🚀 Relativistic Radio Jet

An AGN launches a relativistic jet. Relativistic Doppler boosting: S_obs = S_em · δ^(3+α) where δ = 1/(γ(1−β·cos θ)). Superluminal apparent motion β_app = β·sin θ/(1−β·cos θ).

SpaceInteractive
Jet blobs moving from AGN core · Blob brightness ∝ Doppler boost · Counter-jet is dimmed · P pause · R reset

How it Works

The simulation shows a jet of plasma blobs ejected from an AGN core at relativistic speed β = √(1-1/γ²). The jet is inclined at angle θ to the line of sight. Each blob moves at speed β·c in 3D, but we observe the projected 2D position on the sky.

Due to relativistic time compression: when a blob moves toward the observer, successive light signals have increasingly less travel time, making the blob appear to move faster than it actually does. This produces the superluminal apparent speed β_app = β·sin θ/(1−β·cos θ) in the approaching jet.

Doppler factor: δ = 1 / [γ·(1 − β·cos θ)] Boosted flux: S_obs = S_em · δ^(3+α) [blob] Apparent speed: β_app = β·sin θ / (1 − β·cos θ) Counter-jet: δ_cj = 1 / [γ·(1 + β·cos θ)] Jet/CJ ratio: R = [(1+β·cosθ)/(1−β·cosθ)]^(3+α)

Frequently Asked Questions

What is relativistic Doppler boosting?

Relativistic Doppler boosting amplifies the observed flux from a relativistic jet pointed toward the observer. The Doppler factor δ = 1/(γ(1−β·cos θ)) can be very large for small angles, boosting the flux by δ^(3+α).

What is superluminal motion in radio jets?

Superluminal motion is an optical illusion where jet components appear to move faster than light when the jet points close to the line of sight. The apparent speed β_app = β·sin θ/(1−β·cos θ) can exceed c.

What is the Lorentz factor γ of an AGN jet?

AGN jets have Lorentz factors γ typically 5–50 (β = 0.98 to 0.9998). Extreme blazars have γ > 50, making them enormously bright due to Doppler boosting.

What causes AGN jets to form?

AGN jets are launched by the spinning supermassive black hole at the galaxy center, powered by the Blandford-Znajek mechanism where magnetic field lines extract rotational energy. The jet is collimated by magnetic pressure and hoop stress.

What is a blazar?

A blazar is an AGN whose relativistic jet points almost directly toward Earth. The extreme Doppler boosting makes blazars very bright and variable across all wavelengths. BL Lacertae objects and flat-spectrum radio quasars (FSRQs) are the two main classes.

What is the counter-jet dimming?

The counter-jet (moving away) is Doppler de-boosted, appearing much fainter. The brightness ratio between approaching and receding jet is [(1+β·cosθ)/(1−β·cosθ)]^(3+α), which can be thousands for highly relativistic jets.

What is the optimal angle for superluminal motion?

Maximum apparent speed β_app = γβ occurs at θ_opt = arcsin(1/γ) ≈ arctan(1/(γβ)). For γ=10 this is about 6°. At this angle the apparent speed equals γ times the speed of light.

What is VLBI and how does it measure jet motion?

Very Long Baseline Interferometry (VLBI) combines radio telescopes across Earth to achieve milli-arcsecond resolution. This allows direct imaging of AGN jets and measuring their proper motion between observations years apart, revealing superluminal motion.

What is the spectral index α of a radio jet?

The spectral index α describes frequency dependence: S ∝ ν^(-α). Optically thin synchrotron has α ≈ 0.5-0.8. Doppler boosted flux scales as δ^(3+α) for a blob or δ^(2+α) for a continuous jet.

Why do some jets show a one-sided morphology?

Relativistic Doppler boosting brightens the approaching jet enormously while dimming the counter-jet below detection. For β=0.9 and θ=30°, the jet-to-counter-jet ratio exceeds 1000:1, making the counter-jet effectively invisible.

About this simulation

This scene launches plasma blobs from a supermassive black hole's core along a jet tilted by θ degrees to your line of sight. Because the blobs travel at a Lorentz factor γ close to the speed of light, each pulse of light they emit takes slightly less time to reach you than the last — the geometry that makes the approaching jet blaze with Doppler-boosted light while the counter-jet on the far side fades to near invisibility.

🔬 What it shows

Two streams of ejected blobs — one approaching, one receding — rendered with brightness scaled by the Doppler factor δ, plus the apparent superluminal creep of the approaching blobs across the sky.

🎮 How to use

Drag the Lorentz factor γ and jet angle θ sliders to see β_app and the jet/counter-jet ratio swing wildly; adjust spectral index α to change how strongly flux responds to boosting; use Pause/Reset or the P/R keys to freeze and restart the ejection sequence.

💡 Did you know?

Superluminal motion is a pure projection effect — nothing here actually exceeds light speed. Astronomers first measured apparent speeds of several times c in quasar 3C 273 in the 1970s, which briefly puzzled the field until this geometry was worked out.

Frequently asked questions

Why does the jet slider angle matter so much?

The Doppler factor δ = 1/(γ(1−β·cosθ)) is extremely sensitive to θ when the jet points close to your line of sight — small changes in angle near θ_opt = arcsin(1/γ) swing the boost by orders of magnitude, which the simulation's brightness scaling makes visible instantly.

What does the "Boost S/S₀" readout mean?

It is δ raised to the power (3+α), the factor by which the observed flux of a moving blob is amplified or suppressed relative to its rest-frame emission — this is the number driving how bright the approaching blobs render on the canvas.

Why is the counter-jet barely visible?

The counter-jet uses the same formula with a flipped sign, δ_cj = 1/(γ(1+β·cosθ)), which shrinks rather than grows — for the default γ=10, θ=15° settings the jet/counter-jet ratio easily reaches several hundred to one.

What sets the maximum apparent speed β_app?

β_app = β·sinθ/(1−β·cosθ) peaks at θ_opt = arcsin(1/γ), where it equals γβ. Try dragging θ near that value for your chosen γ to watch the apparent-speed readout hit its ceiling.

Is this how real AGN jets are observed?

Yes — the underlying formulas match those used to interpret Very Long Baseline Interferometry (VLBI) images of blazars and quasars, where astronomers track blob positions across years to measure real proper motions and infer γ and θ.