Constrain the upper limit of the cloud size

Determine the upper limit of the dense-cloud radius in the outflow–cloud bow-shock model for AT 2019avd, given that the synchrotron self-absorption peak becomes relatively insensitive to further increases in cloud radius beyond a characteristic scale.

Background

The hydrodynamical outflow–cloud models indicate that cloud radii of approximately 0.01–0.02 pc can reproduce the observed spectra. Smaller clouds produce higher opacity and shift the synchrotron self-absorption peak to higher frequencies, whereas increasing the cloud radius beyond a certain scale has little effect on the peak frequency. This weak sensitivity prevents the observations from providing a well-defined upper bound on the cloud size.

References

Consequently, the upper limit of the cloud size remains uncertain.

— Radio Emission with Dust: A Bow-Shock Interpretation for the TDE Candidate AT 2019avd  (2609.08324 - Wei et al., 8 Sep 2026) in Section 4.4, “The late-time SED deviation from the outflow-cloud scenario”