# Radial velocity exoplanet search - can mathematical details be explained? (Bayesian periodogram MCMC)

Radial velocity (RV) is one of main methods for exoplanet search.

The popular description of the method sounds simple - one should measure periodic Doppler variation of a spectral line of a star and determine characteristics of orbiting planet (period, minimal mass, etc).

But if you read scientific articles (like this about Proxima b) - the picture is different.

Image from the article:

My current understanding:

A telescope with high-resolution spectrometer observes a specific spectral line of a star. The result is in pairs (Vi,Ti), i=1..N. Here Vi are Doppler variations of radial velocities and Ti are times of observation. Ti are transformed to barycentric times.

Astronomers then use a model to search for a hypothetical planet such that it has a much higher Bayesian probability than model without planet. Much higher usually means 10000 higher in modern publications. If some Keplerian solution (planet's period, mass, eccentricity) satisfies the threshold - one "planet candidate" is found. Let's subtract it from the observations and search is there still high Bayesian probability of another planet.

But I still can't figure out how the math in done.

Questions:*

1. Can mathematical details of the method be explained in simple terms? This work contains some details, but from it I can't understand what is being done.

2. Does complete review of RV method exist online in free access?

3. How exactly is the math done? How does Markov chain Monte Carlo (MCMC) "scan" possible parameters of planet's orbits?

4. How exactly are Bayesian periodograms built?

EDIT

Question: