It is not straightforward to evaluate the average SEP flux even for the modern instrumental epoch of direct space-borne measurements (e.g., Mewaldt et al., 2007). For example, estimates for the average flux of SEPs with an energy above 30 MeV (called f 30 henceforth) for individual cycles may vary by an order of magnitude, from 10 cm–2 s–1 for cycle 21 up to 70 cm–2 s–1 for cycle 19 (Reedy, 2012). Moreover, estimates of the SEP flux were quite uncertain during the earlier years of space-borne measurements because of two effects, which are hard to account for (e.g., Reeves et al., 1992; Tylka et al., 1997). One is related to the very high flux intensities of SEPs during the peak phase of events, when a detector can be saturated because of the dead-time effect (the maximum trigger rate of the detector is exceeded). The other is related to events with high energy solar particles, which can penetrate into the detector through the walls of the collimator or the detector, leading to an enhanced effective acceptance cone with respect to the “expected” one. Since the SEP fluence is defined by major events, these effects may lead to an underestimate of the average flux of SEPs. The modern generation of detectors are better suited for measuring high fluxes. The average f 30 flux for the last five solar cycles (1954 – 2006) is estimated at about 35 cm–2 s–1 (Smart and Shea, 2002; Shea et al., 2006).
The development of the method of cosmogenic isotopes makes it possible to estimate occurrence of extreme SEP events in the past. Some earlier attempts were inconclusive. For example, Usoskin et al. (2006b) found that a typical strong SEP event leaves no distinguishable signature in 14C but may be observed from ice core 10Be records. However, the question of the possible rare occurrence of extreme SEP events on the millennial time scale is important not only from the theoretical point of view, but also for assessment of radiation risks for space-borne missions, especially manned ones. What can be the strongest SEP event originated from the sun, how often they can occur? These questions need to be answered. Several attempts have been made to evaluate that from the cosmogenic isotope data (Lingenfelter and Hudson, 1980; Usoskin et al., 2006b; Webber et al., 2007), but the result was grossly uncertain (Hudson, 2010; Schrijver et al., 2012), mostly because of the large model uncertainties of the radionuclide production.
A new step forward has been done recently by Usoskin and Kovaltsov (2012), who analyzed two 14C and five 10Be records over the last millennia and searched for possible signatures of extreme SEP events.
While the response of 10Be to an SEP event is simply a 1 – 2-yr long peak, because of the simple atmospheric transport/deposition (see Section 3.3.3), the response of 14C has a typical shape shown in Figure 25 – with a sharp peak and exponential decay of the length of several decades, due to the carbon cycle (see Section 3.2.3). Usoskin and Kovaltsov (2012) checked all the available cosmogenic isotope data through the entire Holocene looking for a potential SEP signatures, and came up with a list of candidates of extreme SEP events and assessments of their strength (Table 3).
|1460 – 1462 AD||NGRIP(1460)||1.5 × 1010|
|Dye3 (1462)||9.7 × 109|
|1505 AD||Dye3||1.3 × 1010|
|1719 AD||NGRIP||1 × 1010|
|1810 AD||NGRIP||1 × 1010|
|8910 BC||IntCal09||2.0 × 1010|
|8155 BC||IntCal09||1.3 × 1010|
|8085 BC||IntCal09||1.5 × 1010|
|7930 BC||IntCal09||1.3 × 1010|
|7570 BC||IntCal09||2.0 × 1010|
|7455 BC||IntCal09||1.5 × 1010|
|6940 BC||IntCal09||1.1 × 1010|
|6585 BC||IntCal09||1.7 × 1010|
|5835 BC||IntCal09||1.5 × 1010|
|5165 BC||GRIP||2.4 × 1010|
|4680 BC||IntCal09||1.6 × 1010|
|3260 BC||IntCal09||2.4 × 1010|
|2615 BC||IntCal09||1.2 × 1010|
|2225 BC||IntCal09||1.2 × 1010|
|1485 BC||IntCal09||2.0 × 1010|
|95 AD||GRIP||2.6 × 1010|
|265 AD||IntCal09||2.0 × 1010|
|785 AD||IntCal09||2.4 × 1010|
|Dome Fuji||5.3 × 1010 †|
|M12||4 × 1010 †|
|1455 AD||South Pole||7.0 × 1010 †|
† Upper bound.
The list includes 23 candidates for extreme SEP events with the fluence F30 exceeding 1010 cm–2, viz. the greatest fluence observed for the space era in 1960 (Shea and Smart, 1990). Note that only two of these candidates appear in more than one series – the events of ca. 1460 AD and ca. 780 AD. The former had signatures in two annual 10Be series, NGRIP and Dye3. The later was observed in two 14C series, biennial M12 and 5-yr IntCal09, and in quasi-decadal Dome Fuji 10Be series. The quasi-decadal South Pole 10Be series does not show an increase ca. 780 AD placing an upper limit on the strength of the event.
We note that the event of ca. 775 AD was analyzed using biennial 14C data by Miyake et al. (2012), who suggested that the event was probably caused by -rays from an unknown nearby supernova. This event is confirmed by annual 14C data from a German oak tree (Usoskin et al., 2013). However, because of the use of an inappropriate carbon cycle model, Miyake et al. (2012) grossly (by a factor of 5) overestimated the corresponding 14C production, leading to the need of a supernova. Moreover, this leads to a strong disagreement between 14C and 10Be data sets, since this event is not observed in the South Pole record and is not exceptionally strong in the Dome Fuji record. However, if an appropriate model of the carbon cycle is used, the production of 14C appears in a reasonable range, being consistent with 10Be (Usoskin et al., 2013). Therefore, there is no need to involve such an exotic object as a nearby supernova whose remnants are unknown for us – the event of ca. 775 – 780 AD can be consistently explained by a extreme but not exceptional SEP event.
The integral probability distribution of the occurrence of strong SEP events, as revealed from the cosmogenic isotope data, is shown in Figure 26.
One can see that the break in the distribution marginally hinted in the directly observed SEP events at around F30 = (5 – 7) ×109 cm–2 (nonproportionally fewer strong events observed) is confidently confirmed by the cosmogenic isotope data. In particular, no event with F30 > 2 × 1010 cm–2 was found over the last 600 years using annually resolved 10Be data. It is noteworthy that the idea of an possible extreme Carrington SPE of 1859 AD (McCracken et al., 2001) is discarded (see also Wolff et al., 2012). On the longer time scale of 11 millennia, no event with F30 > 5 × 1010 cm–2 has been found. This gives a new strict observational constraint on the occurrence probability of extreme SPEs.
According to Usoskin and Kovaltsov (2012) practical limits can be set as F30 1, 2 – 3 and 5 × 1010 cm–2 (10, 20 – 30 and 50 times greater than the SEP event of February 23, 1956), for the occurrence probability of 10–2, 10–3, and 10–4 yr–1, respectively. The mean SEP flux is found as 40 (cm2 s)–1 in agreement with estimates from the lunar rocks. On average, extreme SPEs contribute about 10% to the total SEP fluence.
Since energy spectra of SEP and GCR are dramatically different, one may think of a natural spectrometer to separate their effects and thus evaluate their fluxes independently. A spectrometer that is able to separate cosmic rays is lunar (or meteoritic) rocks.
Figure 27 depicts an example of 14C measured in a lunar sample (Jull et al., 1998). The dotted line shows the expected production of radiocarbon by GCR. The production increases with depth due to the development of a nucleonic cascade in the matter, initiated by energetic GCR particles, similar to the atmospheric cascade. Less energetic particles of solar origin produce the isotope only in upper layers of the rock, since their low energy does not allow them to initiate a cascade. On the other hand, thanks to their high flux in the lower energy range, the production of 14C in the upper layers is much higher than that from GCR. Thus, by first measuring the isotope activity in deep layers one can evaluate the average GCR flux, and then the measured excess in the upper level yields an estimate for the SEP flux in both integral intensity and spectral shape. The result is based on model computations and therefore is slightly model dependent but makes it possible to give a robust estimate of the GCR and SEP in the past.
A disadvantage of this approach is that lunar samples are not stratified and do not allow for temporal separation. The measured isotope activity is a balance between production and decay and, therefore, represents the production (and the ensuing flux) integrated over the life-time of the isotope before the sample has been measured. However, using different isotopes with different life times, one can evaluate the cosmic-ray flux integrated over different timescales.
Estimates of the average SEP flux f 30 on different timescales, as obtained from various isotopes measured in lunar samples, are collected in Table 4. Based on isotopes with different life-times (see Table 4) one can evaluate the average flux of SEP on different time scale (see Figure 28). The average f 30 flux for the last five solar cycles (1954 – 2008) is consistent with the average flux estimated in the past for longer timescales from 103 to 107 years (cf. Reedy, 2002, 2012).
|Timescale||Method||Source||Reference||f 30 (cm–2 s–1)|
|1954 – 2008||measurements||space-borne||Reedy (2012)||35|
|104 yr||14C||lunar rock||Jull et al. (1998)||42|
|105 yr||41Ca||lunar rock||Fink et al. (1998)||56|
|5 × 105 yr||36Cl||lunar rock||Nishiizumi et al. (2009)||46|
|106 yr||26Al||lunar rock||Kohl et al. (1978)||25|
|106 yr||26Al||lunar rock||Grismore et al. (2001)||55|
|106 yr||10Be, 26Al||lunar rock||Michel et al. (1996)||24|
|106 yr||10Be, 26Al||lunar rock||Fink et al. (1998)||32|
|106 yr||10Be, 26Al||lunar rock||Nishiizumi et al. (2009)||24|
|2 × 106 yr||10Be, 26Al||lunar rock||Nishizumi et al. (1997)||35|
|5 × 106 yr||53Mn||lunar rock||Kohl et al. (1978)||25|
|2 × 106 yr||21Ne, 22Ne, 38Ar||lunar rock||Rao et al. (1994)||22|
However, this method is not able to provide an estimate of the occurrence rate of extreme SEP events. If one assumes that the entire average SEP flux is produced within one extreme event occurring at half of the isotope’s life-time ago (Reedy, 1996), an upper limit for the occurrence of extreme SEP events can be placed. This is an unrealistically extreme assumption, which may lead to an overestimate by many orders of magnitude, but it sets the very conservative upper limit which cannot be exceeded.
It has been discussed until recently that another quantitative index of strong SEP events (with F30 × 109 cm–2) might be related to nitrate () records measured in polar ice cores. The concentration of nitrates has been measured in polar ice from both the Southern (South Pole, e.g., Dreschhoff and Zeller, 1990) and Northern (Greenland, e.g., Zeller and Dreschhoff, 1995; Dreschhoff and Zeller, 1998) polar caps, depicting pronounced spikes associated with strong SEP events (McCracken et al., 2001). As a result of the analysis a list of large SEP events since 1560 and their fluences have been published (see Table 1 in McCracken et al., 2001) and widely used.
However, as shown by several independent recent studies (Wolff et al., 2012; Usoskin and Kovaltsov, 2012) on the example of the Carrington event (September 1859), the nitrate spikes are not related to SEP events. According to McCracken et al. (2001), the nitrate spike and the associated SEP event was the strongest in the entire record (F30 2 × 1010 cm–2). Wolff et al. (2012) have measured, with high resolution, nitrate content in 14 ice cores from Antarctic and Greenland for a few decades around 1859. Only one Greenland series depicts a spike which can be associated with the event, all other series have no signatures. Moreover, all similar spikes found in Greenland datasets are accompanied by chemical tracers (ammonium, formate, black carbon, etc.) clearly pointing to the anthropogenic source of nitrates – biomass burning plumes. No significant spikes have been found in the Antarctic records. Wolff et al. (2012) concluded that “Nitrate spikes cannot be used to derive the statistics of SEPs.” Another confirmation of this conclusion was made by Usoskin and Kovaltsov (2012), who calculated, from the F30 fluence proposed by McCracken et al. (2001) for the Carrington event, the 10Be production. If the Carrington SEP event was so strong, it would have necessarily left its clear signature in the annually resolved 10Be record, which however contradicts to the real data from NGRIP and Dye3 ice cores.
Thus, the nitrate record in polar ice cannot serve as an index of SEP events. On the other hand, it may be used to study long-term variability of GCR (see Section 3.4).
In this section, estimates of the averaged long-term flux of SEPs are discussed.
Measurements of cosmogenic isotopes with different life times in lunar and meteoritic rocks allow one to make rough estimates of the SEP flux over different timescales. The directly space-borne-measured SEP flux for past decades is broadly consistent with estimates on longer timescales – up to millions of years. The same measurements can provide a very conservative upper estimate for the occurrence rate of extreme SEP events. Terrestrial cosmogenic isotope data in dated archives (tree trunks, ice cores) give a possibility to assess the occurrence rate of strong SEP events on the time scales up to ten of millennia. Measurements of nitrates in polar ice have been shown to be an invalid index of strong SEP events in the past.
Different estimates of the extreme (quantified as the fluence of SEP with energy above 10 MeV) SEP event occurrence probability are summarized in Figure 28).
An analysis of various kinds of data suggests that the distribution of the intensity of SEP events has a break, and the occurrence of extra-strong events (with the F30 fluence exceeding 5 × 1010 cm–2) is unlikely on the multi-millennial time scale.