<p><a href="https://en.wikipedia.org/wiki/Methods_of_detecting_exoplanets#Radial_Velocity" rel="nofollow noreferrer">Radial velocity</a> (RV) is one of main methods for exoplanet search.</p>
<p>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).</p>
<p>But if you read scientific articles (like <a href="https://arxiv.org/abs/1609.03449" rel="nofollow noreferrer">this about Proxima b</a>) - the picture is different.</p>
<p>Image from the article:</p>
<p><a href="https://i.sstatic.net/kM2xk.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/kM2xk.png" alt="enter image description here" /></a></p>
<p><em>My current understanding:</em></p>
<p>A telescope with high-resolution spectrometer observes a specific spectral line of a star. The result is in pairs (V<sub>i</sub>,T<sub>i</sub>), i=1..N. Here V<sub>i</sub> are Doppler variations of radial velocities and T<sub>i</sub> are times of observation. T<sub>i</sub> are transformed to <a href="https://en.wikipedia.org/wiki/Barycentric_Coordinate_Time" rel="nofollow noreferrer">barycentric times</a>.</p>
<p>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 &quot;planet candidate&quot; is found. Let's subtract it from the observations and search is there still high Bayesian probability of another planet.</p>
<p>But I still can't figure out how the math in done.</p>
<p><s><em>Questions:</em>*</p>
<ol>
<li><p>Can mathematical details of the method be explained in simple terms? <a href="https://www.researchgate.net/publication/260483215_Bayesian_search_for_low-mass_planets_around_nearby_M_dwarfs_Estimates_for_occurrence_rate_based_on_global_detectability_statistics" rel="nofollow noreferrer">This work</a> contains some details, but from it I can't understand what is being done.</p>
</li>
<li><p>Does complete review of RV method exist online in free access?</p>
</li>
<li><p>How exactly is the math done?  How does Markov chain Monte Carlo (MCMC) &quot;scan&quot; possible parameters of planet's orbits?</p>
</li>
<li><p>How exactly are Bayesian periodograms built?</s></p>
</li>
</ol>
<p><strong>EDIT</strong></p>
<p><strong>Question:</strong></p>
<p><strong>Does complete review of RV method exist online in free access to read about the details?</strong></p>

CC BY-SA 4.0
2020-10-17T00:58:16.733Z
silly close vote!
uhoh
CC BY-SA 4.0
2020-10-17T01:08:27.957Z
I made some small edits, can you check that the meaning is still clear?
uhoh
CC BY-SA 4.0
2020-10-17T05:34:05.257Z
This questions seems far to broad to me and is asking multiple questions.
ProfRob
CC BY-SA 4.0
2020-10-17T06:48:12.520Z
@Rob Jeffries - my question is "how they do math for RV planet search" :). I admit that proper answer can be too long to write. So I asked whether a good review of the method exists I could read myself. Partial answers are welcome, too. I'll wait for a while, if no satisfiable answer - I can split into several questions. But currently I see all my subquestions are interlinked, and it would be hard to explain periodograms not explaining MCMC. I can be wrong, of course.
Heopps
<exoplanet><radial-velocity>
Radial velocity exoplanet search - can mathematical details be explained? (Bayesian periodogram MCMC)
Heopps
# Radial velocity exoplanet search - can mathematical details be explained? (Bayesian periodogram MCMC)

(Asked by: username_0 on 2020-10-16)

[Radial velocity](https://en.wikipedia.org/wiki/Methods_of_detecting_exoplanets#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](https://arxiv.org/abs/1609.03449)) - the picture is different.

Image from the article:

[![enter image description here](https://i.sstatic.net/kM2xk.png)](https://i.sstatic.net/kM2xk.png)

*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](https://en.wikipedia.org/wiki/Barycentric_Coordinate_Time).

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](https://www.researchgate.net/publication/260483215_Bayesian_search_for_low-mass_planets_around_nearby_M_dwarfs_Estimates_for_occurrence_rate_based_on_global_detectability_statistics) 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:**

**Does complete review of RV method exist online in free access to read about the details?**

**Tags:** exoplanet, radial-velocity
> **Comments:**
> **username_1**: silly close vote!  
> **username_1**: I made some small edits, can you check that the meaning is still clear?  
> **username_2**: This questions seems far to broad to me and is asking multiple questions.  
> **username_0**: @Rob Jeffries - my question is "how they do math for RV planet search" :). I admit that proper answer can be too long to write. So I asked whether a good review of the method exists I could read myself. Partial answers are welcome, too. I'll wait for a while, if no satisfiable answer - I can split into several questions. But currently I see all my subquestions are interlinked, and it would be hard to explain periodograms not explaining MCMC. I can be wrong, of course.  

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## 0 answers

