Orbital phase coverage

The coverage in orbital phase has to be good enough to observe at least one transit event to be able to start with the follow-up analysis. The ideal case is to detect three transit events to be able to determine the orbital period of the planet and to be able to detect weak transit signals in folded light curve data. Observing only one transit event will make follow-up observations more intensive, but a high number of false alarms can be identified in this early stage already reducing the total amount of follow-up observations. Nevertheless a higher number of RV measurements will have to be made to determine the orbital period if only one single transit detection was made. Additional photometric observations will be necessary to make sure that the phases of the radial velocity changes and the transit are the same. Photometric observations at a phase shift of about 0.5 are important to exclude secondary eclipses for binaries where a smaller occultation signal is detected (small star is covered by large star). Approaching 100% orbital phase coverage would be optimal. An advantage of reaching full orbital phase coverage for the suggested orbital period is the possibility to identify grazing eclipses of binaries with a high mass ratio between secondary and primary components due to the gravitational darkening effect (gravitational forces lead to deformed stars which show deformed light curves). In this case ellipsoidal variations in the light curves of binaries with a minimal mass ratio of 0.4 caused could be detected to identify such systems with the photometric data.

Which orbital phase coverage can be obtained for ground-based transit surveys? Several limitations of different origins exist. The most common limitations are:

a) Altitude constraint: As already concluded in section 2.3.2. observations at airmasses > 2 (altitudes < 30 degree) are not recommended because of quickly increasing scintillation noise and stronger extinction effects.

b) Seasonal limitations: Target fields are typically observable night by night for up to 4 months per season from a central European site for more than three hours at a time.

c) High background due to moon: It was assumed that a period between 5 -10 days around full moon has to excluded because stray light worsens the photometric quality. The duration of the excluded period depends on the distance between the target field and the moon and the phase angle of the moon. If the moon is closer to the field than 30 degrees observations are not useful. Also, five days centered on full moon are always excluded due to the brightness of the sky.

Chapter 2: The transit method

Another limitation is added by the use of a German mount (as used for BEST) that limits the maximal duration of the observations to 8-10 hours per night depending on the hardware limitations (collision of mount and telescope tube or CCD) of the mounts used. This is a minor disadvantage because only during the winter period longer observations would be possible.

With these limitations it is possible to observe about 630 hours for 84 nights in four months in spring or autumn from a central European site like the TLS. Target fields with this maximal observability are circumpolar fields that move through the zenith position. A model was developed to estimate the phase coverage of potential transiting exoplanets for the attainable total duration of observations for a chosen target field. The orbital period was chosen to be a free parameter along with the epoch of the transit event. Both parameters were determined in a Monte Carlo approach within given limits of 0.5 to 10 days for the orbital period and all possible epochs within the first and the last observation with a minimal number of epochs of one million to reach a high statistical basis. Detection was defined to be an event of a minimal duration of 1.5 hours that occurred during the observational times.

Figure 2.13.: Orbital phase coverage vs. orbital period for a duty cycle of 80 percent as can be obtained on an observational site with very good meteorological conditions. 100 percent orbital phase coverage for one detection is reached for hypothetical planets with orbits up to 7.5 days. For three detections full phase coverage is obtained for periods of up to 3.5 days. Similar orbital phase coverage can be reached by the OGLE-III campaigns from Las Campanas, Chile.

These simulations were provided for different duty cycles (efficiency of the observations during time not excluded from observations so far). A duty cycle of 100 percent is rather unrealistic. Only very few observational sites (e.g. Chile) feature nearly optimal weather. A duty cycle of 80 percent can be reached there (see OGLE campaigns, Udalski et al. 2002a, 2002c). Thus a duty cycle of 80 percent for a 4-month observational campaign from Chile during spring or autumn is assumed for a realistic simulation of the orbital phase coverage (see Figure 2.13). 100 percent orbital phase coverage for one detection is reached for hypothetical planets with orbits of up to 7.5 days. For periods of about 10 days there is still phase coverage of 95 percent reached which would imply the detection of Hot Jupiter planets with detectable transit signals at least once. For three detections full phase coverage is obtained for periods of up to 3.5 days. Nearly all transits of planets with orbital periods up to

five days could be monitored. Thus an observational site with a duty cycle of 80 percent would be an ideal observational place for a one-site/one instrument transit search concerning sufficient orbital phase coverage.

Most observational sites in Europe with an existing infrastructure allow lower duty cycles of 40 to 60 percent. Thus the orbital phase coverage was simulated for a duty cycle of 50 percent (see result in Figure 2.14). 100 percent orbital phase coverage for one detection is

Figure 2.14.: Orbital phase coverage vs. orbital period for a duty cycle of 50 percent as can be obtained on a typical site with good meteorological conditions like OHP. 100 percent orbital phase coverage for one detection is reached for hypothetical planets with orbits up to 4.5 days. For three detections full phase coverage is obtained for periods of up to 2 days.

Figure 2.15. Number of Jupiter-sized exoplanets detected by RV searches vs. orbital period as given by the Extrasolar Planets Encyclopaedia6. The number peaks at about 3 - 4 days. 24 of 31 planets have an orbital period less than 5 days. The RV measurements are not biased for

Chapter 2: The transit method

orbital periods less than 5 days; the RV precision reached allows detecting Neptune-mass planets in close-in orbits and the RV campaigns are going on for several years now.

for hypothetical planets with orbits up to 4.5 days. For three detections full phase coverage is obtained for periods of up to two days. Thus most of the Hot Jupiter planets will be detected once assuming that most of them have orbital periods up five days as suggested by RV searches (see Figure 2.15.). Three detections could be made for planets with typical orbital periods of three to five days with 50 – 80 % certainty (with an average of 65 % for further calculations).