INTRINSIC PLANETARY FREQUENCIES BASED ON KEPLER OBSERVATIONS William Borucki , NASA Ames
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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
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AN ACCURATE VALUE OF eta-EARTH REQUIRES REMOVING THE MANY BIASES THAT EXIST
• Biases;– Size of star Stellar variability
– Number of transits increases SNR Missed transits affects longest orbital periods
– Planet size Interacting planetary systems vs isolated systems
– Stellar magnitude fast 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
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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.
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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(p1) 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.
p2 =probability that orbital plane is aligned with line-of-sight. (Calculated from a and R*).
pnc =p1*p2; probability that star “n” could have produced candidate “c”
nc,a,R = ∑pnc is an estimate of the number of stars that could have produced the candidate in the (k, a, ∆a, R, ∆R) bin.
Na,R,k is the median vaule of nc,a,R
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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 determinewhich target stars could have produced planets In the bin.Rp > 2 Re and Period < 50 dThreshold for detection; SNR >10 sigma4100< Teff < 6100 KKp < 15Log(g) 4.0 to 4.9
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COMPARISONS OF THE INTRINSIC FREQUENCIES WHEN TEMPERATURE CONSTRAINT IS RELEASED
CONSTRAINING THE RANGE OF STELLAR TEMPERATURES HAS LITTLE EFFECT.
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CHANGING THE DETECTION THRESHOLD LEVEL HAS LITTLE EFFECT ON THE ESTIMATE OF THE INTRINSIC FREQUENCIES
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EFFECTS OF ALL CONSTRAINTS ON SELECTING THE CANDIDATES
The combination of all imposed constraintshas a modest (~ 25%) effect.
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COMPARISON OF INTRINSIC FREQUENCIES FROM HOWARD et al AND BORUCKI et al.
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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.
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BACK UP CHARTS
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INTRINSIC FREQUENCY IS THE OBSERVED NUMBER / PREDICTED NUMBER
a<0.02AU 0.02<a<0.04 0.04<a<0.06 0.06<a<0.08
Rp < 1.25Re
Earth-size
Predicted # of candidates & frequencies;185523.2x10-4
Predicted # of candidates &Frequencies;58162.1x10-3
Predicted # of candidates &Frequencies;34005.3x10-3
Predicted # of candidates &Frequencies;15419.1x10-3
1.25 <Rp<2.0
superEarth-size
Predicted # of candidates & frequencies;324723.4x10-4
Predicted # of candidates & frequencies;127733.5x10-3
Predicted # of candidates & frequencies;75778.1x10-3
Predicted # of candidates & frequencies;51801.1x10-2
2.0<Rp<6.0
Neptune-size
Predicted # of candidates & frequencies;446641.1x10-4
Predicted # of candidates & frequencies;178811.6x10-3
Predicted # of candidates & frequencies;109087.4x10-3
Predicted # of candidates & frequencies;76891.2x10-2
6.0<Rp<15.0
Jupiter-size
Predicted # of candidates & frequencies;752264.0x10-3
Predicted # of candidates & frequencies;358255.3x10-4
Predicted # of candidates & frequencies;195842.0x10-3
Predicted # of candidates & frequencies;124381.2x10-3
15<Rp<22.4
superJupiter-size
Predicted # of candidates & frequencies;
Predicted # of candidates & frequencies;317041.6x10-4
Predicted # of candidates & frequencies;209679.5x10-5
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 starprobabilities to reproduce binned candidate data
a<0.02AU 0.02<a<0.04 0.04<a<0.06 0.06<a<0.08
Rp < 1.25Re
Earth-size
# and list of candidates = 6; 500.05 (1.2, 0.017)977.01 (0.78, 0.014)1128.01 (0.97, 0.019)1150.01 (0.65, 0.015)1169.01 (1.16, 0.015)1367.01 (1.18, 0.013)
# and list of candidates = 12;321.01 (0.93, 0.035)377.03 (1.04, 0.027)665.02 (1.18, 0.028)692.01 (712.01 (952.04 ( 975.01 (: : :
# 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
superJupiter-size
# and list of candidates = 0
# and list of candidates =5;
# and list of candidates = 2;
# and list of candidates = 1;
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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.