Abstract
In this chapter, I present a recipe to detect exoplanet orbits in RV observations in the presence of noise arising from stellar activity. I start by introducing Gaussian processes , which are a powerful and elegant way to model correlated noise. I will start from the very basics of Gaussian distributions, leading up to how I incorporate them in my model to account for stellar activity signals. I then present the model that I use to fit RV observations, and describe the Monte Carlo Markov Chain procedure that I apply to determine the best-fitting parameters of this model.
This chapter uses material from, and is based on, Haywood et al., 2014, MNRAS, 443, 2517.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
This lecture is posted online at http://videolectures.net/gpip06_mackay_gpb/ (link correct as of March 2015).
- 2.
Remember this for later; it provides insight on the form of Eq. 3.16.
- 3.
They cannot be completely identical since the covariance functions used with Gaussian processes are always positive definite, whereas the autocorrelation function oscillates about zero. They are very similar though (see Fig. 3.7), and it would be interesting to find out how they are related.
- 4.
The true anomaly is “the angle between the direction of periastron and the current position of the planet measured from the barycentric focus of the ellipse” (Perryman 2011).
References
Aigrain S, Hodgkin ST, Irwin MJ, Lewis JR, Roberts SJ (2015) Monthly notices of the royal astronomical society 447:2880
Aigrain S, Pont F, Zucker S (2012) Monthly notices of the royal astronomical society 419:3147
Ambikasaran S, Foreman-Mackey D, Greengard L, Hogg DW, O’Neil M (2014) Numerical analysis, pre-print (arXiv:1403.6015)
Baluev RV (2013) Monthly notices of the royal astronomical society 429:2052
Barclay T, Endl M, Huber D, Foreman-Mackey D, Cochran WD, MacQueen PJ, Rowe JF, Quintana EV (2015) Astrophys J 800:46
Chib S, Jeliazkov I (2001) American statistical association portal : marginal likelihood from the metropolis–hastings output. J Am Stat Assoc, 96:453
Crossfield IJM et al (2015) Astrophys J, pre-print (arXiv:1501.03798)
Czekala I, Andrews SM, Mandel KS, Hogg DW, Green GM (2014) Astrophys J, pre-print (arXiv:1412.5177)
Ford EB (2006) Astrophys J 642:505
Foreman-Mackey D, Hogg DW, Morton TD (2014) Astrophys J 795:64
Foreman-Mackey D, Montet BT, Hogg DW, Morton TD, Wang D, Schölkopf B (2015) Astrophys J, pre-print (arXiv:1502.04715)
Gelman A, Carlin JB, Stern HS, Rubin DB (2004) Bayesian data analysis. Chapman and Hall, London. (CRC, Boca Raton)
Gibson NP, Aigrain S, Roberts S, Evans TM, Osborne M, Pont F (2011) Monthly notices of the royal astronomical society 419:2683
Gregory PC (2007) Monthly notices of the royal astronomical society 381:1607
Grunblatt SK, Howard AW, Haywood RD (2015) Astrophys J, pre-print (arXiv:1501.00369)
Haywood RD et al (2014) Monthly notices of the royal astronomical society, 443(3):2517–2531
Jeffreys SH (1961) The theory of probability. Oxford University Press, Oxford
Knutson HA, Charbonneau D, Allen LE, Burrows A, Megeath ST (2008) Astrophys J 673:526
Lomb NR (1976) Astrophys Space Sci 39:447
Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) J Chem Phys 21:1087
Perryman M (2011) The exoplanet handbook by michael perryman
Press WH, Flannery BP, Teukolsky SA (1986) Numerical recipes. The art of scientific computing, Vol 1. Cambridge University Press, Cambridge
Rasmussen CE, Williams CKI (2006) Gaussian processes for machine learning. MIT Press, Massachusetts
Roberts S, Osborne M, Ebden M, Reece S, Gibson N, Aigrain S (2012) Philosophical transactions of the royal society a: mathematical. Phys Eng Sci 371:20110550
Scargle JD (1982) Astrophys J 263:835
Zechmeister M, Kürster M (2009) Astron Astrophys 496:577
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Haywood, R.D. (2016). A Toolkit to Detect Planets Around Active Stars. In: Radial-velocity Searches for Planets Around Active Stars. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-41273-3_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-41273-3_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-41272-6
Online ISBN: 978-3-319-41273-3
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)