A Supernova at 50 pc: Effects on the Earth's Atmosphere and Biota

There are no detections of prompt gamma-ray photons from SNe II. A type IIP is thought to be an explosion inside an extended envelope, which converts much of the energy to visible light. As in Thomas et al. (2016), we find that gamma-ray and X-ray fluxes are too small for substantial effects, in this case, by at least two orders of magnitude. It seems that an SN IIP would have to be at about 5 pc distance in order to have significant effects from these sorts of radiations. (It may be worth noting that Gehrels et al. 2003 estimated a lethal distance of 8 pc, using only photons for the estimate.) An event at 5 pc would likely be only at Gy intervals (Melott & Thomas 2011).

Spectra available for SN2013ej and SN2012aw extend to the hard UV. Scaled to 50 pc distance, the irradiance would be approximately 4 × 10⁻³ W m⁻² at the top of the atmosphere. This is several orders of magnitude smaller than the solar UV irradiance at the top of the atmosphere and thus is unlikely to have any significant impact on the atmosphere or significantly increase UV irradiance at Earth's surface.

There is a large body of evidence that enhanced illumination at night, especially in blue, is detrimental in a number of different ways to many different types of organisms; in 2015 the journal Philosophical Transactions of the Royal Society B devoted an entire issue to this topic (Gaston et al. 2015). Exposure to light during a normally dark period disrupts circadian rhythms, leading to loss of sleep, fatigue, changes in behavior, and other impacts detrimental to individuals and populations (Foster & Kreitzmann 2004; Longcore & Rich 2004; LeGates et al. 2012; Raap et al. 2015; Dominoni et al. 2016). Salmon (2003) and Witherington (1997) discuss disruptions in sea turtle reproduction caused by artificial lighting along beaches. Changes in tree frog foraging behavior have been observed at illuminations above 10⁻³ μW cm⁻² (Longcore & Rich 2004). Sky-glow light pollution has also been associated with disruption of reproduction in frogs and salamanders (Jaeger & Hailman 1973; Buchanan 1993; Rand et al. 1997), coral reef invertebrates (Sweeney et al. 2011), marsupial mammals (Robert et al. 2015), and birds (Kempenaers et al. 2010). Effects have even been noted in plants (Bennie et al. 2016).

Nighttime exposure to artificial lighting has been linked to cancers in animals, including rats (Vinogradova et al. 2009) and humans, including breast cancer (Schernhammer et al. 2001; Stevens 2009) and prostate cancer (Kloog et al. 2009). Evidence also supports a link between nighttime illumination and suppression of immune systems (Bedrosian et al. 2011; Arjona et al. 2012).

Many of the physiological changes associated with nighttime lighting appear to be connected to melatonin production and includes insects (Foster & Kreitzmann 2004; Haim & Zubidat 2015; Jones et al. 2015). Abundant evidence implicates light with wavelengths between 400 and 500 nm in these impacts, and others, both at night and otherwise (Brainard et al. 1984; Lockley et al. 2003; Vandewalle et al. 2007; Zaidi et al. 2007; Wood et al. 2013; Brüning et al. 2016; Marshall 2016).

Brainard et al. (1984) found that irradiance of 0.186 μW cm⁻² of "cool white" fluorescent light caused a decrease in pineal melatonin production in the Syrian hamster (Mesocricetus auratus) and that natural full moonlight irradiance as low as 0.045 μW cm⁻² caused pineal melatonin suppression in some animals, but not all. Lockley at al. (2003) found that 460 nm light at 12.1 μW cm⁻² irradiance caused a suppression of melatonin in humans, while a similar irradiance at 555 nm did not have a similar effect. Wood et al. (2013) found significant melatonin suppression in humans with 57–59 μW cm⁻² of light between 450 and 475 nm.

We examined available spectra of several SNe IIP, including 1999em (Hamuy et al. 2001), 2005cs (Bufano et al. 2009), SN2012aw (Bayless et al. 2013), 2013ej (Valenti et al. 2014); spectral data were downloaded from the Weizmann Interactive Supernova data REPository (http://wiserep.weizmann.ac.il/). After scaling each spectrum to represent a supernova at 50 pc, we find that the irradiance between 400 and 500 nm is roughly between 0.12 and 0.24 μW cm⁻². This is comparable to the lower irradiance values shown to have some effect in animals, but significantly smaller than the values used in human melatonin suppression studies.

To summarize, some physiological effects of blue light in the night sky would be significant for a few weeks. Otherwise, visible and UV photons are of negligible importance.

The propagation of CRs in the Galaxy is determined by the regular and the turbulent component of the GMF. Berezinskii et al. (1990) is an excellent introduction and reference to the physics of CR propagation. The turbulent part of the magnetic field can be characterized by the power-spectrum P(k) and the correlation l_c of its fluctuations with wavenumber k. Assuming a power law $P(k)\sim {k}^{-\alpha }$ for the spectrum, the maximal length L_max of the fluctuations, and the correlation length l_c are connected by l_c = (α–1) L_max/(2α). Moreover, if the turbulent field is isotropic and the regular field can be neglected, then the propagation of CRs can be described by an energy dependent scalar function, the diffusion coefficient D(E): diffusion becomes isotropic if CRs propagate on distances l ≫ L_max, while the energy dependence of the diffusion coefficient is determined by the slope α as D(E) ∼ ${E}^{2-\alpha }$ for energies E ≪ E_cr. Here, the critical energy is E_cr, defined by R_L(E_cr) = l_c with R_L as the Larmor radius of the charged CR. Thus the condition E ≪ E_CR ensures large-angle scattering, while the requirement of l ≫ L_max guarantees that features of anisotropic diffusion are washed out.

Several detailed models for the regular component of the GMF exist and two of the most recent and detailed ones are the Jansson & Farrar (2012a, 2012b) and the Pshirkov et al. (2011, 2013) models. Giacinti et al. (2015) compared both models and found that they lead qualitatively to the same predictions for CR propagation. An important constraint on CR propagation models comes from ratios of stable primaries and secondaries produced by CR interactions on gas in the Galactic disk. In particular, the Boron/Carbon ratio in the CRs has recently been measured by the AMS-02 experiment up to the rigidity 2.6 TV (Aguilar et al. 2016) and agrees nicely with the expectations for Kolmogoroff diffusion, α = 5/3. Using the Jansson–Farrar model, Giacinti et al. (2015) found that the B/C ratio can be reproduced choosing as the maximal length of the fluctuations L_max = 25 pc and α = 5/3, if the turbulent field is rescaled to one-tenth of the value proposed by Jansson & Farrar (2012a, 2012b). For this choice of parameters, CR propagation in the Jansson–Farrar model reproduces a large set of local CR measurements and we will use this choice as our case A. Note also that, while l/L_max = 2 only marginally satisfies the condition l ≫ L_max, the dependence of CR propagation on the concrete realization of the turbulent field is negligible because of the dominating regular field.

In case A, we calculate the trajectories of individual CRs (emitted isotropically by the SN) using the code described and tested in Giacinti et al. (2012), which uses nested grids. For the calculation of the local CR flux, we have divided the nearby Galaxy into cells and saved the length of CR trajectories per cell. Since we are interested here in a nearby SN at the distance of 50 pc, we increased the number of cells compared to Kachelrieß et al. (2015). We divided the Galactic plane into a non-uniform grid with cell size 20 pc × 20 pc at the position of the SN, which gradually increases to 100 pc × 100 pc at distances more than 500 pc. The vertical height of these cells was chosen as 20 pc. This allowed us to simultaneously calculate the flux at various places with differing perpendicular distance to the regular magnetic field line, which goes through the SN. The maximal flux at Earth is obtained if a magnetic field line connects the SN and the Earth. In contrast to Thomas et al. (2016), we study now (in Case A) the case where an SN has the maximal impact on the Earth and place therefore the Earth on the GMF line going through the SN.

At present, the Earth is located in the Local Bubble, a region with diameter 100–200 pc characterized by a local under-density of matter. This bubble was excavated by stellar winds and SNe explosions. It is natural to assume that these plasma flows also partly expelled the regular and turbulent magnetic field. However, neither simulations for the creation of the Local Bubble, which start from a realistic GMF model, nor measurements of the magnetic fields inside the Local Bubble exist. One may speculate that the reduction of the turbulent field found by Giacinti et al. (2015) is partly a local effect caused by the Local Bubble.

Alternatively, one may assume that the SN explosion creating the Local Bubble had a more drastic effect on the local GMF structure, expelling the regular field almost completely and reducing the strength of the turbulent field. As in case B, we assume a purely turbulent magnetic field with strength B = 0.1 μG, as suggested, e.g., by Avillez & Breitschwerdt (2005). Since the regular field vanishes, CRs propagate isotropically and we can apply the diffusion approximation with D(E) = D₀ (E/E₀)^1/3, D₀ = 2 × 10²⁸ cm² s⁻¹, and E₀ = 10 GeV. The CR density n from a bursting source is then given by

$$\begin{eqnarray}&&n(E,r,t)=Q(E)/({\pi }^{3/2}\,{{r}_{\mathrm{diff}}}^{3})\exp (-{r}^{2}/{{r}_{\mathrm{diff}}}^{2}),\end{eqnarray} \tag{ 1 }$$

where Q(E) is the source spectrum and r_diff the effective diffusion distance, which is given by ${{r}_{\mathrm{diff}}}^{2}=4$ D t. The CR intensity I then follows as I = (c/4π) n. In both cases, we assume that the SN injects instantaneously inects the CR energy 2.5 × 10⁵⁰ erg with source spectrum $Q(E)\sim {E}^{-2.2}$ exp (−E/E_c) and cutoff energy E_c = 1 PeV.

The injection would be delayed until the remnant expands enough to release the CR; then the release would not be instantaneous but the approximation is adequate for our purposes. The total CR energy assumed is consistent with modern estimates of typical values for SNe II (Higdon et al. 1998; Kasen & Woosley 2009). It is effectively much larger than that of Gehrels et al. (2003), who approximated the CR flux 10 pc from a supernova by scaling up the normal Galactic cosmic-ray (GCR) flux up by a factor of 100, partly motivated by the estimated energetics of SN1987a (e.g., Honda et al. 1989). We find from our explicit propagation computations given a typical supernova at 50 pc that this value is exceeded at that distance in cases A and B below. However, the CR flux could be arbitrarily low in the case of a coherent magnetic field transverse to the line of sight. Thus, the past magnetic field orientation is extremely important, given the primary importance of CR in determining the result.

The resulting CR intensities on Earth are shown in Figure 1(a) for case A and Figure 1(b) for case B respectively. In Figure 1, we plot flux*E² so that the area under the curve is proportional to the total energy between limits. Times are measured from the release of the CR, minus the photon travel time to the Earth. Case A here shows a very large increase, which is caused by the assumption of a field line connecting the Earth with the supernova, and cannot be compared with anything in Thomas et al. (2016). Case B here is consistent with a nearly fivefold increase over Case C in Thomas et al. (2016), not far off from an inverse-square scaling.

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It can be seen that the major difference from the present-day CR flux is the large amount of energy deposited by CRs in excess of a TeV. Due to the strong energy-dependence of the CR penetration in the atmosphere, this implies penetration and ionization at much greater atmospheric depths than is usual for CRs or flux from solar events (e.g., Melott et al. 2016). Discussion of the effects follows, beginning with atmospheric computation procedures.

Atmospheric ionization can have important impacts on chemistry. Odd-nitrogen oxides (NO_y) are produced, leading to the destruction of the stratospheric ozone and subsequent rainout of HNO₃ (Thomas et al. 2005). Ionization by SN CRs in this work was computed using tables from Atri et al. (2010), generated by CORSIKA. CORSIKA (COsmic Ray SImulations for KAscade) is a package combining high- and low-energy interaction models with a transport scheme for CRs in air. The interaction models are tuned to all kinds of accelerator and CR data. The version used for atmospheric ionization was EPOS 1.61, UrQmd 1.3. This gives an ionization rate (ions cm⁻² s⁻¹) as a function of altitude for different primary proton energies. The tables in Atri et al. (2010) give ionization for primaries with energy from 300 MeV to 1 PeV, for 46 altitude bins, from the ground to 90 km. In this work, we used primary proton energies between 10 GeV and 1 PeV.

Atmospheric chemistry modeling was performed using the Goddard Space Flight Center (GSFC) 2D (latitude–altitude) chemistry and dynamics model. This model has been extensively tested for cases similar to the work presented here (Thomas et al. 2005, 2007, 2008; Ejzak et al. 2007). The model runs from the ground to 116 km in altitude, with approximately 2 km altitude bins, and from pole-to-pole in 18 bands of 10° latitude each. The model includes 65 chemical species, 37 transported species and "families" (e.g., NO_y), winds, small-scale mixing, solar cycle variations, and heterogeneous processes (including surface chemistry on polar stratospheric clouds and sulfate aerosols). We use the model in a pre-industrial state, with anthropogenic compounds (such as CFCs) set to zero. It is important to note that some parameter values in the model (e.g., large-scale winds and temperature fields) are prescribed and tied to modern-day values. While this prevents accurate simulation of the exact conditions at other geologic eras, our results are limited to comparisons between runs with and without external influence, rather than absolute quantities, which should remove most uncertainties.

The ionization rate as a function of altitude for a particular CR case is generated by convolving the CR flux (essentially, the number of incident CR protons at each energy) with the tables from Atri et al. (2010). The results are then translated into production of NO_y, using 1.25 NO_y molecules per ion pair (Porter et al. 1976) at all altitude levels. While not significant for this application, we also include production of HO_x as described in Thomas et al. (2005). The chemical family production rate is read into the GSFC atmospheric chemistry model and the model was then run for 10 years until steady-state conditions were reached, simulating a quasi-steady flux of CRs. We then examine the concentrations of various constituents, especially O₃, comparing a run with SN CR ionization input to a control run without that ionization source.

In both cases, ionization in the lower troposphere exceeds that from normal galactic CRs (Figure 2). Both cases get a significant prompt CR flux within 100 years. In case A, we find a factor of about 10³ increase in ionization, right down to the ground. In case B, we find a factor of about 50 increase in ionization, also down to the surface. These increases, as compared with results in Thomas et al. (2016), are consistent with and as expected from the CR results described near the end of Section 3.1. Increased ionization greater than or comparable to that caused by GCRs could be expected to persist for about 10 kyr in case B, or 1 Myr in case A. Of course, if there was a transverse ordered field, no such effects would be seen. Large ionization should cause an increase in lightning (Erlykin & Wolfendale 2010; Mironova et al. 2015). There have been controversial claims of a connection between atmospheric cloud formation and CRs (Mironova et al. 2015; Svensmark 2015). Since there are many open questions in this research, we cannot offer a conclusion, except to state our results and hope that they offer an opportunity for further research to clarify the question.

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While a full analysis of the atmospheric chemistry changes induced by the SN CRs is beyond the scope of this work, we will discuss some results of the modeling described above. Ozone (O₃) is catalytically depleted by oxides of nitrogen (e.g., Thomas et al. 2005). The loss of ozone in the stratosphere has for decades been viewed as the main source of damage to the biota from astrophysical ionizing radiation events (e.g., Gehrels et al. 2003). In Figure 3, we show the globally averaged change in O₃ column density, comparing a run with SN CR ionization included to a run without that added ionization. Here we show both cases A and B, at one time each. The times chosen (100 years for case A, 300 years for case B) correspond to those with the greatest increase in ionization in the stratosphere, where the greatest impact on O₃ column density occurs. Thus, the results in Figure 3 represent the maximum change in O₃ we would expect from the SN CRs.

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When a new ionization flux is introduced, it takes the atmosphere three to five years to equilibriate at the new value (Ejzak et al. 2007). However, in our cases, the changes in CR flux are generally much more gradual than that. In Figure 3, we show plots of the globally averaged change in O₃ column density, assuming the sudden onset of the peak CR flux value found in Figure 1 to a normal atmosphere. Thus the depletion reached asymptotically after a few years should represent the depletion level from a slowly varying CR flux. In case A (at 100 years), this is about 66% depletion; in case B (at 300 years), it is 25%; in the case of a transverse magnetic field, it should be negligible. We note that our case B at 50 pc is roughly comparable to the values found by Gehrels et al. (2003) for a 10 pc distance; thus we have significantly revised upward the CR atmospheric effects from that publication. For reference, recent anthropogenic O₃ depletion is a few percent, globally averaged.

Reduction in O₃ column density is important for life on Earth's surface and in the oceans since O₃ is a strong absorber of solar UV. Past work modeling effects of nearby gamma-ray bursts found around 35% globally averaged depletion (Thomas et al. 2005), which was suggested to be the "mass extinction level." More recent work (Thomas et al. 2015; Neale & Thomas 2016) has shown that this may be overly pessimistic and that the biological impact is more complex, depending heavily on particular types of organisms and impacts considered. Nonetheless, globally averaged depletions on the order of 60% surely would have an impact.

While a full analysis of the biological impact is beyond the scope of this work, we can make a simple estimate of the increase in biologically active solar UV due to a reduction in O₃ column density. Madronich et al. (1998) developed a power-law relationship between various biological effects and O₃ column density: UV_bio ∼ (O₃)^−RAF, where RAF is a "radiation amplification factor," which varies depending on the specific effect considered. Skin damage (erythema) and skin cancer have RAF values around 1.5, while DNA damage has RAF around 2. We can estimate an enhancement in biologically damaging UV using (O₃'/O₃)^−RAF, where the prime indicates the O₃ column density in the SN case. For case A at 100 years the ratio is about 0.32; with RAF values 1.5 and 2.0, the resulting increase in UV is about 5–10 times normal, respectively. For case B, the increase is about 1.5 times.

While the resulting biological effects are complicated and the ecological impact of any such effects are uncertain, it seems likely that a 5–10 times increase in biologically active UV would have a major impact. It is usually assumed that a globally averaged decrease of 30%–50% would have an impact of mass extinction level. Based on that assumption and modeling performed by work by Gehrels et al. (2003), the "lethal distance" for an SN has been estimated at about 10 pc. If this is an appropriate measure of extinction potential, then our results move this "lethal distance" to 50 pc or more, but only for interstellar conditions similar to that in our case A. For conditions similar to our case B, that distance would be somewhat less than 50 pc, but still larger than 10 pc.

There was not a major mass extinction at the end of the Pliocene. Why not? There are several possibilities. (1) There was an ordered component of the GMF transverse to the line of sight to the supernova(e). This would reduce the CR flux, possibly bringing it down to a negligible enhancement in the extreme limit. We consider this unlikely, due to the energetics of the Local Bubble, but it is possible. (2) The distance estimate used here was wrong; all acknowledge considerable uncertainty in the distance estimates. (3) There was a disordered magnetic field as in case B. This is the most likely condition given the recent ⁶⁰Fe data. In this case, there would be a 50% increase in UVB, dangerous but not major mass extinction levels. (4) Recent detailed studies of phytoplankton productivity in an environment simulating astrophysical ionizing radiation changes in atmospheric transmission have suggested that effects are not as strong as assumed in the past, for a variety of reasons (Neale & Thomas 2016). That work studied only primary productivity, but at the least it indicates that the situation is more complicated than previous work assumed, and that more study is needed before setting a "lethal distance" for supernovae. Our results support the need for more study of this question, since no major mass extinction is observed to coincide with the time of the supernovae. Moderate UV effects could have played a role in the moderate extinction observed then.

The nitrogen oxides produced by ionization in the atmosphere are removed over a timescale of months to years by rain/snow-out of HNO₃. At steady state in our modeling the global annual average deposition above background is about 0.5 g m⁻² for case A at 100 years, and 0.03 g m⁻² for case B at 300 years. These values are about 80 times and 5 times, respectively, that generated by lightning and other nonbiogenic sources in today's atmosphere (Schlesinger 1997). Such an increase is unlikely to have a detrimental effect (Thomas & Honeyman 2008) and in fact would probably be beneficial by providing nitrate fertilizer to primary producers. Thomas & Honeyman (2008) and Neuenswander & Melott (2015) found that deposition of the order of 0.09 g m⁻² following a GRB would likely have a small fertilizer effect on both terrestrial and aquatic life. Therefore, we expect that the deposition found in both cases considered here is very likely to have such an impact.

The majority of particles produced in CR showers do not penetrate to the ground level. These particles lose energy through ionizing the atmosphere and do not reach sea level in sufficient numbers to produce an increase in the average radiation level. There are two species of particles that produce sufficient amounts of cosmogenic radiation at sea level to be easily detected: muons and neutrons.

Muons penetrate to sea level and even below sea level through ocean water and rock. Muons are primarily produced high in the atmosphere because hadron–hadron interactions of CRs produce pions that quickly decay into muons. Muon fluxes at ground level were found by convolving the primary spectra with the table of Atri & Melott (2011). The tables of Atri & Melott (2011) were produced again using CORSIKA, EPOS 1.99, and FLUKA 2008. To reduce computation time, the energy cut for the electromagnetic component was set at 300 MeV. This value should be adequate to produce all hadronic interactions from protons, while greatly reducing the computational load (Atri & Melott 2011). After convolution, these tables produce a muon spectrum at the ground level, which can then be used to find the radiation dose. Radiation doses due to muons have not been calculated for a large range of specific energies as is needed for this work, so approximations must be used. To find the dose from our target muon flux, the energy lost by high energy muons as they travel through water was used (Klimushin et al. 2001). This approximation assumes that the energy lost by muons as they travel through water is similar to the energy lost by traveling through biologic matter. Muons behave similarly to a heavy electron, and in many cases can be approximated as such. For this reason, we use a radiation-weighting factor of 1, which is the same as an electron. Some research suggests that this approximation is inadequate for doses at skin level, but is adequate for the dose experienced by deeper organs (Siiskonen 2008). Through these two approximations, we develop an approximate radiation dose for cosmogenic muons from a given primary spectrum. When the average background CR primary spectrum is used, this method agrees within statistical error with the average radiation background from muons.

Neutrons are predominantly created higher in the atmosphere; however, their lack of charge allows them to penetrate substantially lower before thermalization. Neutrons interact through collisions with nuclei, losing energy with each collision. Once reaching thermal speeds, neutrons remain in the region in which they reach this speed, often in the stratosphere. Some neutrons reach this speed near or at sea level, producing a radiation dose for organisms on the ground. Neutron fluxes at ground level were found by convolving the primary spectrum through the tables of Overholt et al. (2013). These tables were produced from CORSIKA simulations identical to those used to find the muons, with the additional step of using MCNP (Monte Carlo N-Particle Simulator) to simulate low-energy neutron interactions (Overholt et al. 2013). Here MCNP was used to simulate all neutrons below 50 MeV with order of magnitude bins in order to produce sufficient particle flux for minimized statistical error (Overholt et al. 2013). Radiation doses per neutron were found by taking order of magnitude averages of the ionizing radiation dose per neutron from Alberts et al. (2001). These averages were then multiplied by the neutron fluxes at ground level to find the total neutron radiation dose.

We have determined the flux of muons on the ground as a function of energy. The detailed spectrum is not extremely important because the dose for muons only varies slowly with energy. We are normally exposed to an average of 56 muons (m² sr s)⁻¹. In the same units, at 100 years, in case A, the total flux is ∼4.5 × 10⁴; in case B it is ∼3.5 × 10³. The energy spectrum of the muons incident at sea level at this time is shown in Figure 4.

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In Table 1, we show the muon and neutron doses on the ground for Cases A and B. We must compare the increase due to muons and/or neutrons to the total background radiation dose. The radiation dose is capable of producing damage to terrestrial biota; emphatically in case A. The radiation doses exceed the average worldwide radiation background dose from all sources (2.4 mSv yr⁻¹, UNSC 2008) for hundreds to thousands of years, and would be likely to cause increased cancer risk and mutations. The ICRP (International Commission on Radiological Protection) models the risk of getting cancer increases by 5.5% for every 1 Sv of exposure (ICRP 1991). By comparison, the ICRP finds that an annual radiation dose of 1 mSv will only result in a very small health risk after a lifetime of exposure at this level (ICRP 1991). The dose sustained on the Earth during the time period following a supernova would build up a dose of 1 Sv in a time period from about two years (in Case A), to about 30 years (in Case B). Muons are more penetrating than most terrestrial radiation sources, so the change would also be more important in large organisms. Increasing the cancer risk of short-lived (<1 year) organisms by ∼5% and long-lived organisms by a larger factor could have detectable effects on the ecosystem as a whole. Figure 5 shows the time evolution of the dose from muons and neutrons, with horizontal bars to indicate the present level. The effect of neutrons is much less severe than muons. However, their high LET radiation does have the opportunity to produce more double strand DNA breaks, which can be the cause of more congenital malformations (Overholt et al. 2015). The time for return to normal levels is significantly different for Case A (upper bound of shaded region) and Case B (lower bound of shaded region). We note that the muon dose in Case B is about five times larger than the dose in Case C in Thomas et al. (2016). Due to different assumed magnetic field configuration in our Case A here, Case B is the only one that can be directly compared with our previous work, and does correspond approximately to simple inverse-square expectations—in fact better than might be expected in this diffusive approximation.

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We must consider the possibility of radioactivity on the ground. As discussed by Ellis et al. (1996), there are two primary sources.

Cosmogenic isotopes such as ¹⁰Be and ¹⁴C are generated by the actions of CRs in the atmosphere. Using the discussion of Ellis et al. (1996) and considering a source at ∼50 pc, we would expect of the order of 4 × 10⁵ atoms cm⁻² of radionuclides during the passage of CRs generated by events A or B.

Direct deposit of SN-generated isotopes from the $a\sim 10\,{M}_{\odot }$ event at 50 pc can be expected, according to Ellis et al. (1996) to deposit ∼a few×10⁶ atoms cm⁻² assuming that the interstellar medium has been previously cleared by another event (case B); if not, they estimate that the blast wave would stall at about 50 pc (case A). Amounts of various isotopes are tabulated in Ellis et al. (1996), Table 1. These amounts are too small to be significant for the environment, but the direct deposit amounts lie within a range of detection (e.g., Wallner et al. 2016). The 2.6 Ma age of the most recent event indicated by ⁶⁰Fe is too great to have any prospect of detection in ice cores.