Secondary transits and thermal IR

During the secondary transit of a planet, the planet passes behind the disk of its parent star. During the bulk of such a transit, the planet is completely obscured by the star, resulting in a genuinely flat-bottomed transit light curve, with fairly brief ingress and egress portions during which the planet's disk is in the process of being covered or uncovered. For stars of roughly solar size, planets roughly the size of Jupiter, and orbital periods of a few days, the total transit duration is typically two to three hours, and the duration of the ingress/egress phases is 15 to 20 minutes. The short duration of the ingress/egress phase is important, because it means that instruments to observe the secondary transits need only be photometrically stable for these relatively short times.

In visible light, for which almost all of the light from the planet consists of scattered starlight, the depth of the secondary transit dip is too small to be seen by current techniques. Again taking as typical a planet with radius of 1.2 RJup, orbiting a Sun-like star with a period of four days, one finds the total flux Ip scattered by the planet to be

2 a2

where I* is the flux seen from the star, and A is the geometric albedo of the planet. This estimate depends upon Lambertian scattering from the planet, and one can imagine atmospheric effects ("glories" and related phenomena) that might cause enhanced backscattering when the planet is near its full phase. Nevertheless, this estimate must be roughly correct, and it suggests a signal that is discouragingly small for any ground-based observation. (Note, however, that by utilizing the Doppler shift of the scattered radiation from the planet as it moves in its orbit, it is possible to devise an observational scheme that is differential in wavelength. In this way, detection of such small signals may be possible. So far, attempts by Charbonneau et al. (1999) to apply such a method have resulted in interesting upper limits on the albedo A, but no detections.) Space-borne detections may also be possible in the near future (Green et al. 2003), though observations of t Boo with the MOST instrument have as yet proved inconclusive (Matthews 2005).

In the thermal infrared, the situation is much better. Recall that for an object with an effective temperature of 1000 K, the peak photon emission of the black body spectrum falls at about 3.7 ¡m, so that "thermal" wavelengths can be only a few ¡m. In the Rayleigh-Jeans long-wavelength limit, Ip is given by r2 t

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