Issue 
A&A
Volume 549, January 2013



Article Number  A30  
Number of page(s)  14  
Section  Planets and planetary systems  
DOI  https://doi.org/10.1051/00046361/201219601  
Published online  11 December 2012 
TASTE
III. A homogeneous study of transit time variations in WASP3b^{⋆,}^{⋆⋆,}^{⋆⋆⋆}
^{1} Dipartimento di Fisica e AstronomiaUniversità degli Studi di Padova, Vicolo dell’Osservatorio 3, 35122 Padova, Italy
email: valerio.nascimbeni@unipd.it
^{2} INAF – Osservatorio Astronomico di Padova, vicolo dell’Osservatorio 5, 35122 Padova, Italy
^{3} Departamento de Astrofísica, Universidad de La Laguna (ULL), 38206 La Laguna, Tenerife, Canary Islands, Spain
^{4} Universidad de Monterrey, Departamento de Física y Matemáticas, Av. I. Morones Prieto 4500 Pte., San Pedro Garza García, Nuevo León, 66238, México
^{5} Instituto de Astrofísica de Canarias, Vía Láctea s/n, E38200 La Laguna, Tenerife, Canary Islands, Spain
^{6} Astronomical Observatory of the Autonomous Region of the Aosta Valley, Loc. Lignan 39, 11020 Nus (AO), Italy
Received: 15 May 2012
Accepted: 8 October 2012
The TASTE project is searching for lowmass planets with the transit timing variation (TTV) technique by gathering highprecision, shortcadence light curves for a selected sample of transiting exoplanets. It has been claimed that the “hot Jupiter” WASP3b could be perturbed by a second planet. Presenting eleven new light curves (secured at the IAC80 and UDEM telescopes) and reanalyzing thirtyeight archival light curves in a homogeneous way, we show that new data do not confirm the previously claimed TTV signal. However, we bring evidence that measurements are not consistent with a constant orbital period, though no significant periodicity can be detected. Additional dynamical modeling and followup observations are planned to constrain the properties of the perturber or to put upper limits to it. We provide a refined ephemeris for WASP3b and improved orbital/physical parameters. A contact eclipsing binary, serendipitously discovered among field stars, is reported here for the first time.
Key words: techniques: photometric / planetary systems / stars: individual: WASP3
This article is based on observations made with the IAC80 telescope operated on the island of Tenerife by the Instituto de Astrofísica de Canarias (IAC) in the Spanish Observatorio del Teide.
Tables 1 and 3 and Appendix A are available in electronic form at http://www.aanda.org
Photometric data are only available at the CDS via anonymous ftp to cdsarc.ustrasbg.fr (130.79.128.5) or via http://cdsarc.ustrasbg.fr/vizbin/qcat?J/A+A/549/A30
© ESO, 2012
1. Introduction
Most of the extrasolar planets discovered so far are massive, gaseous giant planets. The present trend is to probe ever smaller masses, with the final aim of detecting temperate “superEarths” or Earthsized rocky planets (1−10 M_{⊕}, 1−3 R_{⊕}) around solartype stars. The signal expected from a true Earth analog orbiting a Sun twin is extremely small: ~80 ppm for the photometric transit, and ~10 cm/s for the radial velocity (RV) Doppler shift. In the conventional framework both measurements are required to derive the planetary radius and mass (R_{p}, M_{p}), i.e., the basic quantities necessary to confirm the planetary status of the transiting body, and to characterize it. Achieving a photometric precision of ~20 ppm (which would allow the detection of an Earthlike planet at 4σ level) over the timescale of a transit is within reach of spacebased telescopes only, while a longterm ≲ 20 cm/s RV accuracy is still too ambitious even for the most stable spectrographs, such as HARPS.
A few indirect techniques have been developed to obtain an estimate of M_{p} (or upper limits to it) for a nontransiting planet without the need of RV measurements, the most promising of which is the transit timing variation (TTV) method. By monitoring a known transiting planet with highprecision photometry, the central instant T_{0} of each individual transit can be estimated. The gravitational perturbation of a previously unknown third body, which is not necessarily transiting, can cause a significant variation of the orbital period P (Holman & Murray 2005). The effect is greatly increased if the perturber is locked in a loworder meanmotion resonance with the transiting planet (Agol et al. 2005). The Asiago Search for Transit timing variation of Exoplanets (TASTE) project was started in 2010 to search for TTVs with several groundbased, mediumclass facilities on a sample of carefully selected targets (Nascimbeni et al. 2011a).
The TTV technique has been exploited and already gave interesting results on a number of Kepler mission candidates. Some candidate planets in multiple systems were validated through TTV analysis (Lissauer et al. 2011). In the past few years, some authors have claimed TTV detections also from groundbased facilities, but none is confirmed so far. Among these claims, WASP10b (Maciejewski et al. 2011), WASP5b (Fukui et al. 2011), the intriguing case of HATP13b, which was monitored also by TASTE (Pál et al. 2011; Nascimbeni et al. 2011b; Southworth et al. 2012), and the subject of the present investigation: WASP3b (Maciejewski et al. 2010).
WASP3b is a typical shortperiod (P ≃ 1.8468 days) “hot Jupiter” (1.31 R_{jup}, 1.76 M_{jup}), hosted by an F78 dwarf. It was discovered by Pollacco et al. (2008). Analyzing an O−C (observed − calculated) diagram computed by comparing the T_{0} of fourteen transits with the value predicted by a linear ephemeris, Maciejewski et al. (2010) claimed the detection of a sinusoidal modulation with a period of P_{TTV} ≃ 127.4 days and a semiamplitude of ~0.0014 days ≃2 min. They interpreted this signal as the effect of an outer perturber, identifying three possible orbital solutions in the range 6 − 15 M_{⊕} and P = 3.03 − 3.78 days. No independent confirmation of this claim has been published so far, though both Littlefield (2011) and Sada et al. (2012) discussed the consistence of their data with that TTV modulation.
In this paper we present (Sect. 2) eleven unpublished transits of WASP3b: six of them have been gathered at the IAC80 telescope and five at the UDEM 0.36 m (Universidad de Monterrey, Mexico). We also sifted the literature in search of all the archival photometric data useful for a TTV study (Sect. 3). In Sects. 4 and 5 we describe how both new and archival light curves, for a total of fortynine transits, were reduced and analyzed in a homogeneous way with the same software tools to provide a consistent estimate of the planetary parameters and their uncertainties. This is crucial especially for T_{0}, whose estimate has been shown to be easily biased by the employed analysis technique (Fulton et al. 2011; Southworth et al. 2012). In addition to T_{0}, we also refined the orbital and physical parameters of WASP3b, and computed an updated ephemeris (Eq. (10)) for any future study on this target. In Sect. 5.2 we demonstrate that the TTV claimed by Maciejewski et al. (2010) is not supported by our analysis; instead it is probably due to smallsample statistics. Yet, we point out that the revised O − C diagram displays a complex, nonperiodic structure and is not compatible with a constant orbital period. Finally, in Sect. 6 we discuss the possible origin of this TTV signal, and show that careful dynamical modeling and additional photometric and RV followup is required to confirm the hypothesis and constrain the mass and period of the possible perturber(s).
2. TASTE observations
2.1. IAC80 observations
We observed six transits of WASP3b between 2011 May 7 and Aug. 2, employing the CAMELOT camera mounted on the IAC80 telescope. A log summarizing dates and other quantities of interest is reported in Table 1. Individual transits are identified by an ID code ranging from N1 to N6. IAC80 is a 0.8 m Cassegrain reflector installed at the Teide Observatory (Tenerife, Canary Islands) that is operated by Instituto de Astrofísica de Canarias (IAC). CAMELOT is a conventional imager with a field of view (FOV), equipped with an E2V 4240 2048 × 2048 CCD detector, corresponding to a 0.304′′ pixel scale. The software clock interrogated to save the timestamps in the image headers is automatically synchronized with the GPS time signal.
All observations were carried out with a standard Bessel R filter and the same instrumental setup. Windowing and 2 × 2 binning were employed to increase the dutycycle of the photometric series, as described in Nascimbeni et al. (2011a). A 10.4′ × 3.2′ readout window was chosen to image the target and a previously selected set of reference stars in a region of the detector free from cosmetic defects. The oneamplifier readout was preferred to prevent gain offsets between different channels. Stars were intentionally defocused to a full width at halfmaximum (FWHM) of 10−13 binned pixels (≃6.0−8.0′′) to avoid saturation and minimize systematic errors due to intrapixel and pixeltopixel inhomogeneities (Southworth et al. 2009). Exposure time was set to 20 s (N14) or 15 s (N56), resulting in a net cadence τ = 19−25 s and a ~75−87% dutycycle, with the only exception of N3. On that night, due to software problems, the images were read unbinned and in unwindowed readout mode, decreasing both signaltonoise ratio (S/N) and dutycycle.
The weather was photometric on all nights, except for a few thin veils during N3. Our initial goal was to start the series one hour before the first contact of the transit, and to stop one hour after the last contact, but the amount of pretransit photometry is only a few minutes for the N4 and N6 light curves, and the N1 series was interrupted twenty minutes earlier because of twilight.
2.2. UDEM observations
We observed five transits of WASP3b between 2008 Sep. 3 and 2010 Aug. 15 with the Universidad de Monterrey (UDEM) 0.36m reflector. UDEM is a small private college observatory with the Minor Planet Center Code 720 and is located in the suburbs of Monterrey, México. The data were acquired using standard Bessel I and Sloan zband filters with a 1280 × 1024 pixel CCD camera at 1.0′′ pixel scale, resulting in a FOV of ~. The observations were slightly defocused to improve the photometric precision and avoid saturation. Onaxis guiding was used to maintain pointing stability. Exposure times were set to 30 s for I and 40 s for z. All images were binned 2 × 2 to facilitate rapid readout (~3 s). Each observing session lasted about 4.5 h in order to accommodate the transit event and also to cover about one hour before ingress and one hour after egress. The computer clock was reset to UTC via Internet at the beginning of every observing session to the nearest second.
Fig. 1
Light curves of WASP3b. The ID code of each transit matches the corresponding entry in Table 1. Data points are plotted with the original cadence, except for G1/G2 and Z1/E7, which are binned on 30 s and 300 s intervals for clarity, respectively. The red line is the bestfit model found by JKTEBOP. Transits are offset in magnitude by integer multiples of 0.025. 

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3. Archival light curves
All available archival data were searched for any light curve useful for a TTV analysis, i.e., complete transits of WASP3b with a suitable S/N. Partial transits were rejected, except for a few cases with high S/N and without obvious presence of “red noise” after a visual inspection. We define red noise, following Pont et al. (2006), as correlated noise with a covariance between data points on timescales on the same order of the duration of our transit signal. The transit itself must be modeled and removed from a light curve in order to study the statistical properties of its noise content. Thus, first we analyze the whole sample of light curves in Sect. 5.1, then we discuss how to select a highquality subset for furter analysis in Sect. 5.2 (“ALL” vs. “SELECTED”).
Hereafter we refer to each light curve with the corresponding alphanumeric ID code reported in Table 1. Overall, thirtyeight archival light curves were (re)analyzed in the present study:

Gibson et al. (2008): two transits in 2008 (G12) observed with the RISE camera mounted at the 2.0 m Liverpool Telescope. Both nights were photometric. The second series (G2) ended just before the last contact. The RISE camera filter has a custom wideband 500 − 700 nm, approximately covering both the Johnson R and V passbands.

Tripathi et al. (2010): five transits in 2008/2009 (T15) from two different telescopes (Fred Lawrence Whipple Observatory FLWO1.2 m and University of Hawaii UH2.2 m) and in three Sloan passbands (g, i, z), gathered to complement their highprecision RV measurements. The first two FLWO i transits (T12) are partial, the first one missing the first contact by only few minutes.

Damasso et al. (2010): one complete transit observed in 2009 (D1), with a commercial 0.25 m reflector in a nonstandard R band, as a part of the feasibility study for a project dedicated to the search for transiting rocky planets around M dwarfs.

Maciejewski et al. (2010): six complete transits in the R band from two different telescopes (M13 at Rohzen0.6 m, M46 at Jena0.9 m). The first five observations (M15) were carried out on focused images, a practice resulting in a possible increase of the content of red noise.

Christiansen et al. (2011): six complete (C14, C78) and two partial (C56) transits, extracted from an 18day photometric series secured by the High Resolution Imager (HRI) mounted on the spacecraft EPOXI, as part of the EPOCh project. No filter was employed.

Littlefield (2011): three transits observed with an 11′′ SchmidtCassegrain reflector and without filter (L13). These three light curves correspond to the first, third, and fifth ligh curve presented in the original paper. The S/N of the other curves is too low to include them in the present study.

Zhang et al. (2011): one 2009 transit in the V band from the Weihai1.0 m telescope (Z1).

Sada et al. (2012): four transits secured in 2009 − 2011 by different telescopes: S1 and S34 at the 0.5 m Visitor Center telescope at Kitt Peak National Observatory (KPNO), in the Sloan z band; S2 at the KPNO 2.1 m reflector in the J band, exploiting the FLAMINGO infrared imager.
The first two followup light curves of WASP3b were published by Pollacco et al. (2008): one transit observed at the IAC80 (alternating V and I filters) and one at the Keele0.6 m (R band), both in 2007. Unfortunately, the original light curves are not retrievable anymore and we did not include them in this study. A T_{0} data point is determined by the first term of their published ephemeris: (1)One should be careful, however, because this T_{0} (corresponding to 2007 Feb. 12) is not an independent measurement of a single transit event. Instead, it comes from an ensemble analysis of SuperWASP, IAC80 and Keele0.6 m data. For this reason we adopted T_{0} from Eq. (1) as our first data point in the determination of our new ephemeris, but not in our subsequent TTV analysis (Sect. 5.2). The epoch N of each reported observation in our set is defined according to the ephemeris in Eq. (1), i.e., as the number of transits elapsed since 2007 Feb. 12.
All timestamps were converted to BJD(TDB), i.e., based on barycentric dynamical time following the prescription by Eastman et al. (2010). Each light curve was calibrated in time by identifying the time standard reported in the data headers and (when clarifications were necessary) contacting the authors. Generally speaking, even when the authors report a reliable synchronization source (GPS, NTP, etc.) for their data, it is impossible to carry out an external confirmation of that. The only exception, discussed in Sect. 6, is when two or more independent observations of the same event were performed. Though we did not find any reason to doubt the accuracy of the absolute time calibration of these data, it is worth noting that most of these observations were not performed with the specific goal of a TTV analysis. Thus, the precision achievable on T_{0} could be limited by suboptimal choices made about the instrumental setup. For instance, it is widely known that a “long” (in our case, τ ≳ 60 s) exposure time is one of those limiting factors (Kipping 2010).
When required, light curves in flux units were converted into magnitudes and normalized to zero by fitting a loworder polynomial function to the offtransit data points. In a few cases, the tabulated photometric errors are underestimated up to about 50%, as confirmed by the reduced (χ^{2} being defined as the χ^{2} divided by the number of degrees of freedom of the fit). This is not unusual in highprecision photometry owing to effects that are not accounted for by standard noise models (Howell 2006): poorly modeled scintillation, highfrequency systematics mimicking random errors, stellar microvariability for both target and comparison stars, etc. We dealt with this by rescaling the errors by a factor of , following a common practice (Winn et al. 2007; Gibson et al. 2009). When the photometric errors were not published, the error was assumed to be constant and equal to the scatter σ of the offtransit polynomialcorrected curve. We define the scatter as the 68.27th percentile of the residual distribution from the median, after a 5σ iterative clipping. This measurement is much more robust against outliers than the classical RMS.
4. Data reduction
4.1. IAC80 photometry
The six IAC80 light curves (N16) were reduced with the STARSKY photometric pipeline presented in Nascimbeni et al. (2011a,b) but here upgraded with some improvements. The present version v1.1.002 adopts a new, fully empirical weighting scheme to carry out differential photometry. Reference stars were previously weighted by the amount of scatter measured on their light curves after being registered to the total reference magnitude m_{i} (that is, the weighted mean of the instrumental magnitudes of all comparison stars; Broeg et al. 2005). That was an iterative process. Instead, the updated version first extracts the offtransit part of the series, then constructs a set of “intermediate” light curves of the reference stars by subtracting the magnitude of each of them to the offtransit magnitude of the target. Ideally, those curves should be flat and their RMS should be equal to the quadratic sum , where σ_{t} is the theoretical photometric noise expected on the target (calculated as in Nascimbeni et al. 2011a) and the intrinsic noise of the reference star, defined as at the end of Sect. 3. We therefore estimated the latter as . The individual weights for a given comparison star are then assumed to be . The output of this weighting algorithm is checked during each run against two other weighting schemes: (1) equal weights, i.e., unweighted; and (2) using weights derived from the expected theoretical noise computed for the reference stars. The DSYS and PSYS parameters (as defined in Nascimbeni et al. 2011b) allow us to diagnose “bad” reference stars, and to set their weights to zero. For all the N1N6 transits, the same set of eleven reference stars was employed for consistency reasons. None of them shows signs of variability or higherthanexpected scatter.
A second improvement to STARSKY is a new algorithm developed to deal with light curves with red noise caused by veils, trails, or thin clouds. This happens when the cloud possesses a structure at angular scales on the same order as the FOV, and/or it is moving fast. Even differential photometry can be affected by these events, as the change of transparency can affect the target and the reference stars by a different amount. Of course, this systematic effect is correlated on with the rapidity of transparency changes. and this correlation can be exploited to discard the affected frames. A quantity that we called “numerical derivative of the absolute flux” (NDAF) is evaluated for each frame i of the series (2)where F_{i} is the weighted instrumental flux of the reference stars (F_{i} = 10^{ − 0.4mi}, m_{i} defined as above), and t_{i} is the JD time at the midexposure. When NDAF deviates more than 4σ from its average along the series, the frame is discarded. The first and last frame are ignored by our algorithm.
STARSKY outputs light curves extracted from a set of different photometric apertures. These curves are then detrended by a routine that searches for linear and polynomial correlations between the offtransit flux and several combinations of external parameters such as the position of the star on the detector, the airmass, the FWHM of the stellar profiles, the mean sky level, the reference flux F_{i}, and time. In the following, we describe the reason why we searched for a linear correlation between differential flux and airmass X. We considered the case of two stars (target “t” and reference “r”) with outofatmosphere magnitudes m_{t} and m_{r} and color ξ_{t} and ξ_{r}, respectively. Given the extinction coefficient k and the extinction color term k′, the measured differential magnitude Δm is the difference between the observed magnitudes (3)By grouping the involved terms, and taking into account that X is the only quantity that shows shortterm variations, (4)it is easy to see that systematic effects caused by differential extinction on the “true” (intrinsic) differential magnitude (m_{t} − m_{r}) are linearly proportional to X.
Eventually, we chose the light curve with the smallest amount of scatter σ and the lowest level of red noise estimated from the β parameter as defined by Winn et al. (2008). The overall S/N of an observation can be quantified by rescaling the unbinned photometric σ of the light curve (with a net cadence τ) on a standard 120s timescale, that is, by calculating . With the only exception of N3, the final IAC80 light curves have σ_{120} = 0.67 − 0.95 mmag (Table 1, Fig. 2), only slightly higher than that achieved by Gibson et al. (2008), Tripathi et al. (2010) and Christiansen et al. (2011), with spacebased or much larger facilities. N6 shows a large amount of red noise of unknown origin, which is probably related to colordependent systematics caused by variable atmospheric extinction. For the abovementioned reasons, N3 and N6 were employed in the determination of our new ephemeris, but not in our TTV analysis (Sect. 5).
4.2. UDEM photometry
Standard darkcurrent subtraction and twilight sky flatfield division process were performed for calibration on each image of the UDEM light curves (U15). Aperture differential photometry was carried out on the target star and 4 − 6 comparison stars of similar magnitude (  Δm  ≲ 1.5). The apertures used varied for each date due to defocus and weather conditions, but they were optimized to minimize the scatter of the resulting light curves. We found that the best results were obtained by averaging the ratios of WASP3b to each comparison star. This produced smaller scatter than the method of ratioing the target star to the sum of all the comparison stars. We estimated the formal error for each photometric point as the standard deviation of the ratio to the individual comparison stars, divided by the square root of their number (error of the mean).
After normalizing the target star to the comparison stars and averaging, some longterm systematics as a function of time were found. This is perhaps caused by differential extinction between the transit and comparison stars, which generally have different and unknown spectral types. This variation was removed by fitting a linear airmassdependent function to the outoftransit baseline of the light curve.
Orbital/physical parameters of WASP3b estimated from individual data (sub)sets.
5. Data analysis
5.1. Fitting of the transit model
We chose to analyze all new and archival light curves employing the same software tools and algorithms. Our goal was to obtain a homogeneous estimate of the physical/orbital parameters of WASP3b. In particular we were interested for our TTV analysis in estimating the T_{0} of each transit and its associated error in the most accurate way, avoiding biases caused by different techniques. We avoided estimating T_{0} through heuristic algorithms that assume a symmetric light curve, such as that developed by Kwee & van Woerden (1956). The main reason is that they do not fit for any quantity other than T_{0}. Even more important, they are not robust against outliers, they provide values of T_{0} known to be biased (Kipping 2010) and errors on T_{0} known to be underestimated (Pribullaet al. 2012).
JKTEBOP^{2} (Southworth et al. 2004) is a code that models the light curve of a binary system by assuming both components as biaxial ellipsoids and performing a numerical integration in concentric annuli over the surface of each component. JKTEBOP version 25 was run to fit a model light curve over our data and to derive the four main photometric parameters of the transit: the orbital inclination i, the ratio of the fractional radii k_{r} = R_{p}/R_{ ⋆ }, the sum of the fractional radii Σ_{r} = R_{p}/a + R_{ ⋆ }/a (R_{ ⋆ } is the stellar radius, R_{p} the planetary radius, and a the orbital semimajor axis), and the midtransit time T_{0}. We chose to fit i, k_{r}, Σ_{r} independently for each data set, because in a perturbed system i and Σ_{r} could change over a long timescale, while k_{r} is an important diagnostic of light curve quality: when the photometric aperture is contaminated with flux from neighbors, the transit is diluted and k_{r} becomes smaller. Moreover, an independent fit allows us to highlight correlations between i, k_{r}, Σ_{r} and to derive more reliable global results, as discussed at the end of this section.
We set a quadratic law to model the limbdarkening (LD) effect, naming u_{1} the linear term and u_{2} the quadratic term: I_{μ}/I_{0} = 1 − u_{1}(1 − μ) − u_{2}(1 − μ)^{2} and μ = cosγ, where I_{0} is the surface brightness at the center of the star and γ is the angle between a line normal to the stellar surface and the line of sight of the observer. Southworth (2010), among others, has shown that fixing the values of both u_{1} and u_{2} should be avoided, as it could lead to an underestimate of the errors. On the other hand, most light curves have an S/N too low to let both u_{1} and u_{2} free, and the resulting bestfit results can be unphysical. We set the quadratic term u_{2} always fixed to its theoretical value interpolated from the tables computed by Claret (2000; BVR_{c}I_{c} bands), and Claret (2004; Sloan ugriz), adopting the stellar parameters of WASP3 derived by Pollacco et al. (2008). For all light curves from nonstandard photometry, that is, unfiltered CCD photometry (C18, L13, E1) or from wideband R + V photometry (G12), estimating firstguess LD coefficients is not trivial. As for G12, we interpolated u_{1} = 0.24 and u_{2} = 0.38 from the tables by Claret (2000) by taking the average of the values tabulated for the JohnsonV and CousinR bands, as done by Gibson et al. (2008). We did the same for C18, L13, and E1, assuming that the quantum efficiency of a typical unfiltered CCD usually peaks somewhere in between those two bands.
Then one of the three following procedures was applied:
 1.
On the data sets with a high overall S/N and with two or more transits gathered with the same instrument and filter (G12; T13; T5T6; M13; M45; C18; L13; N15) we first fitted a model with free i, k_{r}, Σ_{r}, T_{0} (and u_{1} fixed at its theoretical value) to the “best” individual light curves to derive a preliminary estimate of their T_{0}. For “best” we mean complete transits with high S/N: our choice is summarized in Table 2, fourth column. Then we phased those curves setting T_{0} = 0. The free parameters i, k_{r}, Σ_{r}, u_{1} were fitted again on the stacked light curve to obtain a highS/N “reference” model of the transit by integrating the information contained in the whole set. We fixed i, k_{r}, Σ_{r}, u_{1} to their bestfit values, and fitted a model with only T_{0} as free parameter on all individual transits, including the lowS/N or partial ones.
 2.
On T4, a highS/N but single light curve, we carried out one simultaneous fit with i, k_{r}, Σ_{r}, T_{0}, and u_{1} as free parameters.
 3.
In all other cases, the data quality did not allow us to constrain u_{1} to values with physical meaning, thus u_{1} was fixed to its theoretical value along with u_{2}. Each transit was then fitted individually to derive i, k_{r}, Σ_{r}, and T_{0}.
As the formal errors derived by least squares techniques are known to be underestimated in presence of correlated noise, we took advantage of two techniques implemented in JKTEBOP to estimate realistic errors: a Monte Carlo test (MC) and a bootstrapping method based on the cyclic permutations of the residuals (RP or “prayer bead” algorithm, Southworth 2008). The errors on all parameters obtained with the RP algorithm are on average significantly larger for most of the archival light curves, suggesting a nonnegligible amount of red noise. We thus conservatively adopted the RP results in our subsequent analysis. Mean values and error bars can be estimated in two different ways: (1) as the arithmetic mean of the RP distribution associated to its standard error ± σ; and (2) as the median of the RP distribution along with its 15.87th (σ_{ − }) and 84.13th percentile (σ_{ + }). The first estimate assumes a Gaussian distribution, while the latter is purely empirical: they should match in absence of red noise.
We adopted as final results the RP median and uncertainties σ_{ + }, σ_{ − } for every fitted parameter except T_{0}. The estimated T_{0} is analyzed in Sect. 5.2 with periodogram techniques that cannot deal with asymmetric error bars, thus for this parameter we adopted the RP means with Gaussian errors ± σ. The bestfit values of Σ_{r}, k_{r}, i and u_{1} modeled on each individual data set are summarized in Table 2. We also show the theoretical value of the linear LD coefficient u_{1, th} as interpolated from Claret (2000, 2004). On all subsets, u_{1} and u_{1, th} agree within ~ 1σ. This holds even for C18, L13, and G1, demonstrating that assumptions previously made on nonstandard “clear” or R + V photometry are reasonable.
Fig. 2
Construction of the bestfit model from the four best light curves of WASP3b observed at IAC80 (on 2011 May 7, May 21, Jun. 26, Jul. 20). The ID# of each transit (N1, N2, N4, N5) matches the corresponding entry in Table 1. Small gray dots represent the data points with the original cadence, while blue circles are binned on 120 s intervals. The red line is the bestfit from JKTEBOP (Table 2). Left panel: individual light curves. Transits are offset in magnitude by a multiple of 0.02 for clarity. Middle panel: residuals from the bestfit model. The reported scatter is evaluated on the binned points as the 68.27th percentile from the median value. Right panel: stack of all four IAC80 light curves with the bestfit model superimposed. The derived parameters are quoted in Table 2. 

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Fig. 3
Geometrical parameters of WASP3b estimated from individual data (sub)sets (Table 2) plotted as black labeled circles in their twodimensional parameter space to highlight the sizeable correlation between Σ_{r}, k_{r}, and i. The blue dashed line in each plot is a weighted linear fit of all points; the blue triangles and the associated error ellipse correspond to the weighted mean ± 1σ computed on the marginal distribution of Σ_{r}, k_{r}, and i (last but one row of Table 2). The red continuous line and squares are computed in the same way as the blue ones, but after removing the outlier labeled “3” from the set (T1,T3; last row of Table 2). 

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In an unperturbed system, the transit parameters Σ_{r}, k_{r}, and i are purely geometrical and should not depend on wavelength or observing technique. Even if the system is suspected of being perturbed, one can check the longterm consistency of Σ_{r}, k_{r}, and i by comparing the bestfit values estimated for independent data sets (Table 2). It is then possible to integrate all extracted information to obtain final quantities of higher precision. We computed the weighted means of all subset estimates of Σ_{r}, k_{r}, and i listed in Table 2, obtaining the result shown in the last but one line of the same table ( ⟨ weighted mean ⟩ _{1}). As pointed out from previous works (e.g., Southworth 2008), these three quantities are correlated with each other, as becomes evident by plotting their individual estimate on planes projected from the threedimensional parameter space (Σ_{r}, k_{r}, i) (Fig. 3). Apart from this, the consistency among all measurements is assessed within the error bars, and we conclude that no variation of Σ_{r}, k_{r}, or i is detectable over the timescale covered by our data. The data point extracted from subset T1,T3 appears as the only probable outlier in two correlation plots out of three. We reevaluated the weighted mean after removing that point ( ⟨ weighted mean ⟩ _{2} in Table 2). The resulting averages are quite similar to those evaluated without removing the outlier, but the uncertainty on k_{r} is smaller. We adopt the second mean as final estimate: More in general, results obtained from subsets T13 (Sloan i) and T56 (Sloan g) slightly but significantly disagree with each other, which was already noted by Tripathi et al. (2010), who attributed this to the presence of residual red noise.
5.2. TTV analysis
The bestfit T_{0} values for each transit after uniform conversion to BJD(TDB) are shown in Table 3 along with their estimated ± 1σ uncertainties (second column). For completeness we also tabulated the median value of T_{0} estimated from the distribution of the RP residuals (third column of Table 3) along with its 15.87th (σ_{ − }) and 84.13th percentile (σ_{ + }).
To check which light curves within our sample are significantly affected by red noise, we considered the two diagnostic parameters β and Σ. The first one is defined as in Winn et al. (2008): the light curve is averaged over M bins containing N unbinned points each, then β is calculated as (8)that is, β is the ratio between the scatter σ_{N} measured on a given temporal scale Δt = Nτ, and the expected noise estimated by rescaling the unbinned scatter σ assuming Gaussian statistics. Ideally, we expect β ≃ 1 for independent and random errors (i.e., pure “white noise”), higher values indicating red noise at time scales ~Δt. The time scales around Δt ≃ 25 min are the most important ones for our purposes, because they correspond to the duration of the ingress/egress part of the WASP3b light curve. As shown by Doyle & Deeg (2004), those are the parts with the highest information content about T_{0}. We chose to compute β on a set of averaging times between Δt = 20 and 30 min, then we took their arithmetic mean as a final estimate for β.
The second diagnostic is Σ. We mentioned above that the distribution of the RP residuals around the bestfit value should be symmetric if the noise budget is dominated by white noise. Hence a “skewed” distribution could highlight a significant amount of red noise. The opposite is not always true: shortterm systematics (Δt ≲ τ) do not necessarily lead to skewed RP residual distributions. We parametrized this “skewness” with the ratio Σ between the largest and the smallest error bar σ of a given data point (9)In principle, Σ ≃ 1 for wellbehaved transits, and Σ ≫ 1 for transits dominated by longterm systematics. Table 3 lists Σ for all employed T_{0}. We found 1.01 < Σ < 1.63 for the eleven TASTE transits (N16, U15). Instead, a few archival data points show unusually high values (e.g., Σ = 8.07 for T2). We investigated this issue by comparing the most significant T_{0} published in the literature (T15; G12; C18; M16) with those derived by our reanalysis (Fig. 4, third panel from the top). We concluded that the vast majority of the published estimate agree within the error bars with ours. Notable exceptions are T1, T2, and G2: they all are partial transits, and T2, G2 have also large Σ. This is exactly what we expected. It indeed demonstrates that when a light curve lacks the offtransit part, its normalization becomes difficult, and even a very small difference in the adopted technique can lead to significantly different T_{0} measurements. We emphasize this conclusion because many TTV studies employ partial transits (some of them even for the most part: among others, Pál et al. 2011 and Fulton et al. 2011). While this is fine when estimating the orbital and physical parameters of the planet, we demonstrated that partial light curves should be included with extreme caution in a TTV analysis. We note that, on average, our error bars are larger than the published ones – sometimes by a factor of two –, confirming our concern that most measurements carried out in the past have been published with underestimated errors due to neglected red noise.
We considered two different samples of measurements for our TTV analysis. The first (“ALL”) includes all the 49 T_{0} listed in Table 3, plus the T_{0} from the ephemeris Eq. (1) from Pollacco et al. (2008). The second sample (“SELECTED”) is a highquality subset of 36 values, selected by excluding Eq. (1) (it does not correspond to an independent measurement of one single transit) and other 13 data points using the following rejection criteria:
 1.
partial light curve: data points lacking between the first and the last contact;
 2.
large scatter: σ_{30} > 1 mmag (σ_{30} defined as the RMS of the residuals after averaging over 30min bins);
 3.
red noise: Σ > 2 or β > 1.2;
 4.
presence of systematics during or close to the transit ingress/egress, as determined by visual inspection of the residuals.
The first step to plot an O − C diagram is to calculate a “reference” linear ephemeris to predict T_{0} at any given epoch. We set the new zero epoch at N2, i.e., our most accurate light curve. The ALL sample was employed to fit a linear model by ordinary weighted least squares, obtaining (10)The uncertainties were evaluated from the covariance matrix of the fit, and were both rescaled by to take into account the real dispersion of the data points around our bestfit ephemeris. In Fig. 4 are plotted the O − C diagrams for ALL (first panel from top) and SELECTED samples (second panel, with a smaller baseline). In both diagrams, the reduced suggests that the measurements do not fully agree with the linear ephemeris in Eq. (10). Yet, there is no evident periodic pattern in our diagrams. We investigated the possibility that this statistically significant scatter is caused by a genuine TTV, either the TTV claimed by Maciejewski et al. (2010) or a different one.
Fig. 4
First panel from the top: O − C diagram for all data points tabulated in Table 3. Second panel: same as above for points selected as in the last column of Table 3. Third panel: comparison between the original T_{0} published by the respective authors (white circles with gray error bars; Table 1) and as reestimated in this work (red triangles and bars) for the subset of highprecision light curves identified in the horizontal axis. Fourth panel: GLS periodogram for the complete sample (red line, highest peak at A) and the selected sample (black line, highest peak at S). The periodicity claimed by Maciejewski et al. (2010) is marked with the M label. 

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We exploited two algorithms to search for periodic signals: the generalized LombScargle periodogram (GLS; Zechmeister & Kürster 2009) and the “fast χ^{2}” algorithm (Fχ^{2}; Palmer 2009). Both these techniques are able to deal with irregularly sampled data with nonuniform weights, and minimize aliasing effects caused by the window function. In addition to this, Fχ^{2} can also search for an arbitrary number of harmonics.
We searched for periodic signals with GLS in the period range P = 4−1000 d, the lower limit being imposed by the Nyquist sampling criterion to avoid aliasing (Horne & Baliunas 1986). The resulting periodograms for both samples are plotted in the fourth panel of Fig. 4. In neither case a prominent peak is visible. The ALL and SELECTED periodograms are quite similar, and their highest peaks stand at P(A) ≃ 6.41 d and P(S) ≃ 11.29 d, respectively. The formal falsealarm probability (FAP) as defined by Zechmeister & Kürster (2009) is 0.023 (2.28σ) for the ALL power peak and 0.076 (1.77σ) for the SELECTED peak, i.e., only marginally significant. However, the formal FAP is derived under the assumption of pure Gaussian noise, which is not our case. To take into account the intrinsic dispersion of our data, we investigated whether these peaks are statistically significant with a resampling algorithm. We generated 10 000 synthetic O−C diagrams with the same temporal coordinates of actual data points by randomly scrambling the O−C values at each generation. A GLS periodogram was then evaluated on each of them with the same settings as applied on real data. The power of the highest peak found in the real data for ALL and SELECTED samples lies at the 12th (−1.17σ) and 38th percentile (−0.31σ) of the distribution of the maximumpower peaks in the synthetic, randomly permutated diagrams. We conclude that neither peak can be considered as statistically significant. In particular, the P(M) ≃ 127 days periodicity claimed by Maciejewski et al. (2010) is not consistent with our data. Instead of a peak, the periodogram range where the P(M) peak is expected is characterized by an extremely low GLS power (fourth panel of Fig. 4, blue region). On the other hand, tests on synthetic O−C diagrams with the same sampling and noise properties of our sample demonstrate that a P = P(M), Δ(O−C) = 0.0014 day signal corresponding to the Maciejewski et al. (2010) claim would be easily detectable from our data.
Fig. 5
Period analysis carried out on the same set of O − C data points analyzed by Maciejewski et al. (2010). Upper left panel: O−C diagram for the selected points. Upper right panel: GLS periodogram as a function of frequency ν, adopting the same plotting limits as Maciejewski et al. (2010). Bottom panel: GLS periodogram as a function of period, adopting wider limits on frequency according to the Nyquist criterion (see text for details). The red vertical line marks the peak claimed by Maciejewski et al. (2010). 

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We set Fχ^{2} to search for periodicities with one or two harmonics in the same frequency range. Results from both samples are quite similar to those obtained above with GLS, with nonsignificant power peaks at periods very close to those previously found in the GLS periodogram.
We also carried out our analysis on a subset of data points corresponding to those analyzed by Maciejewski et al. (2010) by employing the same tools as for our full data set (Fig. 5). When plotted adopting the same frequency limits, the resulting periodogram (and the peak corresponding to the maximum power) perfectly matches those published by Maciejewski et al. (2010, upper right panel of Fig. 5). On the other hand, the upper limit in frequency set by Maciejewski et al. (2010; 0.038P^{1}) is too low according to the Nyquist criterion. In the range 0.038 < ν < 0.5P^{1} many other maxima are as high as the 0.0145P^{1} peak (lower panel of Fig. 5). Following a statistical test similar to the one above described, we discard that peak as not significant and consider it to be caused by to smallsample statistics.
6. Discussion and conclusions
We analyzed eleven unpublished light curves of WASP3b and reanalyzed another thirtyeight archival light curves with the same software tools and procedures. We derived improved orbital and physical parameters for this target (Table 2), and computed a refined ephemeris (Eq. (10)). All individual measurements of the central instant T_{0} were compared with the new ephemeris to search for changes in the orbital period P of the transiting planet. We conclude that available observations of WASP3b, spanning more than four years, are not consistent with a linear ephemeris (). A possible explanation for this scatter is the presence of a perturbing body in the WASP3 planetary system.
It is known that the impact of red noise on highprecision transit photometry is still not fully understood. Previous claims of TTVs have been disproved on this basis (Southworth et al. 2012; Fulton et al. 2011). Could the observed scatter in the O − C diagram of WASP3b be explained in terms of underestimated observational errors or calibration problems? The absolute time calibration of each archival light curve cannot be independently checked. In principle one should trust the authors about that. However, we point out two main clues supporting the autoconsistence of the overall data, and hence the hypothesis of a genuine TTV:

on three different epochs (N = 444, 486, 653 following the Pollacco et al. 2008 ephemeris) multiple observations of the same transit are available. Because they were carried out by different authors at different facilities, they should represent independent measurements of the same quantity. All these data points (marked with a star in the first column of Table 3) agree with each other within their 1σ error bars, suggesting that the uncertainties on T_{0} are correctly evaluated by our pipeline;

some anomalous patterns in the O−C diagrams are confirmed by several different data sets. For instance, nearly all points gathered in 2009 within the range N = 440−510 lie ahead of the T_{0} predicted by our baseline ephemeris (O−C < 0). The only exception is U4, which essentially lies at O−C ~ 0 within its error bar. The weighted mean of these twelve measurements from eight different authors is O−C = −0.00118 ± 0.00016 days. This implies a 7.2σ deviation from a constant orbital period. These patterns can also be detected in highprecision data subsets, such as ours. Among the four best IAC80 transits, the first two (N12) are delayed by 4.3σ (i.e., O−C = 48 ± 11 s) compared with the prediction, while the second two (N45) are ahead of the ephemeris by 2.8σ (O−C = 35 ± 13 s).
Veras et al. (2011) demonstrated that some orbital configurations, especially close to (but not exactly in) meanmotion resonances, can induce quasiperiodic or even chaotic TTVs. In other nonexotic configurations, the periodicity would manifest itself only at time scales >10 yr (Veras et al. 2011). Also when more than one perturber is present whose orbital periods are not commensurable, as in the case of our inner solar system, the resulting TTV would be in general aperiodic (Holman & Murray 2005).
If WASP3b belongs to one of these cases, careful dynamical modeling and additional followup is required to confirm the hypothesis and to constrain the mass and period of the possible perturber(s). Photometric monitoring is still ongoing within the TASTE project, and highprecision RV measurements are planned with HARPSN. As stressed by Meschiari & Laughlin (2010) and Payne & Ford (2011), photometric TTVs and RVs are highly complementary in breaking the degeneracies that are common in the inverse dynamical problem.
We note that recently Montalto et al. (2012) reported an independent analysis of the WASP3 system, presenting also novel photometric data. We did not include these data in our work, nevertheless the conclusions reached by those authors appear very similar to ours.
Acknowledgments
This work was partially supported by PRIN INAF 2008 “Environmental effects in the formation and evolution of extrasolar planetary system”. V.N. and G.P. acknowledge partial support by the Università di Padova through the “progetto di Ateneo #CPDA103591”. V.G. acknowledges support from PRIN INAF 2010 “Planetary system at young ages and the interactions with their active host stars”. Some tasks of our data analysis have been carried out with the VARTOOLS (Hartman et al. 2008) and Astrometry.net codes (Lang et al. 2010). This research has made use of the International Variable Star Index (VSX) database, operated at AAVSO, Cambridge, Massachusetts, USA.
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Online material
Summary of the light curves of WASP3b analyzed in this work.
Central instants of WASP3b transits estimated from all individual light curves.
Appendix A: A new eclipsing variable
A star in the WASP3 field (UCAC3 , , epoch 2000.0; Zacharias et al. 2010), initially chosen as reference star, was found to be variable and was excluded from the reference list. A complete light curve of this variable was assembled by registering the magnitudes on the N12 and N4N6 frames on a common zero point (Fig. A.1, upper panel). When folded on the P ≃ 0.3524 day peak detected in the LombScargle periodogram, the binned curve shows a periodical pattern with equal maxima and slightly different minima, typical of contact eclipsing binaries (W UMatype; Fig. A.1, lower panel). We derived the following ephemeris, setting Φ = 0 at the phase of primary minimum and estimating uncertainties through a bootstrapping algorithm: (A.1)This variable star appears to be unpublished, and we submitted it to the International Variable Star Index (identifier: VSX J183407.3+353859). Colors from catalog magnitudes: V = 15.63, R = 14.99 (NOMAD; Zacharias et al. 2004), J = 14.64, H = 14.34, K_{s} = 14.21 (2MASS; Skrutskie et al. 2006), and proper motions μ_{α}cosδ = −32 mas/yr, μ_{δ} = 19 mas/yr (UCAC3) suggest that this object could be a binary with both components of lateG spectral type.
Fig. A.1
Light curve of a previously unreported R ~ 15 variable star in the WASP3 field, classified as a contact eclipsing binary (see text for details). Top panel: unbinned data points folded on the bestfit period P = 0.353626 days. Different nights are coded in different colors. Bottom panel: same as above, binned on 0.02 intervals in phase. 

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All Tables
Orbital/physical parameters of WASP3b estimated from individual data (sub)sets.
Central instants of WASP3b transits estimated from all individual light curves.
All Figures
Fig. 1
Light curves of WASP3b. The ID code of each transit matches the corresponding entry in Table 1. Data points are plotted with the original cadence, except for G1/G2 and Z1/E7, which are binned on 30 s and 300 s intervals for clarity, respectively. The red line is the bestfit model found by JKTEBOP. Transits are offset in magnitude by integer multiples of 0.025. 

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In the text 
Fig. 2
Construction of the bestfit model from the four best light curves of WASP3b observed at IAC80 (on 2011 May 7, May 21, Jun. 26, Jul. 20). The ID# of each transit (N1, N2, N4, N5) matches the corresponding entry in Table 1. Small gray dots represent the data points with the original cadence, while blue circles are binned on 120 s intervals. The red line is the bestfit from JKTEBOP (Table 2). Left panel: individual light curves. Transits are offset in magnitude by a multiple of 0.02 for clarity. Middle panel: residuals from the bestfit model. The reported scatter is evaluated on the binned points as the 68.27th percentile from the median value. Right panel: stack of all four IAC80 light curves with the bestfit model superimposed. The derived parameters are quoted in Table 2. 

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In the text 
Fig. 3
Geometrical parameters of WASP3b estimated from individual data (sub)sets (Table 2) plotted as black labeled circles in their twodimensional parameter space to highlight the sizeable correlation between Σ_{r}, k_{r}, and i. The blue dashed line in each plot is a weighted linear fit of all points; the blue triangles and the associated error ellipse correspond to the weighted mean ± 1σ computed on the marginal distribution of Σ_{r}, k_{r}, and i (last but one row of Table 2). The red continuous line and squares are computed in the same way as the blue ones, but after removing the outlier labeled “3” from the set (T1,T3; last row of Table 2). 

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In the text 
Fig. 4
First panel from the top: O − C diagram for all data points tabulated in Table 3. Second panel: same as above for points selected as in the last column of Table 3. Third panel: comparison between the original T_{0} published by the respective authors (white circles with gray error bars; Table 1) and as reestimated in this work (red triangles and bars) for the subset of highprecision light curves identified in the horizontal axis. Fourth panel: GLS periodogram for the complete sample (red line, highest peak at A) and the selected sample (black line, highest peak at S). The periodicity claimed by Maciejewski et al. (2010) is marked with the M label. 

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In the text 
Fig. 5
Period analysis carried out on the same set of O − C data points analyzed by Maciejewski et al. (2010). Upper left panel: O−C diagram for the selected points. Upper right panel: GLS periodogram as a function of frequency ν, adopting the same plotting limits as Maciejewski et al. (2010). Bottom panel: GLS periodogram as a function of period, adopting wider limits on frequency according to the Nyquist criterion (see text for details). The red vertical line marks the peak claimed by Maciejewski et al. (2010). 

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In the text 
Fig. A.1
Light curve of a previously unreported R ~ 15 variable star in the WASP3 field, classified as a contact eclipsing binary (see text for details). Top panel: unbinned data points folded on the bestfit period P = 0.353626 days. Different nights are coded in different colors. Bottom panel: same as above, binned on 0.02 intervals in phase. 

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In the text 
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