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A blazar is an active galactic nucleus whose relativistic jet is viewed close to its direction of motion. Relativistic beaming enhances the apparent radiation from approaching material and changes observed variability timescales. Its extreme brightness is therefore affected by orientation as well as by the power supplied by black-hole accretion.

A source's brightness and spectrum do not directly identify the particles responsible for every emission component. Radio through gamma-ray observations and their timing help distinguish candidate mechanisms, while TXS 0506+056 illustrates the additional information supplied by a possible association with high-energy neutrinos.

The 2018 collaboration paper associated the 22 September 2017 neutrino alert with the flaring blazar TXS 0506+056 through directional and multiwavelength observations. Its approximately $3\sigma$ evidence included trial corrections and assumed relationships between neutrino and gamma ray emission. A single association did not establish a production mechanism or explain the entire diffuse neutrino flux.^[ref]

Inverse Compton scattering transfers energy from fast electrons to lower-energy photons. In the Thomson scattering limit the scattering is approximately elastic in the electron's instantaneous rest frame, but the transformations into and out of that frame can greatly increase the photon energy in the original frame.

In a blazar, relativistic jet electrons can scatter their own synchrotron radiation, producing synchrotron self-Compton radiation, or scatter photons from an accretion disk and its surrounding reprocessing material. The two spectral humps constrain electron Lorentz factors, the electron distribution and, with assumptions about geometry and relativistic beaming, the magnetic field. For the same electron population in the Thomson regime, the ratio of inverse-Compton to synchrotron power scales as $u_{\mathrm{ph}}/u_B$ in the plasma rest frame. It does not determine the field without information about the photon energy density and beaming.

In a galaxy cluster, hot thermal electrons scatter cosmic microwave background photons and slightly raise their mean energy, producing the thermal Sunyaev-Zeldovich effect. The spectral distortion measures the line-of-sight integral of electron pressure, approximately $y={\sigma }_T\int n_e{k}_B{T}_{e}d\ell /(m_e{c}^2)$ for nonrelativistic thermal electrons. Combined with X-ray emission, which weights density approximately quadratically, it constrains the gas density, temperature and mass distribution. These are distinct source populations and seed photon fields from the blazar example.

For the power derivation, use an isotropic incident radiation field of total photon energy density $u_{\mathrm{ph}}$ in the laboratory frame. Its stress-energy tensor has $T^{00}=u_{\mathrm{ph}}$ and $T^{zz}=u_{\mathrm{ph}}/3$, with zero mean flux. Boosting to an electron moving at $\beta c$ along $z$ givesThe radiation energy flux in this rest frame is $S_z^{\prime }=c{T}^{\prime 0z}$. Elastic Thomson scattering exerts the drag $F_z^{\prime }={\sigma }_T{S}_z^{\prime }/c$. The parallel three-force has the same value in the laboratory frame, so the electron's positive energy loss rate isThis isotropic inverse-Compton drag assumes photon energies small compared with $m_e{c}^2$ in the electron rest frame, negligible recoil and an isotropic seed field in the specified frame. An anisotropic photon field requires its directional moments; the recoil-dependent differential scattering cross-section of Compton scattering becomes necessary at larger rest-frame energies.

There are two conventions to qualify in the printed expression. First, the density multiplying $4/3$ must be $u_{\mathrm{ph}}$, not literally only the magnetic part of a propagating electromagnetic field. That field has equal electric and magnetic energy densities, so $u_{\mathrm{ph}}=2u_{\mathrm{mag}}$ and the corresponding formula is $P_{\mathrm{IC}}=(8/3){\sigma }_{T}c{u}_{\mathrm{mag}}{\beta }^2{\gamma }^2$. Second, this is net electron energy loss, rather than all incident plus scattered photon energy. At $\beta =0$ an electron still scatters power ${\sigma }_{T}c{u}_{\mathrm{ph}}$, but transfers no kinetic energy to the photons, so the inverse-Compton gain is zero.

For an individual incident photon of energy $\epsilon$, the electron-frame energy is ${\epsilon }^{\prime }=\gamma \epsilon (1-\beta \cos \theta )$. For a head-on photon followed by forward emission in the laboratory,Averaging an isotropic seed field gives $⟨{\epsilon }_{\mathrm{out}}⟩\simeq (4/3){\gamma }^2\epsilon$ for ultrarelativistic electrons. The original plot has an inverse-Compton maximum of order $10^8\mathrm{eV}$, a synchrotron maximum around $10^{-1}\mathrm{eV}$ and a disk component around $1\mathrm{eV}$. ThusThe head-on maximum gives the same order of magnitude, about $5\times 10^3$ to $1.6\times 10^4$. These are approximate readings of a broad spectrum, not precise fitted parameters. Disk and synchrotron seed photons need not be scattered by the same part of the electron distribution, and bulk jet Doppler factors also enter the observed peak relation. The indicated rest-frame seed energies remain well below the electron rest energy in this estimate.

TXS 0506+056 is a blazar studied through a gamma-ray flare associated in direction and time with the high-energy neutrino alert IceCube-170922A. The event motivated coordinated observations across the electromagnetic spectrum, connecting a variable relativistic source with a possible source of energetic neutrinos.^[ref]

An association is a statistical inference involving localization, timing and backgrounds. It does not directly image the neutrino-production site or uniquely determine the jet's particle composition. The physical interpretation must account for the measured photons and neutrino evidence together.