How to use the Binary Mass Function for exoplanets?

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In summary, the Binary Mass Function (BMF) is a statistical tool used to estimate the mass of exoplanets in binary star systems. It works by analyzing the gravitational effects of the binary stars on each other and on the orbiting exoplanet. By measuring the orbital period and the velocity of the stars, astronomers can derive the mass function, which provides a range of possible masses for the planet. This method is particularly useful in cases where direct observation of the planet is challenging, allowing researchers to infer its presence and characteristics based on the behavior of the binary system.
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Astroxzip
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Hi. I am working on a research paper for my high school and I am trying to calculate the mass of an exoplanet using the radial velocity values of its star. However, I am confused as to the binary mass function and what units you would use. I also wanted to know how you would interpret a radial velocity curve to calculate the mass of the exoplanet. Thank you
The paper I am using for my radial velocity values is the following (Table 4)
https://iopscience.iop.org/article/10.1088/0004-637X/810/1/30
Hi. I am working on a research paper for my high school and I am trying to calculate the mass of KELT-8b using the radial velocity values of its star. However, I am confused as to the binary mass function and what units you would use. I was under the impression you would use solar masses however I am getting a mass of 3.48 solar masses which is nothing close to the mass they found in the paper. I also wanted to know how you would interpret a radial velocity curve to calculate the mass of the exoplanet because I figured maybe I found the radial velocity the wrong way. The way I did it was by taking an average of the peaks after graphing it against the time. Thank you
The paper I am using for my radial velocity values is the following (Table 4)
https://iopscience.iop.org/article/10.1088/0004-637X/810/1/30
 
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Here is how to find how something is defined in a scientific paper.
  1. Look for a definition in the paper.
  2. If there is no definition, look for a reference to what you are looking for. Get that paper.
  3. Look for a definition in that paper.
  4. Repeat as needed.
 
  • #3
Vanadium 50 said:
Here is how to find how something is defined in a scientific paper.
  1. Look for a definition in the paper.
  2. If there is no definition, look for a reference to what you are looking for. Get that paper.
  3. Look for a definition in that paper.
  4. Repeat as needed.
Hi. I know how they have defined the radial velocity values. The problem is I do not know how the binary mass function works and what units you need for the function.
 
  • #4
The phrase "binary mass function" does not appear in the paper you cite. Where did you come across the term and how is it defined?
 
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Ibix said:
The phrase "binary mass function" does not appear in the paper you cite. Where did you come across the term and how is it defined?
Ok so, basically the paper I am writing needs me to calculate the mass using radial velocity method. After doing some research, I found the binary mass function in an Astrophysics textbook which I found could work for exoplanets. However the problem is that the units are not defined anywhere which is the main source of issue. As for how it is defined, the binary mass function constrains the mass of the unseen component of a binary system, which in my case is the mass. As for the paper I cited, I used it for the values of the radial velocity, however I am struggling a bit to understand how to condense them into one for my calculations. I ended up taking an average of the five highest values however I think my answer could have deviated due to the method I chose to condense the radial velocity values into one.
 

FAQ: How to use the Binary Mass Function for exoplanets?

What is the Binary Mass Function in the context of exoplanets?

The Binary Mass Function is a mathematical tool used in astrophysics to estimate the masses of binary star systems and their companions, including exoplanets. It relates the observable properties of the system, such as the orbital period and the velocity of the stars, to the masses of the stars and their companions. This function is particularly useful when one of the stars in the binary system is not directly observable.

How can the Binary Mass Function help in determining exoplanet masses?

The Binary Mass Function allows scientists to calculate the minimum mass of an exoplanet based on the gravitational influence it exerts on its host star. By measuring the radial velocity of the star and knowing the orbital period of the planet, researchers can use the mass function to derive the mass of the planet, albeit as a lower limit unless additional information is available.

What parameters are needed to use the Binary Mass Function?

To use the Binary Mass Function, you need the following parameters: the orbital period of the exoplanet, the radial velocity amplitude of the host star, and the mass of the host star if available. The function is typically expressed in terms of these variables, allowing for the calculation of the minimum mass of the companion object.

What are the limitations of the Binary Mass Function?

One limitation of the Binary Mass Function is that it only provides a minimum mass for the exoplanet, as it assumes a circular orbit and does not account for the inclination of the orbit. If the orbital inclination is not known, the actual mass could be significantly higher. Additionally, the method is less effective for systems with very low mass companions or for those where the host star's motion is difficult to measure accurately.

How does the Binary Mass Function compare to other methods of exoplanet mass determination?

Compared to other methods, such as transit photometry or direct imaging, the Binary Mass Function is particularly useful for systems where direct observations of the exoplanet are challenging. While transit methods can provide precise measurements of mass and radius, the Binary Mass Function is advantageous for detecting planets around distant stars or in binary systems. Each method has its strengths and weaknesses, and often, a combination of techniques is used for more accurate characterization of exoplanets.

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