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

SLIDE 1

Reaching out

a Bayesian approach to detecting giant planets beyond the ice line

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

SLIDE 2

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%)
Full characterisation of planetary system architectures.
Put Solar System in context.
Dynamics.
Constraints for halitbitbaiy of interior rocky planets.

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.

SLIDE 3

2 BIG

issues

SLIDE 4

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 different instruments + deal with instrument upgrades.

References: Bouchy et al. (2013), Ségransan et al. (2010), Fischer et al. (2014)

SLIDE 5

1. Instruments

0.6 0.8 1

0.2
0.1

Boisse et al. (2012) ELODIE-SOPHIE

Different instruments + instrument

upgrades.

Fixing the offset value is bad

practice.

Instrument offsets can be included

as model (nuisance) parameters.

Fitting for the parameters freely can

lead to spurious detections or unstable solutions.

The Bayesian sets priors based on

her current knowledge of the instrument. Boisse et al. (2012)

SLIDE 6

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.

Two effects are expected:
Cycle effect on the RVs. Or maybe not?
Varying “ jitter” as activity level changes.

Lovis et al. (2011) Baliunas et al. (1995)

SLIDE 7

2. Stars

2006 2008 2010 2012 2014 Year

40
30
20
10

10 ∆ RV [m s1]

5.4
5.3
5.2
5.1
5.0
4.9
4.8
4.7
4.6

log R0 HK RV log R0 HK BIS FWHM

10

10 20 Bisector Velocity Span [m s1] 5.90 5.95 6.00 6.05 6.10 Full-width at half-maximum [km s1] 103 104 Period [days] 0.0 0.2 0.4 0.6 0.8 1.0 Normalised power RV log R0 HK BIS FWHM Díaz et al. (2015)

Long-term activity evolution well correlated with RV.
Velocity scatter increases with activity level.
Short-term effect much more complex and difficult to model in detail.

HD40307

SLIDE 8 Short-term activity “jitter” (including instrumental noise). “Complex physics”; modelled statistically. i.e., the “jitter” increases with activity. Independent Gaussian measurements errors assumed. Number of parameters: 5 j + (1-3) + 1 + (3 | 5) + 2 Parameter posterior PDF sampled using a MCMC + adaptive PCA algorithm (details in Díaz +2014. Starting point obtained using Genetic Algorithm. Planets and non-“jitter” activity (rotational modulation). Drifts (degree l). Activity cycles modelled as polynomial or Keplerian, using priors based on logR’hk, and a scale factor. a(ti) = α · P log R0 HK 3 (ti) a(ti) = α0 · klog R0 HK(ti) RV at ti measured by instrument k

The model

v(k)

i

= k +

n

X

j=1

kj(ti) + pl(ti) + a(ti) + ✏(k)

i

SLIDE 9 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. Díaz1, D. Ségransan1, S. Udry1, C. Lovis1, F. Pepe1, X. Dumusque2, 1, M. Marmier1, R. Alonso3, 4, W. Benz5,
F. Bouchy1, 6, A. Coffinet1, A. Collier Cameron7, M. Deleuil6, P. Figueira8, M. Gillon9, G. Lo Curto10, M. Mayor1,
C. Mordasini5, F. Motalebi1, C. Moutou6, 11, D. Pollacco12, E. Pompei10, D. Queloz1, 13, N. Santos8, 14, and
A. Wyttenbach1

0.0 0.2 0.4 0.6 0.8 Orbital phase

6
4
2

2 4 6 RV [m s1] Planet b; P = 5.771 d 0.0 0.2 0.4 0.6 0.8 Orbital phase Planet c; P = 13.505 d 0.0 0.2 0.4 0.6 0.8 Orbital phase Activity cycle; P = 3573.568 d 0.0 0.2 0.4 0.6 0.8 Orbital phase

6
4
2

2 4 6 RV [m s−1] Planet b; P = 4.311 d 0.0 0.2 0.4 0.6 0.8 Orbital phase Planet c; P = 9.622 d 0.0 0.2 0.4 0.6 0.8 Orbital phase Planet d; P = 20.418 d 0.0 0.2 0.4 0.6 0.8 Orbital phase Planet f; P = 51.592 d HD1461 HD40307

SLIDE 10

Three new long-period giant planet candidates.

ELODIE SOPHIE

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 "different" instruments.

SLIDE 11

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)

eff

[K] 6010 ± 30 6215 ± 30 5620 ± 27 [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

SLIDE 12

Seeing effect corrected on SOPHIE data

RVc = RV + 1.04*(dRV - <dRV>)

Data analysis: yorbit GA + APCA MCMC SOPHIE+ constants corrected

Bouchy et al. (2013) Coucol et al. (2015) Ségransan et al. (2011); Díaz et al. (2014)

SLIDE 13

Offset priors

0.6 0.8 1

0.2
0.1

ELODIE-SOPHIE ELODIE-SOPHIE: offset priors based on Boisse et al. (2012). SOPHIE-SOPHIE + offset:

N(0, 10 m/s)

v(k)

i

= k +

n

X

j=1

kj(ti) + pl(ti) + a(ti) + ✏(k)

i

SLIDE 14

Activity indexes

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

SLIDE 15 Image credit: ?

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
Effect on RVs is not well

known.

SLIDE 16 Work by J. Rey, I. Boisse, O. Girault

SLIDE 17

The (simplified) model

ELODIE-SOPHIE: offset priors based on Boisse et al. (2012). SOPHIE-SOPHIE + offset:

N(0, 10 m/s)

i.e., the “jitter” increases with activity (as measured by Halpha).

σJi ∝ I[Hα] v(k)

i

= k +

n

X

j=1

kj(ti) + pl(ti) + ✏(k)

i It turns out that in all cases n = 1 is enough.

SLIDE 18 HD191806 HD221585 HD214823

SLIDE 19

HD191806 - k1 vs k1d1

Model k1 Model k1d1 Prior from Boisse+2012

SLIDE 20

HD191806 - k1 vs k1d1

Bayesian model comparison

Hi hypothesis (drift / no drift) D data; I prior information. p(Hk1d1|I, D) p(Hk1|I, D) = p(D|Hk1d1, I) p(D|Hk1, I) ∼ 290 ± 70

Assuming prior odds = 1

Perrakis estimator