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Astron. Astrophys. 338, 479-490 (1998)

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4. Results

The final lightcurve presented here contains 17176 points acquired over three years, and gives a complete phase coverage for CM Dra (Fig. 3) at each of the three observational seasons. A break-down of the observational coverage is given in Table 3 and in Fig. 4. The 'typical rms noise' column in Table 3 is the noise of the final lightcurves from each telescope on good nights. On some very good nights, the rms of the larger telescopes was better than 2 mmag, whereas a noise of about 6 mmag was the cut-off for data to be included into the final lightcurves.

[FIGURE] Fig. 3. Plot of the composite lightcurve of CM Dra against phase, containing the 17176 data points obtained in 1994-1996. The two panels show the same lightcurve with different magnitude scaling


Table 3. Overview of observational coverage for the 3 years 1 Observing coverage is the length of the time for which a usable lightcurve of CM Dra was obtained. Coverage was considered continuous for interruptions of less than 15 minutes. 2 Observations were taken through a redshifted H[FORMULA] filter. 3 Some of these observations were taken in V band.

[FIGURE] Fig. 4. Coverage diagrams of the individual telescopes for 1994-1996

4.1. The noise of the lightcurve

Fig. 5 shows power spectra of the observed data over-plotted with spectra from model planetary transits with periods of 10, 20 and 45 days. The power spectra were calculated by phase dispersion minimization with the program POWER (Kjeldsen, personal communication). For the detection of planetary transits which may be hidden from ordinary view in the noise of the lightcurve, it is important to note the differences in the power spectra. The observational data have a relatively flat spectrum, with a maximum at frequencies around 7 day-1, corresponding to a period of 200 minutes. The power of the planetary transits peaks much more pronounced between 5 and 12 day-1 (corresponding to periods between 1 and 2.5 hours, which is the typical length of planetary transits), and there is little power left at frequencies above 20 day-1. For this analysis, the mutual eclipses of CM Dra, as well as the nightly extinction slopes have been removed which accounts for the absence of power at frequencies below 5 day-1. This also fortuitoisly removes most of the power from signals that appear with the period of CM Dra (such as starspots). As can be seen in Fig. 5, there is very little power left at CM Dra's period of 0.79 day-1. Also absent is the first harmonic at 1.58 day-1, which might be strong, since primary and secondary eclipses have nearly equal amplitudes.

[FIGURE] Fig. 5a-c. Smoothed relative power spectra of the observed lightcurve from 1994-1996 (solid line), over-plotted with power spectra for models of planet transits with 10, 20 and 45 day periods. The unit of the frequency axis is cycles per day. The vertical scale is in milli-magnitudes, however it is important to note that this scale applies only to the observed lightcurve. The power spectrum of the model-transits cannot be scaled to measurable units, since the duration of the transits is very short in comparison with the time between transits, where the model lightcurve has no signal. The models were calculated for the same time-points as the observed data. For both the observed data and the model-lightcurve, low frequent power (nightly extinction) was removed in the same way (see description in Sect. 3). In all cases, the power of the modeled planetary transits is concentrated towards frequencies of 5-15 day-1, whereas the power from the noise in the observed data is relatively flat.

4.2. Eclipse minima timing

An analysis of the minimum times of the mutual eclipses of an eclipsing binary may reveal the presence of a third body in this system. In such a case, the orbital period of the third body should cause periodic changes in the time of the minima, as the distance to the binary system is offset by its motion around the 3-body barycenter. In the CM Dra system, for example, a planet with the mass of Jupiter at a distance of 5 AU would cause a periodic shift of minimum times with an amplitude of 5.5 seconds (Doyle et al. 1997). This method is however unsuitable for the detection of planets with masses significantly smaller than giant planets. The three years of observational coverage of CM Dra contain 16 primary and 19 secondary eclipses, on which the time of minimum brightness could be measured reliably, with uncertainties of less than 10 seconds. Minimum times were measured with the 7 segment Kwee-Van Woerden method (Kwee & Van Woerden 1956). We also re-measured the minimum times of the three eclipses observed by Lacy (1977). Against the epochs cited by Lacy, re-measuring gave discrepancies of 10 and 35 seconds for his two primary eclipses, and a discrepancy of 6 seconds against the one secondary he observed. We therefore prefer to assign new epochs to CM Dra as follows: primary eclipse: JD 2449830.757 00[FORMULA]0.000 01, secondary eclipse: JD 2449831.390 03[FORMULA]0.000 01, and a period of 1.268 389 861[FORMULA]0.000 000 005 days, based on a fit to the 35 minimum times from 1994 to 1996 and the remeasured values for Lacy's primary eclipses. With these new elements, our observed - calculated (O-C) minimum times have a scatter of only about 6 seconds. This small scatter excludes periodic changes in the minimum times with amplitudes larger than 9 seconds and periodicities of less than about 4 years. We therefore cannot support the claim made by Guinan et al. (1998) of a 70.3 day periodic variation in minimum times with an amplitude of 18 seconds, that would have been indicative of a very massive planet (see also Deeg et al. 1998).

4.3. Flares

Several flare events of CM Dra were observed. In Table 4, the time of the peak maximum, the total duration, maximum brightness, the average noise(rms) of that night, and the observing telescope are given. Lacy (1977) already noted the low flare rate of CM Dra compared against the rate of [FORMULA] expected for a Population I flare star. Our observations confirm a low flare rate of [FORMULA] over the 3 years of observations, although only 2 flares were observed in 1995, corresponding to a rate of [FORMULA]. Since only flares with durations of more than several minutes (identified flares had to contain more than one data-point, as spikes of single points may also be caused by cosmic rays hitting near CM Dra) and with amplitudes of [FORMULA] could be identified clearly, the observed flares represent a minimum flare rate. Since CM Dra is a tidally locked system, we cannot derive any information about its age from the flare rate. However, for a relatively fast rotator, CM Dra's flare rate is notably low.


Table 4. List of flares observed in 1994-1996

Since flares introduce a spurious signal into the lightcurve, they have been removed from the final lightcurves that are being used in the further analysis to detect planetary transits.

4.4. Potential planetary transits

The goal of these observations has been the detection of transits from planets orbiting the CM Dra system. The lightcurves were therefore visually scanned for the presence of events which might be indicative of planetary transits. Such events, further called transit candidates, are typified by being temporary faintenings of CM Dra's brightness by a few millimagnitudes, with normal durations of 45 - 90 mins. Transit events may last as long as a few hours, but only if CM Dra is very close to a primary or secondary eclipse in the middle of the event. Several potential transit events have been observed and are included in Table 5. Their light-curves are shown in Fig. 6a-e. It is not possible to derive elements of potential planets (with the exception of their diameter), if any one of these transit candidates is considered isolated, since the duration of a planetary transit depends only weakly on the planetary period. An exception is the transit candidate at JD 2449909.53 (Fig. 6e), where the long transit duration is only compatible with a planet with a period of less than 9 days, or a period between 25 and 32 days. Even if a hypothetical planet has already caused two observed transits, its period will generally still be ambiguous because of the unknown number of orbits completed between the two transits.


Table 5. List of photometric events which might be caused by planetary transits

[FIGURE] Fig. 6. The six planetary transit event candidates from Table 5. The lightcurves are plotted against the phase of CM Dra. The data are shown as squares; the line indicates a smoothing fit to the data. a Event at Heliocentric JD 2449485.395 observed at OHP. b The event centered at JD 2449505.78, observed simultaneously at Lick (squares) and Mees (crosses) observatories. The light drop appears about 10 minutes later in the Lick observations; this delay may be caused by noise in the data. The amplitude in the Lick data is 0.001 mag, whereas in the Mees data it is 0.0014 mag. c Double dip at JD 2449603.33 and 2449603.40. d Dip at JD 2449855.62, occurring shortly after a secondary eclipse. e A long flat dip observed at JD 2449909.53. This event occurred shortly after a primary eclipse that was observed at the beginning of this night, and had a duration of 180-240 minutes.

If there are any short-period ([FORMULA] 60 days) planets around CM Dra, it would not be unlikely that these have already been observed more than twice in our 617 hrs of observational coverage. For example, a planet with a period of 10 days will cause 2 transits (one transit for each component of CM Dra) every 240 hrs, giving an average of 5.1 observed transits within the 617 hours. The exact number of observed transits depends, of course, on the exact period and orbital phase -or epoch- of a planet (at [FORMULA] phase, the planet is crossing in front of the binary barycenter). The numbers of transits that are expected in our actual lightcurve are given in Fig. 7a and b for two examples of hypothetical planets with periods of 10.14 and 45.14 days (the odd periods were chosen to avoid aliasing effects). For a 10.14 day planet, the observed lightcurve would contain between 1 and 12 transits, depending on the planet's phase. A 45.14 day planet could have caused up to 5 transits, but there is also a 15% chance of missing this planet entirely. The probabilities that certain numbers of transits from planets with various periods are within the 617 hrs observational coverage is given in Table 6.

[FIGURE] Fig. 7a and b. The expected number of transits that would have been observed in our actual lightcurve of 617 hrs, for a hypothetical planet with a period of a 10.14 days and b 45.14 days. The clockwise direction is the planet's phase (going from 0 to 360 degrees) and the radial direction gives the number of transits. The phase is defined here as the phase of the planet at JD 2450000.0; phase zero means the planet is in front of the barycenter of CM Dra).


Table 6. The probabilities (in percent) of the number of transits observed within the observational coverage from planets with selected periods. For example, if there is a planet with a period of 30.14 days present, the probability that it has caused 1-2 transits in the observations from 1994-1996 is 53 %

Assuming that we may have already observed transits of a potential planet 3 or more times, we searched for periodicities among the transit candidates, using those shown in Fig. 6a-e, and a few less pronounced candidates. Among these transit candidates, several thousand possibilities for planetary candidates (with 3 or more already observed transits!) were found. Each planetary candidate represents a combination of a possible planetary orbital period and epoch, the later one being defined as the time, when the planetary candidate is crossing in front of the barycenter of CM Dra, as stated. Modeled lightcurves of these planetary candidates (assuming radii of 1.5, 2 and 2.5 RE, and using the model-code that generated the curves shown in Fig. 1) were cross-correlated against the observed lightcurve. This led to a list of several 100 planetary candidates which reasonably fitted the observed lightcurve. For the best 10 of these planetary candidates, transit times were predicted, and pointed observations at these predicted times were undertaken in the Spring of 1997 at the IAC80 telescope. Unfortunately, no transits were observed at any of these predicted times. Except for these 10 tested planetary candidates, however, these results cannot rule out any other planets in this size range yet. Since it is impossible to observe at predicted transit times for the whole list of several 100 planetary candidates, we are currently again engaging in observations that will increase transit coverage in general, in order to reveal further smaller transit candidates. We want to emphasize, that the observed transit candidates of Fig. 6a-e are examples of events that can be caused by planetary transits, but only repeated observation of transits from the same planetary candidate can verify their true nature.

Whereas there are multitudes of planetary candidates that may have caused the light drops reported in Table 5, we note that there are no observed light-drops with amplitudes larger than 0.01 mag. Cross-correlations between model-lightcurves of planetary transits and the observed light-drops showed that in no case can planets much larger than 2.5 RE be responsible for these observed light-drops. Our observational coverage gives a confidence of about 80% that such larger planets with periods of less than 60 days can be excluded. For periods of less than 20 days, this confidence is 98%. If the light-drops of Table 5 and Fig. 6a-e are indeed from planetary transits, they must result from planets with sizes between 1.5 and 2.5 RE.

A signal detection approach was taken for preliminarily assessing confidence in the detectability of planets in this size range within the current data set. For this, 36000 model transits were generated for 2 RE planets with periods of 10 days through 30 days (the habitable zone around CM Dra), and included in the data. Subsequent detection attempts (Fig. 8) showed that 50% of the time, the detection statistic for a 2 RE planet transiting CM Dra would be above the detection statistics generated from our photometric data (the number of times the cross-correlation values for the transit curve were higher than the noisy observational data). Thus, our data from the 1994 through 1996 observing seasons allow us a confidence level of 50% that an actually existing 2 RE planet would have been detected. For a 3 RE planet, a similar test gave 90% confidence.

[FIGURE] Fig. 8. Shown are the generated detection statistics for a hypothetical 2-Earth-Radii planet (right) that would cause transits of 1.5 hours each in our observational light curve (left). The degree of overlap of the two peaks (detection on the right and non-detection on the left) is a measure of detectability of the transit signals - if they overlap completely, no detection is possible. Clearly a detection can take place reliably at least 50% of the time, demonstrating that we have already reached a detection limit well into the terrestrial-sized planet range (a 2-Earth-Radii Planet is 1% the size of Jupiter).

We would like to note, that one transit candidate reported by our group (Martin et al. 1996) turned out to result from a problem with the flatfielding of that night's images. There were also reports (Guinan et al. 1996, 1997) of CM Dra being fainter by 0.08 mag throughout the whole night of June 1, 1996. If this event would have been caused by a planet with about 0.94 Jupiter diameters, the long duration of the transit would indicate a planet with an orbital period of about 2.2 years. For such long periodic planets, the probability that their orbital plane crosses in front of CM Dra, as well as the probability of catching a transit at the right time, are both very low. Most important however, such a planet should have caused periodic variations in the minimum times of CM Dra's primary eclipse of over 10 seconds, which have not been detected (see Sect. 4.2). We never encountered any brightness variations this large and this long in duration (the latter would have been due to our reduction procedure, where we set the brightness of CM Dra relative to its reference stars to zero for each night). Our data are therefore less sensitive to slow-changing atmospheric extinction variations but would miss unusually long transits that began before and ended after the nightly observations. However, since none of the reference stars anywhere near the field has a red color similar to CM Dra, relative brightness changes may have been caused by differential color extinction. In addition, Guinan et al.'s observations were done in I band, which is notorious for variations caused by [FORMULA] in the atmosphere. We believe therefore, that the event reported by them was most likely caused by a night with abnormal extinction, or was due to a flatfielding problem.

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© European Southern Observatory (ESO) 1998

Online publication: September 14, 1998