Lecture 4- Synchrotron emission

General

Radio galaxies - Double radio structure (Cygnus A)

Steeply falling spectra, fainter when observed at higher radio frequencies

produced by highly energetic electrons, travelling near speed of light and interacting with magnetic fields

Linearly polarised

non thermal brightness temperature

Lorentz force

force provided by magnetic field

Electrons moving at reletivistic speeds, so consider the lorentz force in the rest frame of the electron

MAATHS

Energy loss

Lorentz invariant quality, so observer will see same energy loss as the electron sees in its own rest frame

Need to average over all pitch angles

Beamed emission

In electrons rest frame, the emission has a dipole shape

dipole is distorted in the observers frame

the side of the dipole in the direction of motion is boosted because of reletivistic motion

this changes the distribution of the emission

The faster the electron is moving, the larger gamma becomes and the narrower the beam of emission becomes

Observer see emission as super fast pulses emitted every time the electron circles the magnetic field and its velocity is towards the observer

Flashes of emission

length of flashes can be calculated by considering the difference in arrival time between emission at start of pulse and end of pulse

Diagram

Emission from point A needs to travel a distance s further to reach the observer than emission from point B

takes s/c longer

But emission from point B will be produced later by a time s/v

Maths

Energy Distribution

Peak frequency depends on the energy of the electron

average over the distribution of electron energies

Ultra-relativistic electrons follow a power-law distribution

known as Non-thermal distribution

maths, p depends on the mechanism that accelerates the elctrons up to such high energies

Emissivity of syncrotron plasma

Should observe synchrotron emission which dims steeply with frequency, with a power law index