Constraints on nonlinear and stochastic growth theories for type III solarradio bursts from the corona to 1 AU

Existing, competing theories for coronal and interplanetary type III solar radio bursts appeal to one or more of modulational instability, electrostat ic (ES) decay processes, or stochastic growth physics to preserve the elect ron beam, limit the levels of Langmuir-like waves driven by the beam, and p roduce wave spectra capable of coupling nonlinearly to generate the observe d radio emission. Theoretical constraints exist on the wavenumbers and rela tive sizes of the wave bandwidth and nonlinear growth rate for which Langmu ir waves are subject to modulational instability and the parametric and ran dom phase versions of ES decay. A constraint also exists on whether stochas tic growth theory (SGT) is appropriate. These constraints are evaluated her e using the beam, plasma, and wave properties (1) observed in specific inte rplanetary type HI sources, (2) predicted nominally for the corona, and (3) predicted at heliocentric distances greater than a few solar radii by powe r-law models based on interplanetary observations. It is found that the Lan gmuir waves driven directly by the beam have wavenumbers that are almost al ways too large for modulational instability but are appropriate to ES decay . Even for waves scattered to lower wavenumbers (by ES decay, for instance) , the wave bandwidths are predicted to be too large and the nonlinear growt h rates too small for modulational instability to occur for the specific in terplanetary events studied or the great majority of Langmuir wave packets in type III sources at arbitrary heliocentric distances. Possible exception s are for very rare, unusually intense, narrowband wave packets, predominan tly close to the Sun, and for the front portion of very fast beams travelin g through unusually dilute, cold solar wind plasmas. Similar arguments demo nstrate that the ES decay should proceed almost always as a random phase pr ocess rather than a parametric process, with similar exceptions. These resu lts imply that it is extremely rare for modulational instability or paramet ric decay to proceed in type III sources at any heliocentric distance: theo ries for type III bursts based on modulational instability or parametric de cay are therefore not viable in general. In contrast, the constraint on SGT can be satisfied and random phase ES decay can proceed at all heliocentric distances under almost all circumstances. (The contrary circumstances invo lve unusually slow, broad beams moving through unusually hot regions of the corona.) The analyses presented here strongly justify extending the existi ng SGT-based model for interplanetary type III bursts (which includes SGT p hysics, random phase ES decay, and specific electromagnetic emission mechan isms) into a general theory for type III bursts from the corona to beyond 1 AU. This extended theory enjoys strong theoretical support, explains the c haracteristics of specific interplanetary type III bursts very well, and ca n account for the detailed dynamic spectra of type III bursts from the lowe r corona and solar wind.