Title: Science-Operational Metrics and Issues for the ‘Are We Alone?’ Movement
ArXiv ID: 0903.5139
Date: 2009-03-31
Authors: Researchers from original ArXiv paper
📝 Abstract
A movement is underway to test the uniqueness of Earth. Sponsored primarily by NASA, it is enlisting talented researchers from many disciplines. It is conceiving new telescopes to discover and characterize other worlds like Earth around nearby stars and to obtain their spectra. The goal is to search for signs of biological activity and perhaps find other cradles of life. Most effort thus far has focused on the optics to make such observations feasible. Relatively little attention has been paid to science operations--the link between instrument and science. Because of the special challenges presented by extrasolar planets, science-operational issues may be limiting factors for the "Are We Alone?" (AWA) movement. Science-operational metrics can help compare the merits of direct and astrometric planet searches, and estimate the concatenated completeness of searching followed by spectroscopy. This completeness is the prime science metric of the AWA program. Therefore, the goals of this white paper are to present representative calculations involving science-operational metrics, and to promote a science-operational perspective. We urge the Survey Committee to allow this perspective and such metrics to inform its plan for the future of AWA.
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Deep Dive into Science-Operational Metrics and Issues for the "Are We Alone?" Movement.
A movement is underway to test the uniqueness of Earth. Sponsored primarily by NASA, it is enlisting talented researchers from many disciplines. It is conceiving new telescopes to discover and characterize other worlds like Earth around nearby stars and to obtain their spectra. The goal is to search for signs of biological activity and perhaps find other cradles of life. Most effort thus far has focused on the optics to make such observations feasible. Relatively little attention has been paid to science operations–the link between instrument and science. Because of the special challenges presented by extrasolar planets, science-operational issues may be limiting factors for the “Are We Alone?” (AWA) movement. Science-operational metrics can help compare the merits of direct and astrometric planet searches, and estimate the concatenated completeness of searching followed by spectroscopy. This completeness is the prime science metric of the AWA program. Therefore, the goals of this w
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Because of three features, an Earth twin (ET)-the AWA benchmark adopted for the calculations presented here-is the most extreme target in astronomy: low information rate, high variability in position and brightness, and the huge, proximate, unwanted signal of the star. To illustrate, consider a space telescope with aperture D = 16 m, the largest currently under serious discussion. With efficiency ε = 0.2, and resolving power R = 10 in the I band, this telescope would detect 0.1 photons per second from an ET at quadrature at 20-pc distance. The apparent separation of the stellar and planetary images would be 0.05 arcsec or 5 λ/D. Assuming an inner working angle IWA = 3 λ/D-meaning the radius of the photometrically inaccessible region immediately around the star-and assuming a maximum feasible difference in magnitudes between the planet and star ∆mag 0 = 26, set by wavefront instability for an internal coronagraph, or by the starshade accuracy and alignment in the case of an external occultor, such an ET on a random orbit would be detectable 66% of random search epochs. 1 The median time for a detected ET on a partially obscured orbit to become undetectable again-too faint or too close to the star-is two months after detection. Assuming the optics suppress the diffraction wings by factor 10 -10 from the central intensity of the stellar image, and assuming sharpness Ψ = 0.02, some 10 photons of scattered starlight and 1 photon of zodiacal light-assuming 1.0 local zodi and 2.0 exozodiwould be counted with each planetary photon during the exposure time T = 146,000 sec that would be required to obtain a spectrum with photometric signal-to-noise ratio SNR pho = 10 at the oxygen A band (760 nm), as required to measure 20% of Earth's column density of O 2 with 99% confidence. 2 Turning to the astrometric signal, at 20 pc the amplitude of the astrometric wobble of the Sun due to the orbiting ET would be α = 0.15 µas or 0.00064 solar radius. α varies directly with the square root of the stellar luminosity and inversely with the stellar mass. An astrometric data set comprises N measurements of the form (t i , τ i , x i , y i , σ i ): the xy position at epochs t i spread over more than one planetary period, where the exposure time is 0.5 τ i for each of the two quasi-orthogonal directions, and where σ i = σ 0 (τ 0 /τ i ) 1/2 is the positional uncertainty in either direction. The astrometric signal-to-noise ratio is SNR ast = α/σ, where
where τ is the total exposure time. This noise reduction with τ and N is valid only down to the noise floor, or for σ > σ floor , where σ floor is determined by systematic effects. For the Space Interferometry Mission (SIM Lite), a space astrometer currently under study, we use the instrumental parameters are σ 0 = 1.41 µas, τ 0 = 2200 sec, and σ floor = 0.035 µas. 3,4,5,6 Assuming periodogram (power spectrum) analysis of the data set to find weak, periodic signals, the search completeness C(SNR ast , fap) depends on SNR ast and the accepted falsealarm probability fap; for example, C = 0.5 for SNR ast ≃ 6. The sensitivity limit for detection probability C = 0.5 is therefore α min = 6 × σ floor = 0.21 µas, which would be achieved in τ = τ max = 3.6 ×106 sec. For example, an ET at 14.3 pc would be just detectable by SIM Lite under these assumptions, because the required σ = 0.21/6 = 0.035 µas, which is equal to the noise floor.
The mother of all science-operational problems for AWA is the density of stars in the solar neighborhood. If it were higher, Hubble (D = 2.4 m) might have obtained the first spectrum of an ET-if it were capable of 10 -10 contrast, of course.
Figure 1 shows the 7332 stars in a SIM Lite project star list for planet searching. 7 For 7 Thanks to Joe Catanzarite for developing and sharing this star list, which includes all the dwarfs and subgiants within 100 pc in the NStED data base (http://nsted.ipac.caltech.edu/
) with stars cut by these criteria: (1) known from the Washington Double Star Catalog to have a companion closer than 35 mas, (2) known to have a companion between 35 mas and 1.5 arcsec with V magnitude difference < 1, (3) luminosity > 25, (4) fainter than V = 9, (5) chromospheric activity index R HK > 4.3, (6) known to have age < 0.3 Gyr, or (7) with orbital period at Earth’s equilibrium temperature > 4 years.
this list, a telescope with D = 16 m resolves 505 ETs at some time in their orbits and achieves the required SNR p = 10 for the O 2 spectrum in less than T max = 500,000 sec, an arbitrary, “stretch” exposure time. (“ET” now means the same radius and albedo as Earth, but with semimajor axis equal to √ L, where L is the stellar luminosity, which ensures the same equilibrium temperature.)
The exposure time for the O 2 spectrum for the hypothetical Earth-Sun system at 20 pc is close to the median value for the 505 stars: T median = 150,000 sec. Some 117 of the 505 stars suitable for O 2 spectroscopy with a 16-m telescope have ETs detectable by SIM Lite a
