WASP-41 2456402.64891 0.00007 133.0 0.000 23 This work (Danish) WASP-41 2456424.01544 0.00030 140.0 −0.000 05 Tan (ETD) WASP-41 2456698.73202 0.00038 230.0 0.000 40 Masek (ETD) WASP-41 2456765.88379 0.00093 252.0 −0.000 67 Evans (ETD) WASP-41 2456768.93761 0.00041 253.0 0.000 75 Evans (ETD) WASP-41 2456808.61760 0.00009 266.0 −0.000 48 This work (Danish) at Qatar Foundation for Education, Science and Commun on April 23, 2016 WASP-41 2456820.82714 0.00058 270.0 −0.000 55 Evans (ETD) WASP-41 2457153.53964 0.00009 379.0 0.000 19 This work (Danish) WASP-41 2457156.59146 0.00015 380.0 −0.000 39 This work (Danish, PRISM+GEMC) WASP-41 2457159.64436 0.00017 381.0 0.000 11 This work (Danish, PRISM+GEMC) WASP-42 2454554.59925 0.00140 −220.0 0.001 99 This work (WASP-South 2008) WASP-42 2455625.65818 0.00027 −5.0 −0.000 70 This work (TRAPPIST) WASP-42 2455630.64068 0.00029 −4.0 0.000 12 This work (TRAPPIST) WASP-42 2455650.56811 0.00033 0.0 0.000 82 This work (TRAPPIST) WASP-42 2455655.54875 0.00032 1.0 −0.000 22 This work (TRAPPIST) WASP-42 2455645.58567 0.00035 −1.0 0.000 07 This work (Euler) WASP-42 2456437.67306 0.00014 158.0 0.000 04 This work (Danish) WASP-42 2456462.58139 0.00010 163.0 −0.000 04 This work (Danish) WASP-42 2456472.54492 0.00018 165.0 0.000 12 This work (Danish)

WASP-55 2453902.56555 0.00340 −563.0 −0.000 93 This work (WASP-South 2006) WASP-55 2454201.76435 0.00280 −496.0 0.000 73 This work (WASP-South 2007) WASP-55 2454581.34095 0.00220 −411.0 −0.001 15 This work (WASP-South 2008) WASP-55 2454951.98517 0.00210 −328.0 −0.004 15 This work (WASP-South 2009) WASP-55 2455309.24157 0.00170 −248.0 0.001 92 This work (WASP-South 2010) WASP-55 2455715.61277 0.00046 −157.0 0.000 88 This work (Euler) WASP-55 2456416.71548 0.00016 0.0 −0.000 17 This work (Danish) WASP-55 2456778.43544 0.00283 81.0 0.003 83 Lomoz (ETD) WASP-55 2456778.42973 0.00200 81.0 −0.001 88 Lomoz (ETD) WASP-55 2456827.55355 0.00023 92.0 0.000 02 This work (Danish) WASP-55 2457135.68202 0.00019 161.0 0.000 09 This work (Danish)

For WASP-42 there are three timings from data in this work, five For WASP-55 we have 11 timings which yield this ephemeris: from published follow-up light curves and one from WASP-South T = BJD(TDB) 2 456 416.71565(13) + 4.465 6291(11) × E observations in the 2008 season. Whilst there are plenty of WASP- 0 2 South observations from 2006 and 2007, there is no coverage of with χν = 1.10 (accounted for in the errorbars). transits due to the near-integer orbital period of the system. We find Fig. 9 shows the residuals versus the linear ephemeris for each of the ephemeris: our four targets. No transit timing variations are apparent, and there are too few timing measurements for a search for such variations to T = BJD(TDB) 2 455 650.56728(15) + 4.981 6819(11) × E 0 be useful. Our period values for all four systems are consistent with 2 where χν = 1.35 and the errorbars have been inflated to account previous measurements but are significantly more precise due to the for this. addition of new high-quality data and a longer temporal baseline.

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Figure 9. Plot of the residuals of the timings of mid-transit versus a linear ephemeris. The results from this work are shown in blue and from amateur observers at Qatar Foundation for Education, Science and Commun on April 23, 2016 in green. Our re-analysis of published data are shown in black for WASP-South observations and in red for other sources. The grey-shaded regions show the 1σ uncertainty in the ephemeris as a function of cycle number.

7 SUMMARY AND CONCLUSIONS WASP-22, WASP-41, WASP-42 and WASP-55 are four systems containing transiting hot Jupiters with large radii. We have presented high-precision photometry of 13 transits of the four systems, and used these data to refine their measured orbital ephemerides and physical properties. Our light curves of each system contain highly consistent transit shapes, demonstrating the re- peatability of observations taken with the telescope-defocussing method. We find no evidence for transit timing variations in any of the systems, and our new measurements of the system properties are mostly in good agreement with previous determinations based on fewer and less precise data. All four planets have inexplicably larger radii than expected from theoretical models (Bodenheimer et al. 2003; Fortney, Marley &Barnes2007; Baraffe et al. 2008). Fig. 10 compares the positions of the four planets in the mass–radius diagram to the overall sample of planets10 and to predictions from Bodenheimer et al. (2003) for planetary equilibrium temperatures similar to those for the four planets which are the subject of this work. Whilst WASP- 22 b is well represented by models without a heavy-element core, the other three planets are significantly larger than predicted even for coreless gas giants. For comparison, Fig. 11 shows the same Figure 10. Plot of planet radii versus their masses. WASP-22 b, WASP- mass–radius diagram but with the predictions of the Baraffe et al. 41 b, WASP-42 b and WASP-55 b are indicated using black filled circles. (2008) theoretical models for a range of heavy-element mass frac- The overall population of planets is shown using blue open circles without tions, Z. All four planets are larger than model predictions even for errorbars, using data taken from TEPCat on 2015/11/09. The lines show the predicted planet radii of gas-giants from Bodenheimer, Laughlin & Lin Z = 0.02, which yields the largest planetary radii of all the model (2003, their table 1) for two different equilibrium temperatures (1000 K and 1500 K) which bracket the four planets, and for with and without a solid 20 M⊕ core (see key). 10 Data on planetary systems were taken from TEPCat on 2015/11/09. Figs 10 and 11 show only those planets regarded as ‘well-studied’, i.e. excluding planets which have been characterized as part of a large sample of planetary systems without receiving significant individual attention.

MNRAS 457, 4205–4217 (2016) WASP-22, WASP-41, WASP-42 and WASP-55 4215

Spectroscopic measurements of λ are notoriously difficult for cool stars because the amplitude of the Rossiter–McLaughlin effect depends on the vsin i of the host star, which is typically very low below Teff values of roughly 5500 K. Starspot tracking is a major contributor in this domain, with a total of 10 determinations to date (Table 8 and Fig. 12). The host stars have Teff values between 4645 K and 5576 K, so are all cool stars where Rossiter–McLaughlin measurements are difficult (e.g. Albrecht et al. 2011) but stars often show strong spot activity. The orbital obliquity of systems containing cool stars is a useful probe of tidal theory (e.g. Esposito et al. 2014; Mancini et al. 2015), and a statistically significant sample of such measurements is both scientifically important and observation- Downloaded from ally tractable via starspot tracking analyses such as that performed for WASP-41.

ACKNOWLEDGEMENTS This study is based on data collected by MiNDSTEp with the Dan- http://mnras.oxfordjournals.org/ ish 1.54 m telescope at the ESO La Silla Observatory. The op- eration of the Danish 1.54-m telescope is financed by a grant to UGJ from the Danish Council for Independent Research, Natural Figure 11. As Fig. 10 but with different theoretical predictions. The lines Sciences (FNU). The reduced light curves presented in this work show the predicted planet radii of gas-giants from Baraffe, Chabrier & will be made available at the CDS (http://vizier.u-strasbg.fr/)and Barman (2008, their table 4) for four different heavy-element mass fractions at http://www.astro.keele.ac.uk/jkt/. We thank Laetitia Delrez and Z, labelled on the plot. The unbroken lines show predictions for a planet of Marion Neveu-VanMalle for providing published light curves of age 0.5 Gyr, the dashed lines for an age of 1 Gyr and the dotted lines for an WASP-41. J So acknowledges financial support from the Lever- age of 5 Gyr. The lines are colour-coded for clarity. hulme Trust in the form of a Philip Leverhulme Prize. JTR ac- at Qatar Foundation for Education, Science and Commun on April 23, 2016 knowledges financial support from ORAU (Oak Ridge Associated Universities) and NASA in the form of a NASA Post-Doctoral Pro- sets. It is clear that all four planets are more inflated than expected, gramme (NPP) Fellowship. DFE is funded by the UK’s Science and particularly WASP-55, and are therefore good candidates for the Technology Facilities Council. EU-S acknowledges the support of characterization of their atmospheres via transmission spectroscopy CONICYT QUIMAL 130004 project. Funding for the Stellar As- and photometry (e.g. Nikolov et al. 2014; Mallonn et al. 2015). trophysics Centre in Aarhus is provided by The Danish National Re- Two of our transit light curves of WASP-41 show clear evi- search Foundation (grant agreement no. DNRF106). The research dence for spot activity, with one spot crossing event observed on is supported by the ASTERISK project (ASTERoseismic Investi- 2015/05/13 and two on 2015/05/17. We make the assumption that gations with SONG and Kepler) funded by the European Research the spot observed on 2015/05/13 is the same as the second spot ob- Council (grant agreement no. 267864). TCH acknowledges KASI served on 2015/05/17, as the measured spot radii and contrasts research grants #2012-1-410-02, #2013-9-400-00, #2014-1-400-06 agree, and the resulting stellar rotation period and velocity are and #2015-1-850-04. NP acknowledges funding by the Gemini- highly consistent with previous measurements obtained using dif- Conicyt Fund, allocated to project no. 32120036. GD acknowl- ferent methods. The change in longitude of the spot then gives a edges Regione Campania for support from POR-FSE Campania stellar rotation period of 18.6 ± 1.5 d and vsin i of 2.4 ± 0.2 km s−1, 2014–2020. YD, AE, OW and J Su acknowledge support from both at a latitude of approximately 12◦. The change in latitude yields the Communaute´ française de Belgique - Actions de recherche a measurement of the sky-projected orbital obliquity of the system concertees´ - Academie´ Wallonie-Europe. The following internet- of λ = 6 ± 11◦, which is significantly more precise than a previous based resources were used in research for this paper: the ESO measurement obtained via the Rossiter–McLaughlin effect. Digitized Sky Survey; the NASA Astrophysics Data System; the

Table 8. Published measurements of the sky-projected, λ, and true, ψ, orbital obliquities obtained from spot-tracking analyses.

◦ ◦ System Host star Teff (K) λ ( ) ψ ( ) Reference ± +16 +24 +15 +8 HAT-P-11 4780 50 105−12 or 121−21 106−11 or 97−4 Sanchis-Ojeda & Winn (2011) HATS-02 5227 ± 95 8 ± 8 Mohler-Fischer et al. (2013) Kepler-17 5781 ± 85 0 ± 15 Desert´ et al. (2011) Kepler-30 5498 ± 54 −1 ± 10 or 4 ± 10 Sanchis-Ojeda et al. (2012) ± − +22 +9 Kepler-63 5576 50 110−14 145−14 Sanchis-Ojeda et al. (2013) Qatar-2 4645 ± 50 4.3 ± 4.5 Mancini et al. (2014) ± − +14 WASP-4 5540 55 1−12 Sanchis-Ojeda et al. (2011) WASP-6 5375 ± 65 7.2 ± 3.7 Tregloan-Reed et al. (2015) WASP-19 5460 ± 90 1.0 ± 1.2 Tregloan-Reed et al. (2013) WASP-41 5546 ± 33 6 ± 11 This work

MNRAS 457, 4205–4217 (2016) 4216 J. Southworth et al. Downloaded from http://mnras.oxfordjournals.org/

Figure 12. Plot of the sky-projected orbital obliquity angle λ versus the Teff of the host star. The data come from TEPCat, obtained on 2015/11/09, and only the best value for each planetary system is plotted. Green lines show the measurements, graded for clarity from dark to light green depending on the sizeofthe errorbars. Measurements obtained from spot tracking are shown with thicker blue lines. The Teff values proposed as boundaries are shown using a grey dashed +150 line (6250 K; Winn et al. 2010) and a grey shaded region with a dotted line to indicate the value and its uncertainties (6090−110 K; Dawson 2014). Published values of λ have been adjusted by ±180◦ to bring them into the interval [0◦,180◦] (see Crida & Batygin 2014).

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MNRAS 457, 4205–4217 (2016) WASP-22, WASP-41, WASP-42 and WASP-55 4217

16 SUPPORTING INFORMATION Centre of Electronic Imaging, Department of Physical Sciences, The Open University, Milton Keynes MK7 6AA, UK Additional Supporting Information may be found in the online ver- 17Stellar Astrophysics Centre (SAC), Department of Physics and Astronomy, sion of this article: Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark 18Institut d’Astrophysique et de Geophysique,´ UniversitedeLi´ ege,` B-4000 Appendix. (http://www.mnras.oxfordjournals.org/lookup/suppl/ Liege,` Belgium 19Qatar Environment and Energy Research Institute (QEERI), HBKU, Qatar doi:10.1093/mnras/stw279/-/DC1). Foundation, PO Box 5825, Doha, Qatar Please note: Oxford University Press is not responsible for the 20Department of Astronomy, Boston University, 725 Commonwealth Avenue, content or functionality of any supporting materials supplied by Boston, MA 02215, USA the authors. Any queries (other than missing material) should be 21Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, I-80126 Napoli, directed to the corresponding author for the article. Italy 22Universitat¨ Hamburg, Meteorologisches Institut, Bundesstraße 55, Downloaded from 1Astrophysics Group, Keele University, Staffordshire ST5 5BG, UK D-20146 Hamburg, Germany 23 2NASA Ames Research Center, Moffett Field, CA 94035, USA Astronomisches Rechen-Institut, Zentrum fur¨ Astronomie, Universitat¨ Hei- 3Dark Cosmology Centre, Niels Bohr Institute, University of Copenhagen, delberg, Monchhofstraße¨ 12-14, D-69120 Heidelberg, Germany 24 Juliane Maries vej 30, DK-2100 Copenhagen Ø, Denmark Hamburger Sternwarte, Universitat¨ Hamburg, Gojenbergsweg 112, 4NASA Exoplanet Science Institute, MS 100-22, California Institute of Tech- D-21029 Hamburg, Germany 25Dipartimento di Fisica e Astronomia, Universita` di Bologna, Viale Berti

nology, Pasadena, CA 91125, USA http://mnras.oxfordjournals.org/ 5Dipartimento di Fisica ‘E.R. Caianiello’, Universita` di Salerno, Via Gio- Pichat 6/2, I-40127 Bologna, Italy 26 vanni Paolo II 132, I-84084 Fisciano (SA), Italy Main Astronomical Observatory, Academy of Sciences of Ukraine, vul. 6Istituto Internazionale per gli Alti Studi Scientifici (IIASS), I-84019 Vietri Akademika Zabolotnoho 27, UA-03680 Kyiv, Ukraine 27 Sul Mare (SA), Italy European Southern Observatory, Karl-Schwarzschild-Straße 2, D-85748 7Max Planck Institute for Astronomy, Konigstuhl¨ 17, D-69117 Heidelberg, Garching bei Munchen,¨ Germany 28 Germany Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 8Unidad de Astronom´ıa, Facultad de Ciencias Basicas,´ Universidad de 21218, USA 29 Antofagasta, Avenida U. de Antofagasta 02800, Antofagasta, Chile Jodrell Bank Centre for Astrophysics, University of Manchester, Oxford 9SUPA, University of St Andrews, School of Physics and Astronomy, North Road, Manchester M13 9PL, UK 30 Haugh, St Andrews KY16 9SS, UK Finnish Centre for Astronomy with ESO (FINCA), University of Turku, 10Yunnan Observatories, Chinese Academy of Sciences, Kunming 650011, Vais¨ al¨ antie¨ 20, FI-21500 Piikkio,¨ Finland at Qatar Foundation for Education, Science and Commun on April 23, 2016 31 China Department of Astronomy, Ohio State University, 140 W. 18th Ave, Colum- 11Key Laboratory for the Structure and Evolution of Celestial Objects, bus, OH 43210, USA 32 Chinese Academy of Sciences, Kunming 650011, China Department of Physics, Sharif University of Technology, P. O. Box 11155- 12Korea Astronomy and Space Science Institute, Daejeon 305-348, Republic 9161 Tehran, Iran 33 of Korea Planetary and Space Sciences, Department of Physical Sciences, The 13Niels Bohr Institute and Centre for Star and Planet Formation, University Open University, Milton Keynes MK7 6AA, UK of Copenhagen, Øster Voldgade 5, DK-1350 Copenhagen K, Denmark 14INAF – Osservatorio Astrofisico di Torino, via Osservatorio 20, I-10025 Pino Torinese, Italy 15Instituto de Astrof´ısica, Facultad de F´ısica, Pontificia Universidad Catolica´ de Chile, Av. Vicuna˜ Mackenna 4860, 7820436 Macul, Santiago, Chile This paper has been typeset from a TEX/LATEX file prepared by the author.

MNRAS 457, 4205–4217 (2016) Mon. Not. R. Astron. Soc. 000, 000–000 (0000) Printed 28 January 2016 (MN LATEX style ﬁle v2.2)

High-precision photometry by telescope defocussing. VIII. WASP-22, WASP-41, WASP-42 and WASP-55⋆

John Southworth 1, J. Tregloan-Reed 2, M. I. Andersen 3, S. Calchi Novati 4,5,6, S. Ciceri 7, J. P. Colque 8, G. D’Ago 6, M. Dominik 9†, D. F. Evans 1, S.-H. Gu 10,11, A. Herrera-Cruces 8, T. C. Hinse 12, U. G. Jørgensen 13, D. Juncher 13, M. Kuffmeier 13, L. Mancini 7,14, N. Peixinho 8, A. Popovas 13, M. Rabus 15,7, J. Skottfelt 16,13, R. Tronsgaard 17, E. Unda-Sanzana 8, X.-B. Wang 10,11, O. Wertz 18, K. A. Alsubai 19, J. M. Andersen 13,20, V. Bozza 5,21, D. M. Bramich 19, M. Burgdorf 22, Y. Damerdji 18, C. Diehl 23,24, A. Elyiv 25,18,26, R. Figuera Jaimes 9,27, T. Haugbølle 13, M. Hundertmark 13, N. Kains 28, E. Kerins 29, H. Korhonen 30,13,3, C. Liebig 9, M. Mathiasen 13, M. T. Penny 31, S. Rahvar 32, G. Scarpetta 6,5,21, R. W. Schmidt 23, C. Snodgrass 33, D. Starkey 9, J. Surdej 18, C. Vilela 1, C. von Essen 17, Y. Wang 10 1 Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK 2 NASA Ames Research Center, Moffett Field, CA 94035, USA 3 Dark Cosmology Centre, Niels Bohr Institute, University of Copenhagen, Juliane Maries vej 30, 2100 Copenhagen Ø, Denmark 4 NASA Exoplanet Science Institute, MS 100-22, California Institute of Technology, Pasadena, CA 91125, US 5 Dipartimento di Fisica “E.R. Caianiello”, Universitàdi Salerno, Via Giovanni Paolo II 132, 84084, Fisciano (SA), Italy 6 Istituto Internazionale per gli Alti Studi Scientifici (IIASS), 84019 Vietri Sul Mare (SA), Italy 7 Max Planck Institute for Astronomy, Königstuhl 17, 69117 Heidelberg, Germany 8 Unidad de Astronom´ıa, Facultad de Ciencias Básicas, Universidad de Antofagasta, Avenida U. de Antofagasta 02800, Antofagasta, Chile 9 SUPA, University of St Andrews, School of Physics & Astronomy, North Haugh, St Andrews, KY16 9SS, UK 10 Yunnan Observatories, Chinese Academy of Sciences, Kunming 650011, China 11 Key Laboratory for the Structure and Evolution of Celestial Objects, Chinese Academy of Sciences, Kunming 650011, China 12 Korea Astronomy and Space Science Institute, Daejeon 305-348, Republic of Korea 13 Niels Bohr Institute & Centre for Star and Planet Formation, University of Copenhagen, Øster Voldgade 5, 1350 Copenhagen K, Denmark 14 INAF – Osservatorio Astrofisico di Torino, via Osservatorio 20, 10025, Pino Torinese, Italy 15 Instituto de Astrof´ısica, Facultad de F´ısica, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, 7820436 Macul, Santiago, Chile 16 Centre of Electronic Imaging, Department of Physical Sciences, The Open University, Milton Keynes, MK7 6AA, UK 17 Stellar Astrophysics Centre (SAC), Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark 18 Institut d’Astrophysique et de Géophysique, Université de Liège, 4000 Liège, Belgium 19 Qatar Environment and Energy Research Institute (QEERI), HBKU, Qatar Foundation, PO Box 5825, Doha, Qatar 20 Department of Astronomy, Boston University, 725 Commonwealth Avenue, Boston, MA 02215, USA 21 Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, 80126 Napoli, Italy 22 Universität Hamburg, Meteorologisches Institut, Bundesstraße 55, 20146 Hamburg, Germany 23 Astronomisches Rechen-Institut, Zentrum für Astronomie, Universität Heidelberg, Mönchhofstraße 12-14, 69120 Heidelberg, Germany 24 Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112, 21029 Hamburg, Germany 25 Dipartimento di Fisica e Astronomia, Universitàdi Bologna, Viale Berti Pichat 6/2, I-40127 Bologna, Italy 26 Main Astronomical Observatory, Academy of Sciences of Ukraine, vul. Akademika Zabolotnoho 27, 03680 Kyiv, Ukraine 27 European Southern Observatory, Karl-Schwarzschild-Straße 2, 85748 Garching bei München, Germany 28 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA 29 Jodrell Bank Centre for Astrophysics, University of Manchester, Oxford Road, Manchester M13 9PL, UK 30 Finnish Centre for Astronomy with ESO (FINCA), University of Turku, Väisäläntie 20, FI-21500 Piikkiö, Finland 31 Department of Astronomy, Ohio State University, 140 W. 18th Ave., Columbus, OH 43210, USA 32 Department of Physics, Sharif University of Technology, P. O. Box 11155-9161 Tehran, Iran 33 Planetary and Space Sciences, Department of Physical Sciences, The Open University, Milton Keynes, MK7 6AA, UK

28 January 2016

c 0000 RAS 2 Southworth et al.

ABSTRACT We present 13 high-precision and four additional light curves of four bright southern- hemisphere transiting planetary systems: WASP-22, WASP-41, WASP-42 and WASP-55. In the cases of WASP-42 and WASP-55, these are the first follow-up observations since their discovery papers. We present refined measurements of the physical properties and orbital ephemeridesof all four systems. No indications of transit timing variations were seen. All four planets have radii inflated above those expected from theoretical models of gas-giant planets; WASP-55b is the most discrepantwith a mass of 0.63 MJup anda radius of1.34 RJup. WASP- 41 shows brightness anomalies during transit due to the planet occulting spots on the stellar surface. Two anomalies observed 3.1d apart are very likely due to the same spot. We measure its change in position and determine a rotation period for the host star of 18.6 ± 1.5 d, in good agreement with a published measurement from spot-induced brightness modulation, and a sky-projected orbital obliquity of λ =6 ± 11◦. We conclude with a compilation of obliquity measurements from spot-tracking analyses and a discussion of this technique in the study of the orbital configurations of hot Jupiters. Key words: stars: planetary systems — stars: fundamental parameters — stars: individual: WASP-22, WASP-41, WASP-42, WASP-55

APPENDIX A: FULL RESULTS FOR THE LIGHT CURVES ANALYSED IN THIS WORK

The tables in this Appendix contain the detailed results of the JK- TEBOP modelling of the light curves of the four planetary systems. Note that whilst all the results are best ﬁts to the relevant data, some parameters are unphysical (for example some limb darkening coef- ﬁcients imply that the limb of the star produces a negative amount of light). In these cases the unphysical results have not been used but are retained in the tables for completeness.

REFERENCES Anderson, D. R., et al., 2011, A&A, 534, A16 Hellier, C., et al., 2012, MNRAS, 426, 739 Lendl, M., et al., 2012, A&A, 544, A72 Neveu-VanMalle, M., et al., 2015, A&A, in press, arXiv:1509.07750

⋆ Based on data collected by MiNDSTEp with the Danish 1.54 m telescope at the ESO La Silla Observatory. † Royal Society University Research Fellow

c 0000 RAS, MNRAS 000, 000–000 WASP-22, WASP-41, WASP-42 and WASP-55 3

Table A1. Parameters of the JKTEBOP best ﬁts of the WASP-22 I-band light curve from DFOSC, using different approaches to LD. For each part of the table the upper quantities are ﬁtted parameters and the lower quantities are derived parameters. T0 is given as BJD(TDB) − 2456000.0. The light curve contains 674 datapoints.

Linear LD law Quadratic LD law Square-root LD law Logarithmic LD law Cubic LD law

All LD coefﬁcients ﬁxed

+0.0039 +0.0035 +0.0033 +0.0033 +0.0029 rA + rb 0.1294−0.0015 0.1285−0.0006 0.1281−0.0005 0.1282−0.0006 0.1295−0.0025 +0.00088 +0.00059 +0.00061 +0.00055 +0.00052 k 0.09863−0.00050 0.09872−0.00046 0.09902−0.00044 0.09909−0.00041 0.10068−0.00055 +0.96 +0.47 +0.41 +0.40 +1.29 i (deg.) 89.12−0.95 89.95−1.14 89.91−1.16 89.91−1.17 88.68−0.62 uA 0.55 fixed 0.38 fixed 0.12 fixed 0.66 fixed 0.35 fixed vA 0.24 fixed 0.61 fixed 0.28 fixed 0.12 fixed +0.00017 +0.00017 +0.00015 +0.00016 +0.00015 T0 560.75245−0.00017 560.75244−0.00017 560.75243−0.00016 560.75243−0.00017 560.75242−0.00016 +0.0035 +0.0031 +0.0029 +0.0030 +0.0026 rA 0.1178−0.0013 0.1169−0.0006 0.1166−0.0005 0.1166−0.0005 0.1176−0.0022 +0.00045 +0.00036 +0.00035 +0.00035 +0.00032 rb 0.01162−0.00017 0.01154−0.00010 0.01154−0.00009 0.01155−0.00008 0.01184−0.00028 σ (mmag) 1.0234 1.0128 1.0082 1.0079 1.0065 2 χ red 1.0852 1.0654 1.0559 1.0568 1.0610 Fitting for the linear LD coefficient and perturbing the nonlinear LD coefficient

+0.0035 +0.0037 +0.0033 +0.0034 +0.0034 rA + rb 0.1292−0.0021 0.1285−0.0012 0.1284−0.0012 0.1282−0.0010 0.1287−0.0016 +0.00071 +0.00072 +0.00069 +0.00077 +0.00073 k 0.10026−0.00061 0.09950−0.00065 0.09958−0.00057 0.09938−0.00060 0.09979−0.00061 +1.16 +0.82 +0.87 +0.70 +0.99 i (deg.) 88.78−0.82 89.37−0.97 89.31−0.85 89.59−1.03 89.11−0.86 +0.023 +0.034 +0.042 +0.056 +0.027 uA 0.436−0.022 0.325−0.038 0.085−0.040 0.640−0.055 0.410−0.028 vA 0.24 perturbed 0.61 perturbed 0.28 perturbed 0.12 perturbed +0.00014 +0.00016 +0.00016 +0.00015 +0.00015 T0 560.75243−0.00017 560.75243−0.00017 560.75243−0.00015 560.75243−0.00016 560.75243−0.00015 +0.0032 +0.0032 +0.0030 +0.0030 +0.0030 rA 0.1175−0.0019 0.1168−0.0010 0.1168−0.0011 0.1166−0.0009 0.1170−0.0015 +0.00040 +0.00041 +0.00036 +0.00039 +0.00039 rb 0.01178−0.00023 0.01162−0.00014 0.01163−0.00015 0.01159−0.00012 0.01168−0.00018 σ (mmag) 1.0040 1.0076 1.0055 1.0067 1.0051 2 χ red 1.0481 1.0580 1.0527 1.0558 1.0514

Table A2. Parameters of the JKTEBOP best ﬁts of the WASP-22 TRAPPIST light curve from Anderson et al. (2011), using different approaches to LD. For each part of the table the upper quantities are ﬁtted parameters and the lower quantities are derived parameters. T0 is given as HJD − 2455000.0. The light curve contains 843 datapoints.

Linear LD law Quadratic LD law Square-root LD law Logarithmic LD law Cubic LD law

All LD coefﬁcients ﬁxed

+0.0077 +0.0111 +0.0073 +0.0070 +0.0067 rA + rb 0.1333−0.0054 0.1279−0.0026 0.1293−0.0022 0.1284−0.0027 0.1328−0.0054 +0.0017 +0.0015 +0.0013 +0.0013 +0.0012 k 0.0929−0.0013 0.0929−0.0011 0.0931−0.0011 0.0930−0.0012 0.0953−0.0011 +1.9 +1.2 +1.2 +1.3 +1.8 i (deg.) 88.0−1.1 90.0−1.8 88.9−1.3 89.3−1.3 87.8−1.0 uA 0.49 fixed 0.23 fixed 0.07 fixed 0.58 fixed 0.20 fixed vA 0.32 fixed 0.56 fixed 0.27 fixed 0.15 fixed +0.00041 +0.00037 +0.00037 +0.00037 +0.00037 T0 532.72692−0.00039 532.72689−0.00043 532.72690−0.00037 532.72690−0.00039 532.72690−0.00036 +0.0069 +0.0100 +0.0065 +0.0063 +0.0061 rA 0.1220−0.0048 0.1170−0.0023 0.1183−0.0020 0.1175−0.0024 0.1213−0.0049 +0.00085 +0.00108 +0.00071 +0.00071 +0.00072 rb 0.01133−0.00059 0.01086−0.00031 0.01102−0.00028 0.01092−0.00030 0.01156−0.00051 σ (mmag) 2.4033 2.3876 2.3884 2.3878 2.3802 2 χ red 1.1228 1.1058 1.1062 1.1057 1.0970 Fitting for the linear LD coefficient and perturbing the nonlinear LD coefficient

+0.0063 +0.0079 +0.0075 +0.0069 +0.0077 rA + rb 0.1324−0.0053 0.1324−0.0046 0.1331−0.0057 0.1330−0.0053 0.1325−0.0050 +0.0013 +0.0013 +0.0014 +0.0014 +0.0014 k 0.0954−0.0012 0.0949−0.0013 0.0952−0.0012 0.0951−0.0012 0.0951−0.0012 +1.8 +1.8 +1.9 +2.0 +1.9 i (deg.) 87.9−0.9 88.0−1.2 87.8−1.1 87.9−1.0 87.9−1.1 +0.046 +0.063 +0.061 +0.067 +0.059 uA 0.261−0.056 0.086−0.069 −0.075−0.066 0.437−0.071 0.217−0.062 vA 0.32 perturbed 0.56 perturbed 0.27 perturbed 0.15 perturbed +0.00034 +0.00035 +0.00036 +0.00037 +0.00038 T0 532.72691−0.00033 532.72691−0.00039 532.72690−0.00037 532.72690−0.00033 532.72690−0.00035 +0.0057 +0.0070 +0.0069 +0.0062 +0.0068 rA 0.1209−0.0047 0.1209−0.0042 0.1215−0.0050 0.1214−0.0047 0.1210−0.0045 +0.00066 +0.00080 +0.00076 +0.00071 +0.00079 rb 0.01153−0.00053 0.01147−0.00049 0.01157−0.00056 0.01154−0.00053 0.01151−0.00052 σ (mmag) 2.3798 2.3811 2.3800 2.3803 2.3801 2 χ red 1.0974 1.0999 1.0982 1.0987 1.0982

c 0000 RAS, MNRAS 000, 000–000 4 Southworth et al.

Table A3. Parameters of the JKTEBOP best ﬁts of the WASP-22 EulerCam light curve from Anderson et al. (2011), using different approaches to LD. For each part of the table the upper quantities are ﬁtted parameters and the lower quantities are derived parameters. T0 is given as HJD − 2455000.0. The light curve contains 187 datapoints.

Linear LD law Quadratic LD law Square-root LD law Logarithmic LD law Cubic LD law

All LD coefﬁcients ﬁxed

+0.0077 +0.0064 +0.0066 +0.0068 +0.0052 rA + rb 0.1423−0.0075 0.1538−0.0071 0.1575−0.0073 0.1563−0.0071 0.1777−0.0056 +0.00161 +0.00121 +0.00125 +0.00126 +0.00092 k 0.10051−0.00153 0.10191−0.00128 0.10288−0.00133 0.10253−0.00118 0.10527−0.00100 +1.01 +0.65 +0.63 +0.63 +0.41 i (deg.) 86.60−0.79 85.43−0.55 85.06−0.56 85.18−0.56 83.32−0.36 uA 0.49 fixed 0.23 fixed 0.07 fixed 0.58 fixed 0.20 fixed vA 0.32 fixed 0.56 fixed 0.27 fixed 0.15 fixed +0.00037 +0.00035 +0.00038 +0.00038 +0.00042 T0 532.72658−0.00039 532.72662−0.00036 532.72665−0.00040 532.72664−0.00036 532.72676−0.00037 +0.0068 +0.0057 +0.0059 +0.0060 +0.0046 rA 0.1293−0.0066 0.1395−0.0063 0.1428−0.0065 0.1418−0.0063 0.1607−0.0050 +0.00086 +0.00074 +0.00076 +0.00079 +0.00055 rb 0.01299−0.00086 0.01422−0.00077 0.01469−0.00082 0.01454−0.00075 0.01692−0.00065 σ (mmag) 1.0516 1.0695 1.0787 1.0755 1.1202 2 χ red 0.9092 0.9298 0.9453 0.9403 0.9831 Fitting for the linear LD coefficient and perturbing the nonlinear LD coefficient

+0.0080 +0.0109 +0.0090 +0.0094 +0.0086 rA + rb 0.1424−0.0091 0.1381−0.0078 0.1413−0.0094 0.1408−0.0092 0.1412−0.0091 +0.0021 +0.0027 +0.0024 +0.0024 +0.0020 k 0.0994−0.0023 0.0973−0.0023 0.0985−0.0025 0.0982−0.0025 0.0986−0.0025 +1.3 +2.4 +1.9 +1.8 +1.6 i (deg.) 86.7−0.9 87.4−1.4 86.9−1.0 87.0−1.1 86.9−1.0 +0.054 +0.073 +0.076 +0.074 +0.064 uA 0.597−0.057 0.445−0.075 0.270−0.066 0.785−0.082 0.560−0.061 vA 0.32 perturbed 0.56 perturbed 0.27 perturbed 0.15 perturbed +0.00037 +0.00040 +0.00038 +0.00038 +0.00037 T0 532.72654−0.00033 532.72653−0.00036 532.72653−0.00038 532.72653−0.00035 532.72654−0.00036 +0.0071 +0.0096 +0.0080 +0.0081 +0.0076 rA 0.1296−0.0081 0.1259−0.0069 0.1286−0.0082 0.1282−0.0082 0.1286−0.0080 +0.0009 +0.0013 +0.0011 +0.0011 +0.0010 rb 0.0129−0.0010 0.0123−0.0009 0.0127−0.0011 0.0126−0.0011 0.0127−0.0011 σ (mmag) 1.0532 1.0497 1.0517 1.0511 1.0517 2 χ red 0.8909 0.8808 0.8868 0.8847 0.8865

Table A4. Parameters of the JKTEBOP best ﬁts of the WASP-41 I-band light curve from DFOSC, using different approaches to LD. For each part of the table the upper quantities are ﬁtted parameters and the lower quantities are derived parameters. T0 is given as BJD(TDB) − 2457000.0. The light curve contains 628 datapoints.

Linear LD law Quadratic LD law Square-root LD law Logarithmic LD law Cubic LD law

All LD coefﬁcients ﬁxed

rA + rb 0.11445 ± 0.00105 0.11557 ± 0.00098 0.11541 ± 0.00109 0.11599 ± 0.00107 0.11993 ± 0.00090 k 0.13602 ± 0.00037 0.13672 ± 0.00031 0.13714 ± 0.00036 0.13739 ± 0.00033 0.14010 ± 0.00027 i (deg.) 89.07 ± 0.36 88.76 ± 0.23 88.72 ± 0.25 88.59 ± 0.22 87.75 ± 0.12 uA 0.53 fixed 0.31 fixed 0.14 fixed 0.62 fixed 0.30 fixed vA 0.30 fixed 0.54 fixed 0.26 fixed 0.15 fixed T0 153.539421 ± 0.000049 153.539414 ± 0.000052 153.539412 ± 0.000052 153.539410 ± 0.000050 153.539403 ± 0.000049 rA 0.10074 ± 0.00090 0.10167 ± 0.00084 0.10149 ± 0.00093 0.10198 ± 0.00090 0.10520 ± 0.00078 rb 0.01370 ± 0.00016 0.01390 ± 0.00014 0.01392 ± 0.00016 0.01401 ± 0.00015 0.01474 ± 0.00013 σ (mmag) 0.6412 0.6354 0.6288 0.6344 0.6832 2 χ red 1.0754 1.0560 1.0343 1.0531 1.2240 Fitting for the linear LD coefficient and perturbing the nonlinear LD coefficient

rA + rb 0.11546 ± 0.00104 0.11368 ± 0.00079 0.11488 ± 0.00115 0.11453 ± 0.00112 0.11472 ± 0.00117 k 0.13759 ± 0.00044 0.13542 ± 0.00056 0.13657 ± 0.00049 0.13613 ± 0.00060 0.13650 ± 0.00065 i (deg.) 88.63 ± 0.23 89.58 ± 0.48 88.91 ± 0.32 89.08 ± 0.42 88.95 ± 0.39 uA 0.467 ± 0.012 0.352 ± 0.028 0.162 ± 0.039 0.666 ± 0.054 0.443 ± 0.015 vA 0.30 perturbed 0.54 perturbed 0.26 perturbed 0.15 perturbed T0 153.539412 ± 0.000051 153.539418 ± 0.000052 153.539415 ± 0.000053 153.539416 ± 0.000050 153.539415 ± 0.000049 rA 0.10150 ± 0.00088 0.10012 ± 0.00068 0.10107 ± 0.00098 0.10081 ± 0.00094 0.10094 ± 0.00098 rb 0.01396 ± 0.00016 0.01356 ± 0.00013 0.01380 ± 0.00017 0.01372 ± 0.00018 0.01378 ± 0.00019 σ (mmag) 0.6267 0.6321 0.6272 0.6284 0.6272 2 χ red 1.0276 1.0441 1.0289 1.0326 1.0290

c 0000 RAS, MNRAS 000, 000–000 WASP-22, WASP-41, WASP-42 and WASP-55 5

Table A5. Parameters of the JKTEBOP best ﬁts of the Danish Telescope R-band light curve of WASP-41 from Neveu-VanMalle et al. (2015), using different approaches to LD. For each part of the table the upper quantities are ﬁtted parameters and the lower quantities are derived parameters. T0 is given as BJD(UTC) − 2456000.0. The light curve contains 102 datapoints.

Linear LD law Quadratic LD law Square-root LD law Logarithmic LD law Cubic LD law

All LD coefﬁcients ﬁxed

rA + rb 0.11324 ± 0.00052 0.11299 ± 0.00043 0.11278 ± 0.00042 0.11312 ± 0.00047 0.11587 ± 0.00057 k 0.13585 ± 0.00023 0.13641 ± 0.00019 0.13629 ± 0.00019 0.13575 ± 0.00022 0.14015 ± 0.00021 i (deg.) 89.61 ± 0.35 89.71 ± 0.32 89.97 ± 0.31 89.89 ± 0.33 88.36 ± 0.10 uA 0.61 fixed 0.45 fixed 0.28 fixed 0.68 fixed 0.40 fixed vA 0.21 fixed 0.48 fixed 0.12 fixed 0.10 fixed T0 402.648176 ± 0.000036 402.648171 ± 0.000036 402.648170 ± 0.000035 402.648176 ± 0.000035 402.648154 ± 0.000034 rA 0.09970 ± 0.00044 0.09942 ± 0.00037 0.09925 ± 0.00035 0.09960 ± 0.00040 0.10162 ± 0.00049 rb 0.013544 ± 0.000079 0.013562 ± 0.000066 0.013527 ± 0.000063 0.013521 ± 0.000071 0.014243 ± 0.000087 σ (mmag) 0.4947 0.4344 0.4380 0.4649 0.5117 2 χ red 7.2640 5.5664 5.6666 6.4048 7.7330 Fitting for the linear LD coefficient and perturbing the nonlinear LD coefficient

rA + rb 0.11335 ± 0.00068 0.11272 ± 0.00055 0.11280 ± 0.00054 0.11279 ± 0.00058 0.11283 ± 0.00059 k 0.13788 ± 0.00035 0.13654 ± 0.00046 0.13688 ± 0.00030 0.13711 ± 0.00041 0.13709 ± 0.00050 i (deg.) 89.10 ± 0.24 89.96 ± 0.39 89.57 ± 0.36 89.48 ± 0.40 89.47 ± 0.41 uA 0.524 ± 0.007 0.441 ± 0.027 0.255 ± 0.039 0.616 ± 0.052 0.508 ± 0.012 vA 0.21 perturbed 0.48 perturbed 0.12 perturbed 0.10 perturbed T0 402.648162 ± 0.000035 402.648170 ± 0.000036 402.648166 ± 0.000036 402.648165 ± 0.000037 402.648165 ± 0.000037 rA 0.09961 ± 0.00058 0.09918 ± 0.00046 0.09922 ± 0.00046 0.09919 ± 0.00049 0.09923 ± 0.00050 rb 0.013735 ± 0.000114 0.013541 ± 0.000093 0.013581 ± 0.000086 0.013600 ± 0.000095 0.013603 ± 0.000103 σ (mmag) 0.4369 0.4336 0.4334 0.4338 0.4338 2 χ red 5.6346 5.5413 5.5386 5.5500 5.5521

Table A6. Parameters of the JKTEBOP best ﬁts of the TRAPPIST I+z-band light curve of WASP-41 from Neveu-VanMalle et al. (2015), using different approaches to LD. For each part of the table the upper quantities are ﬁtted parameters and the lower quantities are derived parameters. T0 is given as HJD − 2455000.0. The light curve contains 2905 datapoints.

Linear LD law Quadratic LD law Square-root LD law Logarithmic LD law Cubic LD law

All LD coefﬁcients ﬁxed

rA + rb 0.1161 ± 0.0021 0.1157 ± 0.0019 0.1148 ± 0.0017 0.1139 ± 0.0014 0.1212 ± 0.0018 k 0.13537 ± 0.00075 0.13664 ± 0.00058 0.13522 ± 0.00063 0.13490 ± 0.00057 0.13991 ± 0.00054 i (deg.) 88.76 ± 0.53 88.78 ± 0.47 89.13 ± 0.68 89.64 ± 0.59 87.64 ± 0.22 uA 0.51 fixed 0.25 fixed 0.17 fixed 0.65 fixed 0.25 fixed vA 0.30 fixed 0.52 fixed 0.26 fixed 0.15 fixed T0 996.67838 ± 0.00013 996.67833 ± 0.00011 996.67836 ± 0.00013 996.67836 ± 0.00011 996.67835 ± 0.00011 rA 0.1022 ± 0.0018 0.1018 ± 0.0016 0.1012 ± 0.0015 0.1003 ± 0.0012 0.1063 ± 0.0015 rb 0.01384 ± 0.00031 0.01391 ± 0.00027 0.01368 ± 0.00025 0.01353 ± 0.00020 0.01487 ± 0.00026 σ (mmag) 3.4299 3.4117 3.4202 3.4176 3.4164 2 χ red 1.2979 1.2808 1.2890 1.2866 1.2849 Fitting for the linear LD coefficient and perturbing the nonlinear LD coefficient

rA + rb 0.1189 ± 0.0020 0.1162 ± 0.0023 0.1182 ± 0.0022 0.1173 ± 0.0021 0.1186 ± 0.0021 k 0.13901 ± 0.00085 0.13702 ± 0.00094 0.13818 ± 0.00081 0.13763 ± 0.00092 0.13828 ± 0.00092 i (deg.) 87.97 ± 0.31 88.62 ± 0.52 88.16 ± 0.37 88.36 ± 0.39 88.10 ± 0.35 uA 0.357 ± 0.024 0.235 ± 0.039 0.060 ± 0.043 0.553 ± 0.057 0.325 ± 0.028 vA 0.30 perturbed 0.52 perturbed 0.26 perturbed 0.15 perturbed T0 996.67836 ± 0.00011 996.67833 ± 0.00011 996.67834 ± 0.00012 996.67834 ± 0.00011 996.67835 ± 0.00011 rA 0.1044 ± 0.0017 0.1022 ± 0.0019 0.1038 ± 0.0018 0.1031 ± 0.0018 0.1042 ± 0.0018 rb 0.01451 ± 0.00030 0.01401 ± 0.00034 0.01435 ± 0.00033 0.01419 ± 0.00031 0.01440 ± 0.00031 σ (mmag) 3.4148 3.4116 3.4136 3.4128 3.4134 2 χ red 1.2838 1.2806 1.2825 1.2818 1.2824

c 0000 RAS, MNRAS 000, 000–000 6 Southworth et al.

Table A7. Parameters of the JKTEBOP best ﬁts of the FTS light curve of WASP-41 from Neveu-VanMalle et al. (2015), using different approaches to LD. For each part of the table the upper quantities are ﬁtted parameters and the lower quantities are derived parameters. T0 is given as HJD − 2455000.0. The light curve contains 190 datapoints.

Linear LD law Quadratic LD law Square-root LD law Logarithmic LD law Cubic LD law

All LD coefﬁcients ﬁxed

rA + rb 0.1186 ± 0.0053 0.1168 ± 0.0044 0.1181 ± 0.0049 0.1175 ± 0.0048 0.1198 ± 0.0040 k 0.1339 ± 0.0018 0.1342 ± 0.0012 0.1337 ± 0.0015 0.1334 ± 0.0015 0.1367 ± 0.0012 i (deg.) 88.01 ± 0.84 88.25 ± 0.82 88.11 ± 0.80 88.22 ± 0.86 87.63 ± 0.51 uA 0.51 fixed 0.25 fixed 0.17 fixed 0.65 fixed 0.25 fixed vA 0.30 fixed 0.52 fixed 0.26 fixed 0.15 fixed T0 663.96740 ± 0.00026 663.96740 ± 0.00025 663.96740 ± 0.00027 663.96740 ± 0.00022 663.96738 ± 0.00025 rA 0.1046 ± 0.0045 0.1029 ± 0.0038 0.1042 ± 0.0042 0.1037 ± 0.0041 0.1054 ± 0.0035 rb 0.01401 ± 0.00077 0.01381 ± 0.00061 0.01393 ± 0.00070 0.01384 ± 0.00068 0.01441 ± 0.00057 σ (mmag) 2.0708 2.0242 2.0506 2.0481 2.0065 2 χ red 1.1126 1.0526 1.0860 1.0820 1.0335 Fitting for the linear LD coefficient and perturbing the nonlinear LD coefficient

rA + rb 0.1204 ± 0.0046 0.1192 ± 0.0048 0.1201 ± 0.0046 0.1198 ± 0.0047 0.1199 ± 0.0045 k 0.1374 ± 0.0015 0.1363 ± 0.0016 0.1368 ± 0.0016 0.1366 ± 0.0016 0.1368 ± 0.0016 i (deg.) 87.50 ± 0.58 87.74 ± 0.71 87.58 ± 0.60 87.63 ± 0.66 87.61 ± 0.62 uA 0.284 ± 0.064 0.128 ± 0.077 -0.024 ± 0.075 0.460 ± 0.083 0.246 ± 0.063 vA 0.30 perturbed 0.52 perturbed 0.26 perturbed 0.15 perturbed T0 663.96737 ± 0.00024 663.96738 ± 0.00024 663.96738 ± 0.00024 663.96738 ± 0.00023 663.96738 ± 0.00024 rA 0.1059 ± 0.0039 0.1049 ± 0.0041 0.1057 ± 0.0040 0.1054 ± 0.0040 0.1054 ± 0.0038 rb 0.01455 ± 0.00066 0.01429 ± 0.00070 0.01446 ± 0.00066 0.01440 ± 0.00066 0.01442 ± 0.00063 σ (mmag) 2.0066 2.0076 2.0066 2.0069 2.0065 2 χ red 1.0338 1.0349 1.0336 1.0339 1.0335

Table A8. Parameters of the JKTEBOP best ﬁts of the WASP-42 R-band light curve from DFOSC, using different approaches to LD. For each part of the table the upper quantities are ﬁtted parameters and the lower quantities are derived parameters. T0 is given as BJD(TDB) − 2456000.0. The light curve contains 468 datapoints.

Linear LD law Quadratic LD law Square-root LD law Logarithmic LD law Cubic LD law

All LD coefﬁcients ﬁxed

rA + rb 0.0851 ± 0.0023 0.0843 ± 0.0023 0.0845 ± 0.0023 0.0849 ± 0.0023 0.0862 ± 0.0023 k 0.12927 ± 0.00057 0.12847 ± 0.00049 0.12882 ± 0.00051 0.12902 ± 0.00050 0.13052 ± 0.00047 i (deg.) 87.96 ± 0.16 88.05 ± 0.14 88.01 ± 0.15 87.97 ± 0.14 87.78 ± 0.15 uA 0.61 fixed 0.49 fixed 0.33 fixed 0.71 fixed 0.50 fixed vA 0.19 fixed 0.44 fixed 0.20 fixed 0.10 fixed T0 462.581363 ± 0.000087 462.581372 ± 0.000082 462.581366 ± 0.000084 462.581360 ± 0.000083 462.581336 ± 0.000079 rA 0.0754 ± 0.0020 0.0747 ± 0.0020 0.0748 ± 0.0020 0.0752 ± 0.0020 0.0763 ± 0.0020 rb 0.00974 ± 0.00028 0.00960 ± 0.00026 0.00964 ± 0.00027 0.00971 ± 0.00027 0.00996 ± 0.00028 σ (mmag) 0.7388 0.7349 0.7351 0.7344 0.7372 2 χ red 1.0867 1.0702 1.0704 1.0660 1.0701 Fitting for the linear LD coefficient and perturbing the nonlinear LD coefficient

rA + rb 0.0867 ± 0.0023 0.0853 ± 0.0023 0.0856 ± 0.0022 0.0855 ± 0.0024 0.0839 ± 0.0023 k 0.13061 ± 0.00064 0.12936 ± 0.00078 0.12970 ± 0.00065 0.12946 ± 0.00076 0.12985 ± 0.00076 i (deg.) 87.77 ± 0.16 87.92 ± 0.16 87.88 ± 0.15 87.90 ± 0.17 87.95 ± 0.15 uA 0.553 ± 0.018 0.457 ± 0.038 0.298 ± 0.039 0.694 ± 0.049 0.531 ± 0.024 vA 0.19 perturbed 0.44 perturbed 0.20 perturbed 0.10 perturbed T0 462.581342 ± 0.000083 462.581353 ± 0.000081 462.581349 ± 0.000087 462.581351 ± 0.000082 462.581349 ± 0.000085 rA 0.0766 ± 0.0021 0.0756 ± 0.0020 0.0758 ± 0.0020 0.0757 ± 0.0021 0.0743 ± 0.0020 rb 0.01001 ± 0.00029 0.00978 ± 0.00028 0.00983 ± 0.00027 0.00980 ± 0.00030 0.00965 ± 0.00028 σ (mmag) 0.7354 0.7346 0.7347 0.7346 0.7348 2 χ red 1.0663 1.0652 1.0648 1.0647 1.0648

c 0000 RAS, MNRAS 000, 000–000 WASP-22, WASP-41, WASP-42 and WASP-55 7

Table A9. Parameters of the JKTEBOP best ﬁts of the Euler r-band light curve of WASP-42 from Lendl et al. (2012), using different approaches to LD. For each part of the table the upper quantities are ﬁtted parameters and the lower quantities are derived parameters. T0 is given as HJD − 2455000.0. The light curve contains 402 datapoints.

Linear LD law Quadratic LD law Square-root LD law Logarithmic LD law Cubic LD law

All LD coefﬁcients ﬁxed

rA + rb 0.0798 ± 0.0040 0.0826 ± 0.0038 0.0820 ± 0.0040 0.0824 ± 0.0038 0.0919 ± 0.0035 k 0.1287 ± 0.0022 0.1310 ± 0.0015 0.1309 ± 0.0018 0.1311 ± 0.0018 0.1376 ± 0.0010 i (deg.) 88.60 ± 0.69 88.16 ± 0.41 88.23 ± 0.46 88.18 ± 0.42 87.09 ± 0.26 uA 0.70 fixed 0.50 fixed 0.38 fixed 0.75 fixed 0.40 fixed vA 0.22 fixed 0.41 fixed 0.20 fixed 0.10 fixed T0 645.58471 ± 0.00040 645.58464 ± 0.00041 645.58466 ± 0.00039 645.58465 ± 0.00039 645.58440 ± 0.00041 rA 0.0707 ± 0.0034 0.0730 ± 0.0033 0.0725 ± 0.0035 0.0728 ± 0.0033 0.0808 ± 0.0030 rb 0.00909 ± 0.00057 0.00957 ± 0.00053 0.00950 ± 0.00058 0.00955 ± 0.00053 0.01112 ± 0.00047 σ (mmag) 2.0546 2.0483 2.0474 2.0477 2.0832 2 χ red 0.9971 1.0041 1.0026 1.0040 1.0526 Fitting for the linear LD coefficient and perturbing the nonlinear LD coefficient

rA + rb 0.0799 ± 0.0041 0.0789 ± 0.0041 0.0796 ± 0.0042 0.0793 ± 0.0042 0.0796 ± 0.0041 k 0.1289 ± 0.0027 0.1267 ± 0.0030 0.1278 ± 0.0028 0.1273 ± 0.0029 0.1279 ± 0.0028 i (deg.) 88.57 ± 0.71 88.84 ± 0.88 88.67 ± 0.85 88.74 ± 0.92 88.66 ± 0.81 uA 0.694 ± 0.051 0.614 ± 0.066 0.467 ± 0.066 0.854 ± 0.077 0.681 ± 0.056 vA 0.22 perturbed 0.41 perturbed 0.20 perturbed 0.10 perturbed T0 645.58471 ± 0.00040 645.58467 ± 0.00038 645.58469 ± 0.00040 645.58468 ± 0.00039 645.58469 ± 0.00039 rA 0.0708 ± 0.0035 0.0700 ± 0.0035 0.0706 ± 0.0036 0.0704 ± 0.0037 0.0706 ± 0.0034 rb 0.00912 ± 0.00062 0.00887 ± 0.00062 0.00902 ± 0.00063 0.00896 ± 0.00064 0.00903 ± 0.00060 σ (mmag) 2.0537 2.0526 2.0531 2.0530 2.0531 2 χ red 0.9996 0.9988 0.9992 0.9990 0.9991 Fitting for both LD coefﬁcients

rA + rb 0.0799 ± 0.0043 0.0788 ± 0.0043 0.0790 ± 0.0050 0.0789 ± 0.0049 0.0791 ± 0.0049 k 0.1289 ± 0.0028 0.1264 ± 0.0048 0.1257 ± 0.0053 0.1259 ± 0.0053 0.1261 ± 0.0059 i (deg.) 88.57 ± 0.73 88.88 ± 0.94 88.89 ± 0.98 88.89 ± 0.99 88.86 ± 0.91 uA 0.694 ± 0.053 0.610 ± 0.153 0.091 ± 1.018 0.979 ± 0.589 0.670 ± 0.087 vA 0.24 ± 0.45 1.11 ± 1.88 0.35 ± 0.68 0.27 ± 0.58 T0 645.58471 ± 0.00040 645.58467 ± 0.00040 645.58467 ± 0.00041 645.58467 ± 0.00041 645.58467 ± 0.00042 rA 0.0708 ± 0.0037 0.0699 ± 0.0037 0.0702 ± 0.0043 0.0701 ± 0.0042 0.0702 ± 0.0043 rb 0.00912 ± 0.00064 0.00884 ± 0.00067 0.00882 ± 0.00073 0.00883 ± 0.00073 0.00885 ± 0.00071 σ (mmag) 2.0537 2.0526 2.0526 2.0526 2.0528 2 χ red 0.9996 1.0013 1.0015 1.0014 1.0015

c 0000 RAS, MNRAS 000, 000–000 8 Southworth et al.

Table A10. Parameters of the JKTEBOP best ﬁts of the WASP-42 I+z-band light curve of WASP-42 from Lendl et al. (2012), using different approaches to LD. For each part of the table the upper quantities are ﬁtted parameters and the lower quantities are derived parameters. T0 is given as HJD − 2455000.0. The light curve contains 1558 datapoints.

Linear LD law Quadratic LD law Square-root LD law Logarithmic LD law Cubic LD law

All LD coefﬁcients ﬁxed

rA + rb 0.0820 ± 0.0028 0.0825 ± 0.0029 0.0852 ± 0.0027 0.0824 ± 0.0027 0.0866 ± 0.0027 k 0.12736 ± 0.00104 0.12758 ± 0.00086 0.13056 ± 0.00071 0.12759 ± 0.00083 0.13143 ± 0.00060 i (deg.) 88.39 ± 0.30 88.33 ± 0.29 87.89 ± 0.22 88.34 ± 0.27 87.71 ± 0.20 uA 0.57 fixed 0.37 fixed 0.24 fixed 0.67 fixed 0.30 fixed vA 0.26 fixed 0.27 fixed 0.23 fixed 0.12 fixed T0 630.63953 ± 0.00017 630.63952 ± 0.00018 630.63948 ± 0.00017 630.63952 ± 0.00018 630.63946 ± 0.00017 rA 0.0727 ± 0.0024 0.0731 ± 0.0025 0.0753 ± 0.0024 0.0731 ± 0.0024 0.0765 ± 0.0024 rb 0.00927 ± 0.00036 0.00933 ± 0.00037 0.00983 ± 0.00033 0.00933 ± 0.00035 0.01006 ± 0.00033 σ (mmag) 2.5489 2.5447 2.5460 2.5437 2.5569 2 χ red 0.9961 0.9941 0.9964 0.9933 1.0056 Fitting for the linear LD coefficient and perturbing the nonlinear LD coefficient

rA + rb 0.0835 ± 0.0027 0.0826 ± 0.0030 0.0831 ± 0.0028 0.0828 ± 0.0029 0.0830 ± 0.0029 k 0.1293 ± 0.0011 0.1278 ± 0.0013 0.1289 ± 0.0011 0.1282 ± 0.0012 0.1285 ± 0.0011 i (deg.) 88.12 ± 0.25 88.29 ± 0.30 88.18 ± 0.26 88.25 ± 0.29 88.21 ± 0.27 uA 0.485 ± 0.032 0.360 ± 0.047 0.328 ± 0.050 0.649 ± 0.056 0.459 ± 0.037 vA 0.26 perturbed 0.27 perturbed 0.23 perturbed 0.12 perturbed T0 630.63951 ± 0.00018 630.63952 ± 0.00019 630.63951 ± 0.00017 630.63952 ± 0.00018 630.63952 ± 0.00019 rA 0.0739 ± 0.0023 0.0733 ± 0.0026 0.0736 ± 0.0025 0.0734 ± 0.0025 0.0735 ± 0.0025 rb 0.00956 ± 0.00035 0.00937 ± 0.00039 0.00949 ± 0.00036 0.00941 ± 0.00039 0.00945 ± 0.00037 σ (mmag) 2.5410 2.5445 2.5417 2.5431 2.5423 2 χ red 0.9920 0.9947 0.9926 0.9937 0.9931 Fitting for both LD coefﬁcients

rA + rb 0.0835 ± 0.0027 0.0829 ± 0.0026 0.0849 ± 0.0027 0.0849 ± 0.0026 0.0850 ± 0.0025 k 0.1293 ± 0.0010 0.1320 ± 0.0015 0.1324 ± 0.0015 0.1322 ± 0.0016 0.1322 ± 0.0015 i (deg.) 88.12 ± 0.25 87.96 ± 0.22 87.84 ± 0.22 87.84 ± 0.21 87.84 ± 0.22 uA 0.485 ± 0.032 0.818 ± 0.169 1.712 ± 0.577 0.047 ± 0.207 0.638 ± 0.090 vA -0.58 ± 0.26 -2.04 ± 0.94 -0.68 ± 0.33 -0.51 ± 0.25 T0 630.63951 ± 0.00018 630.63949 ± 0.00017 630.63950 ± 0.00018 630.63950 ± 0.00017 630.63950 ± 0.00017 rA 0.0739 ± 0.0024 0.0733 ± 0.0022 0.0750 ± 0.0023 0.0750 ± 0.0023 0.0750 ± 0.0022 rb 0.00956 ± 0.00035 0.00967 ± 0.00036 0.00992 ± 0.00037 0.00992 ± 0.00035 0.00992 ± 0.00036 σ (mmag) 2.5410 2.5379 2.5382 2.5381 2.5383 2 χ red 0.9920 0.9901 0.9903 0.9902 0.9904

c 0000 RAS, MNRAS 000, 000–000 WASP-22, WASP-41, WASP-42 and WASP-55 9

Table A11. Parameters of the JKTEBOP best ﬁts of the R-band light curve of WASP-55 from DFOSC, using different approaches to LD. For each part of the table the upper quantities are ﬁtted parameters and the lower quantities are derived parameters. T0 is given as BJD(TDB) − 2456000.0. The light curve contains 152 datapoints.

Linear LD law Quadratic LD law Square-root LD law Logarithmic LD law Cubic LD law

All LD coefﬁcients ﬁxed

+0.0030 +0.0029 +0.0028 +0.0028 +0.0027 rA + rb 0.1036−0.0007 0.1041−0.0007 0.1036−0.0006 0.1035−0.0006 0.1029−0.0007 +0.00095 +0.00078 +0.00078 +0.00081 +0.00076 k 0.12268−0.00065 0.12253−0.00062 0.12294−0.00060 0.12316−0.00063 0.12430−0.00063 +0.51 +0.47 +0.47 +0.43 +0.47 i (deg.) 89.93−0.87 89.98−0.85 89.97−0.83 89.97−0.86 89.95−0.79 uA 0.55 fixed 0.39 fixed 0.21 fixed 0.64 fixed 0.40 fixed vA 0.28 fixed 0.52 fixed 0.20 fixed 0.14 fixed +0.00019 +0.00018 +0.00019 +0.00020 +0.00021 T0 416.71551−0.00019 416.71550−0.00020 416.71550−0.00019 416.71550−0.00020 416.71550−0.00019 +0.0026 +0.0025 +0.0024 +0.0025 +0.0024 rA 0.0923−0.0006 0.0927−0.0006 0.0923−0.0006 0.0922−0.0006 0.0915−0.0006 +0.00042 +0.00037 +0.00037 +0.00037 +0.00035 rb 0.01132−0.00012 0.01136−0.00011 0.01134−0.00010 0.01135−0.00011 0.01137−0.00010 σ (mmag) 0.9177 0.8779 0.8761 0.8646 0.8291 2 χ red 1.2911 1.1739 1.1685 1.1356 1.0365 Fitting for the linear LD coefficient and perturbing the nonlinear LD coefficient

+0.0024 +0.0025 +0.0025 +0.0027 +0.0027 rA + rb 0.1026−0.0010 0.1029−0.0008 0.1023−0.0008 0.1024−0.0007 0.1024−0.0009 +0.00079 +0.00092 +0.00091 +0.00097 +0.00093 k 0.12590−0.00081 0.12514−0.00081 0.12530−0.00080 0.12528−0.00075 0.12534−0.00090 +0.63 +0.56 +0.50 +0.48 +0.51 i (deg.) 89.42−0.66 89.61−0.76 89.96−0.78 89.93−0.83 89.81−0.84 +0.030 +0.039 +0.050 +0.059 +0.034 uA 0.364−0.031 0.235−0.044 0.065−0.050 0.510−0.054 0.335−0.034 vA 0.28 perturbed 0.52 perturbed 0.20 perturbed 0.14 perturbed +0.00018 +0.00020 +0.00018 +0.00019 +0.00017 T0 416.71549−0.00019 416.71549−0.00019 416.71549−0.00017 416.71549−0.00017 416.71549−0.00017 +0.0021 +0.0022 +0.0022 +0.0023 +0.0024 rA 0.0911−0.0009 0.0914−0.0007 0.0909−0.0007 0.0910−0.0007 0.0910−0.0008 +0.00032 +0.00034 +0.00036 +0.00036 +0.00038 rb 0.01147−0.00015 0.01144−0.00012 0.01140−0.00011 0.01140−0.00011 0.01140−0.00012 σ (mmag) 0.8191 0.8151 0.8165 0.8159 0.8165 2 χ red 1.0089 0.9998 1.0024 1.0011 1.0025

Table A12. Parameters of the JKTEBOP best ﬁts of the I-band light curve of WASP-55 from DFOSC, using different approaches to LD. For each part of the table the upper quantities are ﬁtted parameters and the lower quantities are derived parameters. T0 is given as BJD(TDB) − 2456000.0. The light curve contains 388 datapoints.

Linear LD law Quadratic LD law Square-root LD law Logarithmic LD law Cubic LD law

All LD coefﬁcients ﬁxed

+0.0024 +0.0022 +0.0022 +0.0026 +0.0022 rA + rb 0.1031−0.0006 0.1031−0.0005 0.1029−0.0006 0.1037−0.0006 0.1036−0.0015 +0.00076 +0.00056 +0.00060 +0.00074 +0.00052 k 0.12229−0.00052 0.12287−0.00051 0.12289−0.00050 0.12154−0.00057 0.12478−0.00056 +0.42 +0.37 +0.43 +0.45 +0.85 i (deg.) 89.95−0.81 89.93−0.80 89.95−0.75 89.94−0.79 89.08−0.50 uA 0.49 fixed 0.30 fixed 0.10 fixed 0.65 fixed 0.30 fixed vA 0.25 fixed 0.56 fixed 0.20 fixed 0.12 fixed +0.00018 +0.00016 +0.00016 +0.00017 +0.00015 T0 135.68205−0.00016 135.68204−0.00017 135.68205−0.00016 135.68205−0.00019 135.68204−0.00016 +0.0021 +0.0019 +0.0019 +0.0022 +0.0019 rA 0.0918−0.0005 0.0918−0.0005 0.0917−0.0005 0.0925−0.0005 0.0921−0.0014 +0.00031 +0.00028 +0.00027 +0.00033 +0.00028 rb 0.01123−0.00010 0.01128−0.00010 0.01126−0.00010 0.01124−0.00010 0.01150−0.00020 σ (mmag) 1.0562 1.0359 1.0337 1.0649 1.0341 2 χ red 1.0409 1.0019 0.9965 1.0591 0.9998 Fitting for the linear LD coefficient and perturbing the nonlinear LD coefficient

+0.0023 +0.0024 +0.0023 +0.0022 +0.0022 rA + rb 0.1031−0.0013 0.1028−0.0008 0.1027−0.0008 0.1028−0.0008 0.1028−0.0008 +0.00075 +0.00084 +0.00077 +0.00075 +0.00073 k 0.12431−0.00070 0.12335−0.00070 0.12357−0.00068 0.12360−0.00076 0.12375−0.00072 +0.79 +0.46 +0.58 +0.54 +0.50 i (deg.) 89.27−0.55 89.91−0.78 89.75−0.68 89.67−0.70 89.58−0.74 +0.022 +0.035 +0.049 +0.053 +0.029 uA 0.378−0.025 0.268−0.037 0.058−0.045 0.525−0.054 0.354−0.026 vA 0.25 perturbed 0.56 perturbed 0.20 perturbed 0.12 perturbed +0.00016 +0.00014 +0.00016 +0.00016 +0.00016 T0 135.68204−0.00016 135.68204−0.00015 135.68204−0.00016 135.68204−0.00017 135.68204−0.00014 +0.0020 +0.0021 +0.0020 +0.0019 +0.0019 rA 0.0917−0.0011 0.0915−0.0007 0.0914−0.0007 0.0915−0.0007 0.0915−0.0007 +0.00031 +0.00033 +0.00030 +0.00030 +0.00030 rb 0.01140−0.00017 0.01129−0.00010 0.01129−0.00012 0.01131−0.00011 0.01132−0.00011 σ (mmag) 1.0258 1.0335 1.0294 1.0299 1.0287 2 χ red 0.9816 0.9977 0.9887 0.9899 0.9874

c 0000 RAS, MNRAS 000, 000–000 10 Southworth et al.

Table A13. Parameters of the JKTEBOP best ﬁts of the Ejuler r-band light curve of WASP-55 from Hellier et al. (2012), using different approaches to LD. For each part of the table the upper quantities are ﬁtted parameters and the lower quantities are derived parameters. T0 is given as HJD − 2455000.0. The light curve contains 270 datapoints.

Linear LD law Quadratic LD law Square-root LD law Logarithmic LD law Cubic LD law

All LD coefﬁcients ﬁxed

+0.0031 +0.0026 +0.0028 +0.0024 +0.0024 rA + rb 0.1077−0.0029 0.1036−0.0008 0.1060−0.0023 0.1039−0.0008 0.1092−0.0024 +0.00123 +0.00077 +0.00106 +0.00076 +0.00082 k 0.12238−0.00120 0.12243−0.00065 0.12327−0.00086 0.12267−0.00064 0.12628−0.00088 +0.82 +0.47 +0.91 +0.56 +0.36 i (deg.) 88.59−0.53 89.95−0.78 88.82−0.53 89.48−0.72 88.01−0.31 uA 0.62 fixed 0.36 fixed 0.21 fixed 0.69 fixed 0.35 fixed vA 0.31 fixed 0.53 fixed 0.26 fixed 0.15 fixed +0.00023 +0.00021 +0.00022 +0.00019 +0.00022 T0 715.61170−0.00023 715.61174−0.00021 715.61176−0.00022 715.61176−0.00020 715.61195−0.00022 +0.0027 +0.0022 +0.0024 +0.0022 +0.0021 rA 0.0960−0.0025 0.0923−0.0007 0.0943−0.0020 0.0925−0.0007 0.0969−0.0021 +0.00044 +0.00034 +0.00040 +0.00033 +0.00031 rb 0.01174−0.00042 0.01130−0.00013 0.01163−0.00030 0.01135−0.00014 0.01224−0.00033 σ (mmag) 2.4654 2.4031 2.4153 2.4090 2.3824 2 χ red 6.0533 5.6747 5.7527 5.7102 5.5657 Fitting for the linear LD coefficient and perturbing the nonlinear LD coefficient

+0.0021 +0.0026 +0.0022 +0.0024 +0.0024 rA + rb 0.1115−0.0022 0.1092−0.0026 0.1105−0.0024 0.1101−0.0024 0.1111−0.0022 +0.00088 +0.00098 +0.00091 +0.00089 +0.00092 k 0.12836−0.00088 0.12691−0.00100 0.12761−0.00090 0.12731−0.00095 0.12777−0.00087 +0.27 +0.40 +0.33 +0.34 +0.31 i (deg.) 87.57−0.26 87.95−0.35 87.73−0.27 87.81−0.31 87.67−0.31 +0.028 +0.046 +0.048 +0.053 +0.035 uA 0.298−0.029 0.145−0.048 −0.010−0.050 0.481−0.054 0.261−0.034 vA 0.31 perturbed 0.53 perturbed 0.26 perturbed 0.15 perturbed +0.00020 +0.00020 +0.00020 +0.00021 +0.00020 T0 715.61202−0.00020 715.61199−0.00019 715.61200−0.00019 715.61200−0.00020 715.61199−0.00019 +0.0018 +0.0023 +0.0019 +0.0021 +0.0021 rA 0.0988−0.0019 0.0969−0.0022 0.0980−0.0020 0.0976−0.0021 0.0985−0.0019 +0.00030 +0.00034 +0.00031 +0.00033 +0.00034 rb 0.01268−0.00028 0.01230−0.00036 0.01251−0.00033 0.01243−0.00033 0.01259−0.00031 σ (mmag) 2.3798 2.3745 2.3775 2.3762 2.3771 2 χ red 5.5464 5.5161 5.5335 5.5262 5.5314

c 0000 RAS, MNRAS 000, 000–000