Detection of transits of extrasolar planets with the GAIA new design Noël Robichon DASGAL - CNRS UMR 6633

depth of a transit  m ≈  F/F = (R P /R * ) 2 R Earth = 0.1 R Jup = 0.01 R Sun Earth :  m=10 -4 Jupiter :  m=10 -2 HD :  m=  G >  only Jupiter size objects with GAIA

duration of a transit Dt/P= R * /  a = R * /  M * 1/3 P 2/3 2R * to the observer a V circ = 2  a/P Dt = 2R * /Vcirc Earth : P = 1 yr  Dt/P = Jupiter : P = 11.3 yr  Dt/P = HD : P = 3.5 days  Dt/P = GAIA : # of observations  P < 10 days ( if R P <<R * )

geometric probability of observation p geo =p(  <2R * /a)=2sin(R * /2a) p geo =R * /a=R * /M * 1/3 P 2/3 (if R P <<R * ) star planet cone of transit visibility  a 2R * Earth  p geo = Jupiter  p geo = HD  p geo = 0.1  in favor of very short periods

Simulations mass-M V and mass-radius relations from litterature photometric error  G (G)photometric error R P =1R Jup or 1.3 R Jup Monte Carlo simulation in bins of ( , G, M V, P) Galaxy model (Haywood)  N * ( , G, M V ) scanning law of the satellite  P Nobs/transit (  )P Nobs/transit (  ) probability of having an observable transit star  Pobs (P, M V ) = P geo (M V, P) x 0.01 log(P + /P - )/log(10)0.01 probability of detecting the transit P detec (N, G, M V ) less than 10 % of false detection and N>5 or 7 (3 or 4 ≠ epochs)false detection

Number of transited stars if R P = 1.3 R Jup N pts/transits >max(5, N(#f alse /#t rue <10%)) # of stars with transiting planet Period TOTAL: stars M G bins >11

Number of transited stars if R P = 1.0 R Jup N pts/transits >max(5, N(#f alse /#t rue <10%)) # of stars with transiting planet Period TOTAL: stars M G bins >11

Number of transited stars as a function of G R P = 1.3 R Jup N pts/transits >max(5, N(#f alse /#t rue <10%)) # of stars with transiting planet G M G bins >11

R P = 1.0 R Jup N pts/transit > R P = 1.3 R Jup N pts/transit > R P = 1.0 R Jup N pts/transit >75800 R P = 1.3 R Jup N pts/transit > Summary of the results from simulations

Conclusions simulation predict to detectable transits things to improve: countings of the Galaxy model -> less transited stars better limits in G and M V -> more transited stars better precision in AF photometry -> more transited stars take account of variable stars: spots, grazing eclipsing binaries... detection algorithm recovering unbiased planet distribution = f(P, M P, M * …) unknowns: statistics: % of HJ = f(ST)? properties of planets: radii? P min ?…

Photometric precision  F /F = (RON 2 +SKY+F) 1/2 /F  mag G 0,0001 0,001 0,01 0,  G per AF CCD  mag per MBP transit (sum of 10 bands + MSM)  G per AF transit (9 CCDs) mag has been quadratically added in the simulation G2 star R P =1.3 R Jup G2 star R P =1 R Jup

Simulation of HD for two different T C

distribution of number of points during a transit percentage # of points P=10.25 days (dt/P = 1.7%)  = +5° (170 points) P=3 days (dt/P = 3%)  = +35° (280 points)

,511,522,53 # of stars with planet log P (days) distribution of periods of known systems 4 % of stars have an planetary system  1 % have a planet with P < 30 days minimum period observed: 3 days

,0001 0, probability of having N points greater than p  p=1.5 p=2 p=2.5p=3 N probability