Dan Foreman-Mackey
September 22, 2015
400

Probabilistic modeling and Inference in Astronomy

Guest lecture for "Inference and Representation" at NYU

Dan Foreman-Mackey

September 22, 2015

Transcript

1. Probabilistic modeling and Inference in Astronomy Dan Foreman-Mackey Sagan Fellow,

University of Washington github.com/dfm // @exoplaneteer // dfm.io

// dfm.io

4. I study astronomy. Photo credit NASA Ames/SETI Institute/JPL-Caltech this isn't

what my data look like
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

9. transit radial velocity direct imaging microlensing timing astrometry 1281 616

45 32 20 0 Data from Open Exoplanet Catalogue
10. Data from Open Exoplanet Catalogue 2000 2005 2010 2015 year

of discovery 0 200 400 600 800 1000 number of exoplanets transit RV microlensing direct imaging timing
11. Data from Open Exoplanet Catalogue 2000 2005 2010 2015 year

of discovery 0 200 400 600 800 1000 number of exoplanets transit RV microlensing direct imaging timing ﬁrst public data release from Kepler

17. None
18. 1.0 0.5 0.0 0.5 1.0 time since transit [days] 100

50 0 relative brightness [ppm]

20. Fig. 3.— Calculation of the transit probability. Left.—Transits are visible

by observers within the penumbra of the planet, a cone with opening angle Θ with sin Θ = (R⋆ +Rp )/r, where r is the instantaneous star-planet distance. Right.—Close-up showing the penumbra (thick lines) as well as the antumbra (thin lines) within which the transits are full, as opposed to grazing. are tangent at four contact times tI –tIV , illustrated in Fig- ure 2. (In a grazing eclipse, second and third contact do not occur.) The total duration is Ttot = tIV − tI , the full duration is Tfull = tIII − tII , the ingress duration is ingress and egress. In practice the difference is slight; to leading order in R⋆/a and e, τe − τi ∼ e cosω R⋆ 3 1 − b2 3/2 , (17) Credit Winn (2010) arXiv:1001.2010
21. need to look at the right place at the right

time and measure extremely precise photometry

30. Credit Fabrycky et al. (2012) 12 Fabrycky et al. Figure

16. Kepler-31 phase curves, in the style of ﬁgure 3. For the small inner candidate KOI-952.05, the phase is with respect to terest. The Kepler Follow-up spectra of Kepler-32: one sp servatory and one from Keck are weak due to the faintness cross correlation function be and available models is max ∼ 3900 K and ∼ 3600 K, atmospheric parameters are star is cooler than the library able. Both spectra are con siﬁcation as a cool dwarf ( [M/H]=0.172). We conserva Teﬀ and log g with uncertain a [M/H] of 0± 0.4 based on t By comparing to the Yonse values for the stellar mass ( (0.53 ± 0.04R⊙ ) that are sli the KIC. We estimate a lum and an age of ≤ 9Gyr. Muirhead et al. (2011) h resolution IR spectrum of K a stellar Teﬀ = 3726+73 −67 , [Fe ing their data via Padova m they inferred a considerably l We encourage further detail properties, as these have con directly aﬀect the sizes and The probability of a star u being the actual host is only ity of a physical companion h This latter number is relative all the transit depths are sma be much larger planets hoste ically diluted. This opens up
31. 101 102 orbital period [days] 100 101 planet radius [R

] Data from NASA Exoplanet Archive

33. 101 102 orbital period [days] 100 101 planet radius [R

] Data from NASA Exoplanet Archive
34. 101 102 orbital period [days] 100 101 planet radius [R

] Data from NASA Exoplanet Archive
35. 100 101 102 103 104 105 orbital period [days] 100

101 planet radius [R ] Data from NASA Exoplanet Archive

not exactly

40. None
41. None
42. 4000 2000 0 2000 4000 raw: 301 ppm EPIC 201374602;

Kp = 11.5 mag 10 20 30 40 50 60 70 80 time [BJD - 2456808] 400 0 400 residuals: 35 ppm relative brightness [ppm] 4000 2000 0 2000 4000 raw: 301 ppm EPIC 201374602; Kp = 11.5 mag 10 20 30 40 50 60 70 80 time [BJD - 2456808] 400 0 400 residuals: 35 ppm relative brightness [ppm]
43. 7.2 7.4 7.6 x [pix] 10 20 30 40 50

60 70 80 time [BJD - 2456808] 9.05 9.10 9.15 9.20 y [pix]

45. Anatomy of a transit signal + + + = planet

star space craft detector signal
46. Designing the probabilistic model n Pn xn K Sn stars:

n = 1, · · · , N n Pn xn K Sn planet star space craft detector
47. Designing the probabilistic model planet: star: noise: space craft: physics

and geometry continuous in time → GP CCD, photon noise → Poisson ?? representation:
48. The planet orbit model cba Wikipedia user Gonfer Kepler's Laws

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

of Planetary Motion
50. TRANSIT LIGHT CURVES Vol. 580 mb darkening. The star is

seen edge-on, with the observer off the top of the page. The star has radius , and v is deﬁned as the r∗ d the normal to the stellar surface, while . (b) Transit geometry from the perspective of the observer. m p cos v 3. NONLINEAR LIMB DARKENING s a star to be more centrally peaked in brightness compared to a uniform source. This leads to more ng eclipse and creates curvature in the trough. Thus, including limb darkening is important for computing Reference Mandel & Agol (2002); arXiv:astro-ph/0210099 The planet transit model
51. TRANSIT LIGHT CURVES Vol. 580 mb darkening. The star is

seen edge-on, with the observer off the top of the page. The star has radius , and v is deﬁned as the r∗ d the normal to the stellar surface, while . (b) Transit geometry from the perspective of the observer. m p cos v 3. NONLINEAR LIMB DARKENING s a star to be more centrally peaked in brightness compared to a uniform source. This leads to more ng eclipse and creates curvature in the trough. Thus, including limb darkening is important for computing Reference Mandel & Agol (2002); arXiv:astro-ph/0210099 The planet transit model
52. TRANSIT LIGHT CURVES Vol. 580 mb darkening. The star is

seen edge-on, with the observer off the top of the page. The star has radius , and v is deﬁned as the r∗ d the normal to the stellar surface, while . (b) Transit geometry from the perspective of the observer. m p cos v 3. NONLINEAR LIMB DARKENING s a star to be more centrally peaked in brightness compared to a uniform source. This leads to more ng eclipse and creates curvature in the trough. Thus, including limb darkening is important for computing Reference Mandel & Agol (2002); arXiv:astro-ph/0210099 The planet transit model "…elliptic integral of the third kind…"
53. TRANSIT LIGHT CURVES Vol. 580 mb darkening. The star is

seen edge-on, with the observer off the top of the page. The star has radius , and v is deﬁned as the r∗ d the normal to the stellar surface, while . (b) Transit geometry from the perspective of the observer. m p cos v 3. NONLINEAR LIMB DARKENING s a star to be more centrally peaked in brightness compared to a uniform source. This leads to more ng eclipse and creates curvature in the trough. Thus, including limb darkening is important for computing Reference Mandel & Agol (2002); arXiv:astro-ph/0210099 The planet transit model "…elliptic integral of the third kind…" 1.0 0.5 0.0 0.5 1.0 time since transit [days] 100 50 0 relative brightness [ppm]
54. Designing the probabilistic model planet: star: noise: space craft: physics

and geometry continuous in time → GP CCD, photon noise → Poisson ?? representation:

56. The stellar variability model y ⇠ N(f✓ (t), K↵(t)) Gaussian

Mean Covariance
57. 0 1 2 3 4 5 x 6 4 2

0 2 4 6 y y ⇠ N (f✓ (t), K↵(t))
58. 0 1 2 3 4 5 x 6 4 2

0 2 4 6 y y ⇠ N (f✓ (t), K↵(t))
59. 0 1 2 3 4 5 x 6 4 2

0 2 4 6 y y ⇠ N (f✓ (t), K↵(t))
60. 0 1 2 3 4 5 x 6 4 2

0 2 4 6 y y ⇠ N (f✓ (t), K↵(t))

62. Designing the probabilistic model planet: star: noise: space craft: physics

and geometry continuous in time → GP CCD, photon noise → Poisson ?? representation:

64. Designing the probabilistic model planet: star: noise: space craft: physics

and geometry continuous in time → GP CCD, photon noise → Poisson ?? representation:
65. Designing the probabilistic model n Pn xn K Sn stars:

n = 1, · · · , N n Pn xn K Sn
66. stars: n = 1, · · · , N n

xn K Designing the probabilistic model simple space craft assumption:
67. 4000 2000 0 2000 4000 raw: 301 ppm EPIC 201374602;

Kp = 11.5 mag 10 20 30 40 50 60 70 80 time [BJD - 2456808] 400 0 400 residuals: 35 ppm relative brightness [ppm] 4000 2000 0 2000 4000 raw: 301 ppm EPIC 201374602; Kp = 11.5 mag 10 20 30 40 50 60 70 80 time [BJD - 2456808] 400 0 400 residuals: 35 ppm relative brightness [ppm]

70. 4000 2000 0 2000 4000 raw: 301 ppm EPIC 201374602;

Kp = 11.5 mag 10 20 30 40 50 60 70 80 time [BJD - 2456808] 400 0 400 residuals: 35 ppm relative brightness [ppm]
71. Designing the probabilistic model planet: star: noise: space craft: physics

and geometry continuous in time → GP CCD, photon noise → Poisson data-driven linear model representation:
72. Designing the probabilistic model n Pn xn K Sn stars:

n = 1, · · · , N n Pn xn K Sn

74. 2 0 2 4 (a) raw 4 2 0 (b)

10 ELCs depth: 3.2 ppt 4 2 0 (c) 150 ELCs depth: 2.7 ppt 63 64 65 66 67 time [BJD - 2456808] 4 2 0 (d) conditional depth: 3.7 ppt relative brightness [ppt]

77. stars days of data planet candidates conﬁrmed planets 21,703 80

36 18 K2 Campaign 1 exoplanet discoveries Published: Foreman-Mackey, Montet, Hogg, et al. (arXiv:1502.04715) Montet, Morton, Foreman-Mackey, et al. (arXiv:1503.07866) Schölkopf, Hogg, Wang, Foreman-Mackey, et al. (arXiv:1505.03036)

80. Foreman-Mackey, Montet, Hogg, et al. (arXiv:1502.04715) Montet, Morton, Foreman-Mackey, et

al. (arXiv:1503.07866) Schölkopf, Hogg, Wang, Foreman-Mackey, et al. (arXiv:1505.03036) Probabilistic modeling—combining physical and data-driven models—enables the discovery of new planets using open data and open source software