We present Lightning, a new spectral energy distribution (SED) fitting procedure, capable of quickly and reliably recovering star formation history (SFH) and extinction parameters. The SFH is modeled as discrete steps in time. In this work, we assumed lookback times of 0-10 Myr, 10-100 Myr, 0.1-1 Gyr, 1-5 Gyr, and 5-13.6 Gyr. Lightning consists of a fully vectorized inversion algorithm to determine SFH step intensities and combines this with a grid-based approach to determine three extinction parameters. We apply our procedure to the extensive FUV-to-FIR photometric data of M51, convolved to a common spatial resolution and pixel scale, and make the resulting maps publicly available. We recover, for M51a, a peak star formation rate (SFR) between 0.1 and 5 Gyr ago, with much lower star formation activity over the last 100 Myr. For M51b, we find a declining SFR toward the present day. In the outskirt regions of M51a, which includes regions between M51a and M51b, we recover a SFR peak between 0.1 and 1 Gyr ago, which corresponds to the effects of the interaction between M51a and M51b. We utilize our results to (1) illustrate how UV+IR hybrid SFR laws vary across M51, and (2) provide first-order estimates for how the IR luminosity per unit stellar mass varies as a function of the stellar age. From the latter result, we find that IR emission from dust heated by stars is not always associated with young stars, and that the IR emission from M51b is primarily powered by stars older than 5 Gyr.
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