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Straight power-law integrated spectra from inhomogeneous turbulent re-acceleration

Explain how spatially inhomogeneous turbulent re-acceleration of relativistic electrons in cluster environments can yield a straight power-law integrated radio spectrum, as observed for the Abell 2256 radio halo.

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Background

The Abell 2256 radio halo exhibits significant spatial fluctuations in spectral index and curvature, indicating strong inhomogeneity in the emitting volume. Yet its integrated spectrum remains an almost perfect power law over a wide frequency range. While inhomogeneous turbulence has been explored for radio bridges and halos, existing models do not straightforwardly predict how such spatial complexity integrates into an uncurved power-law spectrum. The authors identify this theoretical gap as an open question requiring further work.

References

An inhomogeneous turbulent scenario has also been explored in the case of radio bridges, where theoretical models based on second-order Fermi re-acceleration predict that the fraction of the synchrotron emitting volume increases at lower frequencies. However, it is still an open question how this process would result in a straight power-law for the integrated spectrum.

— Probing particle acceleration in Abell 2256: from to 16 MHz to gamma rays (2405.09384 - Osinga et al., 15 May 2024) in Section 6.1 (Discussion: Spectral properties of the halo)