Two atmospheric responses to simulated astrophysical ionizing radiation events significant to life on Earth are production of odd-nitrogen species, especially NO2, and subsequent depletion of stratospheric ozone. Ozone depletion increases incident short-wavelength ultraviolet radiation (UVB, 280-315 nm) and longer (>600 nm) wavelengths of photosynthetically available radiation (PAR, 400-700 nm). On the other hand, the NO2 haze decreases atmospheric transmission in the long-wavelength UVA (315-400 nm) and short-wavelength PAR. Here, we use the results of previous simulations of incident spectral irradiance following an ionizing radiation event to predict changes in terran productivity focusing on photosynthesis of marine phytoplankton. The prediction is based on a spectral model of photosynthetic response, which was developed for the dominant genera in central regions of the ocean (Synechococcus and Prochlorococcus), and on remote-sensing-based observations of spectral water transparency, temperature, wind speed, and mixed layer depth. Predicted productivity declined after a simulated ionizing event, but the effect integrated over the water column was small. For integrations taking into account the full depth range of PAR transmission (down to 0.1% of utilizable PAR), the decrease was at most 2-3% (depending on strain), with larger effects (5-7%) for integrations just to the depth of the surface mixed layer. The deeper integrations were most affected by the decreased utilizable PAR at depth due to the NO2 haze, whereas shallower integrations were most affected by the increased surface UV. Several factors tended to dampen the magnitude of productivity responses relative to increases in surface-damaging radiation, for example, most inhibition in the modeled strains is caused by UVA and PAR, and the greatest relative increase in damaging exposure is predicted to occur in the winter when UV and productivity are low.