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

Abstract

[1] 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 very long baseline interferometry observations by Spangler et al. of compact radio sources against the solar wind for heliocentric distances R ≈ 10-50 R . We use the Coles and Harmon model for the inner scale l i (R), which 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, nonexclusive, 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 sunward of the empirical prescription, which was based on observations between 10 and 50 R . 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. These results and interpretations are discussed and compared with earlier work.

The structure of solar radio noise storms

“…The highest T b values of the continua and the smallest sizes of the continua and bursts are of interest: the highest values of T b constrain the emission theories and the smallest sizes put an upper limit to the broadening resulting from the scattering of radio waves by coronal density inhomogeneities (Bastian 1994;Subramanian & Cairns 2011). Up to now, the highest reported T b values are of the order of 10 10 K, in agreement with the maximum predicted from plasma emission models.…”

“…Bastian (1994) and Subramanian & Cairns (2011) have modeled these effects assuming small angle scattering for radiation from compact sources embedded in the corona. The limit of validity of this assumption has been estimated by Bastian to a broadening of 25 arsec.…”

“…Melrose did not specify the origin of fast electrons but Benz & Wentzel, and Spicer ascribed their production to reconnection or to weak shocks associated with newly emerging flux. Subramanian & Becker (2004, 2011) considered a generic second-order Fermi acceleration mechanism for generating these electrons. They found an overall efficiency ∼10 −6 for the emission process.…”

A Study of Density Modulation Index in the Inner Heliospheric Solar Wind During Solar Cycle 23

“…It is also an important ingredient in constructing models for the quantity C 2 N , which is the amplitude of the density turbulence spectrum (Thejappa & MacDowall 2008). In turn, C 2 N is crucial for understanding angular broadening of radio sources due to solar wind turbulence (Janardhan & Alurkar 1993;Bastian 1994;Subramanian & Cairns 2011) and for explaining the rather low brightness temperatures of the solar corona at meter to decameter wavelengths (Thejappa & MacDowall 2008). A crucial role is also played by N in influencing the propagation of energetic electrons, produced by solar flares and other explosive solar surface phenomena, through the heliosphere (Reid & Kontar 2010).…”

Turbulent Density Fluctuations and Proton Heating Rate in the Solar Wind from 9–20 R⊙

“…Many authors use analytical expressions for the structure function that are applicable in the asymptotic limits s ≪ l i or s ≫ l i (Coles et al 1987;Armstrong et al 2000;Bastian 1994;Subramanian & Cairns 2011). However, these expressions are not valid for situations (such as the one we are dealing with in this paper) where the baseline is comparable to the inner scale; i.e., s ≈ l i .…”