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.