INTRINSIC PLANETARY FREQUENCIES BASED ON KEPLER OBSERVATIONS William Borucki, NASA Ames Kepler Mission Objectives; Determine the Frequency of Earth-size and larger planets in the habitable zone of sun-like stars  eta-Earth Determine the size and orbital period distributions of planets. Associate the characteristics of the planets with those of their host stars. Gordon Conference, 21July 2011

AN ACCURATE VALUE OF eta-EARTH REQUIRES REMOVING THE MANY BIASES THAT EXIST Biases; –Size of starStellar variability –Number of transits increases SNRMissed transits affects longest orbital periods –Planet sizeInteracting planetary systems vs isolated systems –Stellar magnitudefast rotating stars Develop & test computational approaches Determine the effects of various parameters & their uncertainties Currently, the effort is focused on calculating the size distributions of planetary candidates. Parameters to consider; –Value of detection threshold –Missed transits due to monthly data downlink –20% of the Kepler star field has only 75% time coverage –Substantial uncertainties in star size cause uncertainties in planet size –Data processing introduces noise for some events –Detection efficiency variations of the data analysis pipeline with planet SNR, period, stellar variability THIS IS A WORK IN PROGRESS

MEASURED VS. INTINSIC DISTRIBUTIONS Correction for selection effects reduces the prominence of the coolest stars, but Shows a clear drop in frequency for K dwarfs and a greatly enhanced frequency of Jupiter-size candidates in orbit around the hotter and more massive stars.

A Search for Earth-size Planets in the Habitable Zone Borucki – Page 4 TRANSFORMATION OF OBSERVED DISTRIBUTIONS TO INTRINSIC DISTRIBUTIONS Each candidate “c” is added to bin of class-size “k” & semi-major axis a, Each of the 153,196 target stars is examined to determine the probability that it could produce the candidate. For each star, snr =(Rp/R*) 2 /CDPP. (CDPP computed for the measured transit duration) Total SNR=snr*√N after N is corrected for missed transits (~0.92). Recognition rate =probability(p 1 ) that a pattern of transits would be recognized if the orbital plane was in the line-of-sight; 50% for SNR =7.0, 86% for SNR=8.0, etc. p 2 =probability that orbital plane is aligned with line-of-sight. (Calculated from a and R*). p nc =p 1 *p 2 ; probability that star “n” could have produced candidate “c” n c,a,R = ∑p nc is an estimate of the number of stars that could have produced the candidate in the (k, a, ∆a, R, ∆R) bin. N a,R,k is the median vaule of n c,a,R

LIST OF CONSTRAINTS & A COMPARISON OF INTRINSIC FREQUENCIES VS. ORBITAL PERIOD FOR BOTH APPROACHES Constraints used in Howard et al calculation; Average of bin characteristics used to determine which target stars could have produced planets In the bin. Rp > 2 Re and Period < 50 d Threshold for detection; SNR >10 sigma 4100< Teff < 6100 K Kp < 15 Log(g) 4.0 to 4.9

COMPARISONS OF THE INTRINSIC FREQUENCIES WHEN TEMPERATURE CONSTRAINT IS RELEASED CONSTRAINING THE RANGE OF STELLAR TEMPERATURES HAS LITTLE EFFECT.

CHANGING THE DETECTION THRESHOLD LEVEL HAS LITTLE EFFECT ON THE ESTIMATE OF THE INTRINSIC FREQUENCIES

EFFECTS OF ALL CONSTRAINTS ON SELECTING THE CANDIDATES The combination of all imposed constraints has a modest (~ 25%) effect.

COMPARISON OF INTRINSIC FREQUENCIES FROM HOWARD et al AND BORUCKI et al.

SUMMARY There are hints of frequency dependencies of candidate sizes on stellar characteristics. The current calculations are; 15% for the sum of Earth-size and superEarth- size, 10.4% for Rp from 2 to 4 Re, 2% for Rp from 4 to 8 Re, 1.1% for Rp from 8 to 32 Re, and a total of 30%. These values are consistent with the approach in Borucki et al ApJ 736,19,2011. A comparison of the current calculations with those of Howard et al show good agreement with some differences probably due to selection effects used in the calculations.

BACK UP CHARTS

INTRINSIC FREQUENCY IS THE OBSERVED NUMBER / PREDICTED NUMBER a<0.02AU0.02<a< <a< <a<0.08 Rp < 1.25Re Earth-size Predicted # of candidates & frequencies; x10 -4 Predicted # of candidates & Frequencies; x10 -3 Predicted # of candidates & Frequencies; x10 -3 Predicted # of candidates & Frequencies; x <Rp<2.0 superEarth- size Predicted # of candidates & frequencies; x10 -4 Predicted # of candidates & frequencies; x10 -3 Predicted # of candidates & frequencies; x10 -3 Predicted # of candidates & frequencies; x <Rp<6.0 Neptune-size Predicted # of candidates & frequencies; x10 -4 Predicted # of candidates & frequencies; x10 -3 Predicted # of candidates & frequencies; x10 -3 Predicted # of candidates & frequencies; x <Rp<15.0 Jupiter-size Predicted # of candidates & frequencies; x10 -3 Predicted # of candidates & frequencies; x10 -4 Predicted # of candidates & frequencies; x10 -3 Predicted # of candidates & frequencies; x <Rp<22.4 superJupiter- size Predicted # of candidates & frequencies; x10 -4 Predicted # of candidates & frequencies; x10 -5 Predicted # of candidates & frequencies; Bin the observed candidate data; size & a for each candidate & number of candidates in each bin Predict the # of candidates = sum of all target star probabilities to reproduce binned candidate data a<0.02AU0.02<a< <a< <a<0.08 Rp < 1.25Re Earth-size # and list of candidates = 6; (1.2, 0.017) (0.78, 0.014) (0.97, 0.019) (0.65, 0.015) (1.16, 0.015) (1.18, 0.013) # and list of candidates = 12; (0.93, 0.035) (1.04, 0.027) (1.18, 0.028) ( ( ( ( : : : # and list of candidates= 18; ………… # and list of candidates = 14; ……………… 1.25 <Rp<2.0 superEarth- size # and list of candidates = 41; # and list of candidates = 45; # and list of candidates = 61; # and list of candidates = 57; 2.0<Rp<6.0 Neptune- size # and list of candidates =5; # and list of candidates=29; # and list of candidates=81; # and list of candidates=92; 6.<Rp<15.0 Jupiter-size # and list of candidates = 3; # and list of candidates = 19; # and list of candidates=39; # and list of candidates=15; 15<Rp<22. 4 superJupite r-size # and list of candidates = 0 # and list of candidates =5; # and list of candidates = 2; # and list of candidates = 1;

INTRINSIC DISTRIBUTIONS VS. SEMI-MAJOR AXIS Results imply intrinsic frequencies are at least as large as: 5% for Earth-size for a ≤ 0.2 AU; 8% for super-Earth-size for a ≤0.25 AU; 18% for Neptune-size for a ≤0.5AU, and 2% for Jupiter-size for a ≤0.5AU. The result implies that there are ~ 34 candidates per 100 target stars.