The large radio lobes of radio galaxies contain ultrarelativistic electrons ( v

Question

The large radio lobes of radio galaxies contain ultrarelativistic electrons (v c), which cool pas- sively. Possible cooling mechanisms include inverse Compton scattering off photons from the cosmic microwave background and synchrotron radiation in an ambient magnetic field. The energy spec- trum of the electrons can be expressed in terms of the distribution of Lorentz factors (i.e., number of electrons per unit volume with a Lorentz factor ), as follows:

n() = nop (1) which is defined in the range 0 < < m, no is a constant and p 2 is the power-law index.

(a) Find the ratio of cooling rates of the electrons relative to that of protons of the same energy in the plasma.

Explanation / Answer

a) In case of ultrarelativistic electrons we consider that photoionization is the main feeder of energy for the galaxies. From maxell distribution of velocity we can use the photoionization rate as

N=cross section* energized particle* particle number density

Again for recombination rate inside the galaxy we get that

np=ne =Xn using rate of ionization

Now in case of galaxies the feeder energy cannot rise indefinitely that means there are some energy loss or cooling mechanism.

Depending on type of galaxy the energy is lost in recombination. Now recombination release energy 3/2KTe from basic concept

then cooling rate C=3/2KTeN

for electron Ce=3/2KTeNe and for proton Cp=3/2KTeNp

then Ce:cp= Ne:Np

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