Constraints on coronal turbulence models from source sizes of noise storms at 327 MHz

We seek to reconcile observations of small source sizes in the solar corona at 327 MHz with predictions of scattering models that incorporate refractive index effects, inner scale effects and a spherically diverging wavefront. We use an empirical prescription for the turbulence amplitude $C_{N}^{2}(R)$ based on VLBI observations by Spangler and coworkers of compact radio sources against the solar wind for heliocentric distances $R \approx$ 10--50 $R_{\odot}$. We use the Coles & Harmon model for the inner scale $l_{i}(R)$, that is presumed to arise from cyclotron damping. In view of the prevalent uncertainty in the power law index that characterizes solar wind turbulence at various heliocentric distances, we retain this index as a free parameter. We find that the inclusion of spherical divergence effects suppresses the predicted source size substantially. We also find that inner scale effects significantly reduce the predicted source size. An important general finding for solar sources is that the calculations substantially underpredict the observed source size. Three possible, non-exclusive, interpretations of this general result are proposed. First and simplest, future observations with better angular resolution will detect much smaller sources. Consistent with this, previous observations of small sources in the corona at metric wavelengths are limited by the instrument resolution. Second, the spatially-varying level of turbulence $C_{N}^{2}(R)$ is much larger in the inner corona than predicted by straightforward extrapolation Sunwards of the empirical prescription, which was based on observations between 10--50 $R_{\odot}$. Either the functional form or the constant of proportionality could be different. Third, perhaps the inner scale is smaller than the model, leading to increased scattering.