A&A 615, A135 (2018) Astronomy https://doi.org/10.1051/0004-6361/201731435 & © ESO 2018 Astrophysics

WASP 0639-32: a new F-type subgiant/K-type main-sequence detached eclipsing binary from the WASP project J. A. Kirkby-Kent1, P. F. L. Maxted1, A. M. Serenelli2,3, D. R. Anderson1, C. Hellier1, and R. G. West4

1 Astrophysics Group, Keele University, Keele, Staffordshire ST5 5BG, UK e-mail: [email protected] 2 Institute of Space Sciences (ICE, CSIC) Campus UAB, Carrer de Can Magrans s/n, 08193 Barcelona, Spain 3 Institut d’Estudis Espacials de Catalunya (IEEC), C/ Gran Capità, 2-4, 08034 Barcelona, Spain 4 Department of Physics, University of Warwick, Coventry CV4 7AL, UK Received 23 June 2017 / Accepted 17 April 2018

ABSTRACT

Aims. Our aim is to measure the masses and radii of the stars in a newly-discovered detached eclipsing binary system to a high preci- sion ( 1%), enabling the system to be used for the calibration of free parameters in stellar evolutionary models. Methods.≈ Photometry from the Wide Angle Search for Planets (WASP) project was used to identify 1SWASP J063930.33-322404.8 (TYC 7091-888-1, WASP0369-32 hereafter) as a detached eclipsing binary system with total eclipses and an orbital period of P = 11.66 days. Lightcurve parameters for WASP0639-32 are obtained using the EBOP lightcurve model, with standard errors eval- uated using a prayer-bead algorithm. Radial velocities were measured from 11 high-resolution spectra using a broadening function approach, and an orbit was fitted using SBOP. Observed spectra were disentangled and an equivalent width fitting method was used to obtain effective temperatures and metallicities for both stars. A Bayesian framework is used to explore a grid of stellar evolution models, where both helium abundance and mixing length are free to vary, and use observed parameters (mass, density, temperature, and metallicity) for each star to obtain the age and constrain the helium abundance of the system. Results. The masses and radii are found to be M1 = 1.1544 0.0043 M , R1 = 1.833 0.023 R , and M2 = 0.7833 0.0028 M , ± ± ± R2 = 0.7286 0.0081 R for the primary and secondary, respectively. The effective temperatures were found to be T1 = 6330 50 K ± +0.8 ± and T2 = 5400 80 K for the primary and secondary star, respectively. The system has an age of 4.2 0.1 Gyr, and a helium abundance in the range 0.251–0.271.± − Conclusions. WASP0639-32 is a rare example of a well-characterised detached eclipsing binary system containing a star near the main-sequence turn-off point. This makes it possible to measure a precise age for the stars in this binary system and to estimate their helium abundance. Further work is needed to explore how this helium abundance estimate depends on other free parameters in the stellar models. Key words. binaries: eclipsing – stars: solar-type – stars: fundamental parameters – stars: evolution

1. Introduction affect the determination of these parameters, in particular the overshooting parameter. They note, following on from an earlier Detached eclipsing binary stars with well-determined parame- paper (Valle et al. 2016), that for binaries where both stars are on ters are one of the best methods for testing stellar evolutionary the main-sequence, the calibration of the overshooting param- models (Lastennet & Valls-Gabaud 2002; Torres et al. 2010). eter is hampered by uncertainties of the order 0.5% in the radii These models play an important role in areas, such as exoplanet and 1% in the masses. This indicates that in order to calibrate research, where they are used to determine the mass and age of the overshooting, binary systems with stars at two different planet-host stars, and in galaxy evolution modelling, where they evolutionary stages must be used and their parameters must be are used to predict the properties of the stars that are observed known to very high precision, (at least 1% in the masses, Valle by surveys of the Milky Way and other galaxies (Schaerer 2013). et al. 2017). The number of well-studied binary systems with Stellar evolutionary models can use different prescriptions to both the required precision, and the required evolutionary state describe complex phenomena such as convection and diffusion. are very few. Excluding AI Phe and TZ For (see below) there The free parameters used in these prescriptions are, in general, is only one other system in the list by Torres et al.(2010) that poorly constrained by the underlying physics, so they are meets these requirements, and can be classed as a solar-type star, either calibrated from observations, or by detailed simulations. that is V432 Aur. This system also has a relatively short 3-day Creating models for stars that are different from the stars used orbital period, meaning there is a strong possibility that tidal in the calibrations, whilst using the same calibrated parameters interactions between the stars would invalidate the assumption values, can introduce systematic errors into the models. As such, that the two stars have evolved independently. Some examples these free parameters are still large sources of uncertainty in which meet the requirements include LL Aqr (Graczyk et al. using stellar models to infer the ages and other properties of 2016), TZ For (Valle et al. 2017), and two binaries in NGC 6791 stars (Lebreton et al. 2014). Recently, research has been pushing (Brogaard et al. 2012). Each have provided a constraint on the to understand these parameters in more detail, with Valle et al. helium abundance of the particular binary system. Kirkby-Kent (2017) looking at how uncertainties on observational data et al.(2016) looked at the binary system AI Phe, and after

Article published by EDP Sciences A135, page 1 of 15 A&A 615, A135 (2018) improving the mass and radius estimates of both stars, looked Table 1. Number of observations removed during initial processing. at how independently varying the mixing length and helium abundance affected the age of the system. Again the precise Reason Points removed observational constraints allowed the helium abundance Yi to be constrained to the range 0.25–0.28. σxs = 0 4870 If meaningful statistics are to be done on the helium abun- ferr > 5*median 2408 dance in low-mass stars, then more systems need to be studied Small field 10 to the same level of precision. This paper details the photomet- Offset 3766 ric and spectroscopic analysis of a newly-discovered detached Remaining 28 566 eclipsing binary system containing an evolved F-type primary and a main-sequence K-type star, which was first identified Notes. Last row states the number of observations remaining. using data from the Wide Angle Search for Planets (WASP; Pollacco et al. 2006). Section2 describes the data that used in the photometric analysis (Sect.3) and the spectra used in The final step looks for data that is significantly offset from the the orbital analysis (Sect.4) and the spectroscopic analysis other data. This technique uses a model generated from 1000 (Sect.5). Section6 combines the lightcurve and spectroscopic bins across the phase-folded data, with the median magnitude in orbit parameters to give masses and radii of the system and each bin used as a reference. The magnitude from each observa- in Sect.7 we investigate how the helium abundance can be tion within a block of data (the observation from one camera on constrained by the precise binary parameters system. Finally, one night) was compared to the expected value within in a phase discussion and conclusion sections follow in Sects.8 and9. bin. If observations differed by more than ten times the uncer- tainties for each phase bin, it was removed, and if more than 80% of data from a block was offset, the entire block was removed. 2. Observations Overall, from the initial 39 621 observations stored in the 2.1. WASP photometry WASP archive, 28 566 remained for use during the analysis. Table1 provides a summary of the number of points removed The WASP project (Pollacco et al. 2006) uses two instruments, during this initial processing stage. one located at the Observatorio del Roque de los Muchachos, La Palma, and the other at Sutherland Observatory, South 2.2. UVES spectra Africa. Each instrument consists of eight wide-field cameras each with a 2048 2048 pixel CCD. In total, 39 621 photomet- The eleven spectra used in this work, were obtained using the ric measurements× were obtained for WASP0639-32 (1SWASP Ultraviolet and Visual Échelle Spectrograph (UVES; Dekker J063930.33-322404.8, TYC 7091-888-1) between May 2006 and et al. 2000) at the Very Large Telescope (VLT), over a period March 2012 by the WASP-South instrument using 200 mm, f/1.8 between 9th October 2014 and 20th January 2015. A wavelength lenses and broadband 400–700 nm filters (Pollacco et al. 2006). range of approximately 500–700 nm, with a small gap at 600 nm, A specialised pipeline (Pollacco et al. 2006) is used to reduce and a signal-to-noise ratio of over 100 was obtained for each the images and the data are subject to a detrending algorithm spectrum. The slit was set to a width of 0.7 arcseconds, resulting described by Collier Cameron et al.(2006). in spectra with a resolving power R = 56990. Each spectrum was The WASP data can suffer from significant amounts of scat- reduced using the standard UVES reduction pipeline (Ballester ter caused by clouds, scattered moonlight, etc. To remove the et al. 2000). affected observations, the photometric data is process by an algo- rithm, that was first described in Kirkby-Kent et al.(2016). We briefly discuss the process here. 3. Photometric Analysis Firstly, each measurement that has the weighting factor, σxs, 3.1. Ephemeris set to zero, is removed. This factor is defined as part of the WASP pipeline (σt(i) in Collier Cameron et al. 2006) and characterises To find the period, P, and time of primary minimum, the WASP the amount of scatter present from external sources. When set to photometry, with very minimal cleaning applied (i.e. only the zero, it indicates the pipeline as has marked the value as miss- points with σxs = 0 where removed), was fitted using JKTEBOP ing or bad. Data where the uncertainty in a flux measurement (Southworth et al. 2004). The surface brightness ratio, sum of was more then five times the median value were also removed. radii, ratio of radii, orbital inclination, and e cos ω and e sin ω One WASP field contained only ten observations, which were parameters were included in the model fitting. The results for the removed as they caused problems when the analysis compared period and time of primary minimum are shown in Eq. (2). data from different nights and seasons. The WASP pipeline provides the flux, f , of WASP0639- HJD Pri. Min. = 2 455 241.33931(26) + 11.658317(5) E. (2) 32 measured using an aperture of 3.5 pixels, and also the uncertainty due to known noise sources (photon-counting The period and time of primary minimum have been kept fixed in all subsequent analysis. Figure1 shows the photometric mea- noise, background subtraction, etc.), ferr. Trends in the data are removed using a detrending algorithm (Collier Cameron et al. surements phase-folded using the ephemeris in Eq. (2), after the 2006), which is described in more detail in Sect. 3.3. The flux processing described in Sect. 2.1. measurements are converted into magnitudes, using the overall median flux as the zero point, and the uncertainties, merr, are 3.2. Lightcurve Modelling calculated using To model the lightcurve we used the same method as described 2 in Kirkby-Kent et al.(2016). It uses the subroutine light ferr 2 from the EBOP lightcurve analysis code (Nelson & Davis 1972; merr = f + σxs . (1) s f Popper & Etzel 1981), with modifications allowing it to be ! A135, page 2 of 15 J.J. A. A. Kirkby-Kent et al.: WASP0639-32: WASP0639-32: A A new new detached detached eclipsing eclipsing binary binary system system

Uncertainty contribution to each parameter from uncertainty in Table 2. Uncertainty contribution to each parameter from uncertainty −0.05 ffi inthe the limb limb darkening darkening coe coefficients.cients. 0.00 0.05 Parameter Original Detrend 0.10 Parameter Original Detrend J 0.0042 0.0042 0.15 J 0.0042 0.0042 Magnitude r 0.00006 0.00003 0.20 rsum 0.00006 0.00003 ksum 0.003 0.003 0.25 k 0.003 0.003 i ( ) 0.005 0.005 −0.2−0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 i (◦) 0.005 0.005 e cos◦ ω 0.000003 0.000005 Phase e cos ω 0.000003 0.000005 e sin ω 0.002 0.002 e sin ω 0.002 0.002 Fig.Fig. 1. 1. Phase-foldedPhase-folded lightcurve lightcurve for for WASP0639-32, WASP0639-32, showing showing data data used used l3 0.005 0.005 forfor lightcurve lightcurve analysis. analysis. l3 0.005 0.005 r1 0.00013 0.00013 r2 0.00013 0.00016 called3.2. Lightcurve directly from Modelling the Python programming language. The e 0.0020 0.0019 parameters used in the EBOP model are optimised using the ω (◦) 0 .7 0.8 least-squaresTo model the lightcurve Levenberg–Marquardt we used the same Python method module, as described MPFIT in light (Kirkby-KentMarkwardt 2009 et al.). (2016). It uses the subroutine from the ebop Thelightcurve model has analysis seven code parameters (Nelson that& Davis were 1972; fitted: Popper surface & Etzel 1981), with modifications allowing it to be called directly positionsWeare (2010). in a Byparticular using a sub-groupffine-invariant will transformations, be updated using the the al- brightness ratio at the centre of the stellar discs, J; sum of the positionsgorithm can of workwalkers with in skewed other sub-groups. distributions. The The probability algorithm that ex- radii,from ther Python= r + programmingr ; ratio of the language. radii, k The= parametersr /r ; inclination, used in the ebopsummodel1 are optimised2 using the least-squares2 1 Levenberg- aplores model the produced parameter by space a set using of parameters, a group of walkers,corresponds which to can the i; e cos ω, e sin ω and third-light, l3. In addition to these fitted best-fitbe split model, allowing is evaluated the process using to bethe run log-likelihood in parallel. function Walker po- parameters,Marquardt Python the fractional module, radii, MPFITr and (Markwardtr , are automatically 2009). cal- The model has seven parameters1 that2 were fitted: surface sitions in a particular sub-group will be updated using the po- culated from rsum and k, while the eccentricity, e, and longitude N 2 sitions of walkers1 in othermn y sub-groups.n(Θ) The2π probability that a brightness ratioω at the centre of thee stellarω discs,e J; sumω of the ln ( ; Θ) = − ln , (3) of periastron, , are calculated from cos and sin . modely produced by a set of parameters, corresponds2 to the best- radii, rsum = r1 + r2; ratio of the radii, k = r2/r1; inclination, L −2 merr,n − merr,n The mass ratio, q = M2/M1, was fixed at 0.67. This value n=1  ! ! i; e cos ω, e sin ω and third-light, l . In addition to these fitted fit model, is evaluatedX  using the log-likelihood function was determined by initially setting3 q = 0.5, fitting a model   parameters, the fractional radii, r1 and r2, are automatically cal- where y is a vector of length N containing the magnitudes gener- and then using the estimates of r1, r2, and the spectroscopic N 2 culated from rsum and k, while the eccentricity, e, and longitude1 ated for a model,1 Θ is am vectory containing(Θ) the2 varyingπ parameters orbit parameters (see Sect.4) as inputs into JKTABSDIM . For Θ = n − n of periastron, ω, are calculated from e cos ω and e sin ω. ln (y; ) ω ω ln 2 (3) WASP0639-32, the mass ratio contributes very little to the over- (J,Lrsum, k, i,−e2cos , e sinmerr,,n and l3−), m ism the observed mag- q = M /M n=1  ! err,n ! all shapeThe mass of the ratio, lightcurves2 meaning1, was variations fixed at 0.67. of 0.01 This will value not nitude and merr isX the standard error on the magnitude. Priors = .   alterwas determined the final best-fit by initially parameters. setting Theq gravity0 5, fitting darkening a model expo- and were applied, but these are only used to prevent the parame- then using the estimates of r , r and the spectroscopic orbit pa- where y is a vector of length N containing the magnitudes gener- nents were fixed at 0.26 and 0.461 2 for the primary and secondary terated exploring for a model, areasΘ is that a vector are unphysical, containing the e.g., varyingrsum or parametersJ being rameters (see Sect. 4) as inputs into jktabsdim1. For WASP0639- less than zero. The MCMC process ran using 150 walkers for component, respectively (Claret & Bloemen 2011). These param- (J, rsum, k, i, e cos ω, e sin ω and l3), m is the observed mag- eters32, the also mass have ratio very contributes little effect very on the little lightcurve to the overall as the starsshape are of 2500 steps, of which the first 200 were discarded to allow for the lightcurves meaning variations of 0.01 will not alter the final nitude and merr is the standard error on the magnitude. Priors nearly spherical in shape. anwere adequate applied, burn-in but these stage. are For only each used of to the prevent walkers, the a parame- starting best-fitAttempts parameters. to include The thegravity limb darkening darkening exponents coefficients were as fixed free point for each parameter was chosen by choosing a number at at 0.26 and 0.46 for the primary and secondary component, re- ter exploring areas that are unphysical, e.g. rsum or J being less parameters in the fitting proved unsuccessful as these coeffi- randomthan zero. from The a MCMC normal process distribution ran using (with 150 a mean walkers of forzero 2 500and cientsspectively are not(Claret well-constrained & Bloemen 2011). by the These data. parameters Instead, the also coef- have variance of 0.01) and adding it to the best-fit parameter. This very little effect on the lightcurve as the stars are nearly spherical steps, of which the first 200 were discarded to allow for an ad- ficients were fixed at values taken from interpolating between methodequate burn-in creates stage. a “ball” For of each walkers of the close walkers, to the a starting best-fit pointsolu- valuesin shape. in the tables by Claret & Bloemen(2011). The Kepler tion; however, during the burn-in stage, the walkers spread out ffi for each parameter was chosen by choosing a number at random passbandAttempts was to used include to approximate the limb darkening the response coe ofcients the WASP as free from this ball. The chains for each parameter were checked to parameters in the fitting proved unsuccessful as these coeffi- from a normal distribution (with a mean of zero and variance of broadband filter. The adopted primary limb-darkening coeffi- ensure0.01) and the adding burn-in it to stage the best-fit was completed parameter. within Thismethod these first creates 200 cients are not well-constrained by the data. Instead, the coeffi- steps and adequate mixing had occurred. We also check for bias cient was up = 0.50 0.05 and us = 0.63 0.03 was adopted a “ball” of walkers close to the best-fit solution, however dur- forcients the were secondary. fixed at To values± account taken for from the uncertaintiesinterpolating± between in the limb- val- in the starting positions by carrying out a run where the walk- ues in the tables by Claret & Bloemen (2011). The Kepler pass- ing the burn-in stage, the walkers spread out from this ball. The darkening coefficients, models were calculated with the fixed ers’chains starting for each positions parameter can werebe distributed checked to by ensure up to three the burn-in times limbband darkeningwas used to parameters approximate varied the response by their of uncertainties. the WASP broad- The the uncertainty on the parameters, as determined by the covari- band filter. The adopted primary limb-darkening coefficient was stage was completed within these first 200 steps and adequate average scatter in the parameters from these models has been ancemixing matrix had occurred. obtained We from also the check best for fit. bias The in burn-in the starting stage posi- for up = 0.50 0.05 and us = 0.63 0.03 was adopted for the sec- this test was longer, but still produced the same distribution. added in quadrature± to the uncertainties± from the best-fit model. tions by carrying out a run where the walkers’ starting positions Tableondary.2 details To account the uncertainty for the uncertainties in each parameter in the limb-darkening due to the Various checks were performed to ensure suitable mixing and ffi can be distributed by up to three times the uncertainty on the pa- uncertaintycoe cients, in models the limb-darkening were calculated coefficients. with the fixed limb darken- convergence. The walkers’ positions were plotted against step ing parameters varied by their uncertainties. The average scatter rameters, as determined by the covariance matrix obtained from As in Kirkby-Kent et al.(2016), the parameter-space is numberthe best to fit. visually The burn-in check stage the mixing for this and test to wasdetermine longer, the but burn- still exploredin the parameters using Markov from chain these Monte models Carlo has been (MCMC), added in in the quadra- form in length. Convergence is checked through a running-mean test. ture to the uncertainties from the best-fit model. Table 2 details produced the same distribution. Various checks were performed of the Python module, emcee (Foreman-Mackey et al. 2013). Weto ensure also check suitable the mixing acceptance and convergence.fraction (mean The = 0.43) walkers’ andauto- posi- Itthe was uncertainty used to ensure in each the parameter lightcurve due solution to the uncertainty was not a in local the correlation length (max = 92) for each run. The auto-correlation limb-darkening coefficients. tions were plotted against step number to visually check the mix- minimum in the parameter space. emcee uses a affine-invariant lengthing and is to a determine measure of the the burn-in number length. of evaluations Convergence needed is checked to have ensembleAs in Kirkby-Kentsampling (stretch-move) et al. (2016), algorithm the parameter-space of Goodman is ex- & independent samples (Foreman-Mackey et al. 2013). Parame- plored using Markov Chain Monte Carlo (MCMC), in the form through a running-mean test. We also check the acceptance frac- Weare(2010). By using affine-invariant transformations, the ter uncertainties= . were calculated using a prayer-bead= method, of the Python module, emcee, (Foreman-Mackey et al. 2013). tion (mean 0 43) and auto-correlation length (max 92) for algorithm can work with skewed distributions. The algorithm againeach run. as Thedescribed auto-correlation in Kirkby-Kent length etis a al. measure(2016). of The the prayer- number exploresIt was used the parameter to ensure thespace lightcurve using a group solution of was walkers, not a which local bead algorithm used 500 shifts, spread evenly across the data, emcee ffi of evaluations needed to have independent samples (Foreman- canminimum be split in allowing the parameter the process space. to be runuses in a parallel. a ne-invariant Walker with starting positions selected randomly from the MCMC anal- ensemble sampling (stretch-move) algorithm of Goodman & Mackey et al. 2013). Parameter uncertainties were calculated us- ysis.ing a The prayer-bead prayer-bead method, algorithm again allows as described robust estimates in Kirkby-Kent of the 1 http://www.astro.keele.ac.uk/jkt/codes/jktabsdim. uncertainties associated with lightcurve parameters (as the stan- 1 http://www.astro.keele.ac.uk/jkt/codes/jktabsdim. et al. (2016). The prayer-bead algorithm used 500 shifts, spread html html dardevenly deviation across the of data, the best-fitwith starting values positions from the selected 500 shifts) randomly and

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TableTable 3. 3.Best-fitBest-fit parameters parameters for for WASP0639-32, WASP0639-32, with with and and without without the the detrendingdetrending applied. applied.

Parameter Original Detrended Difference Parameter Original Detrended Difference JJ 00.4527(72).4527(72) 0 0.4513(71).4513(71) 0 0.0014.0014 rrsum 00.09465(42).09465(42) 0 0.09499(42).09499(42) 00.00034.00034 k sum 0.3949(53) 0.3975(53) −− 0.0026 k 0.3949(53) 0.3975(53) − 0.0026 i (◦) 89.9925(68) 89.9943(67) −0.0018 i (◦) 89.9925(68) 89.9943(67) − 0.0018 eecoscosωω 00.00027(12).00027(12) 00.00026(12).00026(12) 0−0.00001.00001 e sin ω −− 0.0077(44) −− 0.0070(44) −− 0.0007 e sin ω − 0.0077(44) − 0.0070(44) − 0.0007 l3 − 0.007(20)− 0.012(20) − 0.005 l3 0.007(20) 0.012(20) − 0.005 . . −. rr11 00.06785(86)06785(86) 0 0.06797(86)06797(86) 00.0001200012 r 0.02679(29) 0.02702(30) −−0.00023 r22 0.02679(29) 0.02702(30) −0.00023 ee 00.0077(54).0077(54) 0 0.0070(53).0070(53)− 0 0.0007.0007 ωω((◦◦)) 268268.0(4.0(4.8).8) 267 267.9(4.9(4.9).9) 0 0.1.1

Notes.Notes. StandardStandard errors errors on on the the final final two two digits digits of each of each parameter parameter value are given in the parentheses and include the contribution from the value are given in the parenthesesJ. A. Kirkby-Kent and include et the al.: WASP0639-32: contribution A new detached eclipsing binary system fromuncertainties the uncertainties in the limb in darkening the limb co-efficients.darkening coefficients. Table 5. Fitted spectroscopic orbit parameters for WASP0639-32. cients include a fixed binary lightcurve model, L, when they are calculated to allow the variability of an eclipsing to be taken into Parameter Best-fit Parameter Best-fit Fig. 2. Density distribution of the fractional radii, r1 and r2, for Density distribution of the fractional radii, r and r , for consideration. It can be described using value value Fig.WASP0639-32. 2. Grey cross marks the values calculated from1 the best-fit2 WASP0639-32. Grey cross marks the values calculated from the best- values from the fit to the “original” data. 1 fit values from the fit to the ‘original’ data. M K1 (km s− ) 47.32(8) ω (◦) 269.96(12) (k) (k) 1 1 mi = mi + Li c0 ai (5) K2 (km s− ) 69.74(11) B0 (km s− ) 0.85(13) − 1 1 accounts for the correlated noise that can be found within the k=1 γsys (km s− ) 57.46(8) σsys,1 (km s− ) 0.26(7) from the MCMC analysis. The prayer-bead algorithm allows ro- X e 0.0009(+12) σ (km s 1) 0.09(10) WASP data, and varying the starting positions overcomes any e 06 sys,2 − bust estimates of the uncertainties associated with lightcurve pa- where mi and mi are the observed and corrected magnitude (re- − bias that may be present by the choice of initial parameters. Fig- (k) rameters2 (as the standard deviation of the best-fit values from spectively), and ai are the same detrending basis functions as theure2 500shows shifts) the and density accounts distribution for the correlated for r1 and noiser2, that which can has be in Eq. (4). Once calculated, the trends are removed from the ob- For one component, j, the log-likelihood can be written as foundbeen calculated within the from WASP the data,k and andrsum varyingpositions the starting explored positions during e the MCMC. The cut-off in the distribution occurs where the served data and a new model fitted. Initially the best-fit model overcomes any bias that may be present by the choice of initial 2 from Sect. 3.2 was used for L, but the coefficients were calcu- N y Θ parameters.third-light becomes Figure 2 zero,2 shows as there the density strongdistribution correlations for betweenr andk 1 rj,n j,n( rv) 2π 1 lated in an iterative process with slightly different models until ln j(yrv; Θrv) = − ln (6) and l3. The parameters k and rsum are directly related to observ- Fig. 3. Upper panels panels: detrended- the detrended best-fit best-fit model model for WASP0639-32 for WASP0639-32 (grey L −2 2 − 2 r2, which has been calculated from the k and rsum positions ex- each parameter change by less than 0.005% from the previous n=1  sj,n   sj,n  able features in the lightcurve and so there values are well line)(grey plotted line) plotted over the over WASP-South the WASP-South photometry photometry for the primary for the (left primary) and X plored during the MCMC. The cut-off in the distribution occurs model. As before, the same MCMC and prayer-bead analysis      determined. secondary(left) and secondary (right) eclipses. (right) eclipses.Lower panels: residuals,- thewith residuals, the grey with line      where the third-light becomes zero, as there strong correlations Lower panels where yrv is a vector of length N containing the modelled radial wasmarkingthe grey used linezero. asin marking Sect.3.2. zero. between k and l3. The parameters k and rsum are directly related Table 3 contains best-fit parameters for both the original velocities of star j, Θrv is a vector containing the varying param- to3.3. observable Detrending features Investigations in the lightcurve and so there values are model fit and those from the detrending testing. The difference eters (e, ω, γsys, K1, K2, B0, σsys,1, σsys,2) and rj are measured well determined. taken into consideration. It can be described using radial velocities for component j. sj,n are weights for each mea- To help ensure the most accurate parameters possible were betweenTable 4. Radial the two velocities is also for shown WASP0639-32 for ease ofmeasured comparison. using broaden- In all surement that combine the measured internal uncertainties, σ2 obtained from the lightcurve, we have investigated whether the casesing function the diff methoderenceM within is less RaveSpan. that the uncertainties associated with j,n (k) (k) 2 3.3.WASP Detrending detrending Investigations algorithm alters the best-fit parameters for thatm = parameters,m + L so thec0 WASPa , detrending algorithm does not af-(5) and a systematic uncertainty σsys,j, such that i i i − i WASP0639-32. The algorithm locates and corrects for four fect the lightcurvek=1 parameters for WASP0639-32. This is the To help ensure the most accurate parameters possible were ob- HJDX2 450 000 Primary Secondary 2 2 2 trends of systematic errors found across all stars in one field. same conclusion− as was found the analysis1 of AI Phe1 (Kirkby- s = σ + σ . (7) tained from the lightcurve, we have investigated whether the e (km s− ) (km s− ) j,n j,n sys,j It can be described using Kentwhere etm al.i 2016).and mi Theare detrended the observed parameters and corrected have been magnitude used in (k) WASP detrending algorithm alters the best-fit parameters for the(respectively), remaining6939.78595 analysis. and ai are Figure the same3 100 shows.90 detrending the detrended5 basis.61 functions best-fit 2 σsys,j represents a combination of instrumental uncertainty and WASP0639-32.M The algorithm locates and corrects for four modelas in Eq. for WASP0639-32(46939.85977). Once calculated, plotted the 101 against trends.44 the are WASP-South removed−6.86 from pho- the (k) (k) e − stellar jitter for component j. Stellar jitter is more significant for trendsmi, j = m ofi, j systematicc j errorsai, found across all stars in one field.(4) tometry.observed data6940.81320 and a new model fitted.104.62 Initially the10.61 best-fit model 2 − − more evolved stars (Wright 2005), therefore σsys was included It can be describedk=1 using from Sect. 3.2 was used for L, but. the coefficients. were calcu- X 6956.80762 20 29 113 83 separately for each component. The log-likelihood from both lated in an iterative6958.81865 process with 14 slightly.74 different 122.02 models until e M components are summed together as ln = ln 1 + ln 2 where m m(k) (k) 4.each Spectroscopic parameter6985.78700 change Orbit by less than 92.35 0.005% from 7.10 the previous L L L mwherei, j = mi,ij, j and i,cj j areai the observed and corrected magnitude,(4) the labels j = 1, 2 denote the primary and secondary compo- respectively,− for star j at time i. M is the total number of trends, model. As before,6999.65212 the same MCMC 100 and.42 prayer-bead4.35 analysis was k=1 Radial velocity measurements for both stars were made using nent, respectively. The chosen priors place loose constraints on a are basis functionsX detailing the patterns of systematic errors used as in Sect.6999.77011 3.2. 98.29 −3.15 i e the broadening function method (Rucinski 2002;− Rucinski & Lu the chain parameters to prevent the walkers exploring regions wheree mi, j and mi, j are the observed and corrected magnitude, Table3 contains best-fit parameters. for both. the original and c j describes to what extent each basis function affects a 1999; Rucinski7015.77003 1992) in RaveSpan 12 02 (Pilecki 124et al.57 2017). The of the parameter-space that correspond to non-physical values. respectively, for star j at time i. M is the total number of trends, model fit and those from the detrending. testing.. The differ- particular star. broadening function7040.65621 smoothing was 16 set67 to a value 117 of65 3 and a tem- Priors on the semi-amplitude velocities are set to allow explo- ai areUsing basis the functions method detailing described the in patterns Kirkby-Kent of systematic et al.(2016 errors), ence between7042.59910 the two∗ is also shown58.74 for ease of ... comparison. 1 e plate spectrum with parameters of Teff = 6200 K, log g = 4.0, ration between 500 and 500 km s− , and the systemic velocity andeffectivec j describes detrending to what coefficients, extent eachc0, basis were function calculated affects using a par- sin- In all cases the difference is less that1 the uncertainties associ- − 1 [Fe/H]= 0.0 and v sin(i) = 0.0 km s− was used. The measured is restricted to between 200 and 500 km s− . The MCMC used ticular star. ated with that parameters, so the WASP detrending1 algorithm − gular value decomposition (SVD). The effective detrending radialNotes. velocities Typical internalare shown errors: in Table primary, 4. The 0.03spectra km weres− ; secondary, obtained 300 walkers and ran for 1000 steps, with the first 400 steps re- Using the method described in Kirkby-Kent et al. (2016), ef- does not1 affect(*) the lightcurve parameters for WASP0639-32. coefficients include a fixed binary lightcurve model, L, when on0.26 separate km s− . nightsTaken to avoid at phase correlationsφ = 0.504, between duringmeasured the flat section radial of moved as burn-in steps. The chains from each parameter were fective detrending coefficients, c0, were calculated using singu- Thissecondary is the eclipse. same conclusion as was found the analysis of they are calculated to allow the variability of an eclipsing to be velocities. checked via a running-mean to ensure the chains had converged, lar value decomposition (SVD). The effective detrending coeffi- AI Phe (Kirkby-Kent et al. 2016). The detrended parameters Orbital parameters were fitted using sbop, the Spectroscopic and the walkers’ positions were plotted against step number to 2 Produced using corner.py by Foreman-Mackey(2016). have been used in the remaining analysis. Figure3 shows the 2 Produced using corner.py by (Foreman-Mackey 2016). Binary Orbit Program (written by P. B. Etzel), with an MCMC ensure there is suitable mixing. The acceptance fraction (mean= . = wrapper in the form of the Python module emcee, (Foreman- 0 40) and parameter auto-correlation lengths (max 87) are also A135, page 4 of 15 Article number, page 4 of 16page.16 Mackey et al. 2013) to ensure robust uncertainties on the orbital checked. parameters. The following parameters were included in the fit- The resulting orbit parameters are shown in Table 5 and the ting: eccentricity, e; angle of periastron, ω; systemic velocity, resulting model orbits are plotted in Fig. 4. The parameters and v ; and the semi-amplitude of the primary and secondary, K their associated uncertainties are calculated from the 15.9, 50 sys 1 and 84.1 percentiles. The eccentricity is consistent with a circu- and K2 respectively. The orbital period and time of periastron were fixed at the period and time of primary minimum from Eq. lar orbit, but it has been allowed to vary in order for the uncer- (2) because the fitted lightcurve parameters showed that the sys- tainty to be accounted for in K1 and K2. K1 and K2 are the key tem is very close circular. In circular systems degeneracy means parameters used to determine the masses of the stars. Both are it is not possible to fit the eccentricity, angle of periastron and determined directly from the range of the radial velocity curve, time of periastron simultaneously. so their values are well determined. 1 Initial fits showed an average offset of 0.56 km s− between the observed and computed (O-C) measurements for the sec- 5. Spectroscopic Analysis ff ondary star. As such, a constant o set parameter, B0, was fitted 5.1. Disentangling alongside the orbital parameters. It is likely that this offset is due the large difference in the spectral types of the two stars, having We have used our own implementation of the matrix disentan- focused the template on parameters for the hotter, primary star. gling algorithm of Simon & Sturm (1994) to obtain individual The offset will also, in part, be due the effects of differing gravi- spectra of the two stars. This method was adapted to include the tational redshifts and convective blueshifts between the two stars apparent flux ratio between the stars for each observed spectrum (Lindegren & Dravins 2003). as additional parameters in the disentangling. This allows the

Article number, page 5 of 16page.16 J. A. Kirkby-Kent et al.: WASP0639-32: A new detached eclipsing binary system

Table 4. Radial velocities for WASP0639-32 measured using broaden- Table 5. Fitted spectroscopic orbit parameters for WASP0639-32. ing function method within RaveSpan. Parameter Best-fit Parameter Best-fit HJD 2 450 000 Primary Secondary value value − 1 1 (km s− ) (km s− ) 1 K1 (km s− ) 47.32(8) ω (◦) 269.96(12) 1 1 6939.78595 100.90 5.61 K2 (km s− ) 69.74(11) B0 (km s− ) 0.85(13) − 1 1 6939.85977 101.44 6.86 γsys (km s− ) 57.46(8) σsys,1 (km s− ) 0.26(7) . − . +12 1 6940.81320 104 62 10 61 e 0.0009( 06) σsys,2 (km s− ) 0.09(10) 6956.80762 20.29− 113.83 − 6958.81865 14.74 122.02 6985.78700 92.35 7.10 where yrv is a vector of length N containing the modelled radial 6999.65212 100.42 4.35 velocities of star j, Θrv is a vector containing the varying param- 6999.77011 98.29 −3.15 eters (e, ω, γ , K , K , B , σ , σ ) and r are measured − sys 1 2 0 sys,1 sys,2 j 7015.77003 12.02 124.57 radial velocities for component j. sj,n are weights for each mea- 7040.65621 16.67 117.65 2 surement that combine the measured internal uncertainties, σj,n 7042.59910∗ 58.74 ... 2 and a systematic uncertainty σsys,j, such that 1 Notes. Typical internal errors: primary, 0.03 km s− ; secondary, 2 2 2 1 ( ) s j,n = σ , + σ , . (7) 0.26 km s− . ∗ Taken at phase φ = 0.504, during the flat section of j n sys j secondary eclipse. 2 σsys,j represents a combination of instrumental uncertainty and stellar jitter for component j. Stellar jitter is more significant for detrended best-fit model for WASP0639-32 plotted against the 2 more evolved stars (Wright 2005), therefore σsys was included WASP-South photometry. separately for each component. The log-likelihood from both components are summed together as ln = ln 1 + ln 2 where the labels j = 1, 2 denote the primaryL and secondaryL L compo- 4. Spectroscopic Orbit nent, respectively. The chosen priors place loose constraints on Radial velocity measurements for both stars were made using the chain parameters to prevent the walkers exploring regions the broadening function method (Rucinski 1992, 2002; Rucinski of the parameter-space that correspond to non-physical values. Priors on the semi-amplitude velocities are set to allow explo- & Lu 1999) in RaveSpan (Pilecki et al. 2017). The broadening 1 ration between 500 and 500 km s− , and the systemic velocity function smoothing was set to a value of 3 and a template spec- − 1 is restricted to between 200 and 500 km s− . The MCMC used trum with parameters of Teff = 6200 K, log g = 4.0, [Fe/H]= − 1 300 walkers and ran for 1000 steps, with the first 400 steps 0.0, and v sin(i) = 0.0, km s− was used. The measured radial velocities are shown in Table4. The spectra were obtained on removed as burn-in steps. The chains from each parameter were separate nights to avoid correlations between measured radial checked via a running-mean to ensure the chains had converged, velocities. and the walkers’ positions were plotted against step number Orbital parameters were fitted using SBOP, the Spectro- to ensure there is suitable mixing. The acceptance fraction scopic Binary Orbit Program (written by P. B. Etzel), with (mean = 0.40) and parameter auto-correlation lengths (max = 87) an MCMC wrapper in the form of the Python module emcee are also checked. (Foreman-Mackey et al. 2013) to ensure robust uncertainties on The resulting orbit parameters are shown in Table5 and the the orbital parameters. The following parameters were included resulting model orbits are plotted in Fig.4. The parameters and in the fitting: eccentricity, e; angle of periastron, ω; systemic their associated uncertainties are calculated from the 15.9, 50, and 84.1 percentiles. The eccentricity is consistent with a circular velocity, vsys; and the semi-amplitude of the primary and sec- orbit, but it has been allowed to vary in order for the uncer- ondary, K1 and K2, respectively. The orbital period and time of periastron were fixed at the period and time of primary minimum tainty to be accounted for in K1 and K2. K1 and K2 are the key from Eq. (2) because the fitted lightcurve parameters showed that parameters used to determine the masses of the stars. Both are the system is very close circular. In circular systems degeneracy determined directly from the range of the radial velocity curve, means it is not possible to fit the eccentricity, angle of periastron so their values are well determined. and time of periastron simultaneously. 1 Initial fits showed an average offset of 0.56 km s− between 5. Spectroscopic Analysis the observed and computed (O–C) measurements for the sec- ondary star. As such, a constant offset parameter, B0, was fitted 5.1. Disentangling alongside the orbital parameters. It is likely that this offset is due the large difference in the spectral types of the two stars, having We have used our own implementation of the matrix disentan- focused the template on parameters for the hotter, primary star. gling algorithm of Simon & Sturm(1994) to obtain individual The offset will also, in part, be due the effects of differing gravi- spectra of the two stars. This method was adapted to include the tational redshifts and convective blueshifts between the two stars apparent flux ratio between the stars for each observed spectrum (Lindegren & Dravins 2003). as additional parameters in the disentangling. This allows the For one component, j, the log-likelihood can be written as spectrum taken during the secondary eclipse to be included with a flux ratio of zero in the disentangling analysis. It is assumed N 2 that all spectra obtained out of eclipse have the same flux ratio. 1 rj,n yj,n(Θrv) 2π ln (y ; Θ ) = − ln , (6) A simple grid search algorithm was used to optimise this param- Lj rv rv −2 2 − 2 n=1  sj,n   sj,n  eter by finding the value of this flux ratio that minimises the X               A135, page 5 of 15 AA&&AA proofs: proofs:A&Amanuscriptmanuscript 615, A135 no. no.(2018) j0639_paper j0639_paper ) ) 1.2 Primary 1 1.2 Primary 1 120120 − − 1.01.0 100100 0.80.8 80 80 0.60.6 6060 0.40.4 4040 0.20.2 NormalisedFlux NormalisedFlux 0.0 2020 0.0 0 0 1.21.2 SecondarySecondary −−11 Radial Velocity (km s Velocity Radial

Radial Velocity (km s Velocity Radial RMS=0.29 (km s ) −20−20 RMS=0.29 (km s ) 1.01.0 0.00.0 0.20.2 0.40.4 0.60.6 0.80.8 1.01.0 0.80.8 PhasePhase 0.60.6 0.60.6 0.40.4

) 0.0 0.2

) 0.0 0.2 1 1 NormalisedFlux NormalisedFlux − − −0.6−0.6 0.00.0 PrimaryPrimary RMS=0.30RMS=0.30 (km(km ss−−11)) 542.0542.0 542.5542.5 543.0543.0 543.5543.5 544.0544.0 544.5544.5 545.0545.0 0.80.8 WavelengthWavelength (nm)(nm) 0.00.0 −0.8 O-C (km s O-C −0.8 O-C (km s O-C Fig. 5. Disentangled spectra for the primary (upper panel) and sec- Secondary RMS=0.27 (km s−−11) Fig.Fig. 5. 5. DisentangledDisentangled spectra spectra for for the the primary primary (upper (upper panel) panel) and and sec- sec- Secondary RMS=0.27 (km s ) ondary (lower panel) components in WASP0639-32 for a region around 0.00.0 0.20.2 0.40.4 0.60.6 0.80.8 1.01.0 ondaryondary (lower (lower panel) panel) components components in in WASP0639-32 WASP0639-32 for for a a region region around around the Fe I line at 543.452 nm. PhasePhase thethe Fe Fe I I line line at at 543.452 543.452 nm. nm.

Fig. 4. Upper panel: radial velocities for the primary (grey squares) and secondaryFig.Fig. 4. 4. Upper Upper (white panel panel circles)-- Radial Radial components velocities velocities of for for WASP0639-32, the the primary primary (grey (grey with squares) squares) best-fit the5.2.the radial radial Equivalent velocities velocities width are are fitting incorrect, incorrect, or or large large slopes slopes at at the the end end of of a a orbit.andand secondary secondaryLower panels (white (white: residuals circles) circles) components components for each component. of of WASP0639-32, WASP0639-32, Error bars with with include best- best- segment in the continuum of Figure 5 would suggest there was fit orbit. Lower panels - Residuals for each component. Error bars in- segment in the continuum of Figure 5 would suggest there was thefit orbit. internalLower and systematic panels - Residuals uncertainties. for each component. Error bars in- anAn issue automated with the method normalisation. is used to The obtained four spectra a table shown of equivalent in Fig- cludeclude the the internal internal and and systematic systematic uncertainties. uncertainties. an issue with the normalisation. The four spectra shown in Fig- urewidthsure 6 6 are are (EWs) a a representative representative for selected sample sample Fe line of of theof the each set. set. star, independently. Functions from the 2014 version of iSpec (Blanco-Cuaresma root mean square (RMS) residuals between the observed spectra et al. 2014a) are used to first normalise and fit a continuum to spectrum taken during the secondary eclipse to be included with andspectrum the spectra taken reconstructed during the secondary from the eclipse disentangled to be included spectra. This with 5.2.each5.2. Equivalent Equivalent segment of width width disentangled fitting fitting spectrum. A small region around a flux ratio of zero in the disentangling analysis. It is assumed searcha flux algorithmratio of zero forms in the part disentangling of a Python analysis. wrapper thatIt is converts assumed the expected location of the iron line is searched to identify the that all spectra obtained out of eclipse have the same flux ratio. thethat UVES all spectra spectra obtained into the out appropriate of eclipse format have the for same disentangling flux ratio. Anline,An automated automated and cross-match method method the is is atomicused used to to data obtained obtained with the a a table table information of of equivalent equivalent in the A simple grid search algorithm was used to optimise this pa- algorithm.A simple grid First, search the wrapper algorithm re-interpolates was used to the optimise spectra this onto pa- a widthsDoylewidths et (EWs) (EWs) al.(2013 for for) line-list. selected selected In Fe Fe some line line casesof of each each multiple star, star, independently. independently. matches were rameter by finding the value of this flux ratio that minimises the uniformrameter bylogarithmic finding the wavelength value of this scale flux in ratio the that barycentric minimises refer- the Functionsfound,Functions in which from from case the the the2014 2014 one version version closest of theof iSpec iSpec expected (Blanco-Cuaresma (Blanco-Cuaresma wavelength was root mean square (RMS) residuals between the observed spectra enceroot mean frame. square A median (RMS) filter residuals is used between as an initial the observed normalisation, spectra etchosen.et al. al. 2014a) 2014a) Once are area line used used has to to been first first identified, normalise normalise a and and Gaussian fit fit a a continuum continuum profile is fit- to to and the spectra reconstructed from the disentangled spectra. This pointsand the affected spectra by reconstructed cosmic rays from are replaced the disentangled with a median spectra. value, This eachtedeach to segment segment the line of of and disentangled disentangled is used to determine spectrum. spectrum. the A A small small EW for region region a particular around around search algorithm forms part of a Python wrapper that converts andsearch the algorithm spectrum forms is binned part to of provide a Python the wrapper a sampling that converts similar theline.the expected expected Each fit location location has been of of visually the the iron iron checked line line is is searched searched to ensure to to a identify identify sensible the the fit the UVES spectra into the appropriate format for disentangling tothe the UVES original spectra UVES into spectra. the appropriate The disentangling format for is disentangling focused on line,wasline, made. and and cross-match cross-match Any lines that the the were atomic atomic blended data dataor with with were the the significantly information information off- in in algorithm.algorithm. First, First, the the wrapper wrapper re-interpolates re-interpolates the the spectra spectra onto onto a a the Doyle et al. (2013) line-list. In some cases multiple matches small sections of spectrum, 30 Å in length, around specific Fe I setthe from Doyle the et al. continuum (2013) line-list. were removed In some from cases the multiple final selection matches uniformuniform logarithmic logarithmic wavelength wavelength scale scale in in the the barycentric barycentric refer- refer- were found, in which case the one closest the expected wave- and Fe II lines. By choosing a small region around each line, EWs.were found, In total, in there which are case 38 EWsthe one for closest the primary the expected (28 Fe I wave- lines enceence frame. frame. A A median median filter filter is is used used as as an an initial initial normalisation, normalisation, length was chosen. Once a line has been identified, a Gaussian uncertainties from the continuum placement are reduced, com- andlength 10 was Fe II chosen. lines) and Once 19 a EWs line has for thebeen secondary identified, star a Gaussian (16 Fe I pointspoints a affffectedected by by cosmic cosmic rays rays are are replaced replaced with with a a median median value, value, profile is fitted to the line and is used to determine the equiva- pared with a fitting a continuum to the entire spectrum. The linesprofile and is 3 fitted Fe II to lines). the line and is used to determine the equiva- andand the the spectrum spectrum is is binned binned to to provide provide the the a a sampling sampling similar similar lent width (EW) for a particular line. Each fit has been visually processing is done for each observed spectrum, and is done inde- lentAn width EW (EW) fitting for procedure, a particular wrapped line. Each in fitthe has MCMC been visually Python toto the the original original UVES UVES spectra. spectra. The The disentangling disentangling is is focused focused on on checked to ensure a sensible fit was made. Any lines that were pendently for each small wavelength section. Sections of spec- module,checkedemcee to ensure(Foreman-Mackey a sensible fit was et al. made. 2013 Any), was lines used that to deter- were small sections of spectrum, 30 Å in length, around specific Fe I blended or were significantly offffset from the continuum were re- trumsmall were sections processed of spectrum, around each 30 Å iron in length, line present around in specific the line-list Fe I mineblended the or best were effective significantly temperature, o set from surface the continuum gravity, metallicity were re- andand Fe Fe II II lines. lines. By By choosing choosing a a small small region region around around each each line, line, un- un- movedmoved from from the the final final selection selection equivalent equivalent widths. widths. In In total, total, there there of Doyle et al.(2013). Residuals between the observed spectra and microturbulence, (Teff, log g, [Fe/H], and vmic, respectively) certainties from the continuum placement are reduced, compared are 38 EWs for the primary (28 Fe I lines and 10 Fe II lines) and andcertainties reconstructed from the spectra continuum were placement used to search are reduced, for and compared remove forare each 38 EWs star for separately. the primary Initial (28 walker Fe I lines positions and 10 are Fe generated II lines) and by with a fitting a continuum to the entire spectrum. The processing 19 EWs for the secondary star (16 Fe I lines and 3 Fe II lines). remainingwith a fitting cosmic a continuum rays using to the three entire times spectrum. the standard The processing deviation perturbing19 EWs for initial the secondary parameter star estimates (16 Fe I linesby multiplying and 3 Fe II numbers lines). is done for each observed spectrum, and is done independently ofis donethe residuals for each as observed a rejection spectrum, criterion. and is The done affected independently regions drawnAnAn randomlyEW EW fitting fitting from procedure, procedure, a normal wrapped wrapped distribution in in the the by MCMC MCMC step parame- Python Python forfor each each small small wavelength wavelength section. section. Sections Sections of of spectrum spectrum were were emcee are replaced with the fitted values. The spectra were normalised module,tersmodule, (100,emcee 0.05,(Foreman-Mackey(Foreman-Mackey 0.1, and 0.05 for etT eteff al. al., log 2013), 2013),g, [Fe/H], was was used used and to tov de-mic de-, processed around each iron line present in the line-list of Doyle andprocessed the disentangling around each algorithm iron line ispresent run one in thefinal line-list time, using of Doyle the terminerespectively).termine the the best best The e e stepffffectiveective parameters temperature, temperature, are needed surface surface because gravity, gravity, of the metal- metal- dif- et al. (2013). Residuals between the observed spectra and recon- g / v optimalet al. (2013). flux ratio.Residuals Figure between5 shows the an observed example spectra of the and result- recon- licityferentlicity and andscales microturbulence, microturbulence, associated with ( ( theTTeeffff different,, log log g,, [Fe [Fe parameters./H]H] and and vmicmic For,, respec- arespec- given structedstructed spectra spectra were were used used to to search search for for and and remove remove remaining remaining ing disentangled spectra around the Fe I at 543.452 nm, where tively)settively) of parameters, for for each each star starΘsp separately. separately.= Teff, log Initial Initialg, [Fe walker walker/H], vmic positions positions, small are sectionsare gen- gen- cosmic rays using three times the standard deviation of the resid- { } Lcosmic/L = rays0.0513 using. three times the standard deviation of the resid- eratedoferated synthetic by by perturbing perturbing spectrum initial initial are generated parameter parameter around estimates estimates the by by lines multiplying multiplying used for uals2 1 as a rejection criterion. The affffected regions are replaced ualsFigure as a6 rejection compares criterion. the observed The a andected recombined regions are disentan- replaced numbersthenumbers EWdrawn measurements drawn randomly randomly using from from solar a a normal normal abundances distribution distribution from by by Asplund step step pa- pa- with the fitted values. The spectra were normalised and the dis- g / v gledwith spectra the fitted for values. four of The the spectra eleven observed were normalised spectra, and around the dis-the rametersetrameters al.(2009 (100, (100,), MARCS.GES 0.05, 0.05, 0.1 0.1 and and (Gustafsson 0.05 0.05 for forTTeeff etff,, al.log log 2008g,, [Fe [Fe) model/H]H] and and atmo-vmicmic,, entangling algorithm is run one final time, using the optimal flux sameentangling Fe I line algorithm that is shown is run one in Fig. final5.time, The residuals, using the which optimal have flux respectively).spheresrespectively). and the The The line-list step step parameters parameters and atomic are are data needed needed of Doyle because because et al.of of( the the2013 dif- dif-). ratio. Figure 5 shows an example of the resulting disentangled beenratio. scaled Figure up 5 by shows a factor an example of ten so of they the can resulting be seen, disentangled are shown ferentTheferent projected scales scales associated associated rotational with with velocity, the the di diffffverenterentsin i, parameters. parameters. and macroturbulence, For For a a given given spectraspectra around around the the Fe Fe I I at at 543.452 543.452 nm, nm, where whereLL2//LL1 ==00..0513.0513. Θ = T , g, / , v above the spectra. There are no strong features2 in the1 residuals. setvsetmac of ofare parameters, parameters, not fitted,Θ andspsp = theTeeff iSpec’sff,loglog g,[Fe default[Fe/H]H], parameters vmicmic ,, small smallare sections sections used 1 {{ 1 }} LargeFigureFigure spikes 6 6 nearcompares compares the absorption the the observed observed lines and and would recombined recombined indicate the disentan- disentan- radial of(ofv sin synthetic synthetici = 2 km spectrum spectrum s− and v are aremac generated= generated3 km s− around) around when generating the the lines lines used used the sec- for for velocitiesgledgled spectra spectra are for for incorrect, four four of of theor the large eleven eleven slopes observed observed at the spectra, spectra, end of around aaround segment the the thetionsthe EW EW of synthetic measurements measurements spectrum. using using These solar solar parameters abundances abundances are from from not Asplund consider Asplund insamesame the Fe Fe continuum I I line line that that of is is Fig. shown shown5 would in in Figure Figure suggest 5. 5. The The there residuals, residuals, was anwhich issue which etinet al. al. the (2009), (2009), MCMC MARCS.GES MARCS.GES fitting because (Gustafsson (Gustafsson they do et et not al. al. 2008)alter 2008) the model model measured atmo- atmo- withhavehave thebeen been normalisation. scaled scaled up up by by Thea a factor factor four of of spectra ten ten so so shown they they can can in beFig. be seen, seen,6 are are are a spheresEWspheres (Niemczura and and the the line-list line-list et al. 2014 and and). atomic atomicOnce measured, data data of of Doyle Doyle the EWs et et al. al. from (2013). (2013). the v i representativeshownshown above above thesample the spectra. spectra. of the There There set. are are no no strong strong features features in in the the ThesyntheticThe projected projected spectrum rotational rotational sections velocity, velocity,Ws arevsinsin comparedi,, and and macroturbulence, macroturbulence, to the observed residuals.residuals. Large Large spikes spikes near near the the absorption absorption lines lines would would indicate indicate vvmacmac areare not not fitted, fitted, and and the the iSpec’s iSpec’s default default parameters parameters are are used used

A135,ArticleArticle page number, number, 6 of page15 page 6 6 of of 16page.16 16page.16 J.J. A. A. Kirkby-Kent Kirkby-Kent et et al.: al.: WASP0639-32: A new detached eclipsing binary system

Residuals are x10

4

3

2 NormalisedFlux 1

542.5 543.0 543.5 544.0 544.5 545.0 Wavelength (nm)

Fig. 6. Observed (black) and recombined disentangled spectra (grey dashed) around the Fe I line at 543.452 nm for four spectra from WASP0639- 32. The residuals, scaled by a a factor factor of of 10, 10, are are shown shown 0.25 0.25 above above each each spectrum spectrum segment. segment. Plotted Plotted with with an an offset offset of of 1.0 1.0 between between spectra. spectra.

Table 6. Spectroscopic parameters for both components of WASP0639-32 obtained using equivalent width fitting, for cases where the surface 1 1 gravity(v sin i was= 2 free km sand− and wherevmac it was=3 fixed km s− at) photometric when generating values. the sec- This is larger than the trend of Mortier et al. (2013), but maybe tions of synthetic spectrum. These parameters are not consider caused by the small number of Fe II lines. Doyle (2015) notes in the MCMC fitting because they do not alter the measured EW that temperatures determined via the ionisation balance method (Niemczura et al. 2014). OnceParameter measured, the EWs from Primary the syn- are not affected bySecondary the discrepancy in log g but as our equiv- Free Fixed Free Fixed thetic spectrum sections Ws are compared to the observed EWs, alent width fitting includes microturbulence and metallicity, the Wo, to judge the choice of TΘsp.(K) The overall log-likelihood6730 30 func- 6320diff10erent surface 5490 gravities100 may 5420 affect90 these parameters. We there- eff ± ± ± ± tion can be written as log gs 4.65 0.05fore 3.97 ran the 4.88 equivalent0.13 width fitting4.61 procedure with log gs fixed 1 ± ± v (km s− ) 1.61 0.01 1.49 at0.01 3.97 and 2.67 4.61,0.18 for the 2 primary.61 0.18 and secondary, respectively. N mic 2 ± ± ± ± 1 W[Feo,n/H]Ws,n(Θsp) 0.10 02.01π 0.33 The0.01 results0.38 are also0.06 shown0.45 in Table0.05 6. By fixing the surface ln (W; Θ ) = − − ln± − (8) ± − ± − ± L sp −2 σ2 − σ2 gravities of both stars, the effective temperature of primary has n=1  W,n   W,n  been reduced, while it has increased for the secondary. For both X          stars, the metallicity has been reduced. The temperature ratio, where is a vector of length N containing the fitted equiva- EWs, WWo, to judge the choice of Θsp. The overall log-likelihood T90/ transitingT , has increased planet host from stars 0.816 and showed0.019 to that 0.857 the discrepancy0.016. Note, is lent widths, and σ are the uncertainties associated with the 2 1 function can be writtenW as thetemperature uncertainties dependent. on the valuesFor a star in± Table with an 6 do effective not include± temperature uncer- measured EWs. Priors were used to prevent the walkers ex- N 2 taintiesnear 6700 from K, thesystematics difference such is typically as those 0.6 from dex, using which one is specific consis- ploring outside of1 the limitsWo,n setWs by,n(Θ thesp) model atmospheres,2π tent with what we have found for the primary of WASP0639-32. ln (W; Θsp) = − ln , (8) line-list, solar abundance list or set of model atmospheres. Jofre i.e. 4500 < Teff < 7500, 3.5 < log2 g < 5.0, 1.0 < [Fe2 /H] < 1.0 In comparison, the difference between the two surface gravities L −2  σ , − σ ,  et al. (2016) provide a summary of expected uncertainty contri- and 0 < v < 100.n For=1  both theW primaryn − and secondary W n  star, mic X     butionsfor the secondary to the metallicity is smaller for atsystematic 0.27 dex. such This as is these, larger with than one the 100 walkers and 500 steps were used. For both stars, the first where W is a vector of length N containing the fitted EWs, and ontrend the of largest Mortier contributions et al.(2013 being), but the maybe continuum caused placement by the small with 100 steps were removed to allow for adequate burn-in. Auto- σW are the uncertainties associated with the measured EWs. Pri- anumber systematic of Fe of II 0.3lines. dex. Doyle As( the2015 uncertainty) notes that on temperatures the effective deter- tem- correlation lengths are between 50-70 for the different runs, and ors were used to prevent the walkers exploring outside of the peraturemined via of the the ionisation primary star balance is very method small are and not does affected not include by the acceptance fractions are 0.34-0.55. limits set by the model atmospheres, i.e., 4500 < Teff < 7500, potentialdiscrepancy systematics in log g but (as as previously our EW fittingdiscussed), includes we take microturbu- the un- 3.5 effective temperature process could of the aff primaryect the star measured is very smallEWs, and we fromfective the temperature mass and radius, near 6700log g K,MR the= 3 di.974fference0.011 is typically. Discrepan- 0.6 havedoes not compared include thepotential EWs systematics from a synthetic (as previously spectra discussed), generated ciesdex, between which islog consistentg values with derived what from we have spectroscopic± found for analysis the pri- withwe take spectroscopic the uncertainty parameters as 50 similarK. This to has the been two estimatedcomponents from of ± (denotedmary of WASP0639-32.log gs hereafter) In and comparison, more direct the di independentfference between tech- WASP0639-32,variations in the to temperature the spectra when obtained the throughsegment disentangling. width for the niquesthe two have surface been gravities noted before.for the secondaryMortier et is al. smaller(2013) at looked 0.27 dex. at Ongenerated average spectrum the disentangling is altered altered slightly. the This EWs paper of the has primary used star the

Article number, pageA135, 7 of page 16page.16 7 of 15 A&A proofs: manuscript no. j0639_paper

Table 6. Spectroscopic parameters for both components of WASP0639-32 obtained using equivalent width fitting, for cases where the surface gravity was free and where it was fixed at photometric values.

Parameter Primary Secondary Free Fixed Free Fixed T (K) 6730 30 6320 10 5490 100 5420 90 eff ± ± ± ± log gs 4.65 0.05 3.97 4.88 0.13 4.61 1 ± ± vmic (km s− ) 1.61 0.01 1.49 0.01 2.67 0.18 2.61 0.18 [Fe/H] 0.10 ± 0.01 0.33 ± 0.01 0.38 ± 0.06 0.45 ± 0.05 − ± − ± − ± − ± A&A 615, A135 (2018)

250 chosenTable 8. andSpectroscopic EWs measured parameters using for the Procyon line fitting obtained function using withinequiva- iSpec.lent width Each fitting. line was checked to ensure there was no obvious blending. As these EWs were measured from a synthetic spec- 200 trum, an uncertainty is not automatically calculated. The EW- fitting methodParameter needs some uncertaintiesThis work for Literature the MCMC walkers are to exploreT parameter-space(K) 6540 properly.150 As6554 such, an84 uncertainty 150 eff on 1.0 mÅlog wasg assumed for3.94 each±0 EW..10 Using 4.0 solar±0.02 abundances from Asplundv et(km al. s (2009)1) 1 and.52 ± MARCS.GES0.16 1.8 (Gustafsson± 0.11 et al. mic − ± ± 100 2008) model[Fe atmospheres,/H] 0. these00 0 measured.07 +0. synthetic01 0.08∗ EW were Fitted EW Fitted fitted, and the resulting stellar parameters± are shown± in Table 7. The MCMC( ) used 100 walkers and 500 steps. Overall the recov- Notes. ∗ Uncertainty in [Fe/H] from combining different sources of 50 ereduncertainties parameters presented agree in well Table with 3 of those the Jofré usedto et al.generate(2014) paper, the syn- in Primary theticquadrature. spectrum. This is The the metallicitysame approach is slightly as in Heiter lowered et al.( that2015 expected). Secondary but only just outside the 1-σ. 0 We also wanted to ensure the EW fitting method could cor- 0 50 100 150 200 250 0.001 over the range 500–700 nm. A selection of 47 iron lines rectly recover stellar parameters of stars. We measured EWs Measured EW (42 Fe I lines and 5 Fe II lines) were chosen and EWs mea- from the ESPaDOnS spectrum of Procyon A in the Gaia Bench- sured using the line fitting function within iSpec. Each line was mark Star library (Blanco-Cuaresma et al. 2014b) and used the Fig. 7. Comparison between fitted equivalent widths generated using checked to ensure there was no obvious blending. As these EWs theFig. best-fitting 7. Comparison spectroscopic between parametersfitted equivalent for a widths fixed log generatedg (detailed using in EW fitting method described in Sect. 5.2 to estimate its stel- were measured from a synthetic spectrum, an uncertainty is not Tablethe best-fitting6) and the spectroscopic measured equivalent parameters widths for a for fixed both log componentsg (detailed in in lar parameters. The spectrum was first normalised, by dividing automatically calculated. The EW-fitting method needs some WASP0639-32.Table 6) and the Uncertainties measured equivalent on the primary widths equivalent for both components widths are too in through with the continuum. The spectrum was split into seg- smallWASP0639-32. to see. Uncertainties on the primary equivalent widths are too uncertainties for the MCMC walkers are to explore parameter- small to see. ments and a third-degree polynomial was fitted in each segment inspace order properly. to identify As such, the continuum. an uncertainty The on VALD 1.0 mÅ line-list was assumed (Kupka Table 7. Recovered stellar parameters using equivalent width fitting, for for each EW. Using solar abundances from Asplund et al.(2009) Table 7. Recovered stellar parameters using equivalent width fitting, for et al. 2011) was used to select 87 lines (72 Fe I and 11 Fe II lines) equivalent widths measured from a synthetic spectrum. and MARCS.GES (Gustafsson et al. 2008) model atmospheres, equivalent widths measured from a synthetic spectrum. which, from visual inspection, did not appear to be blended. Forthese the measured EW fitting, synthetic again EW we were used fitted, solar and abundances the resulting from stellar As- plundparameters et al. are (2009) shown and in MARCS.GES Table7. The MCMC (Gustafsson used 100 et al. walkers 2008) Parameter Recovered Target modeland 500 atmospheres. steps. Overall The the resolution recovered ofparameters the generated agree spectrumwell with those used to generate the synthetic spectrum. The metallicity is Teff (K) 6210 60 6200 was adjusted to account for the slightly higher resolving power eff (K) 6210 ± 60 6200 σ log g 4.01 ±0.14 4.0 (slightlyR = 65000 lowered instead that of expectedR = 56990). but only Here, just the outside MCMC the used 1- . 200 log 1 4 01 ± 0 14 4 0 v (km s−1) 1.53 ± 0.09 1.5 We also wanted to ensure the EW fitting method could vmic (km s− ) 1.53 0.09 1.5 walkers with 1000 steps each. The first 300 were discarded as [Femic/H] 0.05 ± 0.03 0.0 correctly recover stellar parameters of stars. We measured [Fe/H] −0.05 ± 0.03 0.0 a burn-in stage. For this particular run we allowed both a Voigt − ± andEWs Gaussian from the profile ESPaDOnS to be used spectrum to determine of Procyon the syntheticA in the Gaia EW, Notes. Parameters used to generate the synthetic spectrum are labelled Benchmark Star library (Blanco-Cuaresma et al. 2014b) and Notes. Parameters used to generate the synthetic spectrum are la- and chose the EW from the best fitting profile. As a result, the “Target”. used the EW fitting method described in Sect. 5.2 to estimate belled ‘Target’. MCMC required additional steps but it allowed an improved matchits stellar to the parameters. spectral lines. The spectrumThe results was and firstGaia normalised, benchmark by dividing through with the continuum. The spectrum was split same line-list for both measuring the EW from the spectra and parameters (Heiter et al. 2015; Jofré et al. 2014) are shown into segments and a third-degree polynomial was fitted in each forby lessgenerating than 0.5%, the synthetic and 5% forEWs. the The secondary. same is trueThis for has the not model been in Table 8. The parameters themselves are taken as the median segment in order to identify the continuum. The VALD line-list atmospheresincluded in the and MCMC. solar abundances. value from the distribution, with uncertainties calculated using (Kupka et al. 2011) was used to select 87 lines (72 Fe I and Figure7 shows how the fitted EWs, generated with the the 15.9 and 84.1 percentiles. Overall the measured effective 11 Fe II lines) which, from visual inspection, did not appear to parameters in Table6 where log g was fixed, compare to the temperature, surface gravity and metallicity agree with the lit- 5.3. Testing the equivalent width fitting method be blended. For the EW fitting, again we used solar abundances measured values. Overall, there is good agreement with the mea- erature values. The microturbulence is within 2-σ of the litera- from Asplund et al.(2009) and MARCS.GES (Gustafsson et al. sured values. Any lines that were significantly affected by telluric ture value, which is itself a mean value obtained from multiple To ensure the equivalent width fitting was correctly recovering 2008) model atmospheres. The resolution of the generated spec- absorption were removed before the fitting, as were lines that techniques. equivalent widths, we measured a set of EWs from a syntheti- trum was adjusted to account for the slightly higher resolving were blended with other nearby lines. cally generated spectrum, and required that the estimated stellar power (R = 65 000 instead of R = 56 990). Here, the MCMC To investigate how a poor continuum placement could or parameters matched those used to generate the synthetic spec- 5.4.used Checking 200 walkers effective with temperatures 1000 steps each. The first 300 were the disentangling process could affect the measured EWs, we trum in iSpec. The target parameters used to generate the syn- discarded as a burn-in stage. For this particular run we allowed have compared the EWs from a synthetic spectra generated ff ff thetic spectrum are listed in Table 7. In addition to these parame- Theboth equivalent a Voigt and width Gaussian fitting gives profile two to slightly be used di toerent determine e ective the with spectroscopic parameters similar to the two components of ters, we used The Vienna Atomic Line Database (VALD, Kupka temperaturessynthetic EW, depending and chose on the whether EW from we the choose best to fitting use surface profile. WASP0639-32, to the spectra obtained through disentangling.= g et al. 2011) line-list and atomic data, a resolution of R 57 000 gravitiesAs a result, from the the MCMC spectroscopy, required log additionals, or from steps the but masses it allowed and On average the disentangling altered the EWs of the primary star g and a wavelength step of 0.001 over the range 500-700nm. A radii,an improved log MR. match Therefore to the other spectral methods lines. of The determining results and theGaia ef- by less than 0.5%, and 5% for the secondary. This has not been selection of 47 iron lines (42 Fe I lines and 5 Fe II lines) were fectivebenchmark temperature parameters have ( beenHeiter considered. et al. 2015; Jofré et al. 2014) included in the MCMC. Article number, page 8 of 16page.16 are shown in Table8. The parameters themselves are taken as the median value from the distribution, with uncertainties 5.3. Testing the equivalent width fitting method calculated using the 15.9 and 84.1 percentiles. Overall the measured effective temperature, surface gravity and metallicity To ensure the EW fitting was correctly recovering EWs, we mea- agree with the literature values. The microturbulence is within sured a set of EWs from a synthetically generated spectrum, 2-σ of the literature value, which is itself a mean value obtained and required that the estimated stellar parameters matched those from multiple techniques. used to generate the synthetic spectrum in iSpec. The target parameters used to generate the synthetic spectrum are listed in 5.4. Checking effective temperatures Table7. In addition to these parameters, we used The Vienna Atomic Line Database (VALD; Kupka et al. 2011) line-list and The EW fitting gives two slightly different effective tempera- atomic data, a resolution of R = 57 000 and a wavelength step of tures depending on whether we choose to use surface gravities

A135, page 8 of 15 J. A. Kirkby-Kent et al.: WASP0639-32: A new detached eclipsing binaryJ. system A. Kirkby-Kent et al.: WASP0639-32: A new detached eclipsing binary system

Table 8. Spectroscopic parameters for Procyon obtained using equiva- 1.05 Table 9. Magnitudes used in the fitting with colour-effective tempera- lent width fitting. ture and colour-surface brightness relations. 1.00 Parameter This work Literature 0.95 Band Magnitude Error Teff (K) 6540 150 6554 84 0.90 APASS B 11.193 0.028 log g 3.94 ±0.10 4.0 ±0.02 ± ± APASS V 10.686 0.067 v (km s 1) 1.52 0.16 1.8 0.11 0.85 mic − APASS g0 10.907 0.037 [Fe/H] 0.00 ± 0.07 +0.01 ± 0.08 ∗ APASS r0 10.647 0.021 ± ± 0.80 Observed APASS i0 10.437 0.050 (*) Uncertainty in [Fe/H] from combining different sources of 6600 K Notes. NormalisedFlux 0.75 TYCHOBT 11.265 0.057 uncertainties presented in Table 3 of the Jofré et al. (2014) paper, in 6450 K TYCHOVT 10.718 0.054 quadrature. This is the same approach as in Heiter et al. (2015). 0.70 6300 K 6150 K 2MASS J 9.591 0.023 0.65 2MASS H 9.321 0.026 654.66 655.46 656.26 657.06 657.86 2MASS Ks 9.306 0.019 One of the spectra for WASP0639-32, (taken at HJD = Wavelength (nm) DENIS I 10.128 0.04 2 457 042.59910) was taken during the flat region of the sec- DENIS J 9.578 0.05 ondary eclipse when only the primary star would have been Fig. 8. SyntheticSynthetic spectra spectra of of di differentfferent temperatures temperatures plotted plotted against against the theHα DENIS K 9.251 0.09 visible, therefore, it can treated in the same way as a single Hwingsα wings of the of theprimary primary star. star. WISE W3 9.222 0.031 star spectrum. Figure 8 shows how multiple synthetic spectra, generated using different effective temperatures, compare to the fromTable 9.the Magnitudes spectroscopy, used inlog thegs, fitting or from with thecolour-e massesffective and temper- radii, Hα region of the eclipse spectrum. By looking at the wings of logaturegMR and. Therefore colour-surface other brightness methods relations. of determining the effective convergence. With the surface gravity fixed at 3.97, the resulting the Hα line, we found the best temperature was 6150 150 K, ± temperature have been considered. parameters were, Teff = 6410 130 K, [Fe/H] = 0.14 0.30, which is lower than both estimates from the EW fitting. A sur- 1 ± − ± One of the spectra for WASP0639-32, (taken at and vmic = 1.42 0.80 km s− . While the uncertainties are much . Band Magnitude Error ± face gravity of 3 97 was used to generate the synthetic spectra, HJD = 2 457 042.59910) was taken during the flat region larger than those obtain through the disentangling, the effec- but as this method is insensitive to the surface gravity (Niem- of the secondaryAPASS eclipse B when only 11 the.193 primary 0.028 star would have tive temperature has better agreement with the temperature from ff czura et al. 2014), the chosen value will not a ect the best model been visible, therefore,APASS V it can treated 10.686 in the same 0.067 way as a single the disentangling with fixed surface gravity rather than the spectrum. [Fe/H] was set to 0.15 and microturbulence was set APASS g’ 10.907 0.037 1 − star spectrum. Figure8 shows how multiple synthetic spectra, temperature from the Hα fitting. at 1.56 km s− . The temperature obtained from the Hα line dis- generated usingAPASS different r’ effective 10.647 temperatures, 0.021 compare to the We have also used empirical colour-effective temperature agrees with both temperatures for the primary star in Table 6. H region of theAPASS eclipse i’ spectrum. 10.437 By looking 0.050 at the wings of and colour-surface brightness relations to estimate the effective Balmer line fitting can be very sensitive to continuum placement, α the H line, weTYCHO found the BT best temperature11.265 0.057 was 6150 150 K, temperatures of the individual stars in the binary system, as something that can be difficult to do for échelle spectra due to er- α which is lowerTYCHO than both VT estimates10.718 from 0.054 the EW fitting.± A described in Maxted & Hutcheon(2018). Photometry was taken rors from the merging of different échelle orders. surface gravity2MASS of 3.97 Jwas used 9.591 to generate 0.023 the synthetic from the AAVSO Photometric All-Sky Survey, APASS (B,V, g0, We also fitted Hα lines from three different spectra of Pro- spectra, but as2MASS this method H is insensitive 9.321 to 0.026 the surface gravity r0, and i0), the Two Micron All Sky Survey, 2MASS (JHKs), cyon, that were also taken with the UVES instrument, to inves- (Niemczura et al.2MASS 2014), K thes chosen9.306 value will 0.019 not affect the best Tycho-2 Catalogue (BT and VT ), Deep Near-infrared Southern tigate if the offset could be caused by something in the UVES model spectrum.DENIS [Fe/H] I was set to 10.1280.15 and 0.04 microturbulence Sky Survey, DENIS, (I, J, K), and the Wide-Field Infrared 1 − pipeline. The three spectra all had the same grating as spectral was set at 1.56DENIS km s− . J The temperature 9.578 obtained 0.05 from the Hα Survey Explorer, WISE (W3). See Table9 for the observed val- range and those for WASP0639-32, and they have been reduced line disagreesDENIS with both K temperatures 9.251 for the 0.09 primary star in ues (Epchtein et al. 1997; Høg et al. 2000; Skrutskie et al. 2006; using the same reduction pipeline. Two spectra were taken from Table6. BalmerWISE line fitting W3 can be very9.222 sensitive 0.031 to continuum Henden et al. 2009; Wright et al. 2010). the 092.D-0207(A) program from 2013, and one spectrum from placement, something that can be difficult to do for échelle To fit the observed photometry, the model uses the follow- the 266.D-5655(A) program from 2002. All three spectra pro- spectra due to errors from the merging of different échelle ing parameters– g0,i, the apparent g0-band magnitudes for stars duced temperatures that were consistent with the literature value orders.temperatures of the individual stars in the binary system, as de- i = 1, i = 2 corrected for extinction; Teff,i the effective tempera- shown in Table 8, however in one case (one of the two spectra scribedWe inalso Maxted fitted &Hα Hutcheonlines from (2018). three Photometry different spectra was taken of tures for each star; E(B V), the reddening to the system; σext the taken on the same night) the best temperature was 100 K lower Procyon,from the that AAVSO were Photometric also taken with All-Sky the Survey,UVES instrument, APASS (B,V, to additional systematic error− added in quadrature to each measure- than the literature value. For this particular spectrum, the contin- investigateg’,r’ and i’), if the the Two offset Micron could All be Sky caused Survey, by something 2MASS (JHK in thes), ment to account for systematic errors. Although not used here, ffi uum fitting was more di cult due increased noise in the spec- UVESTycho-2 pipeline. Catalogue The (B threeT and spectra VT), Deep all had Near-infrared the same grating Southern as the model can work with triple systems, in which case there is a trum. As such uncertainties from the continuum placement (at spectralSky Survey, range DENIS, and those (I, J, for K) WASP0639-32, and the Wide-Field and Infrared they have Survey been third g0-band and Teff. The apparent magnitudes for each star are least 100 K) should be fed into the uncertainty on the tempera- ± reducedExplorer, using WISE the (W same3). See reduction Table 9 for pipeline. the observed Two spectra values (Hen- were predicted through the colour-temperature relations of Boyajian ture. takenden et from al. 2009; the Skrutskie 092.D-0207(A) et al. 2006; program Høg from et al. 2000;2013, Epchtein and one et al.(2013). Following the example of Boyajian et al.(2013), As a separate test, the EW-fitting was applied to lines from spectrumet al. 1997; from Wright the 266.D-5655(A) et al. 2010). program from 2002. All three the transformations of Bessell & Brett(1988) and Carpenter the spectrum taken in eclipse. Overall, 45 lines were chosen spectraTo fit produced the observed temperatures photometry, that were the model consistent uses with the follow- the lit- (2001) are used to transform between the photometric systems (40 Fe I and 5 Fe II lines), using the same model atmospheres eratureing parameters– value shown g0,i,in the Table apparent8; however, g0-band in magnitudes one case (one for stars of of Johnson and 2MASS. Cousins IC is used as an approximation and line list. As before, the MCMC used 100 walkers and 500 thei = two1, i = spectra2 corrected taken for on extinction; the same night)Teff,i the the e bestffective temperature tempera- to the DENIS Gunn i0 band and the 2MASS Ks is used as an steps, with the initial 100 steps removed as burn-in, and the same wastures 100 for Keach lower star; than E(B theV), literature the reddening value. to theFor system; this particularσ the approximation to the DENIS K band. Transformations between − ext checks were carried out to ensure suitable mixing and conver- spectrum,additional the systematic continuum error fitting added was in quadraturemore difficult to each due increased measure- Johnson B, V, and Tycho BT and VT magnitudes are carried out gence. With the surface gravity fixed at 3.97, the resulting pa- noisement into the account spectrum. for systematic As such uncertainties errors. Although from thenot continuum used here, by interpolating values in Table 3 of Bessell(2000). V-band rameters were, Teff = 6410 130 K, [Fe/H]= 0.14 0.30 and placementthe model can (at least work with100 tripleK) should systems, be fed in which into the case uncertainty there is a extinction is assumed to be 3.1 E(B V), extinction in the 1 ± − ± ± × − vmic = 1.42 0.80 km s− . While the uncertainties are much larger onthird the g temperature.-band and T . The apparent magnitudes for each star are SDSS and 2MASS bands is calculated using Ar = 2.770 E(B ± 0 eff × − than those obtain through the disentangling, the effective temper- predictedAs a separate through test, the colour-temperaturethe EW-fitting was relationsapplied to of lines Boyajian from V) from Fiorucci & Munari(2003), and the extinction coeffi- ature has better agreement with the temperature from the disen- theet al. spectrum (2013). Following taken in eclipse. the example Overall, of Boyajian 45 lineset were al.(2013), chosen cients to the r0 band come from Davenport et al.(2014). The aver- tangling with fixed surface gravity rather than the temperature (40the Fetransformations I and 5 Fe II lines), of Bessell using & the Brett same (1988) model and atmospheres Carpenter age surface brightness ratio in the WASP band (0.429 0.007) ± from the Hα fitting. and(2001) line are list. used As tobefore, transform the MCMC between used the 100 photometric walkers and systems 500 as an approximation to the V-band ratio, and allowed the exter- We have also used empirical colour–effective temperature steps,of Johnson with and the 2MASS. initial 100 Cousins steps I removedC is used as an burn-in, approximation and the nal error σext account for differences in the two bands. This ratio and colour–surface brightness relations to estimate the effective sameto the checks DENIS were Gunn carried i0 band out and to the ensure 2MASS suitable Ks is mixing used as and an is used as a constraint, by using the V-band surface brightness

Article number, page 9 of 16page.16 A135, page 9 of 15 A&A proofs:A&Amanuscript 615, A135 no. (2018) j0639_paper

0.15 Table 10. Absolute parameters for WASP0639-32. 0.10 Parameter Primary Secondary 0.05 Period (days) 11..658317(5) +12 0.00 e 0..0009( 06) −06 i (◦) 89.9943(67)− −0.05 i (◦) 89.9943(67) a sin ii (R(R ) 26..964(31) a (R ) 26.964(31) −0.10 a (R ) 26.964(31) 2MASS TYCHO2 Mass ratio 0..6785(16) 3 −0.15 APASS9 WISE M sin3 ii (M(M ) 1..1544(43) 0..7833(28) DENIS Observed - Fitted Magnitude Fitted - Observed Mass (M ) 1.1544(43) 0.7833(28) −0.20 Mass (M ) 1.1544(43) 0.7833(28) 9.0 9.5 10.0 10.5 11.0 11.5 Radius (R(R ) 1..834(23) 0..7291(81) Observed Magnitude log g 3.974(11) 4.607(10) log gMR 3.974(11) 4.607(10) Teff (K) 6330(50) 5400(80) ff the observed magnitude and those obtained eff Fig. 9. DiDifferenceerence between the observed magnitude and those obtained log(log(L/L ) 0..685(18) 0..392(28) throughthrough the the fitting fitting of of colour–temperature colour-temperature relations. Uncertainties Uncertainties on on the the d (pc) 323(06)− dK (pc) 323(06) yy-axis-axis include include the the external external error, error, σσext,, added added in in quadrature. quadrature. ext Parallax (mas) 3..10(23)(30) +26 +35 dgaia (pc) 323(+26)(+35) dGaia (pc) 323( 22 )( 29 ) v 1 . − − . . and B–K relations of Graczyk et al.(2017). The parameter-space vsin ii (km s− ) 6.75(7) 4.7(1.1) 1 wasapproximation explored using to the a DENIS maximum K band. likelihood Transformations approach, using between an v (km s−1) 7.96(10) 3.16(4) vsynchsynch (km s− ) 7.96(10) 3.16(4) emceeJohnson(Foreman-Mackey B,V and Tycho B etT and al. 2013 VT magnitudes) MCMC procedure, are carried with out by interpolating values in Table 3 of Bessell (2000). V-band ex- 64 walkers, 1088 steps and 64 burn-in steps. All chains have Notes. Where two uncertainties uncertainties are are given, given, the the first first refers refers to theto the random ran- visuallytinction isinspected assumed to to ensure be 3.1 suitableE(B mixing,V), extinction and via in a the running SDSS × − domerror, error, and the and second the second is the systematic. is the systematic. meanand 2MASS check to bands ensure is convergence. calculated using The Amedianr = 2. acceptance770 E(B frac-V) from Fiorucci & Munari (2003), and the extinction× coefficients− tion for the walkers was 0.392. The total line-of-sight reddening and is shown in Table 10. The magnitude was converted to the to the r band come from Davenport et al. (2014). The average from the0 dust maps of Schlafly & Finkbeiner(2011) is used to 6.Johnson Absolute system parameters using equations from Bessell & Brett(1988) surface brightness ratio in the WASP band (0.429 0.007) as place a prior on ∆ = E(B V) E(B V)map: and Carpenter(2001), and the APASS V-band magnitude, giv- an approximation to the V-band− − ratio,− and allowed the± external jktabsdim3 was used to calculate the absolute parameters for ing K = 9.267 0.097 mag. Although other apparent magnitudes error σ account for differences in the two bands. This ratio WASP0639-32, taking the relative radii and inclination from ext 1 ∆ 0 are available and± give similar distances, for example, d = 310 Pis(∆ used) = as a constraint, by using2 the≤ V-band surface brightness the detrended fit in Table 3, and the semi-amplitude velocitiesB exp( 0.5(∆/0.034) ) ∆ > 0 23 pc and d = 322 21 pc for APASS B,V, respectively, the± and B-K( relations− of Graczyk et al. (2017). The parameter-space and eccentricityV from Table 5. The results are presented in Ta- K-band distance was± chosen as it is the least sensitive to red- was explored using a maximum likelihood approach, using an ble 10. log gMR is used to denote a surface gravity obtained The 0.034 is a constant from Maxted et al.(2014), and is the dening. Also listed in this table, is the parallax from Gaia DR1 emcee, (Foreman-Mackey et al. 2013) MCMC procedure, with directly from the mass and radius of the star. jktabsdim also offset between reddening maps and the values derived from (Gaia Collaboration et al. 2016) and its associated Gaia distance, 64 walkers, 1088 steps and 64 burn-in steps. All chains have calculates a distance estimate using the surface-brightness re- photometry of a number of A-type stars. dGaia for comparison. The distance from the K-band magnitude visually inspected to ensure suitable mixing, and via a running lations of Kervella et al. (2004). The 2MASS Ks apparent mag- The resulting temperatures were T1 = 6340 190 K and agrees well with dGaia. mean check to ensure convergence. The median acceptance± frac- nitude has been used to estimate a distance, dK, to WASP0639- T2 = 5320 170 K with reddening of E(B V) = 0.067 0.036 The quoted uncertainties in the masses are 0.37% and 0.36% tion for the± walkers was 0.392. The total line-of-sight− reddening± 32 and is shown in Table 10. The magnitude was converted to and σext = 0.043 0.017. The parameter values are as the for M and M , respectively, while the uncertainties in the radii from the dust maps± of Schlafly & Finkbeiner (2011) is used to the Johnson1 system2 using equations from Bessell & Brett (1988) median of the posterior distributions, while the uncertainties are are 1.27% and 1.12% for R1 and R2, respectively. For the masses, theplace standard a prior deviations. on ∆ = E(B FigureV)9 showsE(B theV) residualsmap: from the fit. and Carpenter (2001), and the APASS V-band magnitude, giv- − − − ingthisK is the= same9.267 level0. of097 precision mag. Although as was obtained other apparent for the evolved mag- Overall, by taking the weighted mean of the temperatures binary, AI Phe (Kirkby-Kent± et al. 2016), meaning that like AI from each technique for each star (excluding spectroscopy with nitudes are available and give similar distances, for example, dPhe,= the310 parameters23 pc and ofd WASP0639-32= 322 21 pc will for APASSbe suitableB,V forrespec- con- a free surface1 gravity), the effective∆ temperatures0 are found to strainingB the± helium abundanceV ± in stellar evolutionary models. P(∆) = 2 ≤ tively, the4K-band distance was chosen as it is the least sensitive be 6330 exp(50 K and0.5(5400∆/0.034)80 )K for∆ > the0 primary and secondary, Figure 10 shows the correlation between M1 and M2, calculated respectively.(± Note− that in these± calculations, an additional 100 K to reddening. Also listed in this table, is the parallax from Gaia DR1from (GaiaK1, K2 Collaboration, and e values et explored al. 2016) during and its the associated MCMC in Gaia Sect. dis-4. has been added to the uncertainty in the temperature for the pri- The formulae recommended in Torres et al.(2010) were used for tance, dgaia for comparison. The distance from the K-band mag- maryThe 0.034 star obtained is a constant from the fromHα Maxtedfitting, dueet al. to (2014), the uncertainty and is the in the calculation as they are same as the formulae used in JKTAB- nitude agrees well with dgaia. theoffset continuum between placement,reddening maps and the and uncertainty the values derived from EW from fit withpho- SDIM. The period and inclination were fixed for this calculation. The quoted uncertainties in the masses are 0.37% and 0.36% atometry fixed log of ag numberhas been of taken A-type as 50 stars. K. The projected rotational velocity, v sin i, of both stars has forbeenM1 measuredand M2, respectively,using the cross-correlation while the uncertainties technique in ( theBouvier radii The resulting temperatures were T1 = 6340 190 K and are 1.27% and 1.12% for R and R , respectively. For the masses, ± 2013). The spectroscopic1 parameters2 from the fixed log g 6.T2 Absolute= 5320 170 parameters K with reddening of E(B V) = 0.067 0.036 this is the same level of precision as was obtained for the evolved ± − ± solution in Table6, were used to generate synthetic spectra with and σext = 0.043 0.017. The parameter values are as the me- binary, AI Phe (Kirkby-Kent et al. 2016), meaning1 that like AI JKTABSDIM3 was± used to calculate the absolute parameters for v sin i values ranging from 2.0 to 9.0 km s− . The spectra were dian of the posterior distributions, while the uncertainties are the Phe, the parameters of WASP0639-32 will be suitable for con- WASP0639-32, taking the relative radii and inclination from the generated using solar abundances from Asplund et al.(2009), standard deviations. Figure 9 shows the residuals from the fit. straining the helium abundance in stellar evolutionary models. detrended fit in Table3, and the semi-amplitude velocities and MARCS.GES (Gustafsson et al. 2008) model atmospheres and Figure 104 shows the correlation between M and M , calculated eccentricityOverall, from by taking Table5 the. The weighted results aremean presented of the temperatures in Table 10. the VALD line-list (Kupka et al. 2011). Each1 synthetic2 spectrum from K , K and e values explored during the MCMC in Sect. 4. logfromg eachis technique used to denote for each a surfacestar (excluding gravity spectroscopy obtained directly with was cross-correlated1 2 with the NARVAL solar spectrum (Aurière MR The formulae recommended in Torres et al. (2010) were used for froma free the surface mass gravity), and radius the of eff theective star. temperaturesJKTABSDIM arealso found calcu- to 2003) within iSpec to set up a relation between v sin i and the the calculation as they are same as the formulae used in jktabs- latesbe 6330 a distance50 K and estimate 5400 using80 K the for surface-brightness the primary and secondary, relations full-width half-maximum (FWHM) of the cross-correlation respectively.± Note that in these± calculations, an additional 100K dim. The period and inclination were fixed for this calculation. of Kervella et al.(2004). The 2MASS Ks apparent magnitude peak. Each observed spectrum was cross-correlated with the has been added to the uncertainty in the temperature for the pri- has been used to estimate a distance, dK, to WASP0639-32 same solar spectrum and the FWHM was obtained for both stars. mary star obtained from the Hα fitting, due to the uncertainty in After3 http://www.astro.keele.ac.uk/jkt/codes/jktabsdim. taking the mean and standard deviation of the resulting 3thehttp://www.astro.keele.ac.uk/jkt/codes/jktabsdim. continuum placement, and the uncertainty from EW fit with html htmla fixed log g has been taken as 50 K. 44 Produced using corner.py (Foreman-Mackey(Foreman-Mackey 2016 2016).).

A135,Article page number, 10 of page 15 10 of 16page.16 J.J. A. A. Kirkby-Kent Kirkby-Kent et et al.: al.: WASP0639-32: WASP0639-32: A A new new detached detached eclipsing eclipsing binary binary system system

SchlattlThe 2008) microphysics and include used the in initial these helium models abundance, is describedYi, ini- in tialSerenelli metallicity, et al.Z(2013i, and) mixing-length and Weiss & parameter, Schlattl(2008αml),, as but free we pa- rameters.provide a brief summary here. The convection is described by the standardThe model mixing grid length covers theory six of initial Kippenhahn helium abundances, & Weigert(1990Yi =), where0.231, 0 the.251 solar, 0.271 mixing, 0.291, 0 length.311, 0 is.331αmland, = five1.801 differentusing mix- the ing{Grevesse length & parameters, Noels(1993α) solar= 1 composition..598, 1.698} , 1 Due.798 to, 1 the.898 effects, 1.989 of, ml { } yieldingdiffusion, 30 the combinations initial solar in composition total. For each is found pair to of beYi[Feand/H]αmli =, there+0.06 are. Molecular 15 values opacities for Zi, covering from Ferguson a range et from al.(2005 0.00307) com- to 0.0772plement with the equal OPAL spacing opacities in fromlog Z Iglesiasspace. For & Rogers each point(1996 on). anConvective evolutionary mixing track, is described [Fe/H]s is in calculated terms of a usingdiffusive [Fe process,/H]s = logwith10( theZs/X diffusions) log10 coefficient,(0.02439),D wherec, being 0.02439 givenis by the solar value from Grevesse− & Noels (1993). Z and X are the model metal 1 s s fractionDc = α andmlHp modelvc, hydrogen fraction, respectively. The evo-(9) lutionary3 tracks cover a mass range of 0.7-2.0 M in steps of 0.02 M . where vc is the convective velocity and αmlHp is the local mix- ingThe length. microphysics Convective overshootingused in these is described models is by described the diffusive in Serenelliprocess (Freytag et al. (2013) et al. 1996 and)Weiss given by & Schlattl (2008), but we provide a brief summary here. The convection is described by the standard mixing2z length theory of Kippenhahn & Weigert D = D exp − , (10) (1990),0 wheref the h solar mixing length is αml, = 1.801 using the Grevesse & Noelsp ! (1993) solar composition. Due to the ef- fectswhere off diisff ausion, free parameter the initial dictating solar composition the extent of is the found overshoot- to be [Feing,/H]D0i is= the +0 diffusion.06. Molecular coefficient opacities within from the convective Ferguson border et al. Fig. 10. Density distribution showing the correlation between M1 and (2005) complement the OPAL opacities from Iglesias & Rogers Fig. 10. Density distribution showing the correlation between M1 and and z is the distance to the convective border. hp is a function of M2. A grey cross marks the measured values as shown in Table 10. (1996). Convective mixing is described in terms of a diffusive M2. A grey cross marks the measured values as shown in Table 10. the pressure scale height (Hp) and the thickness of the convective process,core (∆R withCZ) given the di asffusion coefficient, Dc, being given by FWHMs, the established relation for each star was used to 2 findThe the projected corresponding rotationalv sin i velocity,, the resultsv sin ofi, of which both are stars shown has 1 ∆RCZ Dhc = HαmlHminpvc 1, . (11)(9) beenin Table measured 10. Also using included the cross-correlation in Table 10 are technique the synchronous (Bouvier p 3 P × H  P !  2013).velocities Thevsynch spectroscopicfor both stars, parameters which are from calculated the fixed in logJKTABg so--   where vc is the convective velocity and αmlHp is the local mix- lutionSDIM. in Comparisons Table 6, were between used tov generatesin i and syntheticvsynch show spectra that with both This definition of hp ensures the overshooting region is limited 1 ing length. Convective overshooting is described by the diffusive vstarssin i arevalues almost ranging rotating from synchronously. 2.0 to 9.0 km For s− the. The primary spectra star were the processgeometrically (Freytag to et a al. portion 1996) ofgiven the by convective region, in cases generateddifference using is sufficient solar abundances to say that is from sub-synchronous, Asplund et al. although (2009), where the convective region is small e.g., where ∆RCZ < Hp MARCS.GESthere maybe systematic (Gustafsson uncertainties et al. 2008) that model have atmospheres not been taken and (Magic et al. 20102z ). If ∆RCZ > Hp, the geometric limit does not theinto VALD consideration, line-list (Kupka which may et al. alter 2011). the Each outcome. synthetic One spectrum example Dhave= D an0 exp effect.− In this case, our choice of f = 0.020 leads to(10) an f hp waswould cross-correlated be the effect of with microturbulence the NARVAL in solarthe synthetic spectrum spectra. (Au- extension of the overshoot! 0.25Hp. rièreA possible 2003)explanation within iSpec for to the set nature up a relation of the primary between isv sin thati and it is The description of atomic∼ diffusion is the same as is where f is a free parameter dictating the extent of the overshoot- theevolving full-width on a timescale half-maximum that is (FWHM) more rapid of than the cross-correlation the timescale for described in Kirkby-Kent et al.(2016), and follows the equations ing, D is the diffusion coefficient within the convective border peak.synchronisation. Each observed spectrum was cross-correlated with the of Burgers0 (1969) and the method of Thoul et al.(1994). The and z is the distance to the convective border. h is a function of same solar spectrum and the FWHM was obtained for both stars. parameterisation of VandenBerg et al.(2012) isp used to include the pressure scale height (H ) and the thickness of the convective After taking the mean and standard deviation of the resulting extra macroscopic mixing byp extending the convective envelope. core (∆R ) given as FWHMs,7. Implication the established for stellar relation evolutionary for each star models was used to find For main-sequenceCZ stars, the effects from stellar winds and the corresponding v sin i, the results of which are shown in Ta- radiative acceleration are not considered in the models. These 7.1. The models ∆R 2 ble 10. Also included in Table 10 are the synchronous velocities heffects= H becomemin 1 relevant, CZ at higher masses and work to limit(11) the vWithfor uncertainties both stars, onwhich the are masses calculated of less in thanjktabsdim 0.5%. Compar- and one p P × H synch atomic diffusion. WithoutP ! the mitigating effects of extra mixing isonscomponent between evolvedv sin i offand ofv theshow main-sequence, that both stars WASP0639-32 are almost   synch or winds, metals on the stellar surface, would become depleted rotatingis a good synchronously. binary system For for the testing primary stellar star the evolutionary difference is mod- suf- Thisby an definition amount of thathp isensures greater the than overshooting what is observed region is (Önehag limited ficientels (Torres to say et that al. is2010 sub-synchronous,). The model tracks although that there we tested, maybe were sys- geometricallyet al. 2014). to a portion of the convective region, in cases tematicproduced uncertainties using the Garching that have Stellar not been Evolution taken into Code consideration, (GARSTEC, where the convective region is small e.g. where ∆RCZ < Hp whichWeiss &may Schlattl alter the2008 outcome.) and include One theexample initial would helium be abundance, the effect (Magic7.2. Input et dataal. 2010). If ∆RCZ > Hp, the geometric limit does ofYi, microturbulence initial metallicity, inZ thei, and synthetic mixing-length spectra. parameter,A possibleα expla-ml, as not have an effect. In this case, our choice of f = 0.020 leads to nationfree parameters. for the nature of the primary is that it is evolving on a anFor extension each star of in the WASP0639-32, overshoot 0. the25H vector. of observed param- ∼ p timescaleThe model that is grid more covers rapid six than initial the timescale helium abundances, for synchronisa-Yi = etersThe is d description= (T, ρ, M of, [Fe/H] atomics), diwhereffusionT is is the the effective same as temper- is de- tion.0.231, 0.251, 0.271, 0.291, 0.311, 0.331 and five different mix- scribedature, ρ inis Kirkby-Kent the mean density, et al. (2016),M is the and mass follows and the[Fe/H] equationss is the { } ing length parameters, αml = 1.598, 1.698, 1.798, 1.898, 1.989 , ofobserved Burgers surface (1969) metal and the abundance. method ofUsing Thoul et al. (1994). The { } yielding 30 combinations in total. For each pair of Yi and αml, parameterisation of VandenBerg et al. (2012) is used to include 3 7.there Implication are 15 values for stellar for Zi, evolutionary covering a range models from 0.00307 extra macroscopic3π mixinga by extending the convective envelope. ρ = , (12) to 0.0772 with equal spacing in log Z space. For each Forn main-sequenceGP2(1 + Q ) stars,R the effects from stellar winds and ra- 7.1. The models n n ! point on an evolutionary track, [Fe/H]s is calculated using diative acceleration are not considered in the models. These ef- With[Fe/H] uncertaintiess = log (Zs on/Xs the) masseslog (0 of.02439) less than, where 0.5% 0.02439 and one iscom- the fectsthe mean become density relevant is a atquantity higher that masses can beand calculated work to limit from the the 10 − 10 ponentsolar value evolved from o ffGrevesseof the main-sequence, & Noels(1993). WASP0639-32Zs and Xs are is the a atomicfractional diffusion. radii rn Without= (Rn/a the) obtained mitigating from effects the oflightcurve extra mixing solu- goodmodel binary metal system fraction for and testing model stellar hydrogen evolutionary fraction, models respectively. (Tor- ortion winds, and Kepler’s metals on laws, the meaning stellar surface, it is independent would become from depleted the mass resThe et evolutionary al. 2010). The tracks model cover tracks amass that we range tested, of were0.7–2.0 producedM in byestimates an amount obtained that is fromgreater the than spectroscopic what is observed orbit. (Önehag In this equa-et al. usingsteps of the 0.02 GarchingM . Stellar Evolution Code, (garstec, Weiss & 2014).tion, R is the radius for star n = 1, 2, a is the semi-major axis

Article number, pageA135, 11 of page 16page.16 11 of 15 A&A 615, A135 (2018) of the orbit, P is the orbital period and G is Newton’s gravita- 2 2 2 χtot, is calculated by summing χ1 and χ2 from the matching age tional constant (Maxted et al. 2015). Qn is a function of the mass slice. The best-fit parameters from the corresponding age-slices ratio (q = M2/M1), where Q1 = q and Q2 = 1/q. The densities are shown in Table 11 are for stars of the same age and with the of the two stars were found to be ρ1 = 0.1873 0.0071 ρ and same initial helium abundance. The primary star was chosen ± ρ2 = 2.023 0.073 ρ for the primary and secondary respec- to define the age of the system as its age was constrained more ± tively. By using M and ρ rather than M and R, the parameters by the observed parameters. Figure 11 demonstrates this, as in the log-likelihood can be assumed to be uncorrelated. The 2 χ1 (solid points) forms a much narrower minimum compared masses used are those stated in Table 10 and the temperatures 2 with χ2 (light grey open points) from the fit to the secondary are the weighted means that calculated at the end of Sect. 5.4. star’s parameters. This is due the evolved nature the primary We use the metallicities from Table6 using a fixed log gs, but star. Stars will spend only a small fraction of their life on the assume uncertainties of 0.1 dex to account take into consider- ± subgiant branch, which in itself is a strong constraint on the age ation some of the uncertainties mentioned in Jofré et al.(2017). of a subgiant star, and the tight observational constraints limit The grid of models described in Sect. 7.1 is quite coarse com- it further. pared with the uncertainties on the masses and densities, and Individually, the hotter primary star strongly favours an there is no interpolation between the models. As such, the uncer- initial helium abundance of Yi = 0.271. A higher helium tainties were increased to 0.0073 and 0.0050, for M1 and M2 abundance means a higher mean molecular weight, which in respectively, to allow more evolutionary tracks to be explored. turn means a higher luminosity (Kippenhahn & Weigert 1990), An uncertainty of 0.005 M , covers a range of 2–σ from the ± and therefore temperature, when M and ρ are fixed. However, centre of a mass bin. with small uncertainties on the temperatures providing such tight constraints, it is the parameters with weaker constraints, 7.3. Bayesian analysis such as αml and [Fe/H] that have to adapt. From the solutions for 2 In order to explore this complex parameter space set out by the the secondary star, the smallest χ is seen for Yi = 0.231, which models, we use a Bayesian framework. The set of model param- is lower than that of the primary component. This solution sacrifices the temperature in order to improve the fit to the eters is given by m = (τ, M, αml, [Fe/H]i), where τ, M, αml, and mass and radius. This value is in fact less than the primordial [Fe/H]i are the age, mass, mixing length, and initial metal abun- dance respectively. The initial metal abundance differs from the helium abundance at the time of the big-bang nucleosynthesis, observed surface abundance due to diffusion. YBBN = 0.2485,(Steigman 2010). If this solution is excluded for The probability distribution function p(m d) is propor- this reason, Yi = 0.271 is the next best solution for the secondary tional to p(m) (d m). (d m) = exp( χ2/2) is| the likelihood star. This matches the value found for the primary. 2 of observing theL | data Ld given| the model− m, assuming the After summing the χ from the individual stars, the best independent observed parameters and Gaussian uncertainties, helium abundance for the system as a whole is 0.271, although where it could be argued that a range between 0.231–0.271 could pro- vide reasonable solutions, using ∆χ2 = 1 as an estimate of a 2 2 2 tot (M Mobs) (ρ ρobs) (T Tobs) 68% confidence interval (Press et al. 1992). We refrain from χ2 = − + − + − 2 σ2 2 quoting a true confidence region due the discontinuous nature σM ρ σT 2 of the helium abundances tested, and because there is no inter- [Fe/H]s [Fe/H]s,obs polation between the individual tracks. Better solutions could + − . (13) exist between the models. Interpolation has not been employed  σ2  [Fe/H]s in these models due to the large number of parameters which Observed parameters are denoted by the “obs” subscript and would need to be considered. If the same estimate of a confi- χ2 each σ represent the uncertainty of the parameter. p(m) is the dence interval for 1 is used then the range of helium abundances = . = . product of the priors on each of the model parameters given by is Yi 0 251–0.291, however Yi 0 291 is disfavoured by the m τ secondary due to a high temperature and high metallicity. p( ) = p( )p(M)p([Fe/H]i). A flat prior is applied to the ini- 2 tial surface metallicity, although this usually has little effect The lowest χtot suggests the age of WASP0639-32 is as the surface metallicity is constrained by the observed value. 4.22 Gyr. Taking the uncertainty of Y into consideration, as 1 χ2 . +0.8 = . ± A very loose prior is used on the age aimed at keeping the in 1, the overall age of the system is 4 2 0.1 Gyr. The Yi 0 231 − star’s age within the age of the universe while allowing room solution was excluded as it is less than YBBN. The age estimate for the models to explore slightly older ages in order provide does not consider the potential effects of different overshooting a more realistic age estimate. The prior on the age is set to efficiencies, f , or different parameterisations of the overshoot- 0 < τ < 17.5 Gyr. ing. The age of the primary star may be particularly sensitive to the overshooting, as its mass places the star on the bound- Each Yi value was considered independently and calculations ary for developing convective cores (1.1–1.2 M ; Lebreton et al. were split into slices of age covering 300 Myr, e.g., 0–300 Myr, 300–600 Myr, etc. and the age is the weighted average over the 2014). A full investigation into the overshooting parameter is bin. This is to allow comparisons between the two stars and not possible with our current set of models, but there are a few to choose results where age and initial helium abundance were simple tests to show how our choice of overshooting may affect common to both star. the age estimate. For the tests, we consider a 1.16 M star, with [Fe/H] = 0.3 and α = 1.70. These are the best tracks for − ml 7.4. Model comparisons the Y = 0.271 solution for the primary star. Figure 12 shows the tracks for three different overshoot parameterisations. The track Once the Bayesian analysis for each star and for each Yi was marked “standard” is the same parameterisation that is described complete, we used the best-fit age from the primary star’s results in Sect. 7.1 and that has been used throughout the modelling so to define the age of the system, and then found the matching age far, i.e., for a 1.16 M star where the geometric cut plays a role to get the parameters for the secondary. The total chi-squared, and the overshooting is partially suppressed. We also present the

A135, page 12 of 15 J. A. Kirkby-KentJ. et A. al.: WASP0639-32:Kirkby-Kent A newet al.: detached WASP0639-32: eclipsing binary system A new detached eclipsing binary system

Fig. 11. Variation of the overall fit to the observed parameters at different ages, for the primary (black) and secondary (grey) com- ponents. Each panel represents models calcu- lated with a different initial helium abundance, which is given by the Yi above the panel. && Fig. 11. Variation of the overall fit to the observed parameters at different ages,AA forAA the proofs: proofs: primary (black)manuscriptmanuscript and secondary no. no. (grey) j0639_paper j0639_paper components. Each panel represents models calculated with a different initial helium abundance, which is given by the Yi above the panel.

Table 11. Best-fit evolutionary models for the primary and matching age model for the secondary, using different initial helium abundances Yi. 0.80.8 PrimaryPrimary SecondarySecondary 0.80.8 Parameter Yi Observed Symbol Unit 0.231 0.251 0.271 0.291 0.311 0.331 Value0.60.6 Error τ 0.70.7 best (Gyr) 5.31 5.05 4.22 4.12 3.55 2.98 --0.40.4 T1 (K) 6317 6297 6330 6340 6380 6356 6330 50 ) ) ) )

⊙ ⊙ [Fe/H] - 0.47 0.35 0.35 0.23 0.23 0.22 0.33⊙ ⊙ 0.10 s,1 − − − − − − − M1 (M ) 1.1539 1.1552 1.1568 1.1568 1.1495 1.1578 1.15440.2 0.00730.2 0.60.6 L/L L/L R1 (R ) 1.8324 1.8281 1.8331 1.8407 1.8503 1.7897 1.834L/L L/L 0.023

ρ1 (ρ ) 0.1866 0.1882 0.1847 0.1847 0.1806 0.2010 0.18730.0 0.00710.0

log( log( 0.50.5 log g1 - 3.97 3.98 3.98 3.97 3.96 4.00 3.974log( log( 0.011 αml1 - 2.043 2.048 1.704 1.921 1.639 1.501 -- Y=0.291Y=0.291 2 −0.2−0.2 χ1 - 1.96 0.53 0.10NoNo 1.37 OvershootingOvershooting 3.31 5.39 -- Y=0.271Y=0.271 0.40.4 T2 (K) 5363 5397 5410StandardStandard 5480 5487 5520 5400−0.4−0.4 80 Y=0.251Y=0.251 [Fe/H]s,2 - 0.53 0.45 0.35 NoNo0 . 26GeometricGeometric0.16 CutCut 0.13 0.45 0.11 Y=0.231Y=0.231 − − − − − − − M2 (M ) 0.7784 0.7746 0.7766 0.7784 0.7795 0.7795 0.7833 0.0050 0.30.3 70007000R2 68006800 (R66006600) 0.724564006400 0.725162006200 0.726360006000 0.731758005800 0.732256005600 0.7339 0.7291 0.008170007000 65006500 60006000 55005500 50005000

ρ2 (ρ ) 2.041 2.027 2.021 1.982 1.979 1.966 2.023 0.073 TTeffeff[K][K] TTeffeff[K][K] log g2 - 4.61 4.61 4.61 4.60 4.60 4.60 4.607 0.010

αml2 - 1.810 1.864 1.880 1.962 1.973 1.754 -- Fig. 12. Evolutionaryχ2 - tracks1.64 in the temperature-luminosity 2.83 2.53 5.07 8.89 plane 11.67 for a -- Fig.Fig. 12. 12. EvolutionaryEvolutionary2 tracks tracks in in the the temperature-luminosity temperature-luminosity plane plane for for a a Fig.Fig. 13. 13.EvolutionaryEvolutionary tracks tracks in in the the temperature-luminosity temperature-luminosity plane plane for for the the 1.16 M star,χ2 with [Fe/H] = 0.3, αml = 1.70, and Y = 0.271, for three 1.161.16 M M star,star,tot with with [Fe [Fe- //H]H] ==− 3.6000..3,3, ααmlml 3.36== 11..7070 2.63 and and YY 6.44== 00..271,271, 12.20 for for 17.06 three three primaryprimary-- (black) (black) and and secondary secondary (grey) (grey) components components for for didifferent difffferenterent helium helium parameterisationsparameterisationsparameterisations of of the the overshooting overshooting−− parameter. parameter. parameter. Crosses Crosses Crosses mark mark mark the the the best- best- abundances.abundances. Dashed, Dashed, YY == 00...291;291291;; solid, YY == 00...271;271271;; dotted, YY == 00..251;251251;; Y = . fitfitfit age age obtained obtained obtained from from the the YY ==000.271.271271fit fit fit in in Table Table 11 11 for for for the the the primary primary primary star star star dot-dashed,dot-dashed, YY == 00...231231.231.. All All tracks tracks are are plotted plotted from from an an age age of of 35 35 Myr. Myr. notin possible WASP0639-32. with our current All set tracks of models, arebut plotted there are from a few an ageis a poor of 40 choice Myr. for the primary star. It also shows that reducing simpleinin WASP0639-32. WASP0639-32. tests to show how Allour All choice tracks tracks of are are overshooting plotted plotted from mayfrom af- an an agethe age level of of 40 40of overshooting Myr. Myr. will haveTracksTracks little e closestff closestect on the the the resulting observed observed mass mass of of each each star star are are plotted. plotted. fect the age estimate. For the tests, we consider a 1.16 M star, age of the system. The same trends are seen for tracks with dif- with [Fe/H] = 0.3 and αml = 1.70. These are the best tracks for ferent helium abundances. Although, only one mass-track has thecase Y=0.271 where solution− there for the is primaryno overshooting star. Figure 12 shows and the casebeen considered where the here, geo- the smallthis uncertainties is0.00.0 beyond on the the observed capabilities of our current grid of models. One ff tracksmetricondaryondary for three cut component component di doeserent overshoot not prefers prefers play parameterisations. a role.a a mixing mixing The The lengthremoval length track masses that that of isthewould is about about geometric restrict solar. solar. the possiblepoint values to for note the overshooting. about this work is the different solar compositionsPrimaryPrimary markedThisThis ‘standard’ is is consistent consistent is the same with with parameterisation the the results results that is from fromdescribed 3D 3DThe radiative radiative effects of masshydrody- hydrody- uncertainties on the overshooting parame- SecondarySecondary incut Sect. means 7.1 and that the has overshooting been used throughout is the overestimated modelling so ter hasfor been the discussed star, and in Valle etused al. (2017).0.50.5 between It is worth the noting spectroscopy (Asplund et al. 2009) and these far,providesnamicnamic i.e. for amodels models 1.16 an M upperstar of of where Magic Magic limit the that etgeometric et al. al. is (2015).approximately (2015). cut plays There There a role isthat is equal some some any uncertainty to degeneracy degeneracy 0.3 H inp the. overshooting used for the primary star models (Grevesse & Noels 1993). This may introduce some andbetweenbetween theFigure overshootingYY 12andand isshows partiallyαα asas thatsuppressed. they they removing both both We also a affff present theectectthe geometric the the temperature, temperature,could affect cut the results parameters but but the the in that are presented for the secondary case where there is no overshootingmlml and the case where the ge- (as they are matched to the age ofdiscrepancies the primary star) and in therefore the modelling of the temperatures, although by 2 1.01.0 ometricaextentextent track cut of of does that the the not is degeneracy degeneracy play a poor a role. choiceThe is isremoval not not for fully fullyof the the geometric understood. understood. primaryχtot star.. However, The The It degeneracyalso degeneracy as discussed shows above, the effect should be small.

using⊙ ⊙ a temperature that is obtained as a weighted mean from cut means the overshooting is overestimated for the star, and pro- 2 thatwouldwould reducing need need to to the be be level explored explored of overshooting in in more more detail, detail, will for for have aFor a strong strong little the lowest effect claim claimχtot solution, on to to the two stars use slightly differ- vides an upper limit that is approximately equal to 0.3 Hp. Figure multiple methods, this discrepancy should be reduced. As the ent mixing-lengths, with the more evolvedρ/ρ ρ/ρ primary star requir- 12thebebe shows made made resulting that removing about about age the the of geometric mixing mixing the system. cut lengths lengths results in The a compared compared track same that trends to to those those are by by seen Magic Magic for 1.51.5 ing a value that is less than themixing solar value. length The smaller parameter sec- has been included as a separate free tracksetet al. al. (2015), (2015), with different but but this this helium is is beyond beyond abundances. the the capabilities capabilities Although, of of our our only current current one parameter for both stars, it is possible that these free parameters mass-trackgridgrid of of models. models. has been One One considered point point to to note note here, about about the this thissmall work work uncertainties is is the the di diffff oner-er- Article number, page 13 ofY=0.291Y=0.291 16page.16 are masking2.02.0 discrepanciesY=0.271Y=0.271 between the models and observations, theentent solarobserved solar compositions compositions masses would used used between betweenrestrict the the the possible spectroscopy spectroscopy values (Asplund (Asplund for the i.e., by pickingY=0.251Y=0.251 a higher/lower mixing length it is possible to find etet al. al. 2009) 2009) and and these these models models (Grevesse (Grevesse & & Noels Noels 1993). 1993). This This Y=0.231Y=0.231 overshooting. The effects of mass uncertainties on the overshoot- a better2.52.5 match to the temperatures. ingmaymay parameter introduce introduce has some some been discrepancies discrepancies discussed in Valle in in the the et modelling modelling al.(2017). ofof It is the the worth tem- tem- Figures70007000 13 and65006500 14 show6000 the6000 best fit55005500 evolutionary50005000 tracks for notingperatures,peratures, that although although any uncertainty by by using using in a a the temperature temperature overshooting that that used is is obtained obtained for the aspri- as a a the three best values of initial heliumTTeffeff[K][K] abundance, for each star. maryweightedweighted star meancould mean from fromaffect multiple multiple the parameters methods, methods, that this this are discrepancy discrepancy presented for should should the The points are plotted with the temperatures and luminosities secondarybebe reduced. reduced. (as As As they the the mixing mixing are matched length length to parameter parameter the age ofhas has the been been primary included included star) as as 2 Fig.fromFig. 14. 14. TableEvolutionaryEvolutionary 10. tracks tracks in in the the temperature-density temperature-density plane plane for for the the andaa separate separate therefore free freeχtot parameter parameter. However, for for as both both discussed stars, stars, above, it it is is possible possible the effect that that should these these primaryprimary (black) (black) and and secondary secondary (grey) (grey) components components for for di difffferenterent helium helium befreefree small. parameters parameters are are masking masking discrepancies discrepancies between between the the models models abundances.abundances. Dashed, Dashed, YY == 00..291;291; solid, solid, YY == 00..271;271; dotted, dotted, YY == 00..251;251; 2 andandFor observations, observations, the lowest χ i.e. i.e.tot solution, by by picking picking the a a two higher higher stars//lowerlower use slightly mixing mixing different length length it it dot-dashed,8.dot-dashed, DiscussionYY == 00..231.231. All All tracks tracks are are plotted plotted from from an an age age of of 35 35 Myr. Myr. mixing-lengths,isis possible possible to to find find with a a better better the more match match evolved to to the the temperatures. temperatures.primary star requiring a TracksTracks closest closest the the observed observed mass mass of of each each star star are are plotted. plotted. valueFiguresFigures that is 13 13 less and and than 14 14 show showthe solar the the best value.best fit fit The evolutionary evolutionary smaller secondary tracks tracks for for The trends in χ2 in Table 11 are quite clear for each star, making componentthethe three three best best prefers values values a mixingof of initial initial length helium helium that abundance, abundance, is about solar. for for each each This star. star. is it possible to identify the preferred values for Yi. However, with consistentTheThe points points with are are the plotted plotted results with with from the the 3D temperatures temperatures radiative hydrodynamic and and luminosities luminosities mod- numberthenumber priors of of ontracks tracks the to to mass meet meet being the the precision precision looser than of of the the the measured measured observed masses masses value, elsfromfrom of Table TableMagic 10. 10. et al.(2015). There is some degeneracy between Y andthereand densities densities is a chance would would the be be fit a a to huge huge the mass challenge, challenge, has been with with sacrificed the the current current in set setorder of of trackstracks reaching reaching 2222 000 000 in in number. number. An An alternative alternative would would be be to to and αml as they both affect the temperature, but the extent of the to provide a better≈≈ match to other parameters such as the temper- degeneracy is not fully understood. The degeneracy would need createatures.create a a A small small finer subsetgrid subset of of ofmodels, models models particularly around around the the in solution solution regards obtained toobtained the mass in in to8.8. be Discussion Discussion explored in more detail, for a strong claim to be made about thisandthis work, work, density using using parameters, a a higher higher resolution. resolution. would allow However, However, the tighter that that is is observation something something the mixing lengths compared to those by Magic et al.(2015), but thatconstraintsthat is is beyond beyond to the the be scope scopeused onof of this this these paper. paper. parameters One One approach approach and would taken taken forenable for the the TheThe trends trends in in χχ22 inin Table Table 11 11 are are quite quite clear clear for for each each star, star, mak- mak- binarybinary system system TZ TZ For, For, was was to to fix fix the the mass mass of of the the stars stars (Valle (Valle et et al. al. inging it it possible possible to to identify identify the the preferred preferred values values for for YYii.. However, However, 2017)2017) as as the the measured measured uncertainties uncertainties were were so so small small ( ( 00..001001MM ,, withwith the the priors priors on on the the mass mass being being looser looser than than the the observed observed value, value, GallenneGallenne et et al. al. 2016). 2016). Valle Valle et et al. al. (2017) (2017) also alsoA135, state state page±± that that 13 this this of 15 is is therethere is is a a chance chance the the fit fit to to the the mass mass has has been been sacrificed sacrificed in in order order notnot valid valid for for uncertainties uncertainties of of the the order order 0 0..0101MM .. The The uncertain- uncertain- toto provide provide a a better better match match to to other other parameters parameters such such as as the the temper- temper- tiesties for for the the stars stars in in WASP0639-32 WASP0639-32 lie lie between between these these two two cases cases atures.atures. A A finer finer grid grid of of models, models, particularly particularly in in regards regards to to the the mass mass (at(at 0 0..00430043MM ),), so so it it is is currently currently unclear unclear if if fixing fixing the the masses masses of of andand density density parameters, parameters, would would allow allow the the tighter tighter observation observation con- con- WASP0639-32WASP0639-32 would would hamper hamper the the determination determination of of the the helium helium straintsstraints to to be be used used on on these these parameters parameters and and would would enable enable the the he- he- abundance.abundance. liumlium abundance abundance to to be be constrained constrained further further by by making making the the best best χχ22 InitialInitial attempts attempts to to determine determine the the age age of of WASP0639-32 WASP0639-32 were were valuevalue more more distinct. distinct. As As a a test, test, the the tracks tracks were were also also fitted fitted using using the the donedone using using the the same same evolutionary evolutionary modelling modelling method method as as was was used used measuredmeasured uncertainties uncertainties on on the the the the masses masses and and densities, densities, and and this this forfor AI AI Phe Phe (Kirkby-Kent (Kirkby-Kent et et al. al. 2016). 2016). Here, Here, both both stars stars were were fit- fit- allowedallowedYYii toto be be constrained constrained to to the theYYii == 00..271271 solution. solution. However, However, tedted simultaneously simultaneously with with the the e effffectsects of of di difffferenterent mixing mixing lengths lengths thethe solutions solutions presented presented very very jagged jagged χχ22 minimisationsminimisations plots plots due due beingbeing explored explored independently independently of of the the initial initial helium helium abundance. abundance. toto the the lack lack of of interpolation interpolation in in the the models models particularly particularly for for the the sec- sec- TheThe lowest lowest χχ22 valuesvalues occurred occurred for for mixing mixing length length that that were were solar solar ondaryondary since since the the model model step-size step-size accounts accounts for for a a larger larger percentage percentage ((ααmlml == 11..78)78) and and∆∆YY == 00..0,0, and and yielding yieldingYYii == 00..257257 with with a a range range ofof the the mass mass for for the the secondary secondary component. component. Storing Storing the the required required ofof 00..020.020. The The two two modelling modelling methods methods use use di difffferenterent chemical chemical ±± ArticleArticle number, number, page page 14 14 of of 16page.16 16page.16 A&A 615, A135 (2018)

Table 11. Best-fit evolutionary models for the primary and matching age model for the secondary, using different initial helium abundances Yi.

A&A proofs: manuscript no. j0639_paper Parameter Yi Observed Symbol Unit 0.231 0.251 0.271 0.291 0.311 0.331 Value Error

0.8 τbest (Gyr) 5.31 5.05Primary 4.22 4.12 3.55 2.98 –– T 0.8 1 (K) 6317 6297Secondary 6330 6340 6380 6356 6330 50 0.6 [Fe/H] – 0.47 0.35 0.35 0.23 0.23 0.22 0.33 0.10 s,1 − − − − − − − M1 (M ) 1.1539 1.1552 1.1568 1.1568 1.1495 1.1578 1.1544 0.0073 0.7 0.4 ) ) R1 (R ) 1.8324 1.8281 1.8331 1.8407 1.8503 1.7897 1.834 0.023 ⊙ ⊙ 0.2 ρ1 (ρ ) 0.1866 0.1882 0.1847 0.1847 0.1806 0.2010 0.1873 0.0071 0.6 L/L L/L log g – 3.97 3.98 3.98 3.97 3.96 4.00 3.974 0.011 0.0 1 log( 0.5 log( αml1 – 2.043 2.048 1.704 1.921 1.639 1.501 –– −0.2 Y=0.2912 χ1 – 1.96 0.53 0.10 1.37 3.31 5.39 –– No Overshooting Y=0.271 0.4 T2 (K) 5363 5397 5410 5480 5487 5520 5400 80 Standard −0.4 Y=0.251 [Fe/H] – 0.53 0.45 0.35 0.26 0.16 0.13 0.45 0.11 No Geometric Cut Y=0.231 s,2 − − − − − − − 0.3 M2 (M ) 0.7784 0.7746 0.7766 0.7784 0.7795 0.7795 0.7833 0.0050 7000 6800 6600 6400 6200 6000 5800 5600 7000 6500 6000 5500 5000 R2 (R ) 0.7245 0.7251 0.7263 0.7317 0.7322 0.7339 0.7291 0.0081 Teff [K] Teff [K] ρ2 (ρ ) 2.041 2.027 2.021 1.982 1.979 1.966 2.023 0.073

log g2 – 4.61 4.61 4.61 4.60 4.60 4.60 4.607 0.010 Fig. 12. Evolutionary tracks in the temperature-luminosity plane for a Fig. 13. Evolutionary tracks in the temperature-luminosity plane for the αml2 – 1.810 1.864 1.880 1.962 1.973 1.754 –– 1.16 M star, with [Fe/H] = 0.3, αml = 1.70 and Y = 0.271, for three primary (black) and2 secondary (grey) components for different helium χ parameterisations of the overshooting− parameter. Crosses mark the best- abundances. Dashed,2 Y = 0.291;– solid, Y = 1.640.271; dotted, 2.83Y = 0. 2.53251; 5.07 8.89 11.67 –– 2 fit age obtained from the Y = 0.271 fit in Table 11 for the primary star dot-dashed, Y = 0χ.231.tot All tracks– are plotted3.60 from an 3.36 age of 35 2.63Myr. 6.44 12.20 17.06 –– in WASP0639-32. All tracks are plotted from an age of 40 Myr. Tracks closest the observed mass of each star are plotted.

0.0 The uncertainties for the stars in WASP0639-32 lie between ondary component prefers a mixing length that is about solar. Primary these two cases (at 0.0043 M ), so it is currently unclear if fixing This is consistent with the results from 3D radiative hydrody- Secondary 0.5 the masses of WASP0639-32 would hamper the determination namic models of Magic et al. (2015). There is some degeneracy of the helium abundance. α ff between Y and ml as they both a ect the temperature, but the Initial attempts to determine the age of WASP0639-32 were extent of the degeneracy is not fully understood. The degeneracy 1.0

⊙ done using the same evolutionary modelling method as was used would need to be explored in more detail, for a strong claim to for AI Phe (Kirkby-Kent et al. 2016). Here, both stars were fit- ρ/ρ 1.5 be made about the mixing lengths compared to those by Magic ted simultaneously with the effects of different mixing lengths et al. (2015), but this is beyond the capabilities of our current being explored independently of the initial helium abundance. grid of models. One point to note about this work is the differ- Y=0.291 2.0 Y=0.271 The lowest χ2 values occurred for mixing length that were solar ent solar compositions used between the spectroscopy (Asplund Y=0.251 (αml = 1.78) and ∆Y = 0.0, and yielding Yi = 0.257 with a range et al. 2009) and these models (Grevesse & Noels 1993). This 2.5 Y=0.231 of 0.020. The two modelling methods use different chemical may introduce some discrepancies in the modelling of the tem- 7000 6500 6000 5500 5000 abundances± meaning direct comparison should not be made, but peratures, although by using a temperature that is obtained as a Teff [K] it worth noting that this value matches the two initial helium weighted mean from multiple methods, this discrepancy should 2 abundances with the lowest χtot in Table 11. The spectroscopic be reduced. As the mixing length parameter has been included as Fig.Fig. 14. 14. EvolutionaryEvolutionary tracks tracks in in the the temperature-density temperature-density plane plane for for the the parameters obtained using a free log g were also tested using the a separate free parameter for both stars, it is possible that these primaryprimary (black) (black) and and secondary secondary (grey) (grey) components components for for different different helium helium method of Kirkby-Kent et al.(2016) to see if the evolution of the free parameters are masking discrepancies between the models abundances.abundances. Dashed, Dashed,YY == 00..291291;; solid, solid,YY ==00..271271;; dotted, dotted,YY ==00..251251;; system differs. With the primary star set with a temperature of and observations, i.e. by picking a higher/lower mixing length it dot-dashed,dot-dashed,YY ==00.231.231.. All All tracks tracks are are plotted plotted from from an an age age of of 35 35 Myr. Myr. Tracks closest the observed mass of each star are plotted. 6730 K, a good fit could not be found. The best solutions were is possible to find a better match to the temperatures. Tracks closest the observed mass of each star are plotted. suggesting a mixing length larger than 2.32, and a helium abun- Figures 13 and 14 show the best fit evolutionary tracks for dances larger than 0.31. Even these solutions were very poor fits, the three best values of initial helium abundance, for each star. thenumber helium of abundancetracks to meet to be the constrained precision of further the measured by making masses the with the models unable to match the densities and temperatures The points are plotted with the temperatures and luminosities best χ2 value more distinct. As a test, the tracks were also fitted of both stars. This highlights the need to ensure accurate and con- from Table 10. and densities would be a huge challenge, with the current set of usingtracks the reaching measured22 uncertainties 000 in number. on An the alternative masses and would densities, be to sistent results for parameters that are used in stellar evolutionary andcreate this a allowed small subset≈Yi to ofbe models constrained around to the theY solutioni = 0.271 obtainedsolution. in modelling. It also highlights that caution should be used if the However, the solutions presented very jagged χ2 minimisations only source for a surface gravity is a spectroscopic value. Mortier 8. Discussion this work, using a higher resolution. However, that is something plotsthat is due beyond to the the lack scope of interpolation of this paper. Onein the approach models taken particularly for the et al.(2013) shows that this issue is most prevalent at tempera- The trends in χ2 in Table 11 are quite clear for each star, mak- forbinary the secondary system TZ since For, was the tomodel fix the step-size mass of accounts the stars for (Valle a larger et al. tures that deviates significantly from the Sun, but as yet, an exact percentage of the mass for the secondary component. Storing the cause has not been found. Porto de Mello et al.(2008) looked at ing it possible to identify the preferred values for Yi. However, 2017) as the measured uncertainties were so small ( 0.001 M , with the priors on the mass being looser than the observed value, requiredGallenne number et al. 2016). of tracks Valle to meet et al. the (2017) precision also of state the± that measured this is the atmospheric parameters for α Centauri A and B. They noted there is a chance the fit to the mass has been sacrificed in order massesnot valid and for densities uncertainties would of the be order a huge 0.01 challenge,M . The uncertain- with the a disagreement between photometric and spectroscopic effective current set of tracks reaching 22 000 in number. An alternative temperature scales for α Centauri A, with the spectroscopically to provide a better match to other parameters such as the temper- ties for the stars in WASP0639-32≈ lie between these two cases atures. A finer grid of models, particularly in regards to the mass would(at 0.0043 be toM create), so a it small is currently subset ofunclear models if fixingaround the the masses solution of derived temperature being higher than those obtained photomet- and density parameters, would allow the tighter observation con- obtainedWASP0639-32 in this work, would using hamper a higher the determination resolution. However, of the helium that is rically. This is similar to what has been found for the primary straints to be used on these parameters and would enable the he- somethingabundance. that is beyond the scope of this paper. One approach star of WASP0639-32. Porto de Mello et al.(2008) suggest non- lium abundance to be constrained further by making the best χ2 takenInitial for the attempts binary to system determine TZ For, the age was of to WASP0639-32 fix the mass of were the local thermodynamic equilibrium (NLTE) effects as a cause for value more distinct. As a test, the tracks were also fitted using the starsdone ( usingValle the et al. same 2017 evolutionary) as the measured modelling uncertainties method as was were used so the offset. As no NLTE effects are considered in the analysis in measured uncertainties on the the masses and densities, and this smallfor AI ( Phe0.001 (Kirkby-KentM , Gallenne etal. et al. 2016). 2016 Here,). Valle both et al. stars(2017 were) also fit- this paper, it is possible that this is the cause of the disagree- state that± this is not valid for uncertainties of the order 0.01 M . ment between the temperatures obtained with the fixed and free allowed Yi to be constrained to the Yi = 0.271 solution. However, ted simultaneously with the effects of different mixing lengths the solutions presented very jagged χ2 minimisations plots due being explored independently of the initial helium abundance. to the lack of interpolation in the models particularly for the sec- A135,The lowest page 14χ of2 values 15 occurred for mixing length that were solar ondary since the model step-size accounts for a larger percentage (αml = 1.78) and ∆Y = 0.0, and yielding Yi = 0.257 with a range of the mass for the secondary component. Storing the required of 0.020. The two modelling methods use different chemical ± Article number, page 14 of 16page.16 J. A. Kirkby-Kent et al.: WASP0639-32: A new detached eclipsing binary system surface gravities. With further data releases to come from Gaia, Freytag, B., Ludwig, H.-G., & Steffen, M. 1996, A&A, 313, 497 it will be possible to obtain model independent effective temper- Gaia Collaboration (Brown, A. G. A., et al.) 2016, A&A, 595, A2 ature measurements using the angular diameter and integrated Gallenne, A., Pietrzynski,´ G., Graczyk, D., et al. 2016, A&A, 586, A35 Goodman, J., & Weare, J. 2010, Commun. Appl. Math. Comput. Sci., 5, 65 fluxes of the stars. Graczyk, D., Smolec, R., Pavlovski, K., et al. 2016, A&A, 594, A92 Graczyk, D., Konorski, P., Pietrzynski,´ G., et al. 2017, ApJ, 837, 7 9. Conclusion Grevesse, N., & Noels, A. 1993, in Origin and Evolution of the Elements, eds. N. Prantzos, E. Vangioni-Flam, & M. Casse, 15 We have determined the masses and radii of the stars in a previ- Gustafsson, B., Edvardsson, B., Eriksson, K., et al. 2008, A&A, 486, 951 Heiter, U., Jofré, P., Gustafsson, B., et al. 2015, A&A, 582, A49 ously unstudied binary system, WASP0639-32, to the precision Henden, A. A., Welch, D. L., Terrell, D., & Levine, S. E. 2009, Am. Astron. Soc. of 0.37% and 0.36% for M1 and M2 respectively and 1.27% and Meeting Abstracts, 214, 669 1.12% for the R1 and R2, respectively. Taking the weighted mean Høg, E., Fabricius, C., Makarov, V. V., et al. 2000, A&A, 355, L27 of the temperature from each technique for each star (excluding Iglesias, C. A., & Rogers, F. J. 1996, ApJ, 464, 943 spectroscopy with a free surface gravity), the effective tempera- Jofré, P., Heiter, U., Soubiran, C., et al. 2014, A&A, 564, A133 Jofré, P., Heiter, U., Worley, C. 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