Short-term effects of solar storms in phytoplankton photosynthesis

The potential short-term influence of a solar radiation storm on microalgal photosynthesis is investigated. We focus on muons from the secondary cosmic rays at sea level, given their high penetrating power. According to NOAA’s classification of solar radiation storms, two kinds of solar storms are considered: moderate/strong and extreme. An exponential decay of muon fluxes down the water column and a direct proportionality between their penetrating power and energy are assumed. This allows obtaining a function of ionizing radiation to be embedded in a physical-mathematical model for photosynthesis previously modified by some of us to include particulate ionizing radiation. It is shown that moderate/strong solar radiation storms can cause a short-term depletion of photosynthesis of up to 61%, while this figure scales to 75% for extreme storms.


Introduction
Planetary bodies in the Milky Way receive considerable doses of ionizing radiation from the astrophysical origin (Melott and Thomas 2011). For example, stellar explosions (supernovae, gamma-ray bursts) deliver high-energy cosmic rays, which can hit the atmosphere and produce fluxes of atmospheric muons and other subatomic particles at ground level, underground, and underwater, deplete the ozone layer, and radioactivate the environment. These phenomena could have caused some of the life extinctions found in the geological record of planet Earth. On the other hand, biological mutations due to such ionizing radiations could have enhanced the fast appearance of new species after the extinctions.
In this paper, we focus on a less energetic but more frequent situation: solar storms. Since they follow a cycle of approximately 22 years (11 years with a given polarity of the Sun's magnetic field and the remaining 11 with the re-verse polarity), several researchers have suggested consequent cyclical biological effects on Earth, mediated by several mechanisms: geomagnetic storms, perturbations of atmospheric chemistry, etc.
Secondary cosmic rays delivered at the planetary surface due to solar storms are a cocktail of particles (protons, neutrons, muons, neutrinos). The issue that neutrinos can cause biological effects is still very controversial, so in this work, we investigate the potential effects on phytoplankton photosynthesis of the particles having the second place in penetrating power (after neutrinos): muons. In fact, several studies acknowledge the high penetration power of high-energy muons, quoting that they can travel through hundreds of meters in the ocean water column. In a former paper (Rodríguez-López et al. 2018), several of us reported the first results on this, using a preliminary modification of a mathematical model for photosynthesis to include the effects of ionizing radiations. In this paper, we report the short-term influence on phytoplankton photosynthesis that a flux of muons coming from a solar storm could do, but now using a more refined modification of the above-mentioned model for photosynthesis (Rodríguez-López et al. 2021).

Materials and methods
We considered the NOAA space weather scales (https:// www.swpc.noaa.gov/noaa-scales-explanation), which di-R. Cardenas rcardenas@uclv.edu.cu vides solar storms into three kinds: radio blackouts, geomagnetic and radiation storms. For our study, based on radiational damages, the most useful are radiation storms, which in turn are classified into extreme (S5), severe (S4), strong (S3), moderate (S2), and minor (S1). They might cause ground-level enhancements (GLE) of ionizing radiation. As an example, we take the September 1989 GLE, the greatest of the space era. This event was detected by surface and some underground muon telescopes indicating the presence of particles with energies up to 30 GeV (Lovell et al. 1998). It classifies as an extreme radiation storm of NOAA space weather scales (https://www.swpc.noaa.gov/ noaa-scales-explanation). To estimate its short-term effect on phytoplankton photosynthesis, we considered a 25% increase in muon flux during the first hour (12:00-13:00 UT) of the muon enhancements as seen in the muon detectors of Deep River and Inuvik. As seen from Fig. 1 in (Lovell et al. 1998), this seems to be a reasonable choice, additionally confirmed by data in Table 2. We also considered a 10% increase in muon flux and average energy, something to be expected in a strong (S3) or moderate storm (S2). It should be emphasized that the appearance of GLE depends not only on storm intensity but also on rigidity cutoff values, etc. Therefore, a severe storm could not cause a GLE, while a moderate storm could cause it.
To quantify the action of solar storms, we used a modification, recently proposed by some of us, of the so-called E model of photosynthesis (Rodríguez-López et al. 2021): where P is the photosynthesis rate at depth z, P S is the maximum possible photosynthesis rate, E PAR (z) is the irradiance of photosynthetically active radiation (PAR) at depth z, E S is a parameter accounting how efficiently the species uses PAR, E * UV (z) is the irradiance of ultraviolet radiation (UV), convolved with a biological action spectrum measuring how much each UV wavelength inhibits photosynthesis (the reason for the asterisk), and f ir (z) is the function formally introduced by some of us in (Rodríguez-López et al. 2021) to represent the influence of ionizing radiation. To account for the effects of UV on photosynthesis, we used a biological action spectrum typical of temperate phytoplankton (Neale 2014, personal communication).
The irradiances of PAR and UV at sea level were calculated with the radiative transfer code Tropospheric Ultraviolet and Visible, developed at the National Centre for Atmospheric Research of USA, free for download (https://www2.acom.ucar.edu/modeling/troposphericultraviolet-and-visible-tuv-radiation-model). It was assumed a solar zenithal angle of 45 degrees (moderate radiational regime), an ozone column of 300 Dobson units, an ocean albedo of 0,065, a cloud layer between 4 and 5 km above sea level with an optical depth of 0,00 (clear sky conditions), aerosols with an optical depth of 0,235 and a single scattering albedo of 0,990. The radiation transfer model in the atmosphere was pseudo-spherical with two streams. The radiation transfer model in the ocean included Lambert-Beer's law of Optics: where E(λ, z) are the spectral irradiances at depth z, E(λ, 0 − ) are the spectral irradiances just below the ocean surface, and K(λ) are the (wavelength-dependent) attenuation coefficients, which were taken from Jerlov's reference tables (Jerlov 1976) and further interpolated according to (Peñate-Alvariño et al. 2010). To get a wide range of potential responses, we used ocean optical types I and III, which are the clearest and darkest in Jerlov's classification. For the same reason, calculations were also made for coastal waters C1 and C9 of the above-mentioned classification. In a further study, we intend to include freshwater ecosystems. We notice that the water types only have an effect on photons (PAR and UV), not on muons.
The increments in muon flux and average energy were first treated separately to weigh their relative importance and then were considered together. As in (Rodríguez-López et al. 2018), the penetration of muons in the ocean was modeled through: where I 0 and I (z) are the particle fluxes (m −2 ) at the ocean surface and depth z, respectively; ρ is the density of water, and l is a parameter measuring the penetrating efficiency of the particles of ionizing radiation (the bigger l, the more penetrating the particle). In this first modeling, it was not considered the disintegration of muons on their way down the water column, and it was assumed that the penetrating power depends linearly on their average energy E : The average energy E SS of muons from solar storms can be written as: where m is a proportionality constant. Thus, the penetrating power l SS of "solar" muons can be stated as follows: Following an ansatz formally analogous to the one used in (Atri and Melott 2011;Rodríguez-López et al. 2013), we propose as the function of ionizing radiation: where the subscript ss means the scenario of the solar storm. Applying equation (6) to (7), we get: For our calculations, we used l = 10 4 kg/m 2 , a typical value for muons from ordinary cosmic rays (Rodríguez-López et al. 2013, 2018. On the other hand, research on muon dosimetry in nonhuman samples is an open issue. However, there are hints that the calculation of effective doses needs to be revisited (Overholt et al. 2015). We calculated the energy E, which a muon would deposit in cells of phytoplankton of several cell diameters d, using the equation: where ρ is the cell density (mostly water), and P is the muon-stopping power in the water. The values of the stopping power of muons in different materials can be found in (Groom et al. 2001).

Results and discussion
For a muon of 3 GeV of energy, quite typical of ordinary cosmic rays, the energy it would deposit while traveling through phytoplankton cells of extreme diameters was calculated using equation (9). Diameters of 0,2 µm (picoplankton) and 2000 µm (mesoplankton) were considered. The energies deposited turned out to be 46 eV and 460 keV, respectively. Moreover, muons from a solar storm would have a higher average energy. On the other hand, it is well known that ultraviolet radiation inhibits photosynthesis. However, ultraviolet photons that our current atmosphere allows to reach the surface of the planet have much less energy (wavelength 280 nm or higher, energy of 4,43 eV or less). Therefore, it sounds plausible to expect some inhibition of photosynthesis from muons from solar storms, though the exact mechanism is unknown. Thus, we apply our formalism presented in the previous section to quantitatively assess the potential inhibition of photosynthesis by a moderate (S2, S3) and an extreme solar radiation storm. The following radiational scenarios were considered: a) the solar storm increments muon flux at sea level up to 10% and 25%, b) the solar storm increments average muon energy at sea level up to 10% and 25% and, c) the solar storm increments both muon flux and average muon energy at sea level up to 10% and 25%.
For the sake of compactness, we only show the plots for the third situation with an increment in muon flux and average energy of 10% ( Fig. 1 to Fig. 4). However, we summarize the results in Table 1. Tables 1 and 2 present relative reductions in photosynthesis at depths from 0 to 100 meters since, in most situations, photosynthesis rates below 100 meters were negligible. It can be seen that, in general, the darker waters will be less affected. This is to be expected, as usually dark waters are more protected against radiational phenomena. On the other hand, in most cases, the increases in average muon energy and muon flux will have relatively similar effects on photosynthesis for moderate/strong storms, while the increase in muon energy is more influential for most cases in extreme storms.

Conclusions
Using our mathematical model to account for the influence of ionizing radiations (such as muons), we found that solar radiation storms can cause a significant short-term depletion of phytoplankton photosynthesis. It was shown that, in general, darker waters would be less affected. Our results especially apply to temperate phytoplankton, as the biological action spectrum was obtained for this kind of microalgae. This short-term depletion does not necessarily mean a high lethality, as photosynthesizers can live for a given time without performing photosynthesis, depending on the species. This study focused on ocean and coastal waters; in the near future, we are considering including freshwater ecosystems.
Author contributions Rolando Cardenas devised the general conception of the work, participated in the calculations and interpretation of results, and wrote the main manuscript text. Madeleine López-Águila, Lien Rodríguez-López and Lisdelys González-Rodríguez participated in the calculations and interpretation of results, and reviewed the manuscript. Javier Borges-Márquez provided the method to calculate the energies (dosis) deposited by muons in phytoplankton cells.
Funding No special funding received, just the salaries earned in their respective institutions.
Data Availability Not applicable.

Declarations
Competing interests The authors declare no competing interests.