7. Optimizing of ground-based transit searches
7.1. General considerations for optimizing ground-based transit searches
To obtain a high probability of detecting a transiting planet the monitoring of as many suitable stars as possible with high photometric precision as often as possible to obtain high phase coverage according to equation 2.19 is required.
One approach to optimize ground-based transit searches is to analyze which kind of target fields have maximal detection probabilities for different instrumental set-ups. Target fields with a wide range of stellar densities exist. The range goes from very crowded fields in stellar clusters and fields close to the Galactic bulge, to crowded target fields centered close to the Galactic plane, to moderately crowded target fields above the Galactic plane and finally, to non-Galactic fields with very low content of stars. None of these kind of target fields should be excluded from transit searches. An optimized target field has to be selected for an existing search system to obtain a sufficient detection probability, or an optimized telescope system has to be chosen to monitor the selected kind of target fields.
An optimized ground-based transit search system has to meet the following requirements: a) The telescope should have a low focal ratio (defined as the focal length divided by
the aperture size) to cover a large field of view (FOV) to observe as many stars as possible simultaneously.
b) The telescope should have a large aperture to limit the exposure times for target fields that contain a high number of faint stars to reach a sampling rate of 6 exposures per hours or better (to get information about the shape of the transit signal),
c) The CCD should have a large format that can cover the full unvignetted image in the focal plane.
d) A pixel size of the CCD sensor is required, that corresponds to the observed point spread function (PSF) of the stars in a way that a compromise is found between large full width half maxima (FWHM) to minimize the influence of intra- and inter-pixel variations (typical for front-illuminated CCDs) and a low number of overlapping PSFs in the total FOV. A Nyquist-sampled PSF with a FWHM of two pixels is thought to be such compromise (Howell & Everett 2001, Bakos et al. 2004). Oversampled images (FWHM > 2.0 pixels) will yield higher background noise and increase the crowding problem. Undersampled PSFs (FWHM < 2.0) will introduce additional noise by pixel-to-pixel and intra-pixel effects. Thus optimal PSFs should have a FWHM of two pixels.
e) The search system has to be placed at one (or more) observing site(s) with good photometric and meteorological conditions to obtain maximal phase coverage and a high number of light curves with high precision.
Concerning a) the telescope with the lowest focal ratio that is technically feasible is a telescope with a focal ratio of 1, as built for the Kepler satellite (Borucki et al. 2003) and the Automated Patrol Telescope (see appendix section A.1.8.). An optimized transit search system should have a similar low focal ratio 1. A Schmidt correction plate should be used to minimize the distortion of the image in the focal plane.
Another aspect is the pixelsize of the available large format CCDs (c,d). The largest commercially available and moderately priced CCD chip is the 4k Kodak KAF16801 chip with a size of 36.9 mm x 36.9 mm and a pixel size of 9 µm. Assuming an instrumental
Chapter 7: Optimizing of ground-based transit searches
Table 7.1.: Parameters of the existing and proposed transit search systems that were used for the analysis sorted in the order of increasing aperture size. For more details about the search systems see appendix section A. Note that for BEST4k the FOV is limited to 3.1 deg x 3.1 deg due to vignetting.
System Aperture [cm] Focal ratio 1/F [deg x deg] FOV CCD size[µm] Pixel [arcsec/pixel] Pixelscale
PASS prototype 2.5 2.0 32 x 32 2k x 2k 14 56.2 KELT 4.2 1.9 26 x 26 4k x 4k 9 22.9 TrES (STARE) 10 2.8 6.1 x 6.1 2k x 2k 14 10.7 BEST 20 2.7 3.1 x 3.1 2k x 2k 14 5.5 BEST4k 20 2.7 3.1 x 3.1 4k x 4k 9 3.5 TEST 30 3.2 2.25 x 2.25 4k x 4k 9 2.0 BEST-2 25 5.0 1.66 x 1.66 4k x 4k 9 1.5 OTSS 45 1.0 4.7 x 4.7 4k x 4k 9 4.1 Figure 7.1.: Quantum efficiency of the Kodak KAF-16801E CCD chip as given by Kodak. The quantum efficiency is much higher than for the Thomson TH7899M CCD used for BEST (see Figure 3.5. for comparison). For the wavelength range up to 750 nm the KAF- 16801E chip shows nearly double quantum efficiency compared to the Thomson chip.
dominated PSF (as is typical for wide-angle systems with a low focal ratio) similar to that reached with the BEST telescope (FWHM = 8.25 arcsec for focused images) for a f/1 telescope a pixel scale of about 4.1 arcsec would be necessary to reach a Nyquist-sampled PSF for this CCD chip. This can be reached by a f/1 Schmidt telescope with a main mirror of 45 cm. The FOV covered by the proposed CCD chip would be 4.7° x 4.7°. This proposed system is referred to as the Optimized Transit Search System (OTSS) in the following discussion.
In the following the detection probabilities for the proposed system will be analyzed. Its performance will be compared with the performance of typical transit search systems which already exist or have been proposed (see Table 7.1.). The systems PASS prototype, KELT, STARE and TEST are operational or in the commissioning phase; more details about the systems can be found in appendix A.
BEST4k is an upgraded BEST system: a CCD with a KAF-16801E chip replaces the current 2k CCD, the FOV is assumed to be the same as for BEST. Comparing the
performances for crowding and photometric noise limits of the BEST system with the performance of the BEST4k system will demonstrate the influence of an optimal choice of the CCD sensor. Additionally the CCD chip has a better quantum efficiency (see Figure 8.1.) compared to the Thomson TH7899M chip used.
BEST-2 is a system to study the variability of stars in the most crowded target fields of the COROT satellite mission consisting of a 25cm F/5 Baker Ritchey-Chretien telescope and a CCD with the KAF-16801E chip. It will be located to the Atacama desert, Chile during 2006. This analysis includes wide-angle searches only. Deeper searches will monitor higher fractions of suitable small stars and thus will have higher detection probabilities (see section 2.3.3.). But the observation of faint stars also implicates some disadvantages. The OGLE search (for details see the appendix A.) observes stars in the magnitude range I = 14 mag to I = 17 mag and is a moderately deep transit search. But the confirmation of candidates of this search program by RV measurements has already shown that it is relatively intensive using 8- 10m class telescopes. For some candidates it was reported that they were too faint to reach enough S/N for conclusive RV measurements (Konacki et al. 2003a, b, 2004; Bouchy et al. 2004a). The planetary parameters derived for the planets show large uncertainties. Furthermore follow-up measurements to determine the composition of the planetary atmosphere with the existing instruments are not possible because of the faintness of the stars. Confirmation by RV measurements can not be determined for searches deeper than OGLE. Only upper limits of the masses will be determinable to rule out that the transit-like signals are caused by grazing eclipsing binaries or brown dwarfs. Furthermore the exclusion of blends will be impossible. Additionally most of the deep searches can only monitor target fields for a few days or weeks. The observational time has to be shared with other scientific projects. Technological and financial efforts are significantly higher for the deep searches than for wide-angle searches. Wide-angle searches can be fully dedicated to transit search.
Aspects of the analysis to optimize wide-angle transit searches will include: how to reach sufficient orbital phase coverage and how to optimize the target field selection to monitor a high number of small target stars with undisturbed signals. Additionally it is important to analyze how the different noise sources will affect the photometric performance of the different systems.