Synchrotron Radiation

Question 1

What must be present from synchrotron?

Answer 1

Relativistic electrons and magnetic field.

Question 2

Why does synchrotron cooling remove high-energy electrons first?

Answer 2

Because power per election is proportional to gamma^2.

P ~ gamma^2 B^2

High gamma electrons radiate much more power and lose energy much faster so high energy end of distribution disappears first which causes spectral aging.

Question 3

Synchrotron cooling time?

Answer 3

t sync ~ 1/gamma B^2

This is through: tsync = energy/power and E =2.718 gamma mec^2 and P = gamma^2B^2

High gamma —> short lifetime
Strong B —> short lifetime

Question 4

Why do we need continuous acceleration?

Answer 4

Cooling times are short for large gamma.
Without it spectrum would steepen and high frequency emission would disappear.

Question 5

What does spectrum shape of Sychrotron radiation look like?

Answer 5

Straight power law in log-log plot au ru no exponential cutoff. No thermal and needs relativistic electrons.

Question 6

Characteristic Frequency

Answer 6

vc ~ gamma^2 eB/mec

vc ~ gamma^2

Bigger gamma gives much higher frequency as well as stronger B.

Frequency in which most power is emitted from relativistic charged particle spiraling in magnetic field.

Question 7

Electron Energy Distribution

Answer 7

N(E) ~ E^-p
N(gamma) ~ gamma^-p

Since E = gamma mec^2 for relativistic electrons.

Produced by shock acceleration.
p = 2-3

Smaller p, more high energy electrons present.

Electron energy distribution tells you how many electrons exist at each Lorentz factor.

Question 8

Resulting photon spectrum

Answer 8

Fv ~ v ^-(p-1)/2

Fv ~ v^-a for spectral slope a, then p = 2a + 1