= Solution
One explanation is an upper <electron> <energy> imposed by the accelerator: finite age, finite confinement size, escape, or a balance of acceleration and losses limits $\gamma$ to $\gamma_{\max}$. Since the <synchrotron critical frequency> scales as $\nu_c\propto B\gamma^2\sin\alpha$, the absence of higher-energy <electrons> produces a corresponding high-<frequency> cutoff, broadened by the single-particle spectrum.
The other is <synchrotron cooling>, with <inverse Compton scattering> often contributing: $\dot\gamma=-b\gamma^2$ gives $t_{\rm cool}=1/(b\gamma)$. High-energy <electrons> disappear fastest, so a population of age $t$ develops a cooling scale $\gamma_b\sim1/(bt)$ and $\nu_b\propto B/(b^2t^2)$. A burst population can develop a strong cutoff. With continuous power-law injection, the simplest steady cooling model instead steepens the <electron> <energy> index by one and the <synchrotron radiation> spectral index by $1/2$, giving a break rather than necessarily an exponential cutoff. The detailed spectral shape therefore distinguishes finite acceleration from aging and injection history.
Back to article page
