Non-Thermal Radiation Chapter 8

Our Goal: Synchrotron Radiation -Produced by relativistic electrons moving an a magnetic field -Sometimes referred to as magnetoBremsstrahlung

The Cause? Remember the Lorentz force for a charged particle moving in a B field (assuming E = 0) F = q v X B (we consider electrons, so q = e) This force is perpendicular to both v and B, so the magnitude is F = e v B sin φ, where φ is the pitch angle between v and B.

Limits If φ = 90 o, the force is maximal and the electron moves in circles around the B field lines. If φ = 0 o, the force is zero and the electron moves freely in the B direction. For intermediate angles, the electron spirals along the field lines.

Radiation An accelerated charged particle loses energy through radiation. Note that electrons graudually slow down for this reason, but on much longer timescales than the period of gyration [the time taken to ‘loop around’ the field lines].

Trapping If there are not frequent particle-particle collisions, the electrons are essentially trapped by the magnetic field (it’s a magnetized plasma) and the resultant emission can inform us about the magnetic fields.

In the Sun

Magnetic Field Strengths in Astro Notice the range: 18 orders of magnitude!

Let’s Start Small: Cyclotron Radiation A slow-moving electron emits cyclotron radiation at the gyrofrequency ν o - the frequency with which it orbits the field lines. This gives rise to polarized emission that depends on our vantage point.

Imagine Looking Along the Field Line The electron will be orbiting circularly, with a centripetal acceleration; this gives rise to circularly polarized emission (i.e. with a rotating E vector).

Looking Perpendicularly The electron will be seen to bob ‘back and forth’ across the B lines, so we will see linearly polarized emission. (and from intermediate angles, we will see elliptically polarized light).

The Implication? Polarization is inherently implied for radiation produced by this kind of process! Of course, the magnetic field within an emitting cloud may be tangled, so the net or overall polarization may be negligible. But in many cases there will be ordered motion on large scales in coherent fields.

Surprise: It’s Monochromatic! Equate the Lorentz force to that required for centripetal acceleration and we discover (p 258) that the gyrofrequency is independent of electron velocity [for non-relativistic velocities] Faster moving electrons move in larger circles, but the period is the same for all electrons.

What Sorts of Radii? Consider Example 8.2. In the Warm Interstellar Medium, we find a radius of gyration of 21 km! This is not “atomic-scale” behaviour.

Promise and Problem If we can detect the monochromatic emission at frequency ν o, we can instantly determine the magnetic field strength. The problem is that it is generally very low and can’t propagate through the ISM or the atmosphere. So this is generally only useful for stronger fields (Sun, planets, pulsars)

The Physical Reality Consider Jupiter, with a strong dipole magnetic field affected also by the solar wind.

Complicated Effects Near the magnetic poles, some electrons are removed (encounter the atmosphere), some are reflected magnetically. Atmospheric bombardment by charged particles, of course, creates auroras – not just on Earth.

An Extra Complication!

Remember that J’s B-Field Sweeps Past Io as J Rotates

Net Effect: the Field Fluctuates from Place to Place, and Over Time …as does the concentration and numbers of electrons (the emitting particles) The net result is that there is no monochromatic emission: it is smeared out into a continuum.

The Net Effect

More Energetic: Synchrotron Emission Consider an electron moving relativistically (that is, with γ >>1. See page 263 for the (simple!) derivation. What we discover is that the gyrofrequency now depends on both B and E (where E is the energy of the relativistic electron, ϒ m e c 2 ).

Immediate Implication For large ϒ, the gyroradius is very large (not surprisingly) and the relativistic gyrofrequency is very low. [See example 8.4, on p 263. For an electron with ϒ = 10 4, the gyroradius in the ISM is ~100 solar radii; the gyro frequency is 20 minutes!!!)

..and a Second Implication The classical radiation pattern emitted by the electron in its rest frame has to be transformed to the frame of the observer. In particular, the radiation is beamed into a narrow cone of angular radius θ = 1 / ϒ oriented in the direction of instantaneous motion. (Consider ϒ = An angle of radians is ~ 20 arcsec!)

Not Done Yet! From a particular vantage point, you see emission only when the electron is moving instantaneously towards you – that is determined by the gyration period. So you expect to see pulses from a given radiating particle. Moreover, you only see its radiation in the forward direction so it is tremendously Doppler shifted.

Summing it All Up (see page 264) There is a critical frequency ν crit above which we see negligible radiation. It depends on ϒ 2 and is in fact very high, much higher than the gyrofrequency. Most of the energy is emitted at ~0.3 ν crit There is also a [very low] fundamental frequency ν f (related to the gyrofrequency): we see it and all its harmonics, so the spectrum is spread out into a continuum.

Net Result A broad-band continuous spectrum It peaks at ν max (about 0.3 ν crit ) There is a cutoff at ν crit Look at example 8.5, on page 265.

So Much for Single Radiators How about an ensemble of electrons of various energies and ϒ factors? To sum this all up, we have to know what the distribution of electron energies is. These relativistic particles do not obey a simple M-B thermal distribution. What instead do they do?

Back to Cosmic Rays These told us that there was a power-law distribution in energy (see next panel for a reminder); that is, N(E) = N o E -Γ where Γ is the energy spectral index

Given That Mix… … we can calculate the emission and absorption coefficients (the latter of which accounts for self-absorption) See page 266 for these coefficients (which depend on a set of calculable constants) and on the resultant source function and optical depth.

The Important Take-Away The optical depth increases with decreasing frequency, so a synchrotron-emitting cloud becomes more opaque at lower frequencies.

Closing the Loop! Stick the Source Function and the optical depth into the Equation of Radiative Transfer to figure out the final spectrum. We get:

Forgive Us! Note the use of α to describe the spectrum through what we call the spectral index. (Here α does not mean the absorption coefficient.)

Implications The specific intensity goes like ν 5/2 in the optically- thick part of the spectrum (low frequencies). The specific intensity falls like α = - (Γ-1) / 2 in the optically thin part (higher frequencies). Note that the spectrum is not flat (as it was in thermal bremsstrahlung).

Diagnostics A spectrum of this form is from a non-thermal source. The spectral index gives you an estimate of Γ, the power spectrum of electron energies. And one can solve for magnetic field strengths etc (see next panel)

Diagnosing the Sources!

Synchrotron Sources Explored (pp ) Important Notes and Findings: 1.Synchrotron radiation is most readily observed in the radio regime - but not only! See next panel

M87 (a giant elliptical)

At its core: an optical ‘jet’

At various wavelengths

Polarized

Alignment! Note the scale of the alignment of the jet in the core of M87. The magnetic fields can explain this: gas outflows along the magnetic/rotation axis of a SMBH, with the rotation axis providing long- term stability.

Scale! The M87 jet extends over 200 parsecs. Are you impressed? Consider the next panel, for a double-lobed radio galaxy.

Schematic

Now a Real One (at radio λ’s)

Consider the Scale!

Hence AGNs, Quasars,…

Other Sources: The Crab Nebula (SNR)

Polarization

A Model

Remember Also Diffuse Synchrotron Emission e.g. in the diffuse medium of our galaxy

On to Something Else! Inverse Compton Radiation Reminder: Compton scattering (the common situation) sees high energy photons scattering off relatively placid electrons The photons lose some energy as they do so

Consider a Relativistic Gas Here we have fast-moving electrons. If low- energy photons impinge – a good example would be the microwave background, at T = 3K - - they can be scattered to higher energy. This enhancement goes like ϒ 2, so can be a very dramatic effect.

Example: See discussion on p273, where electrons with ϒ = 10 4 can up-shift a 1 GHz radio photon into the X-ray part of the spectrum!

And a Consequence The Sunyaev-Zeldovich effect.. Map the sky at radio wavelengths where you are seeing the CMBR (from the z=1000 ‘last scattering’ surface). If the photons pass through a cloud of hot gas (like the X-ray halo of a cluster of galaxies), you may get inverse Compton.

Result? You will see small spots in the CMBR map where the usual BB radiation is distorted. It should correlate with indicators (if any) of the presence of hot gas. (See next panel.) This allows you to probe clusters (and, in a roundabout way, work out their cosmological distances).

SZE vs X-Ray (Hot) gas