Magnetic field in radio lobes of cygnus (mainly just substition work)

In summary, the user is seeking help with their calculations for finding the total energy, magnetic field, lifetime, and average bulk power of the source Cygnus A. They have confirmed their methods with their lecturer but are getting a very high value for the magnetic field. They have provided enough information and are open to receiving further help.
  • #1
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Homework Statement


I have a radio map and radio spectrum of Cygnus A and have been asked to find the total energy of the source, the magnetic field in the lobes, the lifetime of the source and the average bulk power of the jets over the lifetime of the source. I've actually done all of this, apart from that the magnetic field bit requires me to use two different methods. I've used one method and got a value that appears acceptable (in that it makes all other value calculated with the number acceptable), but when working through with the other method (that I confirmed was a correct method with my lecturer) I get a value of about 10^38 T, obviously not in the acceptable range for Cygnus A (or anything ever as far as I know!).

This is due, I believe, to the constants in the equation, as the lecturer had stopped putting these in a few stages earlier and made some substitutions after this, leaving us with just a proportionality.


Homework Equations


So the equation I am attempting to use is:
[tex]B ~ \frac{\Theta^4 \nu^5}{(S_\nu)^2}[/tex] where [tex]\Theta[/tex] is the angular diameter in the sky of the object.

This comes from:
[tex]\frac{S_\nu c^2}{\Omega 2k\nu^2} = \frac{m_ec^2}{3k}(\frac{\nu}{\nu_g})^{\frac{1}{2}}[/tex]

which can be rearranged to give an expression for the relativistic gyrofrequency in terms of the other variables. This is the last point at which there are constants in his derivation (and as a result in my notes too!)

From here I substituted in for the relativistic gyrofrequency with [tex]\nu_g = \frac{eB}{2\pi m_e}[/tex] and for the solid angle with [tex]\Omega = \frac{\pi}{4} \Theta^2[/tex], but are these correct things to substitue with? When I put my values in I get (as I said) a value of about 10^38 T which is clearly wrong. I think I'd be happier to find out that I was using the wrong substitutions that to find out that my basic algebra skills were wrong!

I hope I have provided enough information to try and help you help me, as my tex skills are pretty poor, but if you need any more information I will try and give it to you.

Any help is greatly appreciated!
 
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  • #2


Thank you for reaching out for help with your calculations. It is always important to double check and confirm with your lecturer when there are discrepancies in your results.

From your description, it seems like your substitutions for the relativistic gyrofrequency and solid angle are correct. However, it is possible that there may be a mistake in your algebra or in the values you are using. It may also be helpful to check if there are any units or conversion factors that need to be taken into account.

In cases like this, it can be helpful to go through your calculations step by step and double check each substitution and calculation. You can also try using a different method or approach to see if you get a more reasonable result.

I hope this helps and good luck with your calculations! If you need further assistance, feel free to reach out again.
 

1. What is a magnetic field in radio lobes?

A magnetic field in radio lobes refers to the presence of a magnetic field in the lobes of radio galaxies, such as Cygnus. These lobes are the regions of extended radio emission surrounding the central active galactic nucleus.

2. How is the magnetic field in radio lobes measured?

The magnetic field in radio lobes can be measured through a variety of techniques, such as Faraday rotation measurements, synchrotron emission polarization, and Zeeman splitting. These methods allow scientists to determine the strength and orientation of the magnetic field.

3. What is the role of magnetic fields in radio lobes?

Magnetic fields play a crucial role in the formation and evolution of radio lobes. They provide the energy necessary for the lobes to expand and maintain their shape, as well as confining the high-energy particles that produce radio emission.

4. How do scientists study the magnetic field in radio lobes of Cygnus?

Scientists study the magnetic field in radio lobes of Cygnus through a combination of observations and theoretical models. They use radio telescopes, such as the Very Large Array, to observe the polarized emission from the lobes and analyze the data to infer the properties of the magnetic field.

5. What are some potential applications of studying the magnetic field in radio lobes?

Studying the magnetic field in radio lobes can provide insights into the physical processes that govern the behavior of active galaxies. This information can also be applied to other astrophysical contexts, such as understanding the role of magnetic fields in galaxy formation and evolution.

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