TPF-I SWG Report - Exoplanet Exploration Program - NASA

E X O P L A N E T S CIENCE
Figure 2-8. The variation of signal-to-noise for planet detection as a function of exozodiacal
brightness for three cases: TPF-I for large grain emission; TPF-I for small grain emission; and
TPF-C. The parameter μ LZ is the ratio of surface brightness of the exozodiacal cloud in the
habitable zone of a target star to that of our own zodiacal cloud.
In the absence of more detailed information, the vertical optical depth of the exozodiacal dust in any
system can be parameterized as a factor, μ EZ , times the optical depth of our Solar System's dust cloud.
The emission from exozodiacal dust is then S EZ (r) = 2 μ EZ τ LZ (r) B ν (T(r)) Ω tel , where the factor of two
accounts for the fact that in the exozodiacal case we are looking through the entire cloud and not from the
vantage of the mid-plane as we do locally. By analogy with the local zodiacal cloud (Backman 1998), the
vertical optical depth is assumed to fall off radially as τ LZ (r) = τ LZ (1 AU)r AU -0.3 . We also take
T(r) = T 0 r AU β as the equilibrium temperature for grains heated by stellar radiation and emitting in the
infrared. Typical 1-AU values of (T 0 , β) for large and small silicate grains are (255 K, –0.5) and (362 K,
–0.4), respectively (Draine and Lee 1984; Backman and Paresce 1993; Beichman et al. 2006a). For
reference, it is worth nothing that the integrated signal from a Solar-System-equivalent exozodiacal cloud
is a few hundred times brighter than the signal from an Earth twin. The effect of exozodiacal emission is,
however, reduced by the fringe pattern of the interferometer which attenuates the bright central portion of
the exozodiacal disk. To account for this effect, we incorporate the fringe pattern of a particular nulling
scheme, ξ(θ,ϕ), where θ and ϕ are the radial and azimuthal variables, respectively. In the simplified case
of a face-on disk, the signal reaching the detector, S EZ, Leak , is then given by the integral of S EZ over the
fringe pattern and the telescope solid angle:
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