HOW TO DETECT SMALL PLANETS?
1. Doppler Spectroscopy:
Doppler spectroscopy is used to detect the periodic velocity shift of the stellar spectrum caused by an orbiting giant planet.
(This method is also referred to as the radial velocity method.)
From ground-based observatories, spectroscopists can measure Doppler shifts greater than 3 m/sec due to the reflex motion of the star this corresponds to a minimum detectable mass of 33Me / sini for a planet at 1 AU from
a one solar-mass (1 Mo) star, where i is the inclination of the orbital pole to the line-of-sight (LOS).
This method can be used for main-sequence stars of spectral types mid-F through M. Stars hotter and more massive than mid F rotate faster, pulsate, are generally more active and have less spectral structure, thus making to more difficult to measure their Doppler shift.
The minimum detectable planet mass increases as the square root of the planet's orbital size, as shown in the figure below (the red ascending line).
The planets already detected with this method are indicated by the solid diamonds in the figure below. Note the mass is given in Earth masses, Me.
2. Pulsar Timing:
The first widely accepted detection of extrasolar planets was made by Wolszczan (1994).
Earth-mass and even smaller planets orbiting a pulsar were detected by measuring the periodic variation in the pulse arrival time.
The planets detected are orbiting a pulsar, a "dead" star, rather than a dwarf (main-sequence) star.
What is heartening about the detection is that the planets were probably formed after the supernova that resulted in the pulsar.
Thereby demonstrating that planet formation is probably a common rather than a rare phenomena.
The pulsar planets are indicated by the open diamonds in the figure below.
3. Astrometry:
Astrometry is used to look for the periodic wobble that a planet induces in the position of its parent star. The minimum detectable planet mass gets smaller in inverse proportion to the planet's distance from the star. For a space-based astrometric instrument, such as the planned Space Interferometry Mission (SIM), that could measure an angle as small as 2 micro-arcsec, a minimum planet of mass of 6.6Me could be detected in a 1 year orbit around a 1 Mo star that is 10 pc from the Earth (gray descending line for stars out to 10 pc) and a 0.4 Mj planet in a 4 year orbit (dark-blue descending line for stars out to 500 pc). The FAME mission (Full-sky Astrometric Explorer) has an angular resolution of 50 micro-arcsec and the minimum detectable planet mass for it at 10 pc is shown by the descending orange line.
From the ground, the Keck telescope is being equipped to measure angles as small as 20 micro-arc seconds, leading to a minimum detectable mass in a 1 AU orbit of 66Me for a solar-mass star at 10 pc.
The limitations to this method are the distance to the star and variations in the position of the photometric center due to star spots. There are only 33 non-binary solar-like (F, G and K) main-sequence stars within 10 pc of the Earth. The furthest planet from its star that can be detected is limited by the time needed to observe at least one orbital period. This limit is indicated by the dashed light-blue vertical line chosen to be at 10 years in the figure below. There are no planet detections that have been confirmed using this method.
4. Transit Photometry:
Photometry measures the periodic dimming of the star caused by a planet passing in front of the star along the line of sight from the observer. Stellar variability on the time scale of a transit limits the detectable size to about half that of Earth for a 1 AU orbit about a 1 Mo star or Mars size planets in Mercury-like orbits with four years of observing. Mercury-size planets can even be detected in the habitable-zone of K and M stars. Planets with orbital periods greater than two years are not readily detectable, since their chance of being properly aligned along the line of sight to the star becomes very small.
In the figure below, the white region represents the full range of planet masses and orbits that the Kepler Mission can detect. Giant outer planets that produce a transit signal of 1% ( 120 times that of an Earth, i.e., a SNR >1000) but have orbital periods greater than 2 years can be followed up with Doppler spectroscopy or ground-based photometry (green horizontal line in the figure below).
Giant planets in inner orbits can also be detectable independent of the orbit alignment, based on the periodic modulation of their reflected light. For the 10% of these that have transits, the transit depth can be combined with the mass found from Doppler data to determine the density of the planet as has been done for the case of HD209458b and see if these inner giants are "inflated".
Doppler spectroscopy and astrometry (SIM) measurements can be used to search for any giant planets that might also be in the systems discovered using photometry. Since the orbital inclination must be close to 90° (sin i=1.) to cause transits, there is very little uncertainty in the mass of any giant planet detected.
