TPF-I SWG Report - Exoplanet Exploration Program - NASA

C HAPTER 2
S
EZ
2π
∫
θ max
∫
, Leak
( d)
= 2 dϕ
μEZτ
EZ
( θd)
Bν
( T ( θd))
ξ ( θ,
ϕ)
θdθ
0
0
for a star at a distance d pc. Figure 2-8 (Beichman et al. 2006b) shows an illustrative example of the effect
of EZ emission on the S/N of a TPF-I detection where we have adopted the fringe pattern, ξ(θ,ϕ), for the
Dual Chopped Bracewell interferometer (Lay and Dubovitsky 2004; Lay et al. 2005) and a diffractionlimited
beam size of θ max = 0.6λ/D = 0.5" for a D = 3-m telescope at 12 μm. For a solar-type star at d = 10
pc, the ratio of the exozodiacal contribution to that from the Solar System's own dust is 0.06 μ EZ or 0.24
μ EZ , for large and small grains, respectively. For a particular temperature, smaller grains are located
further from their parent star than the cooler, larger (blackbody) grains; and thus, emission from small
grains is less effectively blocked by the central null of an interferometer. Small grains thus produce more
noise than large grains for a given total exozodiacal brightness. Figure 2-8 shows the variation of S/N as a
function of exozodiacal brightness, μ EZ , for two grain sizes. When the surface density of the exozodiacal
dust, μ EZ , is 10 times that of our Solar System, corresponding to a 20-fold brightness increase, the S/N is
reduced by a factor of ~2–3, necessitating an increase in integration time by a factor of ~4–9 to recover
the original S/N. Since many hours of integration time are needed to detect an Earth-sized planet in the
presence of a μ EZ = 1 cloud, and days to carry out a spectroscopic program, it is clear that studying
systems with μ EZ = 10–20 will be difficult.
A similar analysis can be used to assess the
effects of exozodiacal emission at visible
wavelengths; for details see Beichman et al.
(2006b) or Brown (2005). Figure 2-8 also shows
the variation in S/N for TPF-C assuming a 3.5- ×
8-m telescope observing a planet 25 mag fainter
than a V = 4.5 mag solar twin at 10 pc and a local
zodiacal brightness of 0.1 MJy sr -1 at 0.55 μm
(Bernstein, Freedman, and Madore 2002). As
with the interferometer, the effect of zodiacal
emission in the target system is to lower the S/N
by a factor of ~2–3 at μ EZ = 10. In this particular
example, the relative effect of the exozodiacal
emission is more pronounced for the TPF-C than
for the TPF-I because the interferometer is
dominated by the strong local zodiacal
background until very bright exozodiacal
emission is observed. The intrinsic background
level within the visible-light coronagraph is low
(by assumption of an excellent 10 -10 rejection
ratio) so that the exozodiacal emission quickly
plays a significant role in setting the system
noise.
Figure 2-9. Use of a four-element interferometer
with chopping allows rejection of symmetrical
emission from the zodiacal cloud and allows
detection of three planets.
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