TPF-I SWG Report - Exoplanet Exploration Program - NASA

C HAPTER 5
Table 5-3. Angular Resolution (FWHM of PSF) of the Stretched X-Array
Array Size
Wavelength
6 μm 10 μm 18 μm
120 × 20 m 4.9 mas 8.2 mas 14.8 mas
612 × 102 m 1.0 mas 1.6 mas 2.9 mas
Here we have assumed that the 6:1 aspect ratio of the array is held fixed, which simplifies the input optics
on the combiner. One design option would be to allow for a variable aspect ratio. The nulling baseline
length would be set according to the angle subtended by the inner habitable zone, and the imaging
baseline would be made as larger as possible. Fore general astrophysics without nulling, the imaging
properties of the stretched X-array are depicted in Fig. 5-26.
5.8.5 Optimized Program Completeness
Each star on the TPF-I target list has a habitable zone, which scales by luminosity and is defined as the
region around a star in which liquid water could exist. We model the habitable zone by populating this
region with 1,000 pseudo-planets. The pseudo-planets have random inclination, eccentricity over the
range [0, 0.1], and a semi-major axis in the range of 0.75 L ≤ x≤ 1.8 L . The planets are Earth-like in
size and albedo. Program completeness is then defined to be the fraction of potentially observable planets
that are detected over a mission. Our algorithm selects the most productive of the TPF candidate stars to
observe in each week of the mission. It accounts for multiple visits, solar constraints, variable baselines,
and planet orbital motion, removing many of the assumptions that were necessary in previous analyses.
The procedure for this analysis is shown in Fig. 5-27.
The changes to previous methods of computing completeness include temperature-dependence of the
planet across the habitable zone, a more realistic exozodiacal model, a tapered, wavelength-dependent
representation of the IWA, and the optimization of visit timing. We perform this optimization by
evaluating stars on the completeness per time that is provided by a given observation. We calculate the
curve of completeness vs. integration time fore each star determining the best array size at each point.
Several example curves are shown in Fig. 5-28. The curves start out flat due to overhead and a minimum
integration time needed to observe any pseudo planets. The curves rise and then flatten out at different
levels depending on the stellar type and distance to the star. (the IWA limits the possible planet
observations for stars that are farther.) We define an instantaneous efficiency (change in completeness
per hour, i.e., the red dot indicating the slope of the completeness curve in Fig. 5-28) for all available
stars. The observation time per star is then defined as the time needed to observe the star up to the slope
cut off point (t 1 , t 2 or t 3 in Fig.5-28). The stars are then evaluated on net efficiency (i.e., the green dashed
lines indicating overall completeness per observation time). Those stars with the largest net efficiency are
then selected for a visit.
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