Inclusion of ionizing radiation in a mathematical model for photosynthesis

Ionizing radiation of astrophysical origin might have played an important role in biological evolution during the long course of Earth's evolution. Several phenomena might have induced intense fluctuations in background ionizing radiation, such as highly energetic stellar explosions. There might also be anthropogenic causes for environmental radiation fluctuations, resulting from nuclear industry activities. The inclusion of these effects in a mathematical model for photosynthesis provides a useful tool to account for the damages of the above-mentioned phenomena in vegetal life. Mathematical models for photosynthesis typically only consider ultraviolet radiation and photosynthetically active radiation, as they have been a ubiquitous physical factor in the settlement of vegetal life. In this work a mathematical model for aquatic photosynthesis is modified, from first principles, to include the action of particulate ionizing radiation on the photosynthetic process. After assuming an ansatz allowing to separate damage/repair kinetics of ultraviolet and ionizing radiations, a treatable mathematical expression of the model is obtained. This generalized model is presented as a function of radiometric and photometric magnitudes, making it prone to calibration and useful to apply to aquatic ecosystems under radiational stress due to gamma-ray bursts, cosmic ray bursts, solar storms, or other sources of ionizing radiations.