1. Why searching for other planetary systems ?

The existence of other worlds or planets and the opportunity o live elsewhere than on earth have been discussed since the most ancient times. Nowadays, this matter is associated with the desire to better understand the mechanisms which created the planets. Their detection around other stars will bring additionnal constraints to test the current models of the formation of planetary systems.
Since Descartes,we were left to reconstruct the solar system history only from its current state.
Detection of several different planetary systems will allow us to compare models with more than a unique sample.
This field was open by Epikouros in 300 B. C. but it is only 23 centuries later, with the development of the instruments sensibility, that it became a real research field.
The situation only evolved a few years ago with the discovery of three telluric mass objects in 1993 (Wolzczan, 1994) and four Jupiter mass objects around solar type stars in 1995/96 (Mayor, 1995 and Marcy, 1996).
The first three planets which were discovered around a pulsar, are untypical because they formed in " post-mortem " conditions, which are very different from the ones that prevail in circumstellar discs around young stars but which are also unfitted to an eventual life development.
The other four are, from this point of view, able to help understanding the development of planetary systems by further constraining the models. All the discovered planets to date are closer to the star than Jupiter is to the Sun. This causes serious problems to current models of the gaseous mass giant planets development. We notice, in particular, the pretty frequent presence (in more than 5 % of the cases) of giant planets at only about ten stellar radii, the " hot Jupiters " (see Table 1). This makes us think that the detection of a large number of Jupiters will help a better comprehension of their origin and role in the appearance and evolution of a planetary system.
After the discovery of Jupiters around solar type stars, the next major step is clearly the discovery of telluric objects (complete planets or giant gaseous ones embryo) at an evolution state concomittant or previous to the solar system’s one. Apart from their astrophysical significance, they mean a lot from the exobiology point of view which is dedicated to develop in the future.We are living a fascinating time where the answers to these questions are about to be found thanks to observations.

 Table II.1 : Planetary systems known by April 1997

 Onlybodies with a mass less than to10 M Jup. are reported in order to avoid confusions with brown dwarf planets.
 

 
The case of telluric planets

 The detection of a telluric planet is a major challenge and is expected as the next big step in astronomy. It belongs to a " step-by-step " approach which tries to successively search for :
* giant planets
*telluric planets
*Biologic activity signs
*Cases where this life would have led to signals emission ability

 Their detection around solar type stars is very difficult because of their small masses. Possible detection methods are: coronography, astrometry, radial velocity, timing, gravitational amplification, occultations.
Before the achievement of ambitious spatial projects (interferometers, coronographs), there are only 2 possible methods on a short or mid term for the telluric planets detection, the gravitational amplification and the occultations. As emphasizes in the Townes Report (Comments on the Blue Ribbon Panel on ExNPS, 1996), gravitational amplifications can not allow to determine the statistical frequency of planets at several kpc from the Sun (galactic bulb), while we would need to detect earths, located a few pc from the sun, in order to subsequently study them in a more detailed way.The occultations method or transit method, allows on the contrary to precisely determine the orbital period and the size of the planet. Concerning close enough planets, it would enable to study their atmosphere chemical composition thanks to the differential absorption of the star radiance. Yet this method needs a high precision photometry (10^-3 to 10^-4) and a continuous observation during a long period (several months). Today, these two requirements can not be simulnateously satisfied by observations from the ground.

 That is what we are proposing to do it with COROT

 The photometric method, particulary well adapted to the telluric planets can also detect giant extra-solar planets (detectable by spectroscopy from the ground) and determine their albedo, increasing the scientific return.
Thus it is important to know the frequency of the appearances of these planets in the planetary systems as well as their role in the subsequent system evolution. We should also confirm that the detections of " close Jupiters " like 51 Peg are not artifacts of the spectroscopic method as recently suggested (Gray 1997).
We should notice that ESA and NASA are thinking of very ambitious programs to try to reach the research stage for inhabitable planets and signs of biologic activities. The discovery of telluric planets by COROT would set an " existence theorem " and would give to this mission a strategic significance in these programs.

 Occultations methods or " transits "

 The occultations of a star by one of its planet in orbit around her are characterized by 4 parameter (see Figure II,1) :
The geometric probability, Pr, for a transit to exist, the plane of its orbit must contain the star line of view ; this probability is Pr= R*/a, a being the planetary orbit radius and R* star radius. The transit length, tr, depends on the impact parameter, p, and the orbital period P :     with p=0, tr=(P/p )(R*/a).
The amplitude D F/F=(Rp/R*)² where R_p is the planet’s radius.
The periodicity r=1/P of the photometric decrease is nearly perfect because it is the same as the planetary movement’s one. This property is an important one to identify a serie of transits.
The observation strategy is to photometricaly keep watch over stars for several revolution periods of the searched planets. 3 periods minimum are needed to obtain a firm detectioin
* 1 period waiting for the first occultation
* 1 period determining a precise orbital period and predicting the next occultation
* 1 period confirming this new occultation.

Figure II.1 : the transit

 Table II.2 gives the values of the different parameters of a planet similar to the Earth respectively located at 1 UA and at 0, 1 UA (55 Cnc orbit) from the Sun.

The probability of existence of a transit rises in a nearly linear way with the number of planets existing in a fixed planetary system : this probability goes from 0,47 % for the Earth-Sun system to 2 % for the Earth+Venus+Mercur-Sun system.

 Table II.2 : Parameters characterizing an occultation with an impact parameter p= R*/2
 
 

 
The reflection method

 The motion of a planet around its parent star can modulate the stellar luminosity observed at the Earth. The detection probability is 100 %in this case, while it is only 1 or at best 10 % with the occultations method. Yet, this detection method is only optimal for planets close to their star. It is more efficient than the occultations method for orbital distances less than to 0,2 UA.
The number of photon reflected by a planet whose radius is Rp and albedo is A, located at a distance a from its parent star is (Schneider 1992) :   Np(t)=1/4 N* A (Rp/a)² f(t)
Where N* is the number of photon coming from the star and f(t) is a phase factor depending on the planet orbit.
f(t) = 1 - sin(i) cos(2pt/p) where i is the inclination of the orbit on the sky and P, the orbital period.
The time variations of the number of received photons N, around the average value <N> is
DN = 2 A N* sin(i) (Rp/a)² avec <N> = N* (1 + A(Rp/a)²)
This relative variation enables the observer to determine the planet’s albedo, a being determined from the orbital period, Rp, from a reasonnable model of a giant planet (Guillot, 1996) and sin (i) could be subsequently determined from the ground by a method currently tested. A precaution will still be necessary in order to avoid confusing planet with stellar activity : checking that the modulations don’t loose their phase.
Further, we could plan to study the time variation of these planets’ albedo (Schneider, 1992) and even the chemical composition of their atmosphere (Schneider, 1994) or their exosphere (Chassefière 1996).

 2 the search for telluric planets with COROT

COROTis devoted to stellar photometry, aiming both a high precision and a long observation time, the search for exoplanetsby the transit method can easily be integrated in the payload and in the mission profile.
However COROT is not a mission devoted to telluric exo-planets detection and is not optimized for that purpose, especially because of its small telescope diameter. Nevertheless, we will show that we can hope to achieve a few significant breakthrough in this field.

 The requirements on the photometry

 The decrease of stellar brightness caused by a transit is proportionnal to the ratio of the planet surface to the star’s one. Concerning stars of the same size as the sun, the radiance variation is 1% for the giant planets (Jupiter, Saturn, 51 Peg.), 0.1 % for planets like Uranus or Neptun and 0.01 % for planets like Earth or Venus.
With a telescope diameter D and a global efficiency e, the photons flux per second coming from a star of visual magnitude mv is F* ~ 1.7 10⁹(D/25)(e/0.45)10 ^{-0.4 mv}
The seismology program is setting up D around 27 cm and e near 0,5.
The different sources of noise which arise in the observation of planetary transits are studied below. We will also estimate the importance of spectral types in the detection of the transit signal.

 Noise of stellar origin

 Activity phenomena (stellar spots transit, granulation, eruptions...) cause photometric variations often superior to 100 ppm but with time frequencies different from the transit’s ones. The SSM mission measured the solar flux during long periods of time in 1980, 1984 and 1985. The figure II.2 shows what the transit of planets as big as the main two planets o the pulsar PRS 1257 + 12 into a close orbit around the Sun would be. It is clear in this case that the sun variability wouldn’t bother the transits detection.
An estimate of the fraction of stars which have significant photometric fluctuations, and then which won’t be able to give any results about hypothetic planetary transits, can be done from a few simple hypotheses
• The photometric variability level caused by activity is a " steep " function of the Rossby number Ro = Prot/Tconv, where Prot is the star rotation period and Tconv is the turn-over time scale of the convection.
It can be shown that below the critical value Ro = 0,66, the variability level is between 0,001 and 0,1.
•The variation of Prot, as a function of the spectral type, with a given age, doesn’t depend on the age.
Thus we can use the relationship between Prot and the spectral type measured in the Hyades, Cluster, taken as a reference (Raddick 1987).
• With a fixed spectral type, Prot is increasing like t^1/2, as established by Skumanitch and checked by observation (Soderblom 1983).
Then for every spectral type we can compute the age t_min when the star would have slowed down sufficiently to reduce its activity level     t_min /t_H > (0.66 T_conv/P_rotH )
Here t_H is Hyades’ age (10⁸ years) and P_rotH is the rotation period for this spectral type in the Hyades, Cluster.
When their expected number is larger than 3, the periodicity off the signal allows to lower the constraint on the value of k.

 The results (Table II.3) show that the activity level of the main sequence stars remains low for most part of their life up to the spectral type K5,.
Therefore, in the following estimaties, we only kept stars hotter than K7, wheighting our results with a constant coefficient (0,8) in order to remove the contribution of the youngest stars whose activity level makes the transists detection impossible.
Solar type stars, especially the late spectral type ones, are among the quietest one. Then the expected brightness variations are, the ones caused by a group of spots rotation or otherwise, the ones coming from turbulent motions and from the gravity waves inside the star atmosphere.The variations slower than the maximum transit time will affect the detection of the transit.

 Table II.3 Activity life time as a function of spectral type
 

 
Photon noise
A non-ambiguous detection of a photometric variation DF/F of the order of 10 ^--4 requires a sufficient number of photons to beat the quantum noise. With a given instrument, it leads to a minimum of the detectable stellar flux and, correspondingly, to a maximum distance, Dmax for each spectral type.
In order to identify a serie of transits, photometric decreases need to get out at k times s. We will set up k=6 when only one or two transits are suspected during the observing time of a single field of view (150 j). On the other hand, then concerning six successive transits, individual detections with 2.5s are unambiguous
The limiting magnitude enabling a detection is the result of the characteristics of the telescope, of the CCD and of the awaited transits series. Without any limb darkening and with an impact parameter p=0, it is for COROT :
m_V = 13.6 + 5 log[(DF/F) / 2 10^-4] - 5 log(k / 3) + 2.5 log(tr / 10 ) + 2.5 log C
where tr is the transit time expressed in hours, C is a correction factor which accouns for the CCD chromatic response. The maximal distance is a function of M_V and the star redenning. For a given a spectral type, the number of detectable transits series is :     N_tr = 0.78 N₁₀ (D_max / 10 pc)³ Pr D W / 4 p
where N10 is the number of stars of this spectral type included in a sphere of 10 pc radius (Scalo 1984) around the sun. Pr is the probability that the planet orbital plane is correctly oriented. DW is the solid angle of the studied stellar field. The 0.78 factor comes from the limb darkening effect, for which solar values were chosen, and from the summation of the different impact parameters.

Figure II. 2 : Simulation of the transit of two planets similar to the ones discovered around the pulsar PSR 1257 + 12 orbiting around the Sun.

 Figure II.2 represents the results of a transit simulation. The chosen conditions are : the subjacent solar flux is from the SMM mission of 1985. The planets radii (respectively R_pl/R_Terre = 1.58 and 1.48) are obtained by assuming an inclination of the orbital planet around the pulsar by 60 ° from the sky plane and a density equivalent to the Earth’s one. The two periods are arbitrarily fixed at 20 and 12.5 days, with respectively a =0,144 and 0,106 AU, T=790 and 920 K, assuming T ~ a^1/2 .
After adding the transits to the SMM_85 datas, the inelevant frequencies have been filtered. We should note the perfect equality between the determined orbital periods. It is an important characteristic of the transits. In this particular case, the signal is clearly distinguishes from the noise. 1985 corresponded to a minimum of the solar activity but the signal of the transits is also very easy to distinguish in the 1980 data when the solar activity wasmaximum

 Expected number of transits

 In order to estimate the number of possible transits due to telluric planets, we have to estimate the number of solar type stars escorted a priori with at least one planet. Concerning Jupiter-like planets, this number seems to be of a few % (Marcy 1996). Qualitatively, it is in agreement with Zuckermann’s observations (1995) which claimed that about 10 % of young stars have got an hydrogen cloud. Around the others, the stellar wind has dispersed the hydrogen, preventing Jupiters formation.
Regarding the telluric planets, their formation from Planetesimals is not inhibited by this stellar wind mechanism because it can’t disperse the asteroïd like bodies . Since 50 % of the young stars have a dust disc (Beckwith, 1993), it is reasonnable to a priori assume that half of the stars have got telluric planets and that 20 % of them have got planets whose radius is superior to the earth’s one. Our quantitative estimates are based upon this hypothesis.
We would also like to emphasize that the quantitative estimates shouldn’t be based upon the solar system taken as an example. The planetary systems already found to date have got orbits which are closer than in the solar system (Mayor and Queloz 1995, Marcy and Butler 1996), or the telluric planets mass are superior to the earth ones (Wolszczan, 1994).
We are choosing two examples of telluric planets :
*A telluric planet whose radius is R_pl = 1.58 R_terre (similar to the P1 planet from pulsar PRS 1257 + 12)
*A telluric planet whose radius R_pl = 2 R_terre, located at such a distance from its star that the temperature of a black body would be 600 K (being 0,22 UA for a star similar to the sun).
The estimaties of the number of transits series which could be observed with COROT, in a 1deg² field of view for 150 days, assuming that 20 % of the stars have such planets, are given in table II. 4 and II. 5. By observing, at least, 5 fields of 4 deg² during the mission, we would detect 30 or 40 planets according to the hypothesis made about the size of these bodies.
The scientific breakthrough of such detections woud be an exact knowledge of the planets masses (because sini=1) and especially of their radius, i.e their density and their rocky or gaseous nature.

 Figure II.3 gives the number of expected detections during the COROT nominal mission (2.5 years) if every star has a probability of 20 % to be escorted by a planet with radius R_pl and located at a distance from the star, renormalised at a_r. in the phase space planet radius distance from the star. If every star has got several planets, these numbers add up. We consider the planet temperature as the relevant parameter (the distance from the star being determined from its luminosity) because it allows to clearly express particular physical constraints, as for example the non-sublimation of rocks.
 

Table II. 4a : Planet transit parameters for different spectral types. The planet radius R_pl = 1.58 R_terre at 600K. (a_r = 0.25 UA). n_tr is their average number within 150 days if the orbit plane orientation is adequate. Ntr is the number of expected transits per deg², assuming that 20 % of the stars have a planet of this kind. We only consider spectral types down to K7 because beyond this level, the stars intrinsic variability could prevent from detecting DF/F variations. The total number N_tot is obtained by adding the contributions of the 2 detectors and the 5 field that will be observed by COROT. We only keep from this summation the situations where we can observe at least three transits within 150 days (P £ 60 days) in order to check the planet orbital period equality. The only stars to be kept in the sample are thoses which are sufficiently bright, for the photon noise to remain the dominant source of noise (mv>15.5). Finaly we have multiplied by 0.8 for the reasons explained in the text.

Table II.4b : Calculation, for different spectral types, of the planet transit parameters. The planet radius is R_pl = 2. R_terre a 600K. In the same conditions as in II. 4a.
 

Table II. 4c : as in the two previous tables, estimate of the transits number of " hot Jupiters " with the following hypotheses : Rp radius planet equal to Jupiter’s one, distance from the star varying with the spectral type. With such distance, the planet temperature is equivalent to 51 Peg’s one which is 1340 K. 2 % of the stars are assumed to be escorted by such a planet. All the stars are observed up to mv=16,5. The S/B ratio will be excellent considering the high values of DF/F. The stars M3-M7 have been kept despite their variability because of the large amplitude of the transit signal and the short period which should enable an easy detection.
We can conclude from the table II. 3 that :
If 20 % of the exo-systems have 3 telluric planets whose radius is 1.5 Rearth
with temperature by 300, 500 et 700 K, COROTnominal version would detect
* no 300 K planet (a_r = 1 UA)
* 10 500 K planets (a_r = 0.36 UA)
* 40 700 K. planets (a_r = 0.18 UA)
If 5% of the exo-systems have 3 telluric planets whose radius is 2 Rearth,
at the same temperatures, COROT nominal version would detect
* 1 300 K planet
* 9 500 K planets
* 18 700 K planets
Moreover, it is clear that giant planets like 51 Peg B or 55 Cnc will be very easily detected because they are located up at the to-right of the map. These detections would add complementary pieces of information to the ones already reachable from the ground by giving the planets radius, their sin (i) (equal to 1) and, so, the average planet density. It would allow to definitely be sure about a gaseous or rocky nature.
Planet detecting using reflection
In this case we are dealing with variations within several days or even several weeks. To reach a sufficient S/B, it is necessary to integrate the signal on a longer time (at least 30 days), this would imply stronger constraints on the detectors’ stability.

The table II. 5 shows the S/B that can be reached by COROT in different conditions.

 Table II. 5 : estimations of S/B in different configurations.
 

 
Therefore, COROT, even if it will only be able to marginally detect planetary systems similar to the solar system, is perfectly adapted to the search for telluric planets bigger and hotter than the earth as well as getting significant pieces of information about the physical nature of the "hot jupiters ".

 This discovery would be an extremely interesting step in order to constraint the theories on planetary formation and to provide data to the future exobiology research projects

Figure II. 3 : Map of the planetary space reachable by Corot.

The ioscontours give the expected detections number if 20 % of the stars have planet with a radius R_pl and located at a renormalized distance ar. The renormalization of the distance by the luminosity L_* of the related star :
a_r = a (L_* / Lo)^0.5
leads to a temperature of the planet black body which doesn’t depend on the star any more. The thick outline (blue) corresponds to the basic version of the instrument. The ones in dotted line (red) represent the additionnal detections resulting from the chromatic option (see section II. 3). For clarity the common area of the two regions has been reduced. The solar system’s telluric planets positions, the pulsar PSR 1257 + 12 ones and the ones from the habitable zone are given.

 Choice of the fields of view

Since transits detections can only be done on stars closer than a certain distance, it would be fine to have only this kind of stars in the field. A way to reach this goal is to use the cut off caused by the galaxy scale height. Moreover, it is necessary to have a large number of stars whose magnitude is large enough to allow detection. According to Table II.4, the most interesting stars have mv<16,5. Taking into account the confusion problem, it seems that a good compromise can be reached with a star density less than to 3000/ deg2.
This condition is reached at intermediary galactic latitudes The constraints caused by the orbit of COROT, which will be a low altitude, polar one implies that the observable regions have d ó 7° ( d equatorial declination) then suitable fields are located in the following directions :
b_II=+23 (± 5) Dec équatorial = 0 (± - 7) (l_II = 20 roughly)
b_II=-23 (± 5) Dec équatorial = 0 (± - 7) (l_II = 45 roughly)
b_II=+14 (+ 6/-4) Dec équatorial = 0 (± 7) (l_II = 220 roughly)
b_II=-14 (+ 4/-6) Dec équatorial = 0 (± 7) (l_II = 210 roughly)
(b_II et l_II are the galactic coordinates). These values will be changed some what in order to be compatible with the seismology fields of view.
The stellar density is about 700 to 400 per square degree depending if the field is close to the galactic center or to the anticenter (Besançon model 1997).
In order to roughly have the same objects number in every observed field , it is possible to observe at a lower galactic latitude towards the anticenter. The best positions are given on Figure II. 4.

 Figure II. 4 : Position on the celestial sphere of the fields proposed for the exo-planets goal, in equatorial coordinates (a , d ) Galactic coordinates (l_II, b_II) are drawn as isocontours. The galactic plane is the thick line. The fields must be chosen inside the dark zones. They verify the constraints on galactic latitude (stars optimum density) and declination (imposed by the orbit see chap. V).

 3 Additionnal planetary detections thanks to the chromatic information

The transit of a telluric planet induces a photometric variation of a low amplitude which has to be distinguished from other signals as for instance the ones caused by the star activity or by noises of varius origins.
Two methods exist to distinguish transits from stellar activity. If the planet is close enough to its star to cause at least 3 transits during the observation time of a field (150 days with COROT), the most natural criterion is the strict equality of the intervals between two successive transits (orbital period of the planet).
This is the method previously described and which makes the basic core of the proposed scientific program. Yet, if the planet is located at a longer distance, we can only observe one or two transits and the previous criterion is not applicable any more. We will show that if we have a colored " information ", then it is possible to use the chromaticity of the photometric variations to distinguish planetary transit from stellar activity.
This method is illustrated in Figure II.6. Where the sun chromatic variations, as a function of wavelength, as drawn according to theVIRGO experiment measurements made on the SOHO satellite (Frohlich, 1990). It appears that the chromatic, defined as the ratio of the flux in the blue to the one in the red, depends on the wavelengths used to determine these colours. But the chromatism remains inferior to 1 concerning the planetary transits while it is clearly superior to 1 concerning the solar variations, this being measured during the adequate period of time scales ( 3 to 10 hours).
It doesn’t seem possible to know by another way if the observed variations are caused by a planet or if they are solar variations with the same time structure.

Therefore, the chromatic signature of the planetary transits is very different from the one due to solar type stars luminosity variations.

In order to determine if the chromatic variations of the Sun can be typical for other spectral types these variations can be modeled, assuming they are due to the presence of colder zones (from D T) in the stellar disc (whose temperature is Teff). This way the observed solar chromatism is corredly described with a value of Teff=5800 K, and we find also that the star depends on Teff but not on D T. This is in agreement with the SOHO observations of the Sun. Thus it seems possible to predict the chromatism of the stellar variations with some confidence. It depends on the real temperature of the star but is qualitatively similar to the sun’s one.
A criterion is then obtained with this method. If the blue and red flux can be measured with suffficient accuracy, it is possible to distinguish the variations caused by a planetary transit from the ones caused by stellar activity. This chromaticity criterion will be particulary usefull if only one or two transits are identified within 150 days (a field observation time with COROT) since the periodicity criterion becomes useless. Actually if an event seems identififed, we wouldn’t have any certainty about its nature (i.e) and we wouldn’t know if a particular stellar variation couldn’t have miniced this event. Even if a detection is made at 6 s from the different noises (case of a planet with 2 terrestrial radius at 600 K, around a F0 star of 750 pc), we couln’t conclude about the nature of this event without the chromatic criterion.
This second method enables to significantly rise the space volume of the explored planetary parameters’ phases (Rpl, Tpl). This therefore allows us to increase the chances for COROT to detect planets. In particular, it becomes possible to detect planets located in the habitable zone of A, F G, or K spectral type stars (see Figure II. 3).

 This gives us the opportunity to make a major scientific discovery

 Figure II; 5 : Ratios of the relative chromatic flux variations of a star to its bolometric flux, as a function of the wavelength. Variations caused by the stellar activity are given by measurement made by VIRGO-SOHO in the range of 3 to 10 hours periods. The variations produced by a planetary transit are calculated from the sun center-edge darkening. In the latter case, the possible values band corresponds to different values of the impact parameter (p=0 - 0,8). This ratio seems to be a mean to distinguish the two kinds of phenomena;

 Implementation of the chromaticity criterion

 The splitting of the stellar flux at the focal plane by a dichroïc with two independant detection channels is considered too complex and too expensive for a small mission and therefore can’t be used. Another solution to get the chromatic data with a single focal plane has been studied for the exo-planet.
It is introduced here as an option of the nominal design to be studied more deeply.
The purpose is to include a dispersing element (prism) giving, instead of a defocussed image, a little spectrum (3-4 resolution) with the same number of pixels as the nominal configuration. This solution has got a natural advantage in comparison with the dichroïc solution because the wavelengths defining the spectral bands can be adapted to the spectral type of each star. The additionnal cost introduced by this option seems low but remains to be more precisely studied.
The problem is does the chromatic data can be obtainedwith a sufficient accuracy to discriminating criterion ? In this eventuality, how many news detections can be expected.
The gain of a small spectrum enables to determine the blue and red bands respectively including a fraction X_B and X_R of the N photons obtained duringthe measure of a photometric event. In order to perform the chromatic analysis there are different ways to analyze the blue photons (nimber B) and the red ones (number R) : to make the ratio, the difference or another mathematical combination. Let’s take the simple example of the difference,
Here the random variable (because of the quantum noise)writes :
y = D B /B - D R/R.

Each physical phenomenon i, inducing a flux variation, stellar activity or transit, has a specific chromaticity : D B /B = a _B (i )e , D R/R = a _R(i) e where e = D N/N is the total variation. The a are given in Figure 1.2.5 and the flux are coloured X_B and X_R
The variable y hasa mean value which depends on the nature of the phenomenon :
<y>_tr = e (a _B - a _R) _tr
<y>_stel = e (a _B - a _R) _stel
Its standard deviation, due to the quantum noise, is independant of its nature.
s = (1/X_B + 1/X_R)^1/2/N^1/2
The corresponding probability distributions aretwo Gauss functions, whose standard deviation is s , respectively centered on the mean values <y>_tr and <y>_stel (see Figure II.6).

 Figure II. 6 : Distribution functions of the random variable y (" blue/red ") for the two types of photometric variations : planetary transit and stellar activity (see text).The measure of y will allow to distinguish between the two phenomena with a confidence level which increases with the separation of the two gaussians.

The represented level is 90%.
In order that a measure (realization of y) enables to distinguish between a transit and a stellar activity, with a confidence rate f (for example f-90%) the gaussians have to intersect at y_o that beyond this value, the surface of each gaussian be less than 1-f.
In the case of solar type star, the optimal values for the splitting of the spectrum are X_B = 0.17 and X_R = 0.60. We obtain a confidence level of 80 % or 90 % for, respectively, e N^1/2 = 5.8 or 8.4. Moreover, this latest quantity is also the optimum S/B ratio for the white light detection. It is an optimum because the measurement of the variation D F/F is made within the exact duration of the transit. The corresponding signal is indeed e = D N/N and the associated noise is N^1/2..
In conclusion, if we manage to make measurement blue and red parts of each star only limited by the quantum noise, it is possible to know the origin of a flux variation, planetary transit or stellar activity, with a confidence level of 80 %, 90% or even more when this variation, of white light integrated within the event’s length, is detectable at 5,8 ; 8,4 or more.
Therefore the method is appropriate for the photometric variations which are stronger than the noise but only occur once out of 150 days (a field observation time with COROT).

 Expected number of detections in the habitable zone

 In order to make an estimate of this number we will make the following assumptions :
-20 % of the stars have a planet in the habitable zone (probability of liquid water at their surface)
- 5 fields with 1200 stars each are studied during the whole length of the mission.
We are using a galactic stellar population model (Besançon’s one for example) in a field located at b_II = 20° and l_II = 20°. The number of stars to be monitore is obtained bylimiting mv<16.5 with fields of 4 deg². Inder such an assumption, the only considered signals are the ones detectable at 5.8 sigmas and identified with planetary transits with a confidence level of 80 %.
The expected number of detections has been computed according to the planet radius. Concerning planets in the habitable zone the number is significant for objects whose radius is larger to 1,5 times the earth’s one. For such objects there is, in most cases, only one transit during the observation time (150 days) (see Figure II. 3).
The existence of planets of this size is obviously not established. Nevertheless the formation of such objects is not removed by the current models because the efficiency of the accretion mechanisms depends on the density or the mass of the protoplanetary discs. These " giants " telluric objects could for example appear inside the densest and the most massive discs. Moreover, we can notice that the cores of the giant planets of our solar system have estimated masses comparable to with the size of these planets.
If, in the solar neighborhood, planets exist in the habitable zone around mother stars and have a radius which is at least 1.5 RÅ , the chances to detect something are serious if COROT has a chromatic dispersion device.

 Figure II. 7 : Number of planets located in the star habitable zon eof a star (the planet surface temperature should allow the presence of water), detectable by COROT if the light is dispersed by a prism. We are assuming that 20 % of the stars have a planet of this kind and a radius R_planète.

 1.1.4 Summary of the exo-planets program’s scientific goals

 Currently we only know a few things about the radial distribution and about the mass of the planets which form around stars which differ from the sun. We first thought that the planetary exo-systems should be similar to our solar system but, with the recent discoveries we had to admit that it wasn’t obvious. The new objects we are detecting cause very serious problems to the models of planetary formation models which will certainly know important evolutions within the forthcoming years.
With COROT, it is likely that the discovery of a larger number of extra-solar planets (telluric or " hot jupiters " types) will allow to constrain the planetary formation models more strongly.
For the moment, if we want to estimate the detection opportunities of such objects, we are forced to make hypotheses (finally pretty uncertain) concerning the number, the size and the temperature of these objects.
The uncertainty is high in each case. Yet, concerning the number, we can rely on what we have learnt from the recent discoveries.
We estimate that 5 % of the stars are associated with massive planets, close to their stars which are probably gaseous giant ones. Therefore, according to the current planetary models which tell that the planetesimal accretion processes have come before gas capture (appearance of a rocky core whose mass is around 15 times the earth’s one, followed by a gas gravitationnal capture), we can conclude that the telluric planets formation should occur at least as oftenly.
So our minimal hypothesis about the number of objects will be :

At least 5 % of stars are escorted with telluric planets

Concerning the size and the temperature of the telluric exo-planets, we can only rely on the objects we know : the planets of our solar system or the pulsar PSR 1257+12 ones.
Therefore our hypothesis to estimate the expected transits number is :
there are planets a bit bigger than the earth.

The scientific goals for the COROT-exoplanets mission are the following ones :

Main objective :
To detect telluric planets larger than the earth and with temperature Tpl > 600 K
If the number of transits is larger than 3 during the observation time (150 days), we can use the event’s pure periodicity criterion in order to distinguish planetary transits from artefacts.

Main goal’s consequences :
- Detection and studies of the " hot Jupiters "
(In order to study the eventual existence of giant satellites or planetary rings, it is necessary to change, up on alert, the time sampling).
- Study of the stellar variability

 Additionnal objective

 To detect planets larger than the earth andof temperature 200 K< Tpl < 600 K.

If transit is less than 2, white light photometry is not sufficient to distinguish between planetary transits and stellar variations. A chromatic information enables to remove the ambiguities because the chromatic signature of these two types of events is very different. It is important to note that detections of that kind correspond to objects which are more similar to the ones we know in our solar system (bigger and colder).

Additionnal objectives
- Significant increase of number " hot Jupiters " of detections
- Chromatic study of stellar variability (to be precised subsequently)

Expected number of events

 The expected transits has been computed in the table II. 4 for several planets radius.
With a photometry optimized up to mv=15,5 (which corresponds to the COROT field with 30000 stars observed during the mission) the expected number of events is :
- With the minimal hypothesis :
. 6 planets with Rpl = 1.58 R_earth during the whole mission.
. 10 planets with Rpl = 2.R_earth during the whole mission, with the same distance from the star
- With a more optimistic hypothesis (if 20% of the stars are associated with telluric planets) :
. 25 planets Rpl = 1.58 R_earth during the whole mission.
. 40 planets Rpl = 2 R_earth during the whole mission, with the same distance from the star.

Moreover we are expecting about 35 hot Jupiters during the whole mission.

1.1.5 Summary of the scientific specifications of the exo-planets program

 The exo-planets program brings some additionnal constraints to the mission.
The specifications enabling to reach the main goal are the basic specifications of this program :
- To observe at least 30 000 stars during the whole mission
- To measure the relative flux variations included between 7 10 ^-4 et 5 10 ^-3 with one hour integration times and magnitude varying between 15,5 and 11.

In order to reach the additionnal objectives, there should be :
- a multi-colour observation (prism dispersion)
- a 60 000 stars observation during the whole mission
(we use a degraded photometry upon targets whose magnitude 15,5 <mv<16,5)
This goal is the subject of the option presented here but is not yet accepted.

 In order to optimize the detection chances it is necessary :
(i) to have target stars dense enough (around 1500 to 3000 per square degree) and whose mv is less than or equal to 16,5
(ii) to avoid giant type stars.
These two conditions are satisfied if the galactic latitude of the observations is chosen as to benefit from the natural cut off due to the galaxy height scale.
To sum up, the exo-planets specifications are :
• To observe at least 30 000 (60 000 if possible) stars of the main sequence during the whole mission.
• To measure relative flux variations included between 7 10 ^-4 et 5 10 ^-3 with 1 hour integration times and magnitude varying between 15,5 and 11.
• To observe at intermediate galactic latitudes :
23 degrees ± 10 degrees towards the galactic center
0 degrees ± 10 degrees toward the anticenter
• To observe with several colours if possible (device presented in option)