Planetary transits can be detected through high precision photometric monitoring, as illustrated below:
Schematic
illustration of the dynamics of a planetary transit and the
corresponding light curve (click figure to enlarge)
A planetary transit in front of a stellar disc causes a decrease of the photometric signal d=(Rp/R*)2, where Rp and R* are the radius of the planet and of the star, respectively. For a star like the Sun, the typical relative variations are 10-4 with 13 hour duration for 1 AU orbits, for Earth-size planets, and 10-2 for Jupiter-size bodies. Observations of recurring planetary transits can be used to measure the orbital period P, and therefore the semi-major axis of the orbit, by applying Kepler's third law.
The photometric method has the unique ability to determine the ratio of planet to star radius from the transit's depth. It also has the potential to detect small, Earth-sized planets, and is not limited to slowly rotating stars, like the radial velocity technique.
The figure below clearly shows that the search for terrestrial-size planets (especially those in the habitable zone) is the unique domain of space-based photometry: (space-based) astrometry can tackle higher-mass, longer-period planets, while the radial velocity searches excel for the shorter-period giant planets.
The capabilities of
planetary search methods, shown in the orbital period versus planetary
mass domain. dots: solar-system planets; triangles: extra-solar planets
discovered up to now; dotted lines: astrometric searches; dashed lines:
radial velocity searches; horizontal dashed-dotted lines: photometric
transit searches. As can be be seen, individual transits from Earths
can be detected with accurate (10-4) photometric searches
(the type of data PLATO will naturally produce), while they are
inaccessible for either of the other methods (click figure to enlarge)
The main objective of PLATO for exoplanetary science being to detect planets of all sizes, around all types of stars, and to characterize them completely, transit observations therefore constitute the best and the most unbiased technique.
Besides the direct detection of planetary transits and the measurement of planet sizes, orbital periods and semi-major axis, high precision photometric observations obtained by PLATO will result in the measurement of other critical physical characteristics of extra-solar planets:
- Albedo of close-in planets and detection of stellar reflected light: the albedo is one of the key surface properties of a planet. Accurate photometry will allow the measurement of the albedo of the close-in planets, of which large numbers will be found by PLATO. The fraction of reflected stellar light by a close-in giant exoplanet depends linearly on its albedo A, and the flux variation due to the modulation of the reflected light along the planet orbit is typically
, for a planet
orbiting at about 0.05 AU from its host star. Because the monitoring of
such
targets will cover several hundred planet orbital periods, such a
modulation will be detectable by PLATO down to mV=9 - 10 for albedos as
small as A=0.3.High precision photometric monitoring will therefore allow us to detect giant exoplanets in close-in orbits around stars down to mV= 9 - 10,
even for large inclination angles, where occultations are not visible.
- Physics of planet interiors: follow-up ground-based radial velocity measurements will be used to determine the mass of a large fraction of the detected planets (the inclination, which enters in the mass determined by radial velocity through the sini factor, being accurately constrained
by the presence of transits). The transit depth will measure the ratio of the planet radius to the star radius, and the star radius will be well determined by the seismology measurements. The planet radius will therefore be derived with great accuracy, and we will have a direct measure of the mean density, and thus constraints on the internal structure of the planet.
- Astrometric detection of planets: the star reflex motion induced by planet revolution, which can be measured by accurate radial velocity monitoring, also creates an astrometric wobble, which can be expressed as
,
where w
is the amplitude of the astrometric wobble in micro-arcsec, a is the semi-major axis of the
exoplanet orbit in AU, mpl
and M* the mass of
the planet
and its star (expressed in earth masses and in solar masses,
respectively), and d the
distance to the exoplanetary system in pc.
Thus a 1 MJ
exoplanet, orbiting a 1 solar mass star at 1 AU, placed
at 15 pc, so that the star has mV~6, would induce a 60
micro-arcsec
wobble.If we measure the astrometric position of each star in the surveyed field relative to all other stars in the field, and if the astrometric measurement is limited by photon noise, precisions of about 6 micro-arcsec may be achieved down to mV= 6 after one month of integration. This will be amply sufficient to detect all giant exoplanets with orbits near 1 AU, orbiting nearby bright stars, irrespective of the inclination angle of the orbital plane with respect to the line of sight.
These astrometric measurements, coupled with measurements of reflected stellar light described earlier, will constitute a powerful tool for identifying exoplanetary systems around nearby stars, out to distances of 15 - 20 pc, and therefore can help select targets for future interferometric and coronographic missions.
- Satellites and rings: high precision measurements of planetary transits can be used to detect the presence of satellites and rings of the observed exoplanets. The presence of planetary rings affects the shape and duration of the planetary transits: for a Saturn-like planet at one AU from the parent star, the ingress and egress take one hour for the planet and two hours for the ring. In addition, the planet ingress (egress) starts (ends) steeper for the planet than for the ring. Finally, the projected inclination of the ring with respect to the planet's orbital plane and the ring optical depth can be derived from the transit shape.
Satellites of the observed exoplanets can be detected directly by the shape of the transit curve if they are sufficiently large, or by their perturbation of the transit timing of their parent planet (see below).
- Timing detection of satellites and of further planets: in a system with a known transiting planet, further bodies will cause small distortions to the transiting planet's orbit. These distortions manifest themselves in deviations of the transits from strict periodicity; and will be measurable in data with sufficient signal and temporal resolution. Such timing measurements can be applied to the detection of satellites around transiting planets. For
example, Saturn's moon Titan would cause transit timing variations of Saturn with an amplitude of 30 seconds, whose detection would be within the capabilities of PLATO. Additional non-transiting planets could be detected as well by their influence on the barycenter of the star - transiting planet system, and current ground-based observations are already being analyzed for the presence of such further planets.