Large-scale systematic characterization of transiting exoplanets

Talk given to the astrophysics group at Oxford University

Transcript

1. Large-scale Systematic Characterization of Transiting Exoplanets Dan Foreman-Mackey New York University
2. Large-scale Systematic Characterization of Transiting Exoplanets by Dan Foreman-Mackey New York University
3. Large-scale Systematic Characterization of Transiting Exoplanets Dan Foreman-Mackey CCPP@NYU @exoplaneteer dfm.io dfm
4. Kepler
5. Credit: NASA
6. Study the population of (Earth-like) exoplanets. Reference: kepler.nasa.gov (ish)
7. 1 2 search characterization hierarchical inference 3
8. 1 2 search characterization hierarchical inference 3 AKA noise and systematics
9. Search Aren’t the Kepler team doing this already?
10. Data from: NASA Exoplanet Archive
11. Credit: NASA
12. Object: Kepler-37 linear counts
13. Object: Kepler-37 log counts
14. Object: Kepler-37 pixel time series time flux
15. Object: Kepler-37 pixel time series time flux
16. Kepler-37b
17. Object: Kepler-32 linear counts
18. Object: Kepler-32 log counts
19. Object: Kepler-32 time flux
20. Object: Kepler-32 time flux
21. “raw” relative photometry [ppm]
22. “corrected” (PDC) relative photometry [ppm]
24. “raw” relative photometry [ppm]
25. “corrected” (PDC) relative photometry [ppm]
27. instrumental: pointing, temperature variations, electronic noise, etc. astrophysical: cosmic rays, variable stars, spots, exoplanets, etc. systematics
28. Rappaport et al. 2013 the Host Star alue Uncertainty 433 ±66 .632 ±10% .574 ±10% .721 0.1 −0.2 ... 0.98 ±0.02 0m 03. s14 ... 3′ 14. ′′7 ... 5.38 ... 6.44 ... 5.30 ... 4.93 ... 4.69 ... 3.58 ... 2.99 ... 2.84 ... 4900.00 ... 10022 ±0.000005 − 525d ... 900.358 0.004 5.9 ±0.4 < 1.0 ... > 5 2 σ < 10 2 σ Fig. 5.— Top-left is a typical 29.4-min. LC observation of the target, for one particular frame of 62,000 exposures. The blue pixel at {400, 35} contains KIC 8639919 that is ∼2 magnitudes brighter than the target KOI-2700 located at {398.5, 35.7}. During this quarter, the target fell upon detector module 17 output node 3. Rappaport et al. (2013) pointing & the Kepler PSF
29. Rappaport et al. 2013 the Host Star alue Uncertainty 433 ±66 .632 ±10% .574 ±10% .721 0.1 −0.2 ... 0.98 ±0.02 0m 03. s14 ... 3′ 14. ′′7 ... 5.38 ... 6.44 ... 5.30 ... 4.93 ... 4.69 ... 3.58 ... 2.99 ... 2.84 ... 4900.00 ... 10022 ±0.000005 − 525d ... 900.358 0.004 5.9 ±0.4 < 1.0 ... > 5 2 σ < 10 2 σ Fig. 5.— Top-left is a typical 29.4-min. LC observation of the target, for one particular frame of 62,000 exposures. The blue pixel at {400, 35} contains KIC 8639919 that is ∼2 magnitudes brighter than the target KOI-2700 located at {398.5, 35.7}. During this quarter, the target fell upon detector module 17 output node 3. Rappaport et al. (2013) ble uncertainty of ata. al. (2010). ssuming zero dilu- 00 t is being tran- y to confirm, precision, that th time during ses in flux are Table 1 for the hown in Fig. 6 ted flux series, thin the statis- obtained from st being devel- ained with the study, though xcellent overall Fig. 6.— Epoch-folded transit profile produced from PSF pho- tometry at the pixel level for KIC-2700 (blue curve) and for the nearby bright neighbor star (green curve). There is no trace of the transit in the photometry from the neighboring star. pointing & the Kepler PSF
30. Presearch Data Conditioning (PDC) (yeah it's a strange name) attempts to remove instrumental effects without affecting astrophysical signals (nearby targets are correlated) (nearby targets are uncorrelated)
31. Presearch Data Conditioning (PDC) (yeah it's a strange name) run PCA on nearby light curves fit target using top few components
32. “corrected” (PDC) relative photometry [ppm]
33. instrumental: pointing, temperature variations, electronic noise, etc. astrophysical: cosmic rays, variable stars, spots, exoplanets, etc. remaining systematics
34. How to Proceed?
35. 1 2 median filter BLS
36. Data from: NASA Exoplanet Archive
37. time since transit Object: KIC 2301306 + injected super-Earth Object: KIC 2301306 + injection
38. Object: KIC 2301306 + injected super-Earth time since transit Object: KIC 2301306 + injection
39. Object: KIC 2301306 + injected super-Earth time since transit Object: KIC 2301306 + injection
40. figure generated using: github.com/dfm/triangle.py
41. I would never do THAT
42. Model all the noise!
43. a Gaussian process
44. a Gaussian process
45. 1 2 n yn ˆ yn yn ˆ yn a Gaussian process
46. The data are drawn from a HUGE Gaussian
51. 3 2 1 0 1 2 3 time since transit [days] 3 2 1 0 1 2 3 time since transit [days]
52. time since transit Object: KIC 2301306 + injected super-Earth Object: KIC 2301306 + injection
53. Object: KIC 2301306 + injected super-Earth Object: KIC 2301306 + injection time since transit
54. figure generated using: github.com/dfm/triangle.py
55. figure generated using: github.com/dfm/triangle.py
56. What about real data?
57. KOI 1474 Dawson et al. (2012) my fit to the raw photometry!
59. Search That’s what we were talking about, right?
60. search is a hypothesis test a. compute likelihoods (efficiently) b. vet candidates (robustly) ln " ptransit(data | t(k) 0 , P(k), . . .) pnull(data | t(k) 0 , P(k), . . .) #
61. solve linear system compute determinant GP likelihood ~ 1200 x 1200 O(N3)
62. solve linear system compute determinant GP likelihood ~ 1200 x 1200 O(N3) pre-factorize only depend on hyperparameters
63. solve linear system compute determinant GP likelihood ~ 1200 x 1200 O(N3) pre-factorize only depend on hyperparameters but sparse!!
64. enforce sparsity t ⌃ sparse Cholesky factorization using SuiteSparse cise.ufl.edu/research/sparse/SuiteSparse
65. 100 1000 ms s COMPUTATION TIME NUMBER OF DATAPOINTS O(N⇠2) O(N3) enforce sparsity
66. 0.08s factorization for real Kepler quarter see George github.com/dfm/george C with Python bindings
67. 0.9ms solve for real Kepler quarter see George github.com/dfm/george C with Python bindings
68. search is a hypothesis test a. compute likelihoods (efficiently) b. vet candidates (robustly) ln " ptransit(data | t(k) 0 , P(k), . . .) pnull(data | t(k) 0 , P(k), . . .) #
69. phase log(period)
70. phase log(period) can you spot the planet?
71. phase log(period) can you spot the planet?
72. phase log(period) can you spot the planet?
73. 1 2 search characterization hierarchical inference 3
74. 1 2 search characterization hierarchical inference 3 ✓
75. Hierarchical Inference
76. stars planets n sn rn,k ✓r ✓s xn exoplanets the hard way
77. stars planets n sn rn,k ✓r ✓s xn exoplanets the hard way the Kepler data noise, systematics, “de-trending”
78. stars planets n sn rn,k ✓r ✓s xn exoplanets the hard way exoplanet populations physics, occurrence, formation the Kepler data noise, systematics, “de-trending”
79. stars planets n sn rn,k ✓r ✓s xn exoplanets the hard way exoplanet populations physics, occurrence, formation the Kepler data noise, systematics, “de-trending” characterization parameters of individual systems
80. l Journal, 725:2166–2175, 2010 December 20 doi:10.1088/000 tronomical Society. All rights reserved. Printed in the U.S.A. INFERRING THE ECCENTRICITY DISTRIBUTION David W. Hogg1,2, Adam D. Myers2,3, and Jo Bovy1 logy and Particle Physics, Department of Physics, New York University, 4 Washington Place, New York, NY 10003, USA; d 2 Max-Planck-Institut f¨ ur Astronomie, K¨ onigstuhl 17, D-69117 Heidelberg, Germany 3 Department of Astronomy, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA Received 2010 August 24; accepted 2010 September 25; published 2010 December 6 ABSTRACT rd maximum-likelihood estimators for binary-star and exoplanet eccentricities are biased high, in th e estimated eccentricity tends to be larger than the true eccentricity. As with most non-trivial observ histogram of estimated eccentricities is not a good estimate of the true eccentricity distribution. H p and test a hierarchical probabilistic method for performing the relevant meta-analysis, that is, in e eccentricity distribution, taking as input the likelihood functions for the individual star eccent plings of the posterior probability distributions for the eccentricities (under a given, uninformative ethod is a simple implementation of a hierarchical Bayesian model; it can also be seen as a k The Astrophysical Journal, 725:2166–2175, 2010 December 20 C ⃝ 2010. The American Astronomical Society. All rights reserved. Printed in the U.S.A. INFERRING THE ECCENTRICITY DISTRIBUT David W. Hogg1,2, Adam D. Myers2,3, and Jo Bov 1 Center for Cosmology and Particle Physics, Department of Physics, New York University, 4 Washington Place, 2 Max-Planck-Institut f¨ ur Astronomie, K¨ onigstuhl 17, D-69117 Heidelberg 3 Department of Astronomy, University of Illinois at Urbana-Champaign, Urbana Received 2010 August 24; accepted 2010 September 25; published 2010 D ABSTRACT Standard maximum-likelihood estimators for binary-star and exoplanet eccentricit that the estimated eccentricity tends to be larger than the true eccentricity. As with
81. stars planets n sn rn,k ✓r ✓s xn
82. stars planets n sn rn,k ✓r ✓s xn p ({ x } | ✓ecc) the marginalized likelihood
83. stars planets n sn rn,k ✓r ✓s xn p ({ x } | ✓ecc) the marginalized likelihood
84. n = 1, · · · , N ↵ wn xn p ( xn | ↵ ) = Z d wn p ( xn, wn | ↵ ) = Z d wn p ( xn, wn | ↵ ) p ( wn | xn, ↵0) p ( wn | xn, ↵0) = p ( xn | ↵0) Z d wn p ( wn | ↵ ) p ( wn | ↵0) p ( wn | xn, ↵0)
85. w (j) n ⇠ p ( wn | xn, ↵0) if you have a sampling with interim priors p ( xn | ↵ ) p ( xn | ↵0) = Z d wn p ( wn | ↵ ) p ( wn | ↵0) p ( wn | xn, ↵0) ⇡ 1 J J X j=1 p ( w (j) n | ↵ ) p ( w (j) n | ↵0)
86. w (j) n ⇠ p ( wn | xn, ↵0) if you have a sampling with interim priors p ( xn | ↵ ) p ( xn | ↵0) = Z d wn p ( wn | ↵ ) p ( wn | ↵0) p ( wn | xn, ↵0) ⇡ 1 J J X j=1 p ( w (j) n | ↵ ) p ( w (j) n | ↵0) Just A Sum™
87. 0.0 0.2 0.4 0.6 0.8 1.0 eccentricity e 0.0 0.2 0.4 0.6 eccentricity e 0.0 0.2 0.4 0.6 0.8 1.0 eccentricity e 0.0 0.2 0.4 0.6 eccentricity e 0.0 0.2 0.4 0.6 0.8 1.0 eccentricity e 0.0 0.2 0.4 0.6 eccentricity e 0 0 0 1 2 3 4 5 frequency p(e) 30 stars / ML estimates 0 2 4 6 8 10 frequency p(e) 30 stars / ML estimates 0 1 2 3 4 5 frequency p(e) 30 stars / inferred distribution 0 2 4 6 8 10 frequency p(e) 30 stars / inferred distribut Figure 3. Same as Figure 2, but for just the first 30 ersatz exoplanets. Hogg, Myers & Bovy (2010)
88. “ w (j) n ⇠ p ( wn | xn, ↵0) if you have a sampling with interim priors the big if ”
89. the kplr project a. which parameters? b. choice of interim priors c. interface to results large-scale sampling of parameters for every KOI
90. the “observables” mean stellar flux limb darkening function period phase duration radius ratio impact parameter 1 2/3 4 5 6 7 8
95. 0.00 0.02 0.04 0.06 0.08 0.10 KOI r/R 0.00 0.02 0.04 0.06 0.08 0.10 kplr r/R
96. 1 2 search characterization hierarchical inference 3 ✓
97. 1 2 search characterization hierarchical inference 3 ✓ ✓
98. Dan Foreman-Mackey CCPP@NYU @exoplaneteer dfm.io dfm