Reaching out a Bayesian approach to detecting giant planets beyond - PowerPoint PPT Presentation

Reaching out a Bayesian approach to detecting giant planets beyond the ice line Rodrigo F. Díaz Geneva Observatory rodrigo.diaz@unige.ch Hébrard, Bouchy, Udry, Arnold, Astudillo-Defru, Boisse, Bonfils, Borgniet, Bourrier, Courcol, Delfosse, Deleuil, Demangeon, Ehrenreich, Forveille, Lagrange, Moutou, Rey, Santerne, Santos, Ségransan, Wilson. The National Centres of Competence in Research (NCCR) are a research instrument of the Swiss National Science Foundation

Full characterisation of planetary system architectures. • Put Solar System in context. • Dynamics. • Constraints for halitbitbaiy of interior rocky planets. • How hard is it? • 1 Mjup at 3 AU (5 years): 16 m/s (p(transit) ~ 0.15%) • 1 Mjup at 5.2 AU (12 years): 12 m/s (p(transit) ~ 0.09%) Marcy et al. (2002), Pepe et al. (2007), Wright et al. (2009), Fischer et al. (2009), Moutou et al. (2011), Robertson et al. (2012), Boisse et al. (2012), … etc.

2 BIG issues

1. Instruments • Instrumental stability over many years required. • No single unmodified instrument over > 12 years: • ELODIE (1994 - 2006) —> SOPHIE (2006 - 2011) —> SOPHIE+ (2011 -) • CORALIE (1998 - ); upgraded in 2007 and 2014. • Hamilton@Lick (1987 - 2011); upgraded in 1994, 1998 and 2001. • HIRES@Keck (1996 - ); upgraded in 2004. • HARPS (2004 - ); upgraded recently (2015). • Combine di ff erent instruments + deal with instrument upgrades. References: Bouchy et al. (2013), Ségransan et al. (2010), Fischer et al. (2014)

1. Instruments • Di ff erent instruments + instrument upgrades. • Fixing the o ff set value is bad practice. • Instrument o ff sets can be included Boisse et al. (2012) as model (nuisance) parameters. ELODIE-SOPHIE • Fitting for the parameters freely can Boisse et al. (2012) 0 lead to spurious detections or unstable solutions. -0.1 • The Bayesian sets priors based on her current knowledge of the -0.2 instrument. 0.6 0.8 1

2. Stars • Between 53 - 70 % of old stars in the Solar neighbourhood exhibit large amplitude cycles (Lovis+2011, Baliunas+1998). • Cyclic stars with periods as short as a few years. Lovis et al. (2011) • Two e ff ects are expected: • Cycle e ff ect on the RVs. Or maybe not? • Varying “ jitter” as activity level changes. Baliunas et al. (1995)

2. Stars HD40307 10 -4.6 Díaz et al. (2015) 1.0 6.10 -4.7 20 0 Full-width at half-maximum [km s � 1 ] Bisector Velocity Span [m s � 1 ] -4.8 0.8 Normalised power 6.05 -10 -4.9 ∆ RV [m s � 1 ] 10 0.6 HK log R 0 -5.0 -20 6.00 0.4 -5.1 0 RV -30 5.95 log R 0 0.2 HK -5.2 BIS -10 FWHM -40 -5.3 0.0 RV BIS 5.90 10 3 10 4 FWHM log R 0 HK Period [days] -5.4 2006 2008 2010 2012 2014 Year • Long-term activity evolution well correlated with RV. • Velocity scatter increases with activity level. • Short-term e ff ect much more complex and di ffi cult to model in detail.

The model Activity cycles modelled as polynomial or Keplerian, using priors based on logR’hk, and a Planets and scale factor. non-“jitter” activity a ( t i ) = α · P log R 0 ( t i ) HK RV at t i measured (rotational 3 modulation). by instrument k a ( t i ) = α 0 · k log R 0 HK ( t i ) Drifts (degree l ). n v ( k ) k j ( t i ) + p l ( t i ) + a ( t i ) + ✏ ( k ) X = � k + i i j =1 Short-term activity “jitter” (including Independent Gaussian Number of parameters: instrumental noise). “Complex physics”; measurements errors 5 j + (1-3) + 1 + (3 | 5) + 2 modelled statistically. assumed. Parameter posterior PDF sampled using a MCMC + adaptive PCA algorithm (details in Díaz +2014. Starting point obtained using Genetic i.e., the “jitter” increases with activity. Algorithm.

The HARPS search for southern extra-solar planets. XXXVII. Bayesian re-analysis of three systems. New super Earths, unconfirmed signals, and magnetic cycles. ? R. F. Díaz 1 , D. Ségransan 1 , S. Udry 1 , C. Lovis 1 , F. Pepe 1 , X. Dumusque 2 , 1 , M. Marmier 1 , R. Alonso 3 , 4 , W. Benz 5 , F. Bouchy 1 , 6 , A. Co ffi net 1 , A. Collier Cameron 7 , M. Deleuil 6 , P. Figueira 8 , M. Gillon 9 , G. Lo Curto 10 , M. Mayor 1 , C. Mordasini 5 , F. Motalebi 1 , C. Moutou 6 , 11 , D. Pollacco 12 , E. Pompei 10 , D. Queloz 1 , 13 , N. Santos 8 , 14 , and A. Wyttenbach 1 Planet b; P = 5.771 d Planet c; P = 13.505 d Activity cycle; P = 3573.568 d 6 4 RV [m s � 1 ] 2 0 HD1461 -2 -4 -6 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 Orbital phase Orbital phase Orbital phase Planet b; P = 4.311 d Planet c; P = 9.622 d Planet d; P = 20.418 d Planet f; P = 51.592 d 6 4 RV [m s − 1 ] 2 0 HD40307 -2 -4 -6 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 Orbital phase Orbital phase Orbital phase Orbital phase

Three new long-period giant planet candidates. ELODIE • Stars originally observed with ELODIE but not showing significant trend (i.e. not in the SP5). • Targets observed as part of the SP2: • ~2100-stars volume-limited sample. • Precision of 3 - 4 m/s. • Targets started with SOPHIE and continued with SOPHIE+. Three "di ff erent" instruments. SOPHIE

Targets Parameters HD 191806 HD 214823 HD 221585 Sp. T. (1) ?? G0V G8IV V (1) 8.09 8.06 7.47 B � V (1) 0.64 0.63 0.77 ⇡ (2) [mas] 14 . 41 ± 0 . 50 10 . 25 ± 0 . 68 17 . 40 ± 0 . 60 T (3) [K] 6010 ± 30 6215 ± 30 5620 ± 27 e ff [ Fe / H ] (3) [dex] + 0 . 30 ± 0 . 02 0 . 17 ± 0 . 02 0 . 29 ± 0 . 02 log ( g ) (3) [cgs] 4 . 45 ± 0 . 03 4 . 34 ± 0 . 06 4 . 05 ± 0 . 04 M (3) [M � ] 1.14 1.22 1.19 ?

Bouchy et al. (2013) Seeing effect corrected on SOPHIE data RVc = RV + 1.04*(dRV - <dRV>) SOPHIE+ constants corrected Coucol et al. (2015) Data analysis: yorbit GA + APCA MCMC Ségransan et al. (2011); Díaz et al. (2014)

Offset priors n v ( k ) k j ( t i ) + p l ( t i ) + a ( t i ) + ✏ ( k ) X = � k + i i j =1 ELODIE-SOPHIE 0 ELODIE-SOPHIE: offset priors based on Boisse et al. (2012). -0.1 SOPHIE-SOPHIE + offset: -0.2 N(0, 10 m/s) 0.6 0.8 1

Activity indexes • Scatter in R’ HK very large (~10 times scatter in HARPS). • Alternative given by Halpha index.

• Halpha and Ca II do not probe the same stellar atmosphere height. • On the question of the correlation: • Cincunegui+2007 • Meunier & Delfosse 2009 • Gomes da Silva 2014 • E ff ect on RVs is not well known. Image credit: ?

Work by J. Rey, I. Boisse, O. Girault

The (simplified) model n v ( k ) k j ( t i ) + p l ( t i ) + ✏ ( k ) X = � k + i i j =1 ELODIE-SOPHIE: offset priors based on Boisse et al. (2012). σ Ji ∝ I [ H α ] i.e., the “jitter” increases with activity (as measured by Halpha). SOPHIE-SOPHIE + offset: N(0, 10 m/s) It turns out that in all cases n = 1 is enough.

HD191806 HD214823 HD221585

HD191806 - k1 vs k1d1 Model k1 Model k1d1 Prior from Boisse+2012

HD191806 - k1 vs k1d1 Bayesian model comparison p ( H j | I,D ) = p ( D | H i ,I ) p ( H i | I,D ) p ( D | H j ,I ) · p ( H i | I ) p ( H j | I ) H i hypothesis (drift / no drift) D data; I prior information. Assuming prior odds = 1 Perrakis estimator p ( H k 1 d 1 | I, D ) = p ( D | H k 1 d 1 , I ) ∼ 290 ± 70 p ( H k 1 | I, D ) p ( D | H k 1 , I ) Similar result obtained with other estimators.

HD191806 HD214823 HD221585 Period [d] 1606.5 +/- 7.4 1876 +/- 17 1172 +/- 19 Period [yr] 4.40 +/- 0.02 5.14 +/- 0.05 3.21 +/- 0.05 K [m/s] 140.5 +/- 2.2 281.3 +/- 3.7 27.8 +/- 1.7 0.120 +/- 0.070 ecc 0.261 +/- 0.019 0.154 +/- 0.015 95% HDI: [0.0, 0.3] a [AU] 2.81 +/- 0.11 3.20 +/- 0.13 2.309 +/- 0.085 Msini [Mjup] 8.56 +/- 0.62 19.4 +/- 1.5 1.60 +/- 0.16

HD191806 HD214823 HD221585

Summary • Planet detection beyond the ice line is challenging but worth it. Full characterisation of planet system architectures. • Put Solar System in context. • Constraints for h@b17@b1l17y of interior in rocky planets. • • Combination of instrument knowledge and statistical tools necessary to deal with major issues: Instrument changes / offsets. • Stellar activity evolution (cycles). • • Combined ELODIE - SOPHIE time bases allow constraining long-period objects.