Physics of the Neupert Effect: Estimates of the Effects of Source Energy, Mass Transport, and Geometry Using RHESSI and GOES Data
The ``empirical Neupert effect'' (ENE) is the observed temporal correlation of the hard X-ray (HXR) flux FHXR(t) with the time derivative of the soft X-ray (SXR) flux ḞSXR(t) in many flares. This is widely taken to mean that the energetic electrons responsible for FHXR(t) by thick-target collisional bremsstrahlung are the main source of heating and mass supply (via chromospheric evaporation) of the SXR-emitting hot coronal plasma. If this interpretation were correct, one would expect better correlation between the beam power supply Pbeam(t), inferred from the HXR spectrum, and the actual power Pin(t) required to explain the SXR flux and spectrum, allowing for variations in both emission measure (EM) and temperature T, for radiative and conductive cooling losses, and for complexities of geometry like multiple loops. We call this the ``theoretical Neupert effect'' (TNE). To test if it is true that Pbeam(t) and Pin(t) inferred from data are better correlated than FHXR(t) and ḞSXR(t), we use an approximate approach for a simple single-loop geometry and rough estimates of the particle and energy transport and apply the model to RHESSI and GOES data on four flares. We find that if the beam low cutoff energy E1 is taken as constant, the correlation of Pbeam(t), Pin(t) is no better than that of FHXR(t),ḞSXR(t). While our modeling contains many approximations to cooling and other physics, ignored entirely from ENE data considerations, there seems to be no reason why their order-of-magnitude inclusion should make the TNE worse rather than better, although this should be checked by more accurate simulations. These results suggest that one or more of the following must be true: (1) fast electrons are not the main source of SXR plasma supply and heating, (2) the beam low cutoff energy varies with time, or (3) the TNE is strongly affected by source geometry. These options are discussed in relation to possible future directions for TNE research.