Report - School of Physics

Table 6: Magnitudes and separations for exo-planets predicted for OWL (estimated by Hainaut).
Separations are given in arcsec. Contrast ratios between the planets and the parent star are of
order 10 −8 to 10 −9 . The magnitudes of the planets were taken as follows: Jupiter: real observations;
Earth: real observations of the Earth, and for some wavelength where no observations
were available, constructed by scaling observations of Venus and/or Mars; hot Jupiter: models by
Sudarsky et al. (2003) and Burrows et al. (2004), for a planet with M = 1M J and a = 0.2 AU.
Distance Star Hot Jupiter Earth Jupiter
(pc) (mag) 0.2 AU 1 AU 5 AU
10 4.8 V = 24.1 27.9 25.8
sep = 0.020 0.100 0.500
25 6.8 V = 26.1 29.9 27.8
sep = 0.008 0.040 0.200
50 8.3 V = 27.6 31.4 29.3
sep = 0.004 0.020 0.100
100 9.8 V = 29.1 32.9 30.8
sep = 0.002 0.010 0.050
would be a strong indicator of life (i.e. of photosynthetic biochemistry), while its
absence would not be conclusive evidence for an abiotic world.
Table 8 indicates the S/N that can be expected from a 24 hr OWL observation of
an Earth at 10 pc, in the optical and near-infrared. Clearly, even if Earths exist
at distances as close as only 10 pc, detection and spectroscopy will be challenging
even with OWL. Concerning the number of target stars accessible for investigation
by OWL, the Darwin study identifies some 500 F5–K9 stars out to 25 pc, of which
some 285 are single. There are only some 2–5 G0V–G2V stars within 10 pc, and
some 21 single, non-variable G0V–G4V within 15 pc.
The distance at which an Earth will be observable will depend on various parameters
(Strehl ratio achievable, the performance of nulling/subtraction techniques, e.g.
phase-induced apodization coronography could yield attenuation of 10 −9 , etc.) but
in any case is a strong function of mirror diameter. Assuming, as above, that a
telescope can see a planet beyond an angular distance of 5λ/D from the parent star,
the volume of space explored (i.e. the number of stars) is proportional to D 3 , and the
numbers for G stars go from about 25 for a 30 m telescope to about 900 for a 100 m.
The time to achieve the same S/N for different size telescopes scales as (S/N) −2 ;
the object lies within the uncorrected light from the star, so measurements are in
the background-limited regime, i.e. S ∝ D 2 , background ∝ D 2 , pixel size ∝ D −2
(being diffraction limited) so S/N ∝ D 2 / √ D 2 × D −2 = D 2 and t ∝ D −4 . Thus a
30 m aperture would take 123 times longer than a 100 m to observe an object that
both would separate from the parent star. This is also the reason why a lower limit
of about 70 m diameter is considered useful for spectroscopy of the very nearest
exo-solar systems, and why 30 m telescopes do not include Earth-like exo-planets as
part of their scientific goals.
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