In contrast to searching for extrasolar planets by direct imaging techniques, there are several indirect methods used to find exoplanets. Direct imaging is primarily done in the infrared region of the electromagnetic spectrum since the Star-to-Planet flux ratio is lower in the thermal-IR than it is in the visible. However, because the resolution is lower in the thermal-IR than it is in the visible, a larger telescope aperture is required (resolution ~ wavelength / aperture diameter). A nulling interferometer works as follows: as the interferometer rotates, an exoplanet would pop into and out of the nulls. The theory behind the nulling interferometer is constructive/destructive interference. Another option is to use a free-flying infrared space-based interferometer equipped with an imaging spectrometer (see page on imaging spectroscopy/hyperspectral imaging) to characterize the atmosphere and surface of earth-like planets. The advantages of a free-flying IR interferometer in space is good contrast ratio, and the capability to detect spectroscopic biosignatures. The disadvantage is that multiple spacecraft would be required, and some form of cooling (to reduce detector noise) is required since the interferometer works in the thermal-IR region. The required interferometer baseline required would be about 80 meters. To reduce the size of the baseline needed (to about 8 meters), one could switch to a space-based interferometer working in the visible-near-IR (VNIR) part of the spectrum. A coronagraph or mask would be used to reduce scattered light from the host star. Working in the VNIR offers the advantage of having to use only a single spacecraft and telescope. However, a disadvantage is that the contrast ratio between the planet and star is higher. Furthermore, the thermal-IR, a where where many atmospheric gases are detectable, is no longer available.
A color image of the planetary system produced by combining the J-, H-, and Ks-band images obtained at the Keck telescope in July (H) and September (J and Ks) 2008. The inner part of the H-band image has been rotated by 1 degree to compensate for the orbital motion of the d between July and September. The central region is masked out in the upper images but left unmasked in the lower to clearly show the speckle noise level near d. Image courtesy of Marois et al (2008).
Simulation of Earth and Venus viewed from 10 parsecs in broadband visible light. The space-based imager uses a starshade to suppress light from the host star. The blue planet at the 12 o'clock position is Earth and the white planet at 2 o'clock is Venus. The sequence of simulated images uses an aperture size of 1.5, 2.4, 4.0, and 10 meters, starting from left to right. Simulated images courtesy of Cash et al 2008.
Simulation of Earth from 10 parsecs showing the improvement of detection as the telescope aperture increases. The use of a starshade (e.g. New Worlds Observer or NWO) suppresses the starlight from the host star, allowing the faint exoplanet to be seen. The resolution and quality of images depends upon the diffraction limit of the space-based telescope. The extended light seen in these simulated images is due to exozodiacal dust located within the inner regions of the solar system.
Simulation of an exoplanetary system with Venus, Earth, and Jupiter type planets from 10 parsecs viewed at an inclination of 60 degrees. Note the exozodiacal emission that is spatially extended.
The simulated image with an integration time of 60 hours shown below illustrates what Venus, Earth and Mars would look like using the original DARWIN interferometer. The DARWIN interferometer would consist of 6 telescopes, each with an aperture size of 1.5 meters. The telescope array would have a baseline of 50 meters and be located in a 1 AU orbit. The observing wavelengths would range between 6-17 microns, in the thermal-IR. The field of view of this simulated image is 2 arcsec by 2 arcsec. The host star in this simulation is viewed from a distance of 10 pc. The simulation assumed a zodiacal dust emission similar to the Solar System, and the light from the host star has been nulled. Simulation courtesy of Bertrand Mennesson.
A space-based hypertelescope system using 150 telescopes (each with a 3 meter primary mirror) with baseline separations of 150 km could produce an image of an Earth-like world as viewed from 10 light years away as shown in this simulated image.
The radial velocity technique measures the tiny shift in spectral lines of the host star as a result of its radial motion due to the gravitational influence of any orbiting planetary companions. The radial velocity technique is most sensitive to close-in planets. It yields the orbital period of the planet or planets, and their ambiguous masses (lower limit) because the inclination of the planetary orbit(s) is unknown. If information about the planet(s) inclination(s) is obtained using the transit technique (drop in star's brightness due to the transit of companion(s)), then a true mass can be obtained. The radial velocity signature due to a Jovian type planet at 1 AU would be about 30 m/s, and for an Earth-like planet at 1 AU, the radial velocity signature would be about 10 cm/s. The radial velocity signature can be measured to a high precision as a result of advanced wavelength calibration procedures that utilize iodine absorption cells that allow the superposition of wavelength reference on observed stellar spectra, and the recent introduction of laser frequency combs that will allow wavelength calibration to better than 10 cm/sec. The laser frequency comb provides a wavelength standard by creating a high density array of uniformly spaced emission lines which can be associated with fundamental constants or to the standard second. Current echelle spectrometers have resolutions ranging from 50,000 to 300,000 and can resolve spectral lines with equivalent Doppler widths on order of 1 km/s (or better). These modern spectrometers can monitor changes in radial velocity down to 1 m/s over extended periods.
The diagram below shows the concept of the laser frequency comb, which provides a wavelength calibration using a set of evenly-spaced narrow emission lines while maintaining stability over long time spans.
The astrometric method of exoplanet detection measures the angular motion of the star on the plane of the sky due to the gravitational influence of a planetary companion or companions. The motion of the star is around the system's barycenter of center of mass. The astrometric method is most sensitive to planets orbiting far-out from their host star, so it requires observations over long periods of time (years to decades). This method provides orbital inclinations of planets, and unambiguous masses of any planets. The method is also sensitive to planets in all orbital inclinations. For a Jovian type planet with an orbital period of 3 months, the astrometric signature is about 0.1 milliarcsec, and for an Earth-like planet with a 1 year orbital period, the astrometric signature would be approximately 1 microarcsec. Due to the extremely small astrometric signatures involved, the method is suited to space based observatories. As of to date, no confirmed exoplanets have been detected using the astrometric technique.
The most widely used method to date (e.g. NASA's Kepler mission) is the transit method. A planetary companion passing in front of its host star will result in a slight drop in stellar flux. The transit technique is most sensitive to planets on close-in orbits. The method allows the inclination of the planet's orbit to be determined as well as the unambiguous mass of the planet with additional data from radial velocity measurements. The radius of the planet can be determined using the transit method, and when combined with the mass using the radial velocity, astrometric, or gravitational microlensing method, the density of the planet can be deduced. Also, the composition of the planet's atmosphere can be found using transmission spectroscopy when a portion of the star's light passes through the atmosphere of a transiting planet. If the radius of the star is known from spectroscopic measurements or theoretical stellar models, then the planet's radius can be determined from the equation that gives the drop in brightness due to the transit event. The profile of the drop in brightness depends on the ratio of the radii of the planet and star, the latitude of the transit across the central star, and the star's limb darkening. The orbital period of the planet can be determined from several successive transit events. One of the limitations of the transit method is the requirement for orbital inclinations to be near 90 degrees.
Gravitational microlensing is another indirect method used to detect distant exoplanets. Light from a star (the source) is bent by the curvature of space as its passes by the lensing object (planet) of given mass (general relativistic effect). Advantages of the gravitational microlensing technique include the ability to detect exoplanets at distances up to several tens of kiloparsecs because the technique is independent of the flux from either the source or lens. Instead, the strength of the signal due to the lens (the planet) depends weakly on the planet/primary mass ratio (the signal decreases as the square root of the mass ratio). Microlensing is most sensitive to planets at separations of 1 to 10 AU from their host star, and the entire orbital period does not need to be monitored. The main drawback of the microlensing method is that it is essentially not a repeatable event, and occurs for only a short period of time. This makes followup observations problematic.
Mass-Radius Relationships for Terrestrial Type Exoplanets
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