Why does the spectrum look "hotter" when the plasma expands?
Heat wave analogy: A heat wave (like the Doppler shift) can make two things go up together—e.g. ice cream sales and drowning rates—so they appear correlated. The real cause is the heat wave. Here, transverse expansion is the real cause: it blue-shifts the photons, so the spectrum looks like it has a higher temperature than the true local one. That "measured heat" is the effective temperature Teff.
Takeaway: The "motion blur" of the collision makes the data look more energetic. Toggle "Local" vs "Effective" below to see how expansion stretches the spectrum.
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Photon energy spectrum (dNγ/d²pT dy) — inverse slope → Teff
Transverse expansion uμ (schematic)
Physics takeaway
| Concept | Non-specialist | Expert |
|---|---|---|
| Doppler shift | "Motion blur" that makes data look more energetic | Blue-shift of thermal distribution due to uμ |
| Effective temperature | "Measured heat" including the explosion's speed | Teff ≈ Tlocal √[(1+v)/(1−v)] |
| Energy spectrum | "Light signature" of the exploding nuclear matter | dNγ/d²pT dy vs pT (GeV) |
Validation (causal correlation)
Expansion → spectral hardening is enforced by hydrodynamic causality. No spurious relationships (e.g. Redskins Rule / stork statistics).
Causal check: v → Teff consistent