Chapter 3: Synchrotron Radiation Flashcards
What is synchrotron radiation?
Radiation emitted when an electron gyrates around a magnetic field line
What is the relativistic and non-relativistic gyrofrequency?
The frequency at which the velocity of synchrotron radiation perpendicular to the magnetic field undergoes circular motion.
w_B = eB/(gamma*m_0)
w_g = eB/m_e
What is the magnetic energy density?
U_B = (B^2)/2mu_0
Describe the energy loss rate and what it means for certain particles.
<dE/dt> = -(E^2)(e^4)(B^2)/9(pi)(epsilon_0)(c^5)(m_0)^4
Proportional to E^2 therefore high energy particles lose energy faster
Proportional to (m_0)^-4 so at given energy, electrons are most radiative
Why does an observer only observe radiation for a small part of the particle’s orbit?
Due to the beaming of radiation from relativistic particles
By what factor is the radiation in a synchrotron higher than expected and why?
Gamma squared due to the combo of the beaming effect and the light travel time effect
Below a critical frequency, how can the synchrotron spectrum be described?
A power law of nu^1/3
What assumptions do we make to get the spectrum from an ensemble of electrons?
Assume all radiation comes out at peak frequency, and ignore the theta dependence ie sin(theta)=1
Describe the polarisation of cyclotron radiation.
Direction of electric field vector rotates as electron moves around its orbit, looking parallel to B field, circular polarisation. Looking perpendicular to B field, E field performs SHM, linearly polarised radiation. At angles in between, elliptically polarised.
Describe the polarisation of synchrotron radiation.
Beaming if emission from relativistic particle means emission only detected when particle velocity points (nearly) towards us. Electron only seen at same point throughout its orbit, when acceleration is in same direction. E field in same direction as acceleration, highly linearly polarised radiation. Not totally linear as electron with pitch angles within range 2/gamma will radiate in our direction. Gives small component of circular polarisation
What is the Brightness Temperature?
The temperature that a black body would have to have to give the same intensity of emission at that frequency
Describe synchrotron self absorption.
Defined the spectrum of a synchrotron emission as a power-law S_nu is prop to nu^-alpha and so as we move towards lower freqs, the effective temp of radiation will exceed the effective temp of the radiating electrons. According to the principle of detailed balance, every emission process has an associated absorption process. If there is more energy in radiation than emission, electrons will absorb energy
Describe how the self-absorbed spectrum behaves
Initial rise with nu^(5/2) followed by a turnover and a decrease with nu^(-alpha)
When is the total energy in B and relativistic electrons a minimum?
Corresponds to equipartition of energy between electrons and the magnetic field
What is Compton Scattering?
The scattering of a high-energy photon by a charged particle (usually an electron)
How does Compton Scattering differ from Thomson Scattering?
In Thomson scattering the photon has its direction changed but the energy remains the same. In Compton Scattering the energy of the photon approaches the rest-mass of the electron, the scattering interaction can change the momentum of the photon, meaning the photon loses energy to the particle.
What is Inverse Compton Scattering?
The scattering of low-energy photons by high-energy electrons, producing a high-energy photon and a lower energy electron.
What is the electron energy loss rate for ICS?
-dE/dt = (4/3)(γ^2)(U_photon)(σ_Τ)c
Why is U_B changed to U_photon when calculating the energy loss rate for ICS when compared to Synchrotron?
The electron only cares about the acceleration (ie E) in its rest frame
Why are the energies between ICS and synchrotron radiation different?
There is a max energy photon, of energy 4(γ^2)hν, arising from head-on collision, which is a strict upper limit.
For what values of b (b=B/10nT) does ICS dominate?
b«0.03, for b»0.03 synchrotron losses dominate.
