TPF-I SWG Report - Exoplanet Exploration Program - NASA

C HAPTER 2
would be in atmospheres of different composition and for stars of different spectral type and incident
ultraviolet flux. These uncertainties, however, could be addressed by further modeling studies.
2.4.2 Resolution Needed
This section provides quantitative information on the sensitivity necessary to detect spectral features on
Earth or an Earth-like exoplanet. The equivalent width needed for optimal detection of each chemical
signature in the thermal infrared is given in Figure 2-4 (Kaltenegger et al. 2007). Following standard
practice, the total absorption in the feature is expressed in terms of equivalent width, (i.e., the spectral
width of an equal area of a rectangular line with zero residual intensity and unity continuum). To detect a
spectral feature with optimum signal to noise requires that the full width at half maximum (FWHM) of
the spectrometer should be approximately equal to the FWHM of the spectral features. For an extrasolar
planet this will not be known, but assuming an Earth-analog as a guideline, we can specify these numbers.
We determine equivalent width for these species by integrating the difference between a model spectrum
with and without the chemical of interest. The spectral resolution (λ/Δλ) needed for optimal detection of
each changing spectral feature is given in Figure 2-4. Here λ is the central wavelength of a feature, and Δλ
is the FWHM of the feature after it has been smeared sufficiently to blend any sharp lines yet still retain
its essential overall shape. These numbers are relevant for the design of the TPF-I and Darwin mission.
Note that features like N 2 O would have to be detected on top of another feature, implying an excellent
signal-tonoise ratio (SNR) for detection. This example also illustrates that identification of the continuum
region, as well as potentially overlapping species, is also an important part of biomarker detection, which
in some cases may require higher spectral resolution, in addition to high signal to noise.
2.4.3 Planets Around Different Stars
The interferometric systems suggested for Darwin and the TPF-I mission operate in the mid-IR, and the
coronagraph suggested for TPF-C operates in the visible. For the former it is thus the thermal emission
emanating from the planet that is detected and analyzed, while for the latter the reflected stellar flux is
measured. This means, that if you want to observe Earth-like planets in the Habitable Zone (HZ) around a
given star, the thermal flux will to first order be constant for a given planetary size, while the reflected
stellar flux will scale with the brightness of the star. The suppression of the primary’s thermal emission
will, on the other hand, be progressively easier for later and later spectral types. The contrast ratio is a
factor of about 4 more for FV stars, 30 less for KV stars, and about 300 less for MV stars compared to the
Sun–Earth contrast ration in the IR (Kaltenegger, Eiroa et al. 2007). Surprisingly enough, it may thus be
easier for the IR interferometer concept to detect a habitable Earth around an M-Dwarf than around
something more akin to our own Sun. This is true for interferometric systems like Darwin and TPF-I that
can be adapted to each individual target system, since the HZ moves closer and closer to the star for later
and later stellar types. The baseline of the interferometers have to increase to resolve M-star planetarysystems
at larger distances, a constraint that is taken into account for the M target systems at largest
distance in the target star catalogue.
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