Data Analysis Techniques for Next-Generation RV Surveys

Michigan State Astronomy Seminar talk. Overview of techniques for analyzing radial velocity data to infer properties of exoplanets.

Transcript

1. May 20, 2015 PhD Thesis Defense Data Analysis Techniques for Next-Generation Radial Velocity Surveys Center for Exoplanets and Habitable Worlds Benjamin Nelson (Data Science Scholar) Collaborators Kat Deck (Caltech), Debra Fischer (Yale), Eric Ford (PSU), Andrew Howard (Hawaii), Howard Isaacson (Berkeley), Matt Payne (CfA), Seth Pritchard (UT San Antonio), Paul Robertson (PSU), Kaspar von Braun (Lowell), Jason Wright (PSU) MSU Astro Seminar 10/28/15
2. Outline History of Exoplanet RVs Challenges with Parameter Estimation - Bayesian (MCMC) with science examples Challenges with Stellar Activity - Controversial claims - Model Comparison - Keplerian Fitting Challenge MSU Astro Seminar 10/28/15
3. The Radial Velocity Method Video Source: h-p://www.eso.org/public/videos/eso1035g/ MSU Astro Seminar 10/28/15
4. Story of RVs Inferred From The 55 Cancri Dataset &QF$ H E F I G MSU Astro Seminar 10/28/15
5. Story of RVs Inferred From The 55 Cancri Dataset &QF$ H E F I G <1995: sparse observations MSU Astro Seminar 10/28/15
6. Story of RVs Inferred From The 55 Cancri Dataset &QF$ H E F I G <1995: sparse observations 1995: ??? MSU Astro Seminar 10/28/15
7. Story of RVs Inferred From The 55 Cancri Dataset &QF$ H E F I G <1995: sparse observations 1995: 51 Peg b (Mayor & Queloz) 1998: 55 Cnc b (Butler+) MSU Astro Seminar 10/28/15
8. Story of RVs Inferred From The 55 Cancri Dataset &QF$ H E F I G <1995: sparse observations 1995: 51 Peg b (Mayor & Queloz) 1998: 55 Cnc b (Butler+) 2002: 55 Cnc c and d (Marcy+) MSU Astro Seminar 10/28/15
9. Story of RVs Inferred From The 55 Cancri Dataset &QF$ H E F I G <1995: sparse observations 1995: 51 Peg b (Mayor & Queloz) 1998: 55 Cnc b (Butler+) 2002: 55 Cnc c and d (Marcy+) 2002-2004: Keck, HJST, HET start searches 2004: 55 Cnc e (McArthur+) MSU Astro Seminar 10/28/15
10. Story of RVs Inferred From The 55 Cancri Dataset &QF$ H E F I G <1995: sparse observations 1995: 51 Peg b (Mayor & Queloz) 1998: 55 Cnc b (Butler+) 2002: 55 Cnc c and d (Marcy+) 2002-2004: Keck, HJST, HET start searches 2004: 55 Cnc e (McArthur+) 2008: 55 Cnc f (Fischer+) MSU Astro Seminar 10/28/15
11. Story of RVs Inferred From The 55 Cancri Dataset &QF$ H E F I G <1995: sparse observations 1995: 51 Peg b (Mayor & Queloz) 1998: 55 Cnc b (Butler+) 2002: 55 Cnc c and d (Marcy+) 2002-2004: Keck, HJST, HET start searches 2004: 55 Cnc e (McArthur+) 2008: 55 Cnc f (Fischer+) 2010: New period for 55 Cnc e (Dawson & Fabrycky) MSU Astro Seminar 10/28/15
12. Sampling Aliases Dawson, EPRV 2015, tinyurl.com/nhlv4fq MSU Astro Seminar 10/28/15
13. Sampling Aliases Dawson, EPRV 2015, tinyurl.com/nhlv4fq MSU Astro Seminar 10/28/15
14. Sampling Aliases 2.816 day 2.796 day 0.7365 day Dawson & Fabrycky 2010 candidate yearly daily 2-day (harmonic) real data MSU Astro Seminar 10/28/15
15. oklo.org Pushing to Lower Exoplanet Masses MSU Astro Seminar 10/28/15
16. Han et al. 2014 RV Detected Planets by the Year 1995 MSU Astro Seminar 10/28/15
17. Han et al. 2014 RV Detected Planets by the Year 2000 MSU Astro Seminar 10/28/15
18. Han et al. 2014 RV Detected Planets by the Year 2005 MSU Astro Seminar 10/28/15
19. Han et al. 2014 RV Detected Planets by the Year 2010 MSU Astro Seminar 10/28/15
20. Han et al. 2014 RV Detected Planets by the Year 2015 MSU Astro Seminar 10/28/15
21. Challenges with Parameter Estimation MSU Astro Seminar 10/28/15
22. HD 12661 RVs: Butler+ 2006 github.com/dfm/triangle.py p1 e1 p2 e2 e1 p2 e2 p1 plot made with Systemic Console (Meschiari+ 2009) Simple Keplerian System MSU Astro Seminar 10/28/15
23. GJ 876 RVs: Rivera+ 2005 e1 p2 e2 p1 github.com/dfm/triangle.py p1 e1 p2 e2 plot made with Systemic Console (Meschiari+ 2009) Complex N-body System MSU Astro Seminar 10/28/15
24. ? github.com/dfm/triangle.py p1 e1 p2 e2 e1 p2 e2 p1 GJ 876 RVs: Rivera+ 2005 plot made with Systemic Console (Meschiari+ 2009) Complex N-body System MSU Astro Seminar 10/28/15
25. Frequentist Methods: Bootstrap RVLIN (Wright & Howard 2009): Get to chi-square minimum with LM BOOTTRAN (Wang+ 2012): Bootstrap to get uncertain\es in model parameters Disadvantages: - long orbital periods - poor phase coverage Time Velocity MSU Astro Seminar 10/28/15
26. Difficul\es with mul\ple modes, correlated parameters, high-dimensional parameter spaces… h-p://www.normalesup.org/~athiery/files/animatedgif/MALA.gif Bayesian Methods: MCMC MSU Astro Seminar 10/28/15
27. 3URSRVHGGLVSODFHPHQW  VFDOHG &DQGLGDWHIRUXSGDWH 3URSRVDO L M N Radial velocity Using N-body Differential evolution MCMC Nelson+ 2014a (ter Braak 2006) N-body image source: oklo.org MSU Astro Seminar 10/28/15
28. 3URSRVHGGLVSODFHPHQW  VFDOHG &DQGLGDWHIRUXSGDWH 3URSRVDO L M N Radial velocity Using N-body Differential evolution MCMC Nelson+ 2014a (ter Braak 2006) N-body image source: oklo.org MSU Astro Seminar 10/28/15
29. &DQGLGDWHIRUXSGDWH L Nelson+ 2014a x y DEMCMC MSU Astro Seminar 10/28/15
30. &DQGLGDWHIRUXSGDWH L M N Nelson+ 2014a x y DEMCMC MSU Astro Seminar 10/28/15
31. 3URSRVHGGLVSODFHPHQW  VFDOHG &DQGLGDWHIRUXSGDWH L M N Nelson+ 2014a x y DEMCMC MSU Astro Seminar 10/28/15
32. 3URSRVHGGLVSODFHPHQW  VFDOHG &DQGLGDWHIRUXSGDWH 3URSRVDO L M N Nelson+ 2014a x y DEMCMC MSU Astro Seminar 10/28/15
33. L M N 3URSRVDO Nelson+ 2014a x y DEMCMC MSU Astro Seminar 10/28/15
34. L M N 3URSRVDO Nelson+ 2014a x y DEMCMC MSU Astro Seminar 10/28/15
35. DEMCMC is much more efficient than tradi\onal MCMC, especially for model parameter distribu\ons with mul\ple modes or highly covariant structure. Performance most sensi\ve to number of Markov chains. Best choice: number of Markov chains ≈ 3 × number of dimensions Sidenote: emcee3 will have differen\al evolu\on! (Foreman-Mackey et al. 2013) Nelson+ 2014a Take-away points for DEMCMC MSU Astro Seminar 10/28/15
36. -XSLWHU DQDORJ &QF$     H E F I G 'LVWDQFH $8 WUDQVLWLQJ a KDELWDEOH ]RQH" 55 Cancri MSU Astro Seminar 10/28/15
37. Over 40 model parameters ~5 minute integration timestep We apply RUN DMC to 1418 RV observations spanning ~23 years Nelson+ 2014b Lick: Fischer+ 2014 Keck: Fischer+ 2008 HET: Endl+ 2012 HJST: Endl+ 2012 55 Cancri: It’s Tricky! MSU Astro Seminar 10/28/15
38. Kozai’d to death Nelson+ 2014b 55 Cancri: Dynamics in Probabilistic Framework 1. Mutual Inclination 2. Better Mass Estimates 3. Alignment and Formation MSU Astro Seminar 10/28/15
39.     F E G 'LVWDQFH $8 *-  H GD\V GD\V GD\V GD\V Gliese 876 MSU Astro Seminar 10/28/15
40.     F E G 'LVWDQFH $8 *-  H GD\V GD\V GD\V GD\V https://github.com/dtamayo/OGRE Gliese 876 MSU Astro Seminar 10/28/15
41. Nelson+ 2015 Gliese 876: Dynamics in Probabilistic Framework 1. Mutual Inclination 2. Mean-motion resonances 3. Chaos MSU Astro Seminar 10/28/15
42. RV Error Budget Wavelength Calibration PSF Stability Instrumental Errors Stellar Noise Detectors ? ? Visualization credit: Lars Buchhave (CfA), Debra Fischer (Yale) MSU Astro Seminar 10/28/15
43. RV Error Budget Stellar Noise Visualization credit: Lars Buchhave (CfA), Debra Fischer (Yale) MSU Astro Seminar 10/28/15
44. RV Error Budget SCREWED! Visualization credit: Lars Buchhave (CfA), Debra Fischer (Yale) MSU Astro Seminar 10/28/15
45. Challenges with Stellar Activity MSU Astro Seminar 10/28/15
46. Challenges with Stellar Activity Type of Activity Timescale RV Amplitude Oscillations < 15 min a few m/s Granulation 15 min - 2 days a few m/s Active Regions 10-50 days 40-140 cm/s Magnetic Cycles ~10 years 1-20 m/s Dumusque+ 2011 MSU Astro Seminar 10/28/15
47. Stellar Activity Masquerading as Planets MSU Astro Seminar 10/28/15
48. Stellar Activity (Gliese 581) *- E F    G G  H  J I   MSU Astro Seminar 10/28/15
49. MSU Astro Seminar 10/28/15 Stellar Activity (Gliese 581) *- E F    G G  H  J I  
50. MSU Astro Seminar 10/28/15 Stellar Activity (Gliese 581) *- E F    G G  H  J I  
51. MSU Astro Seminar 10/28/15 Stellar Activity (Gliese 581) *- E F    G G  H  J I  
52. MSU Astro Seminar 10/28/15 Stellar Activity (Gliese 581) *- E F    G G  H  J I   32
53. MSU Astro Seminar 10/28/15 Stellar Activity (Gliese 581) *- E F    G G  H  J I   32
54. MSU Astro Seminar 10/28/15 Stellar Activity (Gliese 581) *- E F    G G  H  J I   32
55. MSU Astro Seminar 10/28/15 Stellar Activity (Gliese 581) *- E F    G G  H  J I   32
56. Stellar Activity (Kapteyn’s Star) Image source: http://www.sci-news.com/astronomy/science-kapteyn-b-c-two- exoplanets-kapteyns-star-01965.html MSU Astro Seminar 10/28/15
57. Stellar Activity (Kapteyn’s Star) Image source: http://www.sci-news.com/astronomy/science-kapteyn-b-c-two- exoplanets-kapteyns-star-01965.html MSU Astro Seminar 10/28/15
58. Stellar Activity (Kapteyn’s Star) Image source: http://www.sci-news.com/astronomy/science-kapteyn-b-c-two- exoplanets-kapteyns-star-01965.html MSU Astro Seminar 10/28/15
59. Nelson+ 2015 Stellar Activity (Gliese 876) MSU Astro Seminar 10/28/15
60. Nelson+ 2015 Stellar Activity (Gliese 876) 1 95d 1 365d ⇡ 1 128d MSU Astro Seminar 10/28/15
61. Baluev 2011 ê ç Rivera+ 2010 Nelson+ 2015 Stellar Activity (Gliese 876) MSU Astro Seminar 10/28/15
62. p(d|M) = Z p(✓|M)p(d|✓, M)d✓ Fully marginalized likelihood (FML) Prior Likelihood The probability of a radial velocity dataset {d} being generated from some model M parameterized by {θ} is given by… To choose between two competing models M1 and M2 , take the ratio of their FMLs… Bayes Factor = p(d|M2) p(d|M1) Bayesian Model Comparison MSU Astro Seminar 10/28/15
63. p(d|M) = Z p(✓|M)p(d|✓, M)d✓ Fully marginalized likelihood (FML) Prior Likelihood The probability of a radial velocity dataset {d} being generated from some model M parameterized by {θ} is given by… There are efficient ways to do this! Nested Sampling (Feroz+ 2008) Transdimensional MCMC (Brewer & Donovan 2015) Geometric Path Monte Carlo (Hou+ 2015) Importance Sampling (Nelson+ 2015) Bayesian Model Comparison MSU Astro Seminar 10/28/15
64. Seth Pritchard (PSU/UT San Antonio) FML = Z p(✓)p(d|✓)d✓ = Z p(✓)p(d|✓) g(✓) g(✓)d✓ Importance Sampling To Compute FML MSU Astro Seminar 10/28/15
65. Seth Pritchard (PSU/UT San Antonio) FML = Z p(✓)p(d|✓)d✓ = Z p(✓)p(d|✓) g(✓) g(✓)d✓ Importance Sampling To Compute FML MSU Astro Seminar 10/28/15
66. Seth Pritchard (PSU/UT San Antonio) [ FML ⇡ 1 N X ✓i ⇠g(✓) p(✓i)p(d|✓i) g(✓i) FML = Z p(✓)p(d|✓)d✓ = Z p(✓)p(d|✓) g(✓) g(✓)d✓ Importance sampling with MCMC samples: Guo 2012, Weinberg+ 2013 Importance Sampling To Compute FML MSU Astro Seminar 10/28/15
67. Competing Model Tournament Bracket Bayes factor Round 1: inner 3 planets vs. outer 3 planets ~1031 Round 2: inner 3 planets vs. inner 3 planets + ~120 day sinusoid ~109 Round 3: all 4 planets vs. inner 3 planets + ~120 day sinusoid ~30 Round 4: all 4 planets vs. all 4 + putative 5th planet ~103 Nelson+ 2015 And the best Gliese 876 model is… MSU Astro Seminar 10/28/15
68. Competing Model Tournament Bracket Bayes factor Round 1: inner 3 planets vs. outer 3 planets ~1031 Round 2: inner 3 planets vs. inner 3 planets + ~120 day sinusoid ~109 Round 3: all 4 planets vs. inner 3 planets + ~120 day sinusoid ~30 Round 4: all 4 planets vs. additional 5th planet ~103 Nelson+ 2015 And the best Gliese 876 model is… MSU Astro Seminar 10/28/15
69. MSU Astro Seminar 10/28/15
70. MSU Astro Seminar 10/28/15
71. MSU Astro Seminar 10/28/15
72. MSU Astro Seminar 10/28/15
73. •  RV surveys are pushing out ~30 year orbital periods and RV precision is getting below 1 m/s. •  Some multi-planet systems require high-dimensional (30-40) models and n- body integrations. But we have efficient code to deal with their data! •  We can infer very detailed dynamical properties of exoplanet systems (e.g. mutual inclination, resonant/secular interactions, chaotic motion). •  Stellar activity is becoming a problem in the 1 m/s regime but there seem to be some promising tractable methods (e.g. Gaussian processes to model activity, Bayes factors for model comparison) •  Keplerian Fitting Challenge: https://rv-challenge.wikispaces.com/ Summary MSU Astro Seminar 10/28/15
74. Supplemental Material MSU Astro Seminar 10/28/15
75. Burn-in phase… Autocorrela\on length… …as a func\on of ensemble size, number of planets, dynamical strength, etc. Nelson+ 2014a Things to Look Out For in MCMC MSU Astro Seminar 10/28/15
76. How should we model closely spaced cadence observa\ons? Two extreme assump\ons: 1.  Treat them as independent 2.  Treat them as perfectly correlated Nelson+ 2014b Correlation Between RVs MSU Astro Seminar 10/28/15
77. Nelson+ 2014b No Additional Detected Planets in 55 Cancri MSU Astro Seminar 10/28/15
78. 37% Libra\ng &QF$ H E F I G $b $c = 180 Nelson+ 2014b Apsidal Alignment of Planets “b” and “c” MSU Astro Seminar 10/28/15
79. &QF$ H E F I G $b $c = 180 28% Circula\ng Nelson+ 2014b Apsidal Alignment of Planets “b” and “c” MSU Astro Seminar 10/28/15
80. &QF$ H E F I G $b $c = 180 35% Ambiguous Nelson+ 2014b Apsidal Alignment of Planets “b” and “c” MSU Astro Seminar 10/28/15
81. Nelson+ 2014b MSU Astro Seminar 10/28/15
82. Seth Pritchard (PSU/UT San Antonio) [ FML ⇡ 1 N X ✓i ⇠g(✓) p(✓i)p(d|✓i) g(✓i) FML = Z p(✓)p(d|✓)d✓ = Z p(✓)p(d|✓) g(✓) g(✓)d✓ Importance Sampling with MCMC Samples MSU Astro Seminar 10/28/15
83. Seth Pritchard (PSU/UT San Antonio) [ FML ⇡ 1 N X ✓i ⇠g(✓) p(✓i)p(d|✓i) g(✓i) FML = Z p(✓)p(d|✓)d✓ = Z p(✓)p(d|✓) g(✓) g(✓)d✓ MSU Astro Seminar 10/28/15 Importance Sampling with MCMC Samples
84. Seth Pritchard (PSU/UT San Antonio) [ FML ⇡ 1 N X ✓i ⇠g(✓) p(✓i)p(d|✓i) g(✓i) FML = Z p(✓)p(d|✓)d✓ = Z p(✓)p(d|✓) g(✓) g(✓)d✓ [ FML ⇡ k N X ✓i ⇠g⌧ (✓) p(✓i)p(d|✓i) g⌧ (✓i) MSU Astro Seminar 10/28/15 Importance Sampling with MCMC Samples
85. Seth Pritchard (PSU/UT San Antonio) [ FML ⇡ 1 N X ✓i ⇠g(✓) p(✓i)p(d|✓i) g(✓i) FML = Z p(✓)p(d|✓)d✓ = Z p(✓)p(d|✓) g(✓) g(✓)d✓ fraction of MCMC samples in ⌧ : fMCMC [ FML ⇡ 1 N ⇥ fMCMC X ✓i ⇠g⌧ (✓) p(✓i)p(d|✓i) g⌧ (✓i) Guo 2012, Weinberg+ 2013 Importance Sampling with MCMC Samples
86. *- F E G H Kozai’d to death Nelson+ 2015 Mutual Inclination of Planets “d” and “b” MSU Astro Seminar 10/28/15
87. Adapted from Rivera+ 2010 L = c 3 b + 2 e = 0 *- F E G H Rivera+ 2010 The Gliese 876 Laplace Planets MSU Astro Seminar 10/28/15
88. Adapted from Rivera+ 2010 L = c 3 b + 2 e = 0 *- F E G H Nelson+ 2015, MNRAS MSU Astro Seminar 10/28/15 The Gliese 876 Laplace Planets
89. Adapted from Rivera+ 2010 L = c 3 b + 2 e = 0 *- F E G H Are we actually observing this? Nelson+ 2015, MNRAS MSU Astro Seminar 10/28/15 The Gliese 876 Laplace Planets
90. Migrate a system into low libration (~20 degrees) Matt Payne (CfA) Generate synthetic RVs … Nelson+ 2015 Simulating a Laplace Resonance MSU Astro Seminar 10/28/15
91. Nelson+ 2015 Simulated Data Recover The True Libration! MSU Astro Seminar 10/28/15
92. Nelson+ 2015 Kat Deck (Caltech) Chaotic Motion in Gliese 876 MSU Astro Seminar 10/28/15