**High Precision Radial Velocities**

**Pedro Figueira**

CAUP

The search for extrasolar planets started and prospered under the auspices of the Radial Velocity (RV) method. With roughly 90% of all extrasolar planets detected by RV, it is the workhorse of planetary detections. And while the first discoveries were only possible thanks to contemporaneous technological breakthrough, today RV surveys drive the design of new spectrographs. The motivation for obtaining precise measurements goes beyond planetary searches, being fundamental for topics such as asterosismology and the study of the variability of fundamental constants.

In this advanced course I will describe how to calculate precise RVs and interpret them. It will be composed of four lessons of one hour each:

- 27 October: RV Definition, RV Application, and Spectrographs;
- 3 November: Theory of RV Calculation;
- 10 November: Calibrating a Spectrograph - in practice;
- 17 November: RV Signal analysis and interpretation.

It will be aimed at graduate students and researchers willing to gather hands-on knowledge on the subject. It requires virtually no previous knowledge of the topic and only elementary algebra and optics to follow; each lesson will always build up on the previous ones. A bibliography will be provided along with each topic, for the interested reader to explore.

27 October 2010

In this first lesson I will start by introducing the subject of Radial Velocities with its definition and examples of application. We will then discuss how a spectrograph works. We will break it into its principal components and study how they define the properties of the collected spectra. I will conclude by showing these properties in the context of some state-of-the-art spectrographs, and list those available within ESO.

3 November 2010

In this second class we will learn how to evaluate the RV information content of both a spectral line and a spectrum using different methods. We will then learn how to compute the Cross-Correlation Function and define some of its properties. We will finish by reviewing some of the practical difficulties and pitfalls of this method.

10 November 2010

We will explore the differences between the two concurrent methods for calculating RVs: the cross-correlation with a template spectrum and the deconvolution of a superposed reference. We will discuss the advantages and limitations of each and how each one of them is suited for a particular type of spectrographs. We will conclude by presenting frequency combs, a much more stable calibrator than current ones, now under development.

17 November 2010

In this last talk we will address the issue of signal reconstruction from a set of RVs. This lesson will be strongly biased towards my domain of expertise, discussing mostly the identification of planetary signals and their characterization. Several diagnosis complementary to RV determination will be discussed as well.