Understanding Heating in Active Region Cores through Machine Learning I. Numerical Modeling and Predicted Observables

To adequately constrain the frequency of energy deposition in active region cores in the solar corona, systematic comparisons between detailed models and observational data are needed. In this paper, we describe a pipeline for forward modeling active region emission using magnetic field extrapolations and field-aligned hydrodynamic models. We use this pipeline to predict time-dependent emission from active region NOAA 1158 as observed by SDO/AIA for low-, intermediate-, and high-frequency nanoflares. In each pixel of our predicted multi-wavelength, time-dependent images, we compute two commonly-used diagnostics: the emission measure slope and the time lag. We find that signatures of the heating frequency persist in both of these diagnostics. In particular, our results show that the distribution of emission measure slopes narrows and the mean decreases with decreasing heating frequency and that the range of emission measure slopes is consistent with past observational and modeling work. Furthermore, we find that the time lag becomes increasingly spatially coherent with decreasing heating frequency while the distribution of time lags across the whole active region becomes more broad with increasing heating frequency. In a follow up paper, we train a random forest classifier on these predicted diagnostics and use this model to classify real AIA observations of NOAA 1158 in terms of the underlying heating frequency.