Detecting more than 1 exoplanet using Radial Velocity Method.

In summary, the radial velocity method of detecting exoplanets involves analyzing the motion of a star and detecting variations in light wavelengths due to Doppler shift. Multiple planets orbiting a star can be detected by observing two superimposed sinusoidal curves on the resulting velocity graph. The process involves constructing a model of the system and determining the number, size, and distance of planets needed to match the observed graph. However, if the orbital periods are in a 1:2 resonance, it becomes difficult to distinguish between multiple planets and a single planet with an elliptical orbit.
  • #1
avito009
184
4
How do we detect if there is more than 1 exoplanet orbiting a star using radial velocity method?

I read this but I didnt understand it. Can someone explain the answer in Laymans terms?

"Multiple planets will cause a stars radial velocity curve to show two periods: a long gradual change due to the outer planet, and a shorter, sharper change due to the inner planet. The two periods are superimposed on each other, giving the radial velocity curve a complex shape".
 
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  • #2
Imagine there's just a single planet in a circular orbit. It and the star both orbit their mutual centre of mass, and the motion of the star causes variations in detected light wavelengths due to Doppler shift. This let's you calculate the radial velocity.
If you draw a graph of the star velocity against time, in the case above you'd get a sinusoid with the period reflecting that of the planet's orbital period.

Now, imagine another planet, with a different orbital period. If, again, it were the only planet, it'd generate another sinusoid, but with a different period(and depending on mass - amplitude).

With both the planets present, you'd have a velocity graph that represents both of the graphs superimposed, like so:
sinfreq.gif

As with any other function addition, you just take the value(V) of the first one at any given time, and add it to the value of the second one at that time, and plot the result on a new graph.

The more planets you add, the more complex the resulting function becomes. This one is for a simulated system resembling that of Jupiter and its Galilean moons:
challenge3.4.jpg


Elliptical orbits produce a somewhat different velocity graph than a simple sine function, but the principle is the same.

How the detection process works, is you draw the function* from observations, and then try to construct such a model of the system that would result in matching the graph. You try to figure out how many, how large, and how distant planets you need to add for all of their contributions to add up to what you see.

*that's not entirely accurate, but let's not get into details
 
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  • #3
Note that if the periods are in 1:2 resonance, the resulting orbit is hard to distinguish from a single planet on an elliptical orbit.
 
  • #4
snorkack said:
Note that if the periods are in 1:2 resonance, the resulting orbit is hard to distinguish from a single planet on an elliptical orbit.
Care to explain? I thought the first picture in post #2 represented two planets in 1:2 resonance?
 
  • #5
Bandersnatch said:
Care to explain? I thought the first picture in post #2 represented two planets in 1:2 resonance?
Like this:
http://arxiv.org/pdf/0809.1275v2.pdf
for example see Figure 2, page 19, and Figure 4, page 21. The second sinusoid shows itself as sharpening one peak and flattening the opposite maximum - if the inner planet is small enough, not even a secondary maximum curvature - and that´s roughly what orbital eccentricity would show. Small deviations from the expected mathematical curve shape are lost in the noise.
 

1. How does the Radial Velocity Method detect exoplanets?

The Radial Velocity Method detects exoplanets by measuring the slight changes in a star's velocity caused by the gravitational pull of orbiting planets. As a planet orbits its star, the star will also move in a small orbit around their mutual center of mass. This motion causes a slight shift in the star's spectral lines, which can be detected using spectroscopy.

2. What is the minimum number of exoplanets that can be detected using the Radial Velocity Method?

The minimum number of exoplanets that can be detected using the Radial Velocity Method is one. However, this method is most effective at detecting multiple exoplanets in a single system, as each planet's gravitational pull will contribute to the overall velocity signal.

3. How do scientists differentiate between the signals of multiple exoplanets using the Radial Velocity Method?

Scientists can differentiate between the signals of multiple exoplanets by analyzing the periodicity of the velocity measurements. Each planet will have a unique orbital period, and the combination of signals from multiple planets will create a complex but predictable pattern.

4. Can the Radial Velocity Method detect the presence of smaller exoplanets?

Yes, the Radial Velocity Method can detect the presence of smaller exoplanets. However, it is more challenging to detect smaller planets using this method as their gravitational pull on the star is weaker and thus produces a smaller velocity signal. Additionally, the presence of multiple planets can also make it more difficult to detect smaller planets.

5. What are the limitations of using the Radial Velocity Method to detect exoplanets?

One limitation of using the Radial Velocity Method is that it is most effective for detecting exoplanets with relatively short orbital periods. Planets with longer orbital periods will produce smaller and more challenging to detect velocity signals. Additionally, this method is less effective for detecting exoplanets with highly inclined or eccentric orbits.

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