Probabilistic modeling and Inference in Astronomy

Transcription

1 Probabilistic modeling and Inference in Astronomy Dan Foreman-Mackey Sagan Fellow, University of Washington github.com/dfm // dfm.io

2 Dan Foreman-Mackey Sagan Fellow, University of Washington github.com/dfm // dfm.io

3 I study astronomy. Photo credit NASA Ames/SETI Institute/JPL-Caltech

4 this isn't what my data look like I study astronomy. Photo credit NASA Ames/SETI Institute/JPL-Caltech

5 Why Astronomy? simple but interesting physical models precise open-access data observational only

6 Why Astronomy? simple but interesting physical models precise open-access data observational only no chance of financial gain ever

7 ex o plan et ˈeksōˌplanət/ noun. a planet that orbits a star outside the solar system. Credit Google

8 How do we find & study exoplanets?

9 transit radial velocity direct imaging microlensing timing astrometry Data from Open Exoplanet Catalogue

10 number of exoplanets transit RV microlensing direct imaging timing year of discovery Data from Open Exoplanet Catalogue

11 number of exoplanets transit RV microlensing direct imaging timing first public data release from Kepler year of discovery Data from Open Exoplanet Catalogue

12 the transit method

13 Credit NASA/European Space Agency

14 Jupiter Credit NASA/European Space Agency

15 Jupiter Earth Credit NASA/European Space Agency

16 that's not what most stars look like!

17

18 relative brightness [ppm] time since transit [days]

19 everything is against us!

20 Credit Winn (2010) arxiv:

21 need to look at the right place at the right time and measure extremely precise photometry

22 Kepler Credit NASA

23 Credit NASA

24 Credit Carter Roberts

25 Credit NASA

26 Kepler-32

27 Kepler-32

28 Kepler-32

29 Kepler-32

30 Credit Fabrycky et al. (2012)

31 planet radius [R ] orbital period [days] Data from NASA Exoplanet Archive

32 that looks pretty good

33 planet radius [R ] orbital period [days] Data from NASA Exoplanet Archive

34 planet radius [R ] orbital period [days] Data from NASA Exoplanet Archive

35 planet radius [R ] orbital period [days] Data from NASA Exoplanet Archive

36 May 2013 The Kepler Mission goes up in flames * not exactly

37 Kepler RIP Credit NASA

38 introducing: K2 cbna Flickr user Aamir Choudhry

39 K2 Credit NASA

40

41

42 relative brightness [ppm] EPIC ; Kp = 11.5 mag 4000 raw: 301 ppm residuals: 35 ppm time [BJD ] time [BJD ]

43 7.6 x [pix] y [pix] time [BJD ]

44 Can we find planets using K2?

45 Anatomy of a transit signal = planet star space craft detector signal

46 Designing the probabilistic model planet P n star S n detector n x n K stars: n =1,,N space craft

47 Designing the probabilistic model representation: planet: star: noise: space craft: physics and geometry continuous in time GP CCD, photon noise Poisson??

48 The planet orbit model Kepler's Laws of Planetary Motion cba Wikipedia user Gonfer

49 The planet orbit model Kepler's Laws of Planetary Motion cba Wikipedia user Gonfer

50 The planet transit model Reference Mandel & Agol (2002); arxiv:astro-ph/

51 The planet transit model Reference Mandel & Agol (2002); arxiv:astro-ph/

52 The planet transit model " elliptic integral of the third kind " Reference Mandel & Agol (2002); arxiv:astro-ph/

53 The planet transit model relative brightness [ppm] " elliptic integral of the third kind " time since transit [days] Reference Mandel & Agol (2002); arxiv:astro-ph/

54 Designing the probabilistic model representation: planet: star: noise: space craft: physics and geometry continuous in time GP CCD, photon noise Poisson??

55 The stellar variability model

56 The stellar variability model Gaussian Covariance y N(f (t), K (t)) Mean

57 6 4 2 y y N(f (t), K (t)) x

58 6 4 2 y y N(f (t), K (t)) x

59 6 4 2 y y N(f (t), K (t)) x

60 6 4 2 y y N(f (t), K (t)) x

61 The stellar variability model

62 Designing the probabilistic model representation: planet: star: noise: space craft: physics and geometry continuous in time GP CCD, photon noise Poisson??

63 The noise model Credit NASA

64 Designing the probabilistic model representation: planet: star: noise: space craft: physics and geometry continuous in time GP CCD, photon noise Poisson??

65 Designing the probabilistic model P n S n n x n K stars: n =1,,N

66 Designing the probabilistic model simple space craft assumption: n x n K stars: n =1,,N

67 relative brightness [ppm] EPIC ; Kp = 11.5 mag 4000 raw: 301 ppm residuals: 35 ppm time [BJD ] time [BJD ]

68 time [BJD ]

69 time [BJD ]

70 relative brightness [ppm] EPIC ; Kp = 11.5 mag 4000 raw: 301 ppm residuals: 35 ppm time [BJD ]

71 Designing the probabilistic model representation: planet: star: noise: space craft: physics and geometry continuous in time GP CCD, photon noise Poisson data-driven linear model

72 Designing the probabilistic model P n S n n x n K stars: n =1,,N

73 Designing the probabilistic model P n S n n x n K

74 (a) raw 0 relative brightness [ppt] (b) 10 ELCs (c) 150 ELCs depth: 3.2 ppt depth: 2.7 ppt (d) conditional depth: 3.7 ppt time [BJD ]

75 Can we find planets using K2?

76 Yes.

77 K2 Campaign 1 exoplanet discoveries 21, stars days of data planet candidates confirmed planets Published: Foreman-Mackey, Montet, Hogg, et al. (arxiv: ) Montet, Morton, Foreman-Mackey, et al. (arxiv: ) Schölkopf, Hogg, Wang, Foreman-Mackey, et al. (arxiv: )

78 XKCD/1555

79 XKCD/1555

80 Probabilistic modeling combining physical and data-driven models enables the discovery of new planets using open data and open source software Foreman-Mackey, Montet, Hogg, et al. (arxiv: ) Montet, Morton, Foreman-Mackey, et al. (arxiv: ) Schölkopf, Hogg, Wang, Foreman-Mackey, et al. (arxiv: )