© ESO, 2011

1. Introduction

The NASA Kepler mission has been operational for more than one and a half years now (see Borucki et al. 2010, for a description of the mission and some first results). Its major science goal is to detect exoplanets, in particular Earth-like planets. Similar to the CoRoT mission (Fridlund et al. 2006; Auvergne et al. 2009), the transit method is used to detect signatures of exoplanets. This method requires the precise and continuous monitoring of large numbers of stars. As a consequence, a gold mine of variable star light curves at μmag precision is being produced. The nominal maximum time span of the data will be four years, while this is only some 150 days for CoRoT. Kepler will thus allow us to explore much longer timescales than CoRoT, while CoRoT’s denser time sampling (512 s versus 29.4 m) is more suited to probing the short-period variability domain.

We performed a global variability analysis of the public Kepler Q1 data, which was released on 15 June 2010, using automated supervised classification and extractor methods. Statistics on the number of variables and estimates of the class populations are presented. Special attention is paid to the detection of eclipsing binaries, and in particular, pulsating stars in eclipsing binary systems. The latter can provide us with model-independent constraints on astrophysical parameters such as mass and radius, which constitute essential input for asteroseismological studies. Since we find several new γ Dor and δ Sct candidates, we investigate the observational properties of these samples in more detail and compare them with those of known γ Dor and δ Sct stars in order to see if the improved precision leads to an extension of the observational instability strips. We also evaluate the samples of objects assigned to the new rotational modulation and stellar activity classes now considered by our classifiers, after CoRoT provided us with appropriate light curves to define these two classes.

To conclude, we briefly present a comparison of some Kepler light curves with ground-based TrES data of the same targets that we analysed using similar methods. The classification results are made available to the astronomical community in electronic form, since they are very useful for target selection and for studying different statistical aspects of the Kepler data.

2. Data description

The data analysed in this work include all  ~150 000 public Kepler light curves, measured in the first quarter of the mission. The total time span of the light curves is about 33 days, with a sampling interval of 29.4 min (long-cadence data). Only a small fraction of the light curves were measured in short-cadence mode, where the sampling interval equals  ~1 min. Kepler is observing in white light, with a bandpass of 430−890 nm FWHM. The observed stars have magnitudes ranging from 9 to 16. We used the corrected fluxes for our analysis, since they suffer less from instrumental systematics, and most outliers had already been removed from the data. To complement the light curve information and to evaluate our results, we also used the 2MASS colour indices present in the KIC catalogue (Kepler input catalogue).

Fig. 1 Two examples of light curves showing eclipses, as detected with our dedicated extractor method. The presence of additional variability in these light curves (possibly due to spots) caused them to be missed as binaries by our regular classifiers.

3. Methodology

Our methodology is similar to the one applied in Blomme et al. (2010), and described in more detail in Debosscher et al. (2009). Basically, we describe the main characteristics of each light curve by performing a Fourier-decomposition, including a maximum of three independent frequencies, each with a number of overtones. The Fourier parameters are then fed to the supervised classifier, where they are compared to the parameters of template light curves (training set) belonging to several known stellar variability classes. Class assignment is done in a probabilistic way, since light curves can share the characteristics of several variability classes at the same time. We keep improving the capabilities of the classifiers, and have now extended our training set to be able to recognize light curves showing the signs of rotational modulation and activity. We used the clustering results obtained from the CoRoT data, as presented in Sarro et al. (2009), to define these two new classes. Their template data consist of CoRoT exoplanet field light curves for now, but they will be extended in the future, since Kepler will provide many new examples. The definition of these new classes is still somewhat experimental, but as will be shown further on, good results are obtained with both classes.

We have also extended the methods to improve the detection of (single-)eclipses in light curves, regardless of the presence of other variability. It concerns an automated extractor method that complements the results of our supervised classification. The method is described in more detail in the following section.

3.1. Eclipsing binary detection

Our classifiers are able to identify eclipsing binaries in a reliable way, provided that several orbital periods are sampled by the light curves, or that enough measurements during eclipse are present. Otherwise, their signatures in the Fourier spectrum are very weak and difficult to identify with an automated method. Those cases are likely to be missed by the classifier. The presence of additional variability in the light curve, either instrumental or intrinsic to the object, hampers the detection of eclipses even more; therefore, we have developed an extractor method for those cases, which effectively complements the other classifiers. This method also allows us to detect eclipses when the orbital period of the binary is similar to or even equal to the period of the additional variability in the light curve. Basically, eclipses are detected as downward outliers in a high-pass filtered version of the light curve. The high-pass filtering removes the low-frequency content of the light curves, including instrumental trends and long-timescale variability. The resulting filtered version of the light curve only retains the high-frequency content, including part of the highly non-sinusoidal eclipse signal (the higher harmonics of the orbital frequency). As an additional advantage, several combination frequency peaks are removed as well (e.g. combinations of low frequencies that are filtered out, and higher frequencies). This effectively makes the high-frequency region in the amplitude spectrum less contaminated. The filter works by convolving the original light curve y(t_i,i = 1,N) with a sinc-function k(t_i), resulting in a new light curve Y(t_i): $\mathit{Y}\mathrm{\left(}{\mathit{t}}_{\mathit{i}}\mathrm{\right)}\mathrm{=}\mathrm{(}\mathit{y}\mathrm{\ast }\mathit{k}\mathrm{)}\mathrm{\left(}{\mathit{t}}_{\mathit{i}}\mathrm{\right)}\mathrm{=}\sum _{\mathit{j}\mathrm{=}\mathrm{1}}^{\mathit{N}}\mathit{y}\mathrm{\left(}{\mathit{t}}_{\mathit{j}}\mathrm{\right)}\mathrm{\ast }\mathit{k}\mathrm{(}{\mathit{t}}_{\mathit{i}}\mathrm{-}{\mathit{t}}_{\mathit{j}}\mathrm{)}\mathit{,}$(1)where k(t) is defined as $\mathit{k}\mathrm{\left(}\mathit{t}\mathrm{\right)}\mathrm{=}\frac{\sin \mathrm{\left(}\mathrm{2}\mathit{\pi ft}\mathrm{\right)}}{\mathrm{2}\mathit{\pi ft}}\mathit{,}$(2)with f the cutoff frequency, to be defined by the user. In our application to the Kepler data, we used a cutoff frequency of 1.5 d^-1. All frequencies above this value will be removed from the light curve. This technique is well known in electronic filtering systems. It is based on the mathematical result that convolution with a sinc-function in the time domain corresponds to multiplication with a rectangular bandpass function in the Fourier domain. The resulting light curve Y(t_i) is a low-pass filtered version of the original light curve y(t_i). The desired high-pass filtered version y_hf(t_i) is then obtained as ${\mathit{y}}_{\mathrm{hf}}\mathrm{\left(}{\mathit{t}}_{\mathit{i}}\mathrm{\right)}\mathrm{=}\mathit{y}\mathrm{\left(}{\mathit{t}}_{\mathit{i}}\mathrm{\right)}\mathrm{-}\mathit{Y}\mathrm{\left(}{\mathit{t}}_{\mathit{i}}\mathrm{\right)}\mathit{.}$(3)We now scan y_hf(t_i) for groups of downward outliers using box-plot statistics. This method has the advantage of being less sensitive to the underlying statistical distribution of the data. In the application to the Kepler data, we flagged the light curve if more than ten outliers were detected this way. This flag was then combined with the usual classification labels. Figure 1 shows two examples of eclipsing binaries detected using this method, while Fig. 2 illustrates the filtering process for one of the light curves. The filter will remove any kind of variability with frequencies below the cutoff value, but the eclipse detection only works well if the additional variability (not related to the eclipses) is confined to a frequency region below the cutoff frequency of the filter and if the eclipse signal has sufficient power (in the form of higher harmonics) above the cutoff frequency.

Fig. 2 Filtering process illustrated for KIC 4357272. The top plot shows the amplitude spectrum before (in black) and after the high-pass filtering (in red). The signal below the cutoff-frequency of 1.5 d-1 has been completely removed, while the signal at higher frequencies is retained, and now has a lower noise level. The middle plot shows the original light curve (black circles) with its low-frequency part superimposed (red curve, signal below 1.5 d-1). The high-pass filtered version is then obtained by subtracting the red curve from the original light curve, as shown in the bottom plot. The eclipses are now clearly visible and easily detectable with automated methods.

The value of the cutoff frequency we chose proved to be a good compromise between removing sufficient low-frequency content of the light curves (hampering the eclipse detection) and not removing too much high-frequency content, since the latter contains part of the eclipse signal. Given that we are especially interested in detecting pulsators in eclipsing binary systems (see Sect. 4.3), in particular γ Dor and SPB type, this cutoff value will remove most of the pulsation signal for those targets, making the detection of eclipses possible in these cases. At the expense of computation time, different cutoff values can be tried, and the eclipse detection can be done on different filtered versions of the light curves. For example, a higher cutoff frequency can be chosen to detect eclipses in the presence of higher frequency pulsations (otherwise, the filter will not remove any “disturbing” variability). However, higher cutoff values also remove more of the eclipse signal, and not enough power might remain to detect them. To avoid this and to limit the computation time, we performed an additional outlier detection step at the end of the light curve analysis procedure. The automated procedure removes a maximum of three different frequencies from the light curve (with each a maximum of four harmonics), in three consecutive prewhitening steps. This way, we only filter out the dominant signal, irrespective of its frequency. The residuals are then again checked for downward outliers, indicative of eclipses. It is clear that a combination of techniques is needed to detect all kinds of eclipse signals, even more so because additional variability on several timescales can be present as well. Our regular classifier reliably detects “pure” eclipsing binary light curves, irrespective of their orbital period, and the extractor methods can detect eclipses in the presence of additional variability, or when the eclipse signal is too faint to cause clear signatures in the Fourier spectrum. That the extractor scans the (filtered) light curve for outliers implies that it is well-suited to detecting detached system, with highly non-sinusoidal light curves. Close binaries, showing sinusoidal-like light curves, are better detected with the regular classifier.

4. Classification results

4.1. Number of variables

Following the application of our automated methods, we estimated the number of periodic variables in the dataset and constructed samples of good candidate members for the major stellar variability classes we included in our classifier.

Variability estimates are listed in Table 1, and they can be compared to Table 4 in Debosscher et al. (2009), where we made the same estimates for the CoRoT exofield database. A detailed description of the variability selection criteria can be found there. In short, we take a light curve to be variable if at least one of the three highest peaks in the amplitude spectrum is significant (significance parameter P_fi < P_max) and has a frequency value above a certain threshold (f_i > f_min). We list the resulting percentages for a few combinations of f_min and P_max. If we compare these with a short CoRoT observing run having approximately the same time span as the Kepler data, we find a significantly smaller fraction of variables. Kepler’s noise levels per measurement are significantly lower, as shown in Blomme et al. (2010), but the time sampling is not as dense: 29.4 min versus 8.5 min or even 32 s for a significant fraction of the CoRoT data. Probably, the estimates for CoRoT, though conservative, were still influenced by instrumental effects, amongst other things caused by the passage through the South Atlantic Anomaly (Auvergne et al. 2009). This passage causes impacts of charged particles on the CCDs, influencing the pixel responses in several ways. Measured flux levels can temporary increase or decrease, and this translates to discontinuities in the light curves. We refer to, e.g., Mislis et al. (2010) for a more detailed description of these instrumental effects. Often, several discontinuities are present in a single CoRoT light curve, causing peaks in various regions of the amplitude spectrum, but always with significant power at frequencies below 0.15 d^-1. Figure 3 plots the fraction of objects with significant variability (P-value of the dominant frequency f₁ below 0.1) and with a corresponding amplitude below a certain threshold, as a function of this threshold value. It is clear that the majority of variables have very low amplitudes, which can only be reliably detected using space-based instruments. This figure can be compared with Fig. 6 in Debosscher et al. (2009), where similar results were obtained (they are included in Fig. 3).

Fig. 3 Fraction of objects with f1 ≥ 0.1,0.15 d-1, Pf1 ≤ 0.1, and having an amplitude below a certain threshold value, as a function of the threshold value (in magnitude). The dotted curve represents the results obtained for CoRoT (Debosscher et al. 2009).

4.2. Class statistics

Table 2 summarizes the class statistics, including the remaining numbers of objects using different thresholds for the contamination level (taken from the KIC catalogue) of the light curves. We determined the number of good candidates for each class by first selecting the clearest variables assigned to each class using the criteria described in the previous section (P_f1 ≤ 0.1). Next we imposed limits on the Mahalanobis distance to the training class centre for the remaining sample (similar to sigma clipping). We retained only those candidates having a Mahalanobis distance below 1.5. In short, this distance measure is a multi-dimensional generalization of the one-dimensional statistical or standard distance (e.g. distance to the mean value of a Gaussian in terms of sigma). This distance can be used effectively to retain only the objects that are not too far from the class centre in a statistical sense. More details on this distance measure can be found in Debosscher et al. (2009). Note that our classifiers take more variability classes into account than those listed in Table 2. The full list of classes and their abbreviations used by our current classifiers can be found in Appendix A, while a description of the properties of the pulsators is available in Chapter 2 of Aerts et al. (2010). We only list results here for those classes expected to be populated in the Kepler field and whose typical variability behaviour is detectable with the current time span of the light curves. Similar to CoRoT, there are few classical pulsators, owing to the Kepler target selection procedure, which mainly favoured G-type stars on or near the main-sequence.

Fig. 4 Light curves and amplitude spectra of two objects in the binary list presented by Prša et al. (2011), and classified by us as δ Sct stars.

Fig. 5 An eclipsing binary containing a γ Dor or SPB-type pulsator. So far, only one eclipse has been detected, but future data releases might reveal more eclipses.

No good Cepheid candidates have been identified, but some candidates might show up when longer datasets become avaliable. Of the few RR Lyr light curves we identified, the majority turned out to be heavily contaminated. In fact, they all showed the variability of RR Lyrae itself, which falls in the Kepler field and whose brightness causes bleeding on the CCDs (Kolenberg, priv. comm.). This illustrates that users of the Kepler data must carefully check whether their targets are contaminated or not. The presence of a neighbouring variable can introduce variability in the light curve of nearby targets, because part of the flux of the neighbouring variable might be included in the pixel mask. More RR Lyr stars are present in the Kepler observing field, but their light curves are not included in this public data release. They belong to the asteroseismology dataset, part of which was analysed by us in Blomme et al. (2010). Some first Kepler results on those RR Lyr stars are described in Kolenberg et al. (2010).

Recently, a list of binaries in the Kepler Q1 data was made available by Prša et al. (2011). Since they only focused on binaries and used dedicated methods to detect them, we compared our sample of binaries with their results. Their list contains 1879 objects, of which 1767 are present in the public Q1 dataset. Here, we have only compared the results for the public light curves. We identified 1156 out of the 1767 objects as eclipsing binary or ellipsoidal variable using our global supervised classification method. The additional application of our dedicated extractor method increased the count to 1550 (88%), which is very good agreement given the difference in the methodology and the wide diversity of variability classes we consider. We have manually checked the objects we did not recognize as binaries with either method (in total 217): about half of those are clearly eclipsing binaries so they slipped our eclipse detection criteria. Their light curves have either very shallow eclipses or they have a very uncommon morphology not recognized by the current version of our classifier. Some 30 light curves have been confused with pulsators by our classifier: these are short period binaries with nearly sinusoidal light curves. They are confused with monoperiodic RR Lyr pulsators of subtype RRc or β Cep pulsators. The true nature of the remaining half of the 217 light curves in the list is less clear without any additional information. About ten of those show amplitude changes, indicative of rotational modulation, but the majority of the light curves resemble those of pulsating variables and are classified as such by our regular classifier. It is well known that light curves of close binaries can indeed be confused with those of RRc, high-amplitude δ Sct and β Cep pulsators. About 30 light curves are almost sinusoidal, and the majority are classified by our methods as δ Sct or β Cep. More investigation is needed to be certain about those cases, but if some of them turn out to be pulsators, they are probably RRc or δ Sct types (given that the massive β Cep stars are rare, see also Sect. 4.4). Remarkably, about 40 of the 217 light curves clearly show multiperiodic pulsations and are classified by us with high probability as δ Sct stars. Visual inspection of those light curves and their amplitude spectra showed they are clear δ Sct candidates indeed, as can be seen for two cases in Fig. 4. We have also checked the orbital periods they list for those cases, and these turn out to be twice the value of the main pulsation period we detected in the amplitude spectrum.

4.3. Variables in eclipsing binary systems

We detected several objects showing both clear eclipses and additional variability in their light curves. In some cases, multiperiodic variability is present, indicative of SPB, γ Dor or δ Sct type non-radial pulsations. Those objects deserve our special attention, and for some of them, spectroscopic follow-up is planned. By combining the Kepler light curves with ground-based spectra, it is possible to derive the orbital elements of the binary system, and model-independent estimates of stellar masses and radii. Those are key parameters for asteroseismological studies, and they are difficult to derive otherwise. Some nice examples are shown in Figs. 5−7 and another one from the KASC sample (KIC 11285625) was already shown in Gilliland et al. (2010). Figure 5 shows an object classified as a γ Dor star, and the eclipse was detected using our extractor method. The amplitude spectrum clearly shows several significant frequencies in the range 1−2 d^-1. The total time span of the data is yet too short to have high enough frequency resolution for asteroseismological studies. Figure 6 shows an eclipsing binary featuring both primary and secondary eclipses, and additional variability of SPB or γ Dor type. From the distance between the eclipses, we can see that it is an eccentric system. Note the similarity with KIC 11285625 in Gilliland et al. (2010). This object was classified as γ Dor by our regular classifier, and the eclipses were detected with our extractor method. Figure 7 shows an intriguing light curve with several phenomena occurring at the same time. The unusual combination of variability on different timescales caused this object to be assigned to the stellar activity class with low probability (see further for a description of this class), but the eclipses were detected using our extractor method.

Fig. 6 An eclipsing binary featuring both primary and secondary eclipses, and additional variability of SPB or γ Dor type, with a main frequency of 0.44 d-1.

Fig. 7 An intriguing light curve, showing several phenomena at the same time: eclipses followed by a sudden and short-lived increase in brightness, modulation of the light curve at a period that might be a subharmonic of the orbital period, and additional (pulsational) variability on shorter timescales.

The light curves of those systems are difficult to identify in a single step with a supervised classifier, since different phenomena are present at the same time, and their relative strengths can vary a lot. For example, a light curve with eclipses and additional pulsations will be classified as pulsating variable if the amplitude of the pulsation(s) in the Fourier spectrum is greater than the amplitude of the orbital peaks due to the eclipses (e.g. for KIC7422883). The reverse situation will cause the light curve to be classified as eclipsing binary. The situation is not that clear cut, when both phenomena have comparable strength in the Fourier spectrum. The current version of the classifier takes the three most significant frequency peaks into account (each with a maximum of four harmonics), and the first one may be related to the pulsations, while the others are related to the eclipses. This confuses the classifier, especially if the orbital period is very different from the pulsation period(s) (e.g. not in the same range as the typical pulsation periods for the type of variable present in the binary system). In these cases, the class labels have to be treated with caution (e.g. for KIC8719324). Therefore, we used the results of our eclipsing binary extractor to complement the classification results for detecting those objects.

In total, we could identify about 14 candidate pulsators in eclipsing binary systems. Of those, five are classified as SPB or γ Dor, and indeed they show pulsations of that type. They are flagged by the extractor method, indicating the presence of at least one eclipse in the high-pass filtered version of the light curve. Five objects have been identified as eclipsing binary by the classifier, and the additional variability was discovered by visual inspection of the binary sample. The remaining four objects are flagged by the binary extractor method (but not recognized as binary by the normal classifier), and the additional variability was again discovered by visual inspection.

4.4. Samples of candidate non-radial pulsators

Since we find many new candidate non-radial pulsators, we have examined some group properties of the samples. Our classifiers only use information obtained from the Kepler light curves (white light), and therefore cannot reliably distinguish δ Sct and β Cep pulsators or SPB and γ Dor pulsators. Their pulsation spectra are often very similar, but their positions in the Hertzsprung-Russell diagram are very different. We therefore use the 2MASS magnitudes from the KIC catalogue to analyse the samples in more detail. To better answer the question of how many stars are truly good candidate members for those four classes, we compared the 2MASS colour indices of the stars in our sample with those of bona-fide class members from the literature. In fact, we first determined the observational instability domain of those classes in 2MASS colour space. For the β Cep class and the SPB class, we used the extensive tables compiled by P. De Cat (available at http://www.ster.kuleuven.be/~peter/Bstars/), for the δ Sct class, we used the catalogue by Rodríguez et al. (2000), and for the γ Dor class we used the lists presented in Cuypers et al. (2009), Aerts et al. (1998), and Handler (1999).

For each of the combinations β Cep/δ Sct and SPB/γ Dor, we made 2MASS J − H versus H − K colour plots showing both the bona-fide literature samples and the candidate Kepler samples we obtained with our classifiers. We first cleaned our samples to retain only the best candidates, to see whether they fall in the regions occupied by known class members. Cleaning was done by imposing limits on the Mahalanobis distance to the training class centre, as described in Sect. 4.2.

We also investigated the interstellar reddening in the Kepler field to check whether significant colour shifts are present and might hamper our conclusions. The effects of interstellar absorption are relatively small for the H, J, and K infrared photometric bands. We estimated E(H − K) and E(J − H) for the majority of the Kepler stars by using the derived extinction values A_V from the Kepler field description available on the NASA MAST archive (Multimission Archive at STScI), in combination with the ratios A_band/A_V presented in Rieke & Lebofsky (1985). In Figs. 8 to 10 and Figs. 12 to 13, the average reddening vectors for the Kepler samples are indicated. For every star with available extinction values, we estimated E(H − K) and E(J − H). The components of the reddening vector are then constructed by taking the sample average of E(H − K) and E(J − H). Typically, the standard deviations of E(H − K) and E(J − H) for each Kepler sample are only about one third of their average values, thus justifying that we only show the average reddening vectors. We did not estimate the reddening for the bona-fide literature samples, since these samples contain nearby objects (mainly measured by HIPPARCOS) and are less influenced by reddening compared to the Kepler samples.

Fig. 8 Comparison in 2MASS colour space of samples of bona-fide SPB and γ Dor stars, and the candidates we find in the Kepler data. The blue star symbols represent bona-fide SPB stars, red squares represent bona-fide γ Dor stars, and the green triangles represent our sample of candidate SPB/γ Dor stars. The estimated average reddening vector for the Kepler sample is indicated with the black arrow.

Fig. 9 Comparison in 2MASS colour space of samples of bona-fide δ Sct and β Cep stars, and the candidates we find in the Kepler data. The blue star symbols represent bona-fide β Cep stars, red squares represent bona-fide δ Sct stars, and green triangles represent our Kepler sample of β Cep/δ Sct stars. The estimated average reddening vector for the Kepler sample is indicated with the black arrow.

Fig. 10 Objects assigned to the rotational modulation class, plotted in 2MASS colour space (red squares). For comparison, we also plotted our Kepler δ Sct sample (blue stars), the same as shown in Fig. 9. The estimated average reddening vector for the Kepler rotational modulation sample is indicated with the black arrow.

Figure 8 shows the results for the SPB/γ Dor classes. Clearly, most of our candidates fall nicely within the expected colour region of the γ Dor class when taking the effects of reddening into account, they are likely to be good candidates. This is not surprising, given that γ Dor stars are less massive (1.5 to 1.8 M_⊙) than SPB stars (2 to 7 M_⊙), hence much more abundant according to the initial mass function (see e.g. Scalo 1986). Given that we did not consider any colour information to classify the stars, this is a very nice result, showing that these classes of non-radial pulsating stars can be identified reliably using well-sampled white-light photometric time series. We conclude that our method can separate SPB/γ Dor candidates from other variability types and that we need colour information only in a second stage, to differentiate between SPB and γ Dor. We should also find at least some SPB candidates, given the large sample of stars. Indeed, a few of our candidates fall within the SPB domain in colour space and are likely SPB stars. Their visual magnitudes also do not exclude their SPB nature: these are bright objects and can only be present at the bright end of the Kepler sample.

Figure 9 shows a similar plot for the β Cep/δ Sct classes. The majority of our δ Sct candidates fall within the expected colour region for this variability class, when taking the effects of reddening into account, they are likely to be good candidates. This again illustrates the quality of our classification based on a single Kepler light curve alone. We do not expect to find many β Cep candidates, again based on the initial mass function (β Cep stars have masses in the range 8−18 M_⊙, while δ Sct stars have masses in the range 1.5−2.5 M_⊙), but also given their high luminosities: most Kepler targets are too faint to be β Cep stars, so they would have to be at a distance placing them outside the Milky Way! We should find even fewer β Cep than SPB candidates. Only one or two of our candidates fall nicely into the β Cep domain, and the visual magnitude is within the range of those of known galactic β Cep stars. Their light curves indeed show clear pulsations with frequencies in the β Cep range, making them convincing candidates. Spectroscopic observations are required to confirm their nature, also for the few SPB candidates we find.

About 4000 objects in the Kepler Q1 public dataset are present in the asteroseismology dataset as well (KASC, see Gilliland et al. 2010). We have also checked how many of our candidates are present in the corresponding class lists of the asteroseismology dataset, since candidate lists of these variables were made prior to the Kepler mission (the objects in the KASC dataset are distributed over several working groups, according to their suspected variability type). We found that only 36 out of our 295 best SPB/γ Dor candidates, and 75 out of our 313 best β Cep/δ Sct candidates, are present in the asteroseismology dataset. None of the 36 γ Dor candidates was present in the γ Dor sample of the asteroseismology data, while 55 out of the 75 β Cep/δ Sct candidates are present in the δ Sct sample. Clearly, we find many more good candidate pulsators in the public dataset that are not present in the asteroseismology set. By imposing less stringent limits on the Mahalanobis distance to the class centres, our sample sizes even increase, but we would include less obvious candidates and more false positives. This results is an increased scatter of the sample in 2MASS colour space. The border cases are also of interest, however, since we expect to find them at the borders of the pulsational instability strips, thus helping to better constrain them. Longer Kepler time series of these stars are thus immensly important for a better understanding of stellar structure and evolution.

Fig. 11 Two examples of Kepler light curves of objects assigned to the rotational modulation class, but clearly occupying a different region in 2MASS colour space (see Fig. 10). The first example belongs to the biggest subgroup and the second example belongs to the small subgroup.

Fig. 12 The same plot as Fig. 10, but now with the HIPPARCOS sample of semi-regular variables shown as well (green triangles). The estimated average reddening vector for the Kepler rotational modulation sample is indicated with the black arrow.

Fig. 13 The same plot as Fig. 10, now with our Kepler sample of objects assigned to the stellar activity class overplotted (green triangles). The estimated average reddening vector for the Kepler stellar activity sample is indicated with the black arrow.

Fig. 14 Two examples of Kepler light curves of objects assigned to the stellar activity class.

4.5. Rotational modulation and stellar activity

Both the rotational modulation and stellar activity classes are recent additions to our training set, and it is therefore important to assess how well these variability types can be distinguished from the many other forms of stellar variability. Cross-validation tests performed on our training set show that we can distinguish those light curves from the other training classes. However, to check the real performance of the classifier for these new classes, a large and completely independent data set has to be used. Since the Kepler Q1 public data contain more than 150 000 light curves of excellent quality and are expected to contain many objects showing the signatures of activity and rotational modulation, this is an ideal dataset for this purpose.

Fig. 15 Some examples of objects for which we found a match between the Kepler and TrES data. From top to bottom, the TrES and Kepler light curves of, respectively: an eclipsing binary, a γ Dor candidate, and a δ Sct candidate. The TrES light curves have been phased for visibility reasons according to the dominant frequency found in the data.

We made a selection of the best rotational modulation candidates, again by imposing limits on the Mahalanobis distance to the class centre. Using a cutoff-value of 1.5, we still retain almost 2000 candidates. Those candidates are plotted in 2MASS colour space in Fig. 10. For comparison, we also plot the same δ Sct sample as shown in Fig. 9, to show where the sample is located in the colour diagram with respect to the other classes. We can see that the rotational modulation sample is separated very well from the pulsator classes, while we did not use any colour information in the classification process. Also apparent is the clear subgroup visible in the upper right corner of the diagram. We have visually checked several light curves of objects located in both subgroups, revealing that these two subgroups really contain different kinds of objects. Typical examples of both groups are shown in Fig. 11, illustrating the periodicity in the light curves. Many objects in the biggest group show very clear signs of rotational modulation in their light curves, similar to the CoRoT light curves in the training set for this class. The objects in the small subgroup all exhibit clear long-term variability, with relatively large amplitudes. These are very red objects, and some of the light curves resemble those of semi-regular variables. In Fig. 12, we compare the position of these objects in the colour diagram to the regions occupied by semi-regular variables detected by the HIPPARCOS mission (Perryman & ESA 1997). The small rotational modulation subgroup clearly falls within the semi-regular region. They are not classified as semi-regular variables with our methods, but this is due to the insufficient time-span of the current light curves. Further investigation and time series with a longer time span are needed to shed more light on this group of variables.

Including this new class clearly constitutes an improvement of our classification capabilities, since many of those variables are present, and they can now be recognized clearly. Most of our candidates are located in the cool regions of the colour diagram, where we expect to find those stars. We do see some contamination of red giant stars in the sample of candidates though, suggesting that we need to tweak the classification parameters to avoid this confusion. With the many good examples of light curves present in the Kepler data, we plan to improve the definition of this class.

For the stellar activity class, we used a similar limit on the Mahalanobis distance to the class centre to select the best Kepler candidates, retaining about 1200 objects. More than 19 000 objects are assigned to this class in total, which is not surprising given the expected abundances of active main-sequence stars in the Kepler sample. Figure 13 shows the position of the best candidates in 2MASS colour space. The δ Sct and rotational modulation candidates are shown as well for comparison. The activity sample occupies the same region in colour space as the rotational modulation sample, corresponding to cool main-sequence stars. We indeed expect to find many active stars in this region. The activity sample is very well separated from the pulsator classes in colour space, again without using colour information in the classification process. Figure 14 shows two typical examples of light curves that ended up in the activity class. They show rather irregular variability (compared to the rotational modulation class) with long quasi-periods and small amplitudes, similar to the CoRoT light curves in the training set. Some objects in the sample show stricter periodic light curves, similar to those assigned to the rotational modulation class. The differences between those classes are based on light-curve morphology rather than on astrophysical grounds, since stellar activity and rotational modulation due to spots are related phenomena, occurring for stars in the same regions of the Hertzsprung-Russell diagram. Therefore, overlap between those classes is present, but the more regular light curves, with clear signs of stellar spots, will end up in the rotational modulation class. We believe it is useful, however, to keep the subdivision, since the light curves of both subclasses can have a very different morphology. Mixing those together in one class would degrade the classification performance. Another reason to keep the subdivision is that we can reliably identify the “simpler” light curves showing clear signs of rotational modulation, the latter being better suited to studying, e.g., stellar rotation and perform spot modelling.

5. Comparison with TrES ground-based data

Part of Kepler’s field-of-view overlaps one of the fields observed by the ground-based TrES survey (Trans-Atlantic Exoplanet Survey). The goal of this survey was to detect transiting planets using a network of three ten-centimetre optical telescopes. About 26 000 TrES light curves of the overlapping Lyr1 field have been analysed using adapted automated classification methods (Blomme et al. MNRAS, accepted). We did a cross-matching based on coordinates and magnitudes to identify common objects in both the TrES and Kepler datasets. Using a maximum search radius of 2 arcmin, we found 9963 matches. It is interesting to compare the quality of the light curves and to see how well the classifiers performed on data having a much higher noise level and containing daily gaps due to the day-night rhythm, in view of future ground-based surveys containing time-series data. For the 9963 matching objects, we compared the dominant frequency detected in the TrES light curve with the one detected in the Kepler light curve. Frequencies are taken to be equal if their difference is smaller than the frequency resolution obtainable with the Kepler light curves: |f_1,Kepler − f_1,TrES| < 1/T, with T the total time span of the Kepler light curves (the time span of the TrES light curves is about twice that of Kepler). We only considered frequencies higher than 0.6 d^-1, to assure that f/Δf is sufficiently large (minimal value of  ~20). This way, we found 119 confident frequency matches amongst the 9963 common objects in both databases. We then checked how many of those were assigned the same variability class by our classifiers. The results are summarized in Table 3. In total, 48 out of the 119 objects are assigned to the same class. The remaining 71 objects are either assigned to different classes or classified as “MISC” (Miscellaneous) in both cases. Amongst those are also four objects classified as δ Sct from the TrES data and classified as eclipsing binary from the Kepler data. This concerns short period binaries whose orbital period is in the same range as the pulsation periods of typical δ Sct stars. These illustrate that the higher quality of the Kepler data improved the classification of those targets (indeed turned out to be binaries).

Figure 15 shows some examples of variables whose classification from TrES and Kepler are equal: both the TrES and the Kepler light curves are plotted for an eclipsing binary with additional variability, a candidate γ Dor pulsator and a candidate δ Sct pulsator. The TrES light curves have been phased according to the dominant frequency found in the data for visibility reasons. These ground-based data have a much poorer quality than the Kepler data, and the variability is very difficult to see by eye in the original light curve. Nevertheless, those objects were classified correctly using the TrES data, showing the robustness of our methods. For the pulsating stars, we also find exactly the same dominant frequency peaks in the TrES and Kepler light curves, showing the reliability of the frequencies and the stability of the pulsation modes. The latter is very useful when doing asteroseismological studies of individual objects, since analysing two independent datasets is the best way to be certain about detected frequencies. Obviously, the Kepler data allow many more significant frequencies to be detected than the TrES data do, but we could at least verify the reliability of the three most dominant frequencies in ground-based data that were assembled with a completely different goal than asteroseismology, and, along with it, the suitability of target selection for follow-up dedicated studies of the best class candidates.

6. Conclusions

We have presented a global variability study of the public Kepler data, measured in the first quarter of the mission. In total, we analysed more than 150 000 light curves using automated classification and extractor methods. This database is unprecedented, because we never before had access to such a large sample of very-well sampled light curves with such high photometric precision. It is therefore an excellent dataset for doing statistical studies of the relative class populations of variable stars of all kinds and better constraining their instability domains.

To improve our detection capabilities, we introduced two “new” classes in our classification scheme: variables showing rotational modulation and active stars. We also supplemented our classifiers with a dedicated extracted method for eclipsing binaries, to improve the detection of faint eclipses and eclipses in light curves containing other variability as well. The method proves to be very effective: we could significantly increase the number of detected binaries and identified several pulsating stars in eclipsing binary systems. These pulsating stars are of special interest in the field of asteroseismology.

We presented variability estimates and class statistics, which are compared with similar studies of the CoRoT exoplanet data. The results for the relative class populations are fairly similar, since both missions focus on main-sequence targets, with the goal of detecting earth-like planets. This implies that the number of classical pulsators, such as RR Lyr and Cepheids in the datasets, are small, compared to the number of non-radial pulsators, such as δ Sct and γ Dor.

The samples of candidate non-radial pulsators we identified were evaluated by using 2MASS colour indices. We compared the position of our candidates in the colour diagram with those of known class members from the literature. The results convincingly show that our samples contain many new class members for the δ Sct and γ Dor classes, a few very good SPB candidates, and one or two candidates for the β Cep class. The use of colour indices allowed us to distinguish between δ Sct /β Cep and SPB/γ Dor, while this is not possible using only the light curve information. Our classifiers are, however, very capable of separating those combinations of two classes from other variability types, as confirmed by the well-constrained regions the candidates occupy in colour space.

We have positively evaluated the performance of our classifiers for the new rotational modulation and activity classes. Many good candidates could be identified for both classes, and they occupy well-defined regions in colour space, corresponding to cool main-sequence stars. This is where we expect to find these types of variability. We also discovered a clear subgroup in our rotational modulation sample, containing redder objects whose light curves show long-term variability. The nature of these objects needs to be investigated further, but we have strong indications that they are semi-regular variables.

Future work includes more detailed object studies and a spectroscopic follow up of selected non-radial pulsators, especially pulsating stars in eclipsing binary systems. We also plan to keep updating our training set used for the supervised classification, by including high-quality Kepler light curves once the true class membership is confirmed spectroscopically. A detailed clustering analysis of the Kepler database, as in Sarro et al. (2009) for the CoRoT data, is planned as well, since it contains so many excellent light curves. When more Kepler data has been released, we will have access to longer time series for most objects, allowing us to identify and study long-period variables as well.

Acknowledgments

We would like to express our special thanks to the numerous people who helped making the Kepler mission possible. The research leading to these results has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007–2013)/ERC grant agreement No. 227224 (PROSPERITY), from the Research Council of K.U. Leuven (GOA/2008/04), from the Fund for Scientific Research of Flanders (G.0332.06), and from the Belgian federal science policy office (C90309: CoRoT Data Exploitation, C90291 Gaia-DPAC). This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. Some or all of the data presented in this paper were obtained from the Multimission Archive at the Space Telescope Science Institute (MAST). STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. Support for MAST for non-HST data is provided by the NASA Office of Space Science via grant NNX09AF08G and by other grants and contracts. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France.

References

Appendix A: Stellar variability classes

All Tables

All Figures

	Fig. 1 Two examples of light curves showing eclipses, as detected with our dedicated extractor method. The presence of additional variability in these light curves (possibly due to spots) caused them to be missed as binaries by our regular classifiers.
In the text

Fig. 2 Filtering process illustrated for KIC 4357272. The top plot shows the amplitude spectrum before (in black) and after the high-pass filtering (in red). The signal below the cutoff-frequency of 1.5 d-1 has been completely removed, while the signal at higher frequencies is retained, and now has a lower noise level. The middle plot shows the original light curve (black circles) with its low-frequency part superimposed (red curve, signal below 1.5 d-1). The high-pass filtered version is then obtained by subtracting the red curve from the original light curve, as shown in the bottom plot. The eclipses are now clearly visible and easily detectable with automated methods.

In the text

	Fig. 3 Fraction of objects with f1 ≥ 0.1,0.15 d-1, Pf1 ≤ 0.1, and having an amplitude below a certain threshold value, as a function of the threshold value (in magnitude). The dotted curve represents the results obtained for CoRoT (Debosscher et al. 2009).
In the text

	Fig. 4 Light curves and amplitude spectra of two objects in the binary list presented by Prša et al. (2011), and classified by us as δ Sct stars.
In the text

	Fig. 5 An eclipsing binary containing a γ Dor or SPB-type pulsator. So far, only one eclipse has been detected, but future data releases might reveal more eclipses.
In the text

	Fig. 6 An eclipsing binary featuring both primary and secondary eclipses, and additional variability of SPB or γ Dor type, with a main frequency of 0.44 d-1.
In the text

	Fig. 7 An intriguing light curve, showing several phenomena at the same time: eclipses followed by a sudden and short-lived increase in brightness, modulation of the light curve at a period that might be a subharmonic of the orbital period, and additional (pulsational) variability on shorter timescales.
In the text

Fig. 8 Comparison in 2MASS colour space of samples of bona-fide SPB and γ Dor stars, and the candidates we find in the Kepler data. The blue star symbols represent bona-fide SPB stars, red squares represent bona-fide γ Dor stars, and the green triangles represent our sample of candidate SPB/γ Dor stars. The estimated average reddening vector for the Kepler sample is indicated with the black arrow.

In the text

	Fig. 9 Comparison in 2MASS colour space of samples of bona-fide δ Sct and β Cep stars, and the candidates we find in the Kepler data. The blue star symbols represent bona-fide β Cep stars, red squares represent bona-fide δ Sct stars, and green triangles represent our Kepler sample of β Cep/δ Sct stars. The estimated average reddening vector for the Kepler sample is indicated with the black arrow.
In the text

	Fig. 10 Objects assigned to the rotational modulation class, plotted in 2MASS colour space (red squares). For comparison, we also plotted our Kepler δ Sct sample (blue stars), the same as shown in Fig. 9. The estimated average reddening vector for the Kepler rotational modulation sample is indicated with the black arrow.
In the text

	Fig. 11 Two examples of Kepler light curves of objects assigned to the rotational modulation class, but clearly occupying a different region in 2MASS colour space (see Fig. 10). The first example belongs to the biggest subgroup and the second example belongs to the small subgroup.
In the text

	Fig. 12 The same plot as Fig. 10, but now with the HIPPARCOS sample of semi-regular variables shown as well (green triangles). The estimated average reddening vector for the Kepler rotational modulation sample is indicated with the black arrow.
In the text

	Fig. 13 The same plot as Fig. 10, now with our Kepler sample of objects assigned to the stellar activity class overplotted (green triangles). The estimated average reddening vector for the Kepler stellar activity sample is indicated with the black arrow.
In the text

	Fig. 14 Two examples of Kepler light curves of objects assigned to the stellar activity class.
In the text

	Fig. 15 Some examples of objects for which we found a match between the Kepler and TrES data. From top to bottom, the TrES and Kepler light curves of, respectively: an eclipsing binary, a γ Dor candidate, and a δ Sct candidate. The TrES light curves have been phased for visibility reasons according to the dominant frequency found in the data.
In the text