- Covered thus far. - Specific Intensity, mean intensity, flux density, momentum flux. - Emission and absorp>on coefficients, op>cal depth

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1 - Covered thus far - Specific Intensity, mean intensity, flux density, momentum flux - Emission and absorp>on coefficients, op>cal depth - Radia>ve transfer equa>on - Planck func>on, Planck spectrum, brightness temperature - Kirchhoff s Law, principle of detailed balance, Einstein coefficients - ScaKering

2 Sun from Mars Sun from Earth - Average distance of Mars from the Sun is ~1.5 AU How much longer should you expose a photo of the Sun from Mars than a photo of the Sun from Earth?

3 Sun from Mars Sun from Earth - Average distance of Mars from the Sun is ~1.5 AU How much longer should you expose a photo of the Sun from Mars than a photo of the Sun from Earth? - Answer: The same amount of 5me!

4 Energy flowing through unit area into unit solid angle in unit frequency in unit time Brightness or specific intensity Mean intensity: Flux density:

Charged par>cle accelera>on Atomic and molecular transi>ons

Interac>on with magne>c fields Interac>on with the E- field of EM

transi>ons Vibra>onal transi>ons Bremsstrahlung (free- free

emissions Thomson scaaering, Compton scaaering, Inverse Compton

5 Charged par>cle accelera>on Atomic and molecular transi>ons Interac>on with the Coulomb fields of other charged par>cles Interac>on with magne>c fields Interac>on with the E- field of EM waves Bound- bound transi>ons Bound- free transi>ons Rota>onal transi>ons Vibra>onal transi>ons Bremsstrahlung (free- free emission) Cyclotron emission, Synchrotron emission, some coherent emissions Thomson scaaering, Compton scaaering, Inverse Compton ScaAering - Determine emission and absorp>on coefficients and solve transfer equa>ons

At radio frequencies, the emission is due to relativistic electrons spiralling in magnetic field lines synchrotron radiation Electrons have a power law energy distribution with

6 At radio frequencies, the emission is due to relativistic electrons spiralling in magnetic field lines synchrotron radiation Electrons have a power law energy distribution with typically α~-0.75 High frequencies (optically thin) Low frequencies (optically thick) In the case of complex spectra above, multiple components of varying angular size contribute

Radio emission is produced due to acceleration of electrons by

7 Radio emission is produced due to acceleration of electrons by positive ions, i.e., free-free emission (Bremsstrahlung) with jνff and ανff to be derived later in the course. For now Spectral index, α, defines the frequency dependence of the emission, such that Spectrum rises as ν2 at low frequencies and flattens at higher frequencies. Why? Recall High frequencies (optically thin) Low frequencies (optically thick)

D = εe B = μh B = magnetic flux density E = electric field D = electric displacement field H = magnetic field strength v = velocity c = speed of light μ = magnetic permeability ε = dielectric

8 D = εe B = μh B = magnetic flux density E = electric field D = electric displacement field H = magnetic field strength v = velocity c = speed of light μ = magnetic permeability ε = dielectric constant j = current density ρ = charge density in the non-relativistic limit, the Lorentz force exerted on a particle with charge q, of velocity, v in an electric field, E and magnetic field B: - the force due to the magnetic field is always perpendicular to both the direction of the velocity vector and the field

9 - The rate of work done by fields on a particle is - v (vxb) = 0 because B works perpendicular to motion - For non-relativistic particles - generalizing to total force on a volume element containing many charges, the force per unit volume is: where ρ and j are the charge and current density - Rate of work done by the field per unit volume = rate of change of mechanical energy per unit volume due to the fields

10 field - Poynting Theorem Deriviation: (R&L 2.1) - The rate of change of mechanical energy per unit volume plus the rate of change of field energy per unit volume equals minus the divergence of the field energy flux - electromagnetic field energy per unit volume Poynting Vector

11 Integrating over volume element The rate of change of total energy within volume, V, is equal to the net inward flow of energy - Electrostatics: both E and B decrease like r -2. This implies S decreases like r -4 and thus the integral goes to zero since the surface area increases only as r 2. - However for time varying fields E and B decrease like r -1, and therefore the integral can contribute a finite amount to the rate of change of energy of the system. This energy flowing in (or out) at large distances is called electromagnetic radiation.

3145 Topics in Theoretical Physics - radiation processes - Dr J Hatchell. Multiwavelength Milky Way

Multiwavelength Milky Way PHY3145 Topics in Theoretical Physics Astrophysical Radiation Processes Dr. J. Hatchell, Physics 406, J.Hatchell@exeter.ac.uk Textbooks Main texts Rybicki & Lightman Radiative