TIL Physics 18: Why Synchrotron Radiation Dominates Radio AGNs

Synchrotron radiation is a key process in the radio emission from active galactic nuclei (AGNs). It is produced when fast-moving electrons spiral around magnetic field lines, emitting energy as they accelerate. This process is especially important in the radio bands but becomes less significant at higher energies like X-rays and gamma rays. Why does this happen?

I. What Is Synchrotron Radiation?

A charged particle (like an electron) moving in a magnetic field B experiences a force that makes it spiral, emitting radiation. For very fast (relativistic) electrons, this is called synchrotron radiation.

The force is given by:

F = q (v × B)

II. The Synchrotron Frequency

The typical frequency of synchrotron radiation is:

νsync ≈ γ² (e B) / (2π me c)

• γ: Electron energy (Lorentz factor)
• e: Electron charge
• B: Magnetic field strength
• m_e: Electron mass
• c: Speed of light

Higher energy electrons and stronger magnetic fields produce higher frequency radiation.

III. Synchrotron Cooling

Electrons lose energy as they emit synchrotron radiation. The cooling timescale is:

tsync ≈ 6π me c / (σT γ B²)

• High-energy electrons (large γ) cool quickly.
• Strong magnetic fields (large B) also speed up cooling.

Electrons that could emit X-rays or gamma rays lose energy too fast to fill large regions.

IV. Why Synchrotron Dominates in the Radio

• Typical AGN jets: B ≈ 10^-5–10^-3 G, γ ≈ 10³–10⁴
• Synchrotron peaks in the radio to infrared
• Cooling times are long, so emission fills large areas

V. Why It Fades in X-rays and Gamma Rays

• To emit X-rays: need γ ≥ 10⁷
• Such electrons cool in hours or days
• Emission is only possible in small, energetic regions
• Other processes (like inverse Compton scattering) take over at high energies

VI. Order-of-Magnitude Illustration

Take an electron with γ = 1000 in a magnetic field of B = 100 μG. Plug into:

νsync ≈ γ² (e B) / (2π me c)

Calculate:

νsync ≈ 106 × (2.8 × 106 Hz) ≈ 2.8 GHz

This aligns perfectly with observed AGN jet radio emission.

Regime	Synchrotron?	Examples
Radio	Yes	AGN jets, supernovae
Infrared	Yes	Starbursts, AGN tori
Optical	Sometimes	M87 jet, blazars
X-ray	Rare	Crab Nebula, GRB afterglows
Gamma-ray	No	Usually other processes

VII. Conclusion

Synchrotron radiation dominates the radio emission from AGNs because electrons can emit at these frequencies for long times and over large regions. At higher energies, electrons lose energy too quickly, so other processes become more important.

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