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CoRoT 105906206: a short-period and totally eclipsing binary with a Delta Scuti type pulsator

Eclipsing binary systems with pulsating components allow the determination of several physical parameters of the stars, such as mass and radius, that, when combined with the pulsation properties, can be used to constrain the modeling of stellar interiors and evolution. Hereby, we present the results of the study of CoRoT 105906206, an eclipsing binary system with a pulsating component located in the CoRoT LRc02 field. The analysis of the CoRoT light curve was complemented by high-resolution spectra from the Sandiford at McDonald Observatory and FEROS at ESO spectrographs, which revealed a double-lined spectroscopic binary. We used an iterative procedure to separate the pulsation-induced photometric variations from the eclipse signals. First, a Fourier analysis was used to identify the significant frequencies and amplitudes due to pulsations. Second, after removing the contribution of the pulsations from the light curve we applied the PIKAIA genetic-algorithm approach to derive the best parameters that describe the orbital properties of the system. The light curve cleaned for pulsations contains the partial eclipse of the primary and the total eclipse of the secondary. The system has an orbital period of about 3.694 days and is formed by a primary star with mass M1 = 2.25 +/- 0.04 solar masses, radius R1 = 4.24 +/- 0.02 solar radii, and effective temperature Teff1 = 6750 +/- 150 K, and a secondary with M2 = 1.29 +/- 0.03 solar masses, R2 = 1.34 +/- 0.01 solar radii, and Teff2 = 6152 +/- 162 K. The best solution for the parameters was obtained by taking into account the asymmetric modulation observed in the light curve, known as the O'Connell effect, presumably caused by Doppler beaming. The analysis of the Fourier spectrum revealed that the primary component has p-mode pulsations in the range 5-13 c/d, which are typical of Delta Scuti type stars.


Introduction
The study of eclipsing binary systems has gained a new perspective since the beginning of the CoRoT space mission (Baglin et al. 2006). The superb photometry achievable from space, combined with ground-based spectroscopy, allows a precise and independent determination of mass and radius of the components, among other parameters. In particular, by studying pulsating stars in eclipsing binaries, such as the Classical γ Dor and δ Sct type variables, one takes advantage of this parameter determination for the asteroseismic modeling of stellar structure and evolution. The CoRoT observations unveiled several targets suitable for this kind of research.
δ Sct type variables are stars located in the classical instability strip on the H-R diagram with effective temperatures in the range 6300 < T eff < 9000 K, luminosities 0.6 < log (L/L ⊙ ) < 2.0, and masses between 1.5 and 2.5 M ⊙ . Their evolutionary stages range from pre-main sequence to just evolved off the main se-quence (about 2 mag above the ZAMS). They exhibit radial and/or non-radial pulsations, with low-order gravity (g) and/or pressure (p) modes with pulsation periods ranging from ∼15 min to ∼8 h (see e.g. Rodríguez & Breger 2001;Buzasi et al. 2005;Uytterhoeven et al. 2011, and references therein).
Hence, δ Sct type stars are an interesting class of objects since they lie in the transition region between stars having a convective (M < 2 M ⊙ ) or a radiative (M > 2 M ⊙ ) envelope. Their masses are in a range where stars are developing a convective zone so they are useful for a better understanding of the mechanisms responsible for driving the pulsations. In this work we describe the analysis of CoRoT 105906206, an eclipsing binary system showing properties typical of δ Sct type variables.
Sections 2 and 3 present the details of the photometric and the spectroscopic observations, respectively. Section 4 describes how we derive the parameters of the system through the analysis of the light and radial-velocity curves, and Sect. 5 provides additional physical properties. The resulting pulsation frequencies are discussed in Sect. 6, and our final remarks and conclusions are in Sect. 7.

CoRoT photometry
CoRoT 105906206 was observed during the second "Long Run" in the direction of the Galactic centre (LRc02), which lasted about 161 days. According to the information in the ExoDat database (Deleuil et al. 2009), this relatively bright target (V = 11.784 ± 0.044 mag) has a small level of contamination (L 0 = 0.0077, where L 0 is the ratio between contaminant and total fluxes) and thus was not removed from the observed flux. We used in our analysis a white light curve, which is the sum of the three chromatic light curves from the CoRoT three-color photometry (Auvergne et al. 2009). These colors (red, green, and blue channels) do not represent any standard photometric system. They were implemented to help with the identification of false alarms, which can mimic the transit of a planet in front of the main target.
The original time series, containing about 388 000 points, was detrended to remove long-term variations, and was cleaned from outliers using a sigma-clipping algorithm. Points flagged according to the description of Gruberbauer (2008) were also excluded. Only a few measurements (corresponding to about 0.5 days) were made in the long-integration mode (512 s) and they were not used in our analysis. The resulting light curve contains about 341 000 points collected in the short-integration mode (32 s), from HJD = 2 454 573 to 2 454 717 days. A portion of the processed light curve is shown in Fig.1.

High-resolution spectroscopy
We collected high-resolution spectra of CoRoT 105906206 using two instruments: the Sandiford Echelle Spectrograph (McCarthy et al. 1993) attached at the Cassegrain focus of the 2.1-m telescope of McDonald Observatory (Texas, USA), and the fiber-fed FEROS Echelle Spectrograph (Kaufer et al. 1999) mounted on the MPG/ESO 2.2-m telescope at La Silla Observatory (Chile).
Six Sandiford spectra were taken over 6 consecutive nights in May 2011 under fairly good sky conditions, with seeing typically varying between 1.0 and 2.0 ′′ . We set the grating angle to cover the wavelength range 5000-6000 Å and used the 1.0 ′′ wide slit, which yields a resolution of R ∼ 47 000. We adopted an exposure time of 1200-1800 sec and traced the radial velocity drift of the instrument by acquiring long-exposed (T exp = 30 sec) ThAr spectra right before and after each epoch of observation.
Nineteen additional spectra were acquired in June-July 2011 with FEROS, which provides a resolution of R ∼ 48 000 and covers the wavelength range ∼3500-9200 Å. The sky conditions were photometric throughout the whole observation run, with seeing between 0.6 and 1.0 ′′ . Exposure times ranged between 1200 and 1800 seconds.
The spectra were reduced using IRAF 1 standard routines and the FEROS automatic pipeline for order identification and extraction, background subtraction, flat-field correction and wavelength calibration. The radial velocities of the two components, together with their uncertainties, were derived with the fxcor task of IRAF by cross-correlating each spectrum with a reference template. The standard stars HD 168009 (Udry et al. 1999) and HD 102870 (Nidever et al. 2002), both observed with the same instrumental set-up, were used as template for Sandiford and FEROS spectra, respectively. Figure 2 shows the crosscorrelation function (CCF) peaks fitted by a double Gaussian curve. The uncertainty in each radial-velocity measurement, and whether one or a double Gaussian is fitted, depend on the separation of the peaks.
In the beginning of our study, we made a visual comparison of our spectra with the Digital Spectral Classification Atlas of R. O. Gray 2 , which suggested a spectral type F3 for the primary star, corresponding to an effective temperature of about 6800 K. This is the value we used in this work, though it was afterward improved by the spectroscopic analysis of the primary decomposed spectrum, obtained through the disentangling method (see Sect. 3.1). At any rate, both determinations are in very good agreement with each other. Concerning the secondary companion, it gives only a small contribution to the total flux, as can be seen in Fig. 2.
The derived radial velocities and the estimated uncertainties of the two stars of CoRoT 105906206 are listed in Table 1 and plotted in Fig. 3, together with the best-fit models computed with the PHOEBE code (PHysics Of Eclipsing BinariEs, Prša & Zwitter 2005) for both primary and secondary components. Besides Keplerian motion, the models also consider the Rossiter-McLaughlin (R-M) effect.

Spectral decomposition
The VO-version 3 of the KOREL program (Hadrava 2004(Hadrava , 2009) was used to decompose the FEROS spectra into the individual stellar components. The method of spectral disentangling was first introduced by Simon & Sturm (1994) and later on reformulated by Hadrava (2004) in the Fourier space.
The quality of the spectral disentangling with KOREL strongly depends on the quality of the derived line shifts of the components (radial velocities). To determine these shifts as precise as possible, we excluded the broad Balmer lines from this step of the analysis. From visual inspection, we could only find one line of the secondary component in the spectra, Mg ii at 5183 Å. A first KOREL solution was computed on a small interval around this wavelength and then the region was extended to the range 4915 to 5500 Å, also allowing for variable line strengths in the program. Any further extension in wavelength did not improve the accuracy of the results. Due to the low frequency problem, typical of Fourier transform-based disentangling programs like KOREL (see e.g. Hensberge et al. 2008), slight undulations occurred in the computed continua of the decomposed spectra. Therefore, we applied KOREL to overlapping 20 nm wide bins, where we fixed the orbital parameters and time variable line strengths to the values obtained before. Only in the case of broad Balmer lines did we chose wider bins. Each piece of decomposed spectrum, which covers in total a wavelength range from 4410 to 6860 Å, was corrected for slight continuum undulations using spline fits. Finally, all bins were merged using weighting ramps for the overlapping parts.
KOREL delivers the decomposed spectra of the components normalized to the common continuum of both stars. A renormalization to the individual continua of the components can only be done by assuming a value for their flux ratio. Since this value is very low, the line depths of the secondary are very sensitive to the flux ratio. This, in addition to the very low signal-to-noise 3 http://vokorel.asu.cas.cz/app/ (S/N) of the decomposed secondary spectrum, prevented us from its analysis. In the case of the primary component, small deviations from the true flux ratio cause only a second order effect.
For the spectral analysis of the primary component we assumed a flux ratio of 0.07 that was estimated from the light curve solution (the ratio between the bolometric luminosities listed in Table 2). We used the ATLAS9 plane-parallel and LTE model atmospheres (Kurucz 1993), and calculated synthetic spectra using SPECTRUM, a stellar spectral synthesis code (Gray & Corbally 1994). We convolved the synthetic spectra with a Gaussian profile having a FWHM = 0.11 Å, to account for the spectrograph resolution, and adopted a surface gravity of log g = 3.53 ± 0.01 dex, as derived from the modeling of the eclipsing binary.
We derived the effective temperature by fitting the wings of the Hα and Hβ Balmer lines, and the iron abundance ([Fe/H]) and micro-turbulence velocity (υ micro ) by applying the method described in Blackwell & Shallis (1979) on isolated Fe i and Fe ii lines. The results are T eff,1 = 6750 ± 150 K, [Fe/H] = 0.0 ± 0.1 dex, and υ micro,1 = 2.5 ± 0.8 km s −1 . We also measured the projected rotational velocity υ sin i of the stars i) by fitting the CCF profile of individual FEROS spectra using the rotation profile described in Gray (1976), which was convolved with the instrumental profile, and ii) by fitting the profile of several clean and unblended metal lines. We derived υ 1 sin i = 47.8 ± 0.5 km s −1 and υ 2 sin i = 19 ± 3 km s −1 from the CCF peaks for both primary and secondary stars, and υ 1 sin i = 46 ± 2 km s −1 from the metal lines of the decomposed spectrum of the primary. As a matter of fact, the value of υ sin i that we derive here is a mixed of velocity fields including stellar rotation, macro turbulence, and pulsations. However, given the large rotation rate of these stars, macro-turbulence and pulsation broadening are second order effects. We also derived the abundance of chemical elements other than iron using the decomposed spectrum of the primary star. However, the continuum undulations produced by the disentangling procedure, though we tried to correct them, may still affect the abundance determination, specially for heavy elements, which have a small number of spectral lines available. Nevertheless, for elements lighter than Fe, the abundances mostly follow the solar values (Asplund et al. 2005).

Light and radial-velocity curve analysis
The binary model for both light and radial-velocity curve of CoRoT 105906206 were computed with PHOEBE, a tool for eclipsing binary modeling based on the Wilson-Devinney code (Wilson & Devinney 1971). The search for the best model was performed with the PIKAIA subroutine (Charbonneau 2002), a genetic-algorithm based approach. PIKAIA maximizes a usersupplied function (= 1/χ 2 ) by minimizing the chi-square χ 2 between model and data. Starting with a so-called "population", formed by a given number of "individuals" which, in turn, are formed by sets of parameters randomly selected within a given range of the parameter space. These sets of parameters are encoded as strings to form a "chromosome-like" structure, and represent the first trial solutions. The initial solutions (or "parents") then evolve through subsequent "generations" of possible solutions (the "offsprings"), following rules similar to typical processes of the biological evolution (breeding, crossover, mutation). In equivalence to the natural selection, only solutions that provide small values of χ 2 are passed to the next generations, and the final solution is achieved after some condition is satisfied.
Our supplied function evaluates the χ 2 between the observed light curve and the models computed for a set of free parameters that characterize the orbital and physical properties of a binary system. Following the same procedure described in Maceroni et al. (2014), we implemented this function in a FORTRAN-based routine, FITBINARY, which makes use of Wilson-Devinney routines to compute the binary models. In our FITBINARY code we adopt the PIKAIA 1.2 new version, an improvement of PIKAIA 1.0 that includes additional genetic operators and algorithm strategies. In particular, the new version allows several mutation modes such as a fixed or an adjustable mutation rate based either on fitness (the value of 1/χ 2 com-

Fig. 5.
Reduced chi-square between model and data as a function of the eight free parameters of the light curve model computed using the PIKAIA genetic algorithm during the search for the best solution. From left to right, and from top to bottom: secondary effective temperature, orbital inclination angle, surface potentials, primary gravity darkening, surface albedos, and beaming factor. paring best and median individuals) or on distance (the metric distance between best and median population clustering). We normally adopted an initial population with 100 individuals evolving through 200 generations, a mutation mode of one-point+creep and adjustable rate based on fitness, and a full generation replacement with elitism. The other control parameters were normally kept fixed at their default values (see the related documentation in the PIKAIA Homepage 4 ).
In the prewhitening process, described in detail in Sect. 4.2, (i) we first remove an initial binary model from the processed light curve (the one resulting from the cleaning steps of Sect. 2), then (ii) we identify the significant frequencies in the amplitude spectrum of the time series with oscillations only, (iii) we subtract the frequencies from the processed light curve, and finally (iv) we search for an improved solution for the binary model applied to the light curve with the eclipses only. These steps are repeated until there is no improvement on the last solution. However, by using this procedure to treat the whole data set (of about 144 days) we did not find any satisfying solution and the remaining residuals still had clearly visible oscillations. This does not happen if we apply the same procedure to a segment of light curve, since the residuals in this case are at least 2.5 times smaller. Hence, we divided the light curve into 8 segments of about 20 days each, and apply the procedure of prewhitening to each one separately. In the following sections we present the results obtained using the first segment of the light curve, and at the end of the paper we comment on the comparison with what we obtain using the other segments. 4 http://www.hao.ucar.edu/modeling/pikaia/pikaia.php

Preliminary solutions
First, using PHOEBE and the radial-velocity data only, we searched for a good solution to the orbital model by changing the orbital period P, the semi-major axis a, the secondary-toprimary mass ratio q, and the barycentric velocity υ γ . Then, keeping fixed the derived values (except P), we improved the orbital period and, with PIKAIA, we searched for a solution that best fits the light curve data by changing the secondary effective temperature T eff,2 , the orbital inclination angle i, and the surface potentials Ω 1 and Ω 2 . The eccentricity e and the longitude of periastron ω 0 were kept fixed at zero, and the primary effective temperature T eff,1 was set to 6800 K (according to our estimate performed in Sect. 3). The ratio between orbital and rotation periods was fixed to f = 1.0 for both companions. Later on, with our estimate of the projected rotation velocity from the CCF peaks (see Sect. 3.1), we derived P rot,1 = 4.44 ± 0.07 days and P rot,2 = 3.63 +0.53 −0.74 days (assuming coplanarity between equatorial and orbital planes, as discussed in Sect. 7), which yielded f 1 = 0.83 ± 0.01 and f 2 = 1.02 +0.15 −0.21 . However, these new values did not significantly affect the results already found for the parameters.
Concerning the limb darkening, we adopted a square-root law with two coefficients x LD and y LD for each component, which also depend on the passband intensities. For a given set of photospheric parameters, PHOEBE interpolates the limb darkening coefficient tables computed for CoRoT passbands (see Maceroni et al. 2009). For both stars, the bolometric luminosity L, mass M, radius R, and surface gravity log g were computed rather than adjusted, where R represents the radius of a sphere with the same volume as the modeled star.
This first preliminary solution model for a detached binary, which is shown in Fig. 4a, is based on the cleaned light curve de-  Table 2. The solid lines indicate the solution that minimizes χ 2 . scribed in Sect. 2, including the pulsations and other kind of periodic patterns. The curve was binned using an average of 1000 points in both time and flux in the phase-folded space. The gravity darkening and surface albedo coefficients were kept fixed at β = 0.32 and A = 0.60 for purely convective envelopes (Lucy 1967), adopting T 4 eff ∝ g β . Claret (1999) computed the gravity darkening as a function of mass and degree of evolution of the star, which resulted in a smooth transition between convective and radiative energy transport mechanisms. Therefore, in a second step, the gravity darkening (except β 2 ) and surface albedos were set as free parameters as a tentative to improve the fit (see Fig. 4b). Since the primary luminosity dominates the observed flux, the models are independent of the secondary gravity darkening, and therefore β 2 was kept fixed (see Table 2).
As can be seen in Fig. 4b, more clearly in the residuals plot, there is a modulation pattern, commonly referred to as the O'Connell effect (O'Connell 1951), in which the flux maximum after the deeper eclipse is larger than the maximum after the shallower eclipse (see also Milone 1968;Davidge & Milone 1984). Some attempted explanations for this asymmetric modulation are the presence of spots on the surface of a chromosphericaly active star, circumstellar clouds of gas and dust, or a hot spot created by mass transfer. Given the physical configuration of this system, however, both stars are nearly spherical (see Sect. 5) and thus the scenario of mass transfer can be safely excluded from the list of possible causes of the O'Connell effect. Another possible explanation instead is the so-called Doppler beaming, in which the orbital movement of the star modifies its apparent luminosity, beaming the emission of photons in the direction of the observer. The relation (adapted from Loeb & Gaudi 2003) between emitted (F 0,λ ) and observed (F λ ) flux is: where B is the beaming factor (see also Zucker et al. 2007;Bloemen et al. 2011). B depends on the wavelength of the observations and on the physical characteristics of the star. In a binary system, since the stars move in opposite directions with respect to the observer, the net beaming effect represents the difference in flux between the components. Therefore, there is no modulation caused by the Doppler beaming if the binary components have the same mass and the same spectral type. In order to account for and remove this modulation pattern from the observed light curve, we searched for a binary model in which the emitted flux is transformed according to Eq. 1 and the beaming factor is set as a free parameter (see Fig. 4c and Table 2).

Final solution, uniqueness, and uncertainties
The plots in Figs. 4a, 4b and 4c are based on the light curve with the oscillations still present. These include those originating from stellar pulsations, and other sources such as the orbital period of the CoRoT satellite (103 min.) and its harmonics. We use an iterative procedure for the prewhitening. First we find the best fit to the light curve setting the secondary effective temperature, orbital inclination angle, surface potentials, the albedo coefficients of both components, the primary gravity darkening, and the beaming factor as free parameters (Fig. 4c). After that we subtract this model from the observed data so that only oscillations remain. Fig. 7. Evolution of the radius of the system components in the mass range M 1,2 ± 2σ(M 1,2 ) (shaded regions, from Table 2) for three values of chemical composition. The darker regions represent the intersection with R 1,2 ± 2σ(R 1,2 ) (horizontal lines, also from Table 2). The vertical lines indicate the limits in age according to the constraint of coevality of the two stars.
We then use Period04 (Lenz & Breger 2005), a program developed for the analysis of time series, to compute the Fourier spectrum and to search for the frequency, amplitude, and phase of each sinusoidal component of the signal. To establish the number of components that give a significant contribution to the signal, we apply the commonly-used criterion of S/N > 4, i.e., only frequencies having an amplitude 4 times the local noise are considered. It is worth noting that, in order to avoid spurious frequencies in the amplitude spectrum, small gaps in the time series were filled in with artificial points that follow a polynomial function fitted to adjacent regions of each gap. A noise consistent with the dispersion of the adjacent regions was applied to each point. More details on the pulsation frequencies are described in Sect. 6.
Finally, the significant frequencies (according to the criterion mentioned above) are subtracted from the cleaned light curve leaving only the eclipses and the modulation of the binary. Again, using PIKAIA and PHOEBE, we improve the preliminary values of T eff,2 , i, Ω 1 , Ω 2 , A 1 , A 2 , β 1 , and B. The procedure is repeated until the χ 2 value between model and data does not decrease significantly.
We also tried to account for the individual flux contribution of each star to the observed pulsations during and out of the eclipses. However, since the primary star is the pulsating component (we will get to this conclusion in Sect. 6) and dominates the observed flux, the influence of the secondary component on the observed pulsations is negligible, being smaller than the noise. We were thus unable to see any difference in the pulsations amplitude in-and out-of-eclipses, and the pulsation frequencies found were equally subtracted from the entire light curve.
The minimization algorithms employed by PHOEBE are the commonly used Levenberg-Marquandt and Nelder & Mead's downhill simplex, both nonlinear optimization methods affected by the problem of remaining stuck at local minima. In the PIKAIA genetic algorithm, mutation and crossover allow the population to move away from local solutions. Figure 5 plots the reduced chi-square χ 2 red = χ 2 /ν (where ν = N − n − 1 is the number of degrees of freedom for N observation points and n fitted parameters) as a function of the free parameters of the light curve model, for a wide range of the parameter space. Note that PIKAIA tries several local solutions (pattern of points vertically assembled), and progressively moves towards the global minimum. In any case, we preferred to carry out more than one iteration, and also around a shorter range of the parameter space, to better constrain the solutions to provide the minimum χ 2 .
To estimate the uncertainties in the parameters we performed Markov chain Monte Carlo (MCMC) simulations using the Metropolis algorithm (see e.g. Gelman et al. 2003;Ford 2005). This method is based on a bayesian inference in the sense that the posterior (or desired) probability distribution p(x|d) of a set of parameters x given the observed data d is proportional to the product of a prior knowledge of the probability distribution of the parameters p(x) and a factor exp [−χ 2 (x)/2], which depends on the χ 2 goodness of the fit adopting the model x. For the prior probability function we adopted a Gaussian distribution, centered around an initial set of x and having initial arbitrary variances. The idea is to construct a parameter space that approximates the desired probability distribution. To do so, we generate a chain (or sequence) formed by sets of random parameters that are sampled according to the prior probability distributions. If a set of parameters x ′ yields a χ 2 smaller than the previous one, The acceptance rate can be adjusted by multiplying the initial variances by a scaling factor, in order to optimize the number of accepted solutions. We redefine this scaling factor every 100 steps of the simulations to achieve a ratio of about 0.25 between the accepted and the total number of generated solutions, which is an optimal value for a multi-dimension space (see Gelman et al. 2003). During a first phase of tests, which is called the burn-in phase, the variances of the prior distributions are constantly updated, being computed from the posterior distributions themselves. The uncertainty on the data is also adjusted to ensure that the value of minimum χ 2 is equal to the number of degrees of freedom. The burn-in solution is then discarded and a new simulation begins. After reaching a certain number of accepted solutions, the posterior probability distributions become stable and the chain converges towards the desired distribution. Figure 6 plots the distributions of the eight free parameters that we used to model the light curve of CoRoT 105906206. We discarded the first 15% of the accepted solutions and the histograms contains 40,000 points each. The parameters of the bestfit solution and their uncertainties are listed in Table 2. They represent the median values and the 68% confidence limits shown in the figure, and are in very good agreement with the best solution found with PIKAIA. It is worth noting that, since T eff,2 is correlated with T eff,1 (because of the degeneracy between the effective temperatures and the passband luminosities), the uncertainty estimated for the secondary temperature also accounts for the one estimated for the primary star. The final light curve model is shown in Fig. 4d.

Physical properties of CoRoT 105906206
Besides the parameters that come directly from the fits of the light and radial-velocity curves, the masses (M 1 and M 2 ), radii (R 1 and R 2 ), and surface gravities (log g 1 and log g 1 ) of the two stars are also calculated. Using the values of radius and effective temperature, we can calculate the luminosities (L 2 and L 1 ). All these parameters, together with the limb darkening coefficients (x LD,1 , x LD,2 , y LD,1 , y LD,2 ), are listed in Table 2. The resulting model is for a detached binary, whose components are both nearly spherical. For the primary, the radius in the direction toward the secondary is about 4% larger than the radius in the direction of the stellar pole. For the secondary this value is only about 0.3%. This shows that even the primary star is far from reaching the Roche lobe.
In order to estimate the age of the system, we used the Yonsei-Yale (Y 2 ) evolutionary tracks (Yi et al. 2003), interpolated in mass and chemical composition, drawn on the radius vs. age diagram. This kind of diagram allows us to see the evolution of the stellar radius with time, and is preferred over using the placing of the stars in the H-R diagram because in eclipsing binary systems we have a precise determination of mass and radius of the components. We checked the effective temperatures of each star that come from the evolutionary models and they are consistent with those derived from our spectral and light curve analyses. Figure 7 shows the radius vs. age diagrams for three values of metallicity in the range [Fe/H] ± 2 σ([Fe/H]), from Sect. 3.1, plotted for masses and radii in the range M 1,2 ± 2σ(M 1,2 ) and R 1,2 ± 2σ(R 1,2 ), both from Table 2. Applying the constraint of coevality of the two stars, we found the age of this binary system to be 859 +79 −67 Myr. These are 1σ uncertainties though, for clarity in the figure, the diagrams were constructed within two standard deviations in metallicity, mass, and radius. The sharp vertical drops correspond to the second gravitational contraction at the end of main-sequence stars. To compute the evolutionary tracks, an overshoot parameter α OV = 0.2 H P (units of the pressure scale height) is adopted when a convective core develops (see Yi et al. 2003, and references therein). Figure 8 shows the amplitude spectrum of CoRoT 105906206, computed using Period04 after subtracting the final binary model from the light curve. We searched for significant peaks up to the Nyquist frequency, but none was found beyond 25 d −1 . A total of 220 frequencies with S/N > 4 was identified, and Table 3 lists the first 50, together with the amplitudes and phases, and the respective formal errors computed according to Montgomery & O'Donoghue (1999). We also searched for possible frequency combinations, including also the orbital fre-quency (F orb = 0.270667 d −1 ). The most evident are listed in the last column of this table. We identified a few combinations involving the orbital frequency and the most dominant peaks F 1 , F 2 , F 3 , and F 5 , which seem to be genuine p-mode frequencies.

Pulsation properties
A few overtones of the orbital period are still present in Fig. 8, and are also indicated in Table 3. They are probably residuals of the prewhitening process, but have small amplitudes.
The typical properties of δ Sct type variables in terms of effective temperature, luminosity, mass, evolutionary stage, and pulsation frequency range are all present in the primary component of CoRoT 105906206, as one can see in Table 2 and in the list of dominant frequencies in Table 3. As an rough estimate of the frequency range of the pulsations, we applied the relation between the frequency of a given radial mode F puls , the stellar mean density ρ, and the pulsation constant Q: From the fundamental to the fifth radial mode we have 0.033 Q 0.013 (Stellingwerf 1979), which yields 5.2 F puls 13.2 d −1 if we use the values of mass and radius of the primary star, a range that contains the most significant frequencies seen in Fig. 8. The same computation for the secondary star yields frequencies in the range 22 F puls 56 d −1 , which are not observed in the amplitude spectrum. This confirms that the identified pulsation modes belong the primary component.
From the theoretical point of view, a non-adiabatic analysis of an equilibrium model with the physical properties of the primary component, performed with the non-adiabatic oscillation code MAD (Dupret et al. 2005), provides excited modes with frequencies in the typical domain of δ Sct type stars, namely: from 5.2 to 17.0 d −1 in the fundamental mode (ℓ = 0), from 4.0 to 16.6 d −1 in the ℓ = 1 mode, and from 4.2 to 16.7 d −1 in the ℓ = 2 mode, which are in line with the observed range of pulsation frequencies.

Final remarks and conclusions
The study of CoRoT 105906206 unveiled an eclipsing binary system in which the primary component pulsates in the range of frequencies typical δ Sct type variables, a result that agrees with the derived values of effective temperature, luminosity, mass, and stage of evolution. Moreover, from the theoretical point of view, a non-adiabatic analysis of a model matching the physical properties of the primary star gives excited frequencies of the most relevant modes (ℓ = 0, 1, and 2) in the same frequency range of the observed pulsations.
By allowing the surface albedos and gravity darkening to vary as free parameters we have improved the solution for the binary model in comparison with the model found by keeping them fixed. In particular, our estimate of β 1 is in agreement with the calculations of Claret (1999) for the gravity darkening as a function of the effective temperature for a 2 M ⊙ star.
An interesting characteristic of this system is the presence of the O'Connell effect, an asymmetric photometric modulation pattern that we interpreted as due to the Doppler beaming of the emitted flux. We have quantified this effect by means of the beaming factor B, whose value depends on the passband of the photometric observations and on the physical properties of the stars. Using equations from Mazeh & Faigler (2010), our Eq. 1, and some of the parameters in Table 2, we obtain B = 2.00 ± 0.05, which is in fair agreement with the beaming factor derived from the light curve model (see Table 2). The α beam factor used in those equations was set to unity. This factor accounts for the effect of the stellar light being shifted out or into the observed passband. According to Faigler & Mazeh (2011), the value of α beam may range from 0.8 to 1.2 for F, G, and K stars observed with the CoRoT passband. The same beaming factor listed in Table 2 is obtained setting α beam = 0.8.
The fact the primary star rotates with a sub-synchronous velocity may generate some doubt on our determination of the rotation period, and motivates us to provide some tentative explanations. A spin-orbit misalignment, for example, would lead to an overestimation of P rot,1 . However, using Eq. 22 of Hut (1981) applied to the parameters derived for this system, and assuming that the primary component rotates as a rigid body, we can estimate the ratio of orbital to rotational angular momentum to be α ∼ 30. In Fig. 4 of that paper, for this value of α the time scale for circularization is much longer than the time for alignment. Therefore, if e = 0, which is the case of our system, no misalignment is expected. Another explanation could be the loss of angular momentum due to mass transfer. However, the system components are both nearly spherical and far from filling the Roche lobe. The most plausible explanation seems to be the radius expansion of the primary component related to its stage of evolution. This star is passing through a region on the H-R diagram of roughly constant luminosity, decreasing effective temperature, and increasing radius. According to the grid of stellar models with rotation of Ekström et al. (2012), a star of about 2 M ⊙ that has just evolved off the main sequence will pass through a phase of decreasing equatorial velocity before reaching the base of the giant branch (see their Fig. 9). Though these models were computed for single stars, and not specifically for a star with the same parameters as the primary component of our system, they give us an indication that a decrease in the rotation rate is possibly taking place.
The division of the light curve into 8 segments of about 20 days each was necessary to identify the bona fide pulsation frequencies. A shift of the frequency phases with time seems to disturb the identification of frequencies in the whole time series. We performed several tests in order to check the existence of phase shifts in the pulsation frequencies and to identify any periodical variation. However, even if phase shifts are indeed present, no clear periodical variation was found. We are not able to explain the origin of this variation, though we think that it is likely intrinsic to the star. The data reduction process and an instrument related effect could be the cause, but we have applied the same method to several other light curves of both CoRot and Kepler systems, and we did not see the same behavior before.
We derived our results based on the first of the eight segments. We tested the others by proceeding with the prewhitening steps, which led to new solutions for the binary models, and to the identification of pulsation frequencies in each segment. A comparison of the fitted parameters shows very good agreement and low dispersion among the segments. The mean values are: T eff,2 = 6162 ± 13 K, i = 81.66 ± 0.15 • , Ω 1 = 4.27 ± 0.02, Ω 2 = 7.89 ± 0.05, β 1 = 0.52 ± 0.02, A 1 = 0.77 ± 0.11, A 2 = 0.06 ± 0.08, and B = 1.48 ± 0.04. The dispersions are all smaller than the estimated uncertainties, and the values agree with those in Table 2. Regarding the analysis of the pulsation frequencies, the peaks with higher amplitudes in Fig. 8 (> 1 × 10 −3 ) were normally identified in all the eight segments of light curve, in particular the four genuine p-modes (F 1 , F 2 , F 3 , and F 5 ) listed in Table 3. Small shifts in amplitude, probably related to the phase shifts, were also observed among the segments. We believe it would be useful to have more spectra collected during the eclipses in order to allow the modeling the Rossiter-McLaughlin effect. This would confirm whether the spin-orbit axes are indeed aligned, as we suspect, and reinforce the possibility of radius expansion of the primary star due to its stage of evolution. The gathering of more spectra, with higher S/N, would also improve the precision achieved in the spectroscopic analysis, yielding to an accurate abundance determination of el-ements other than iron. We also believe that the behavior of the amplitude and phase variations is still not well understood. The development of more robust programs and methods for the analysis of time series is required to properly deal with this kind of data, in which a large number of observation points and pulsation frequencies are present. also very grateful for the referee report to this work, which has contributed a lot to largely improve our manuscript. This research has made use of the ExoDat Database, operated at LAM-OAMP, Marseille, France, on behalf of the CoRoT/Exoplanet program, and was accomplished with the help of the VO-KOREL cloud service, developed at the Astronomical Institute of the Academy of Sciences of the Czech Republic in the framework of the Czech Virtual Observatory (CZVO) by P. Skoda and L. Mrkva using the Fourier disentangling code KOREL by P. Hadrava. We acknowledge the generous financial support by the Istituto Nazionale di Astrofisica (