4.1 Integral and Differencial Spectra of Primary and Secondary Cosmic Rays

4.2 Estimation of the Power Index of GLE N 69 on January 20, 2005

4.1 Integral and Differencial Spectra of Primary

and Secondary Cosmic Rays

Particle detectors located on the Earth’s surface measure the intensities of secondary cosmic rays reaching detector location. These intensities depend on the latitude and altitude of detector location and on the intensity of primary cosmic rays incident on the Earth’s atmosphere. This, so called integral flux of secondary particles (measured from all directions beyond a threshold determined by cutoff rigidity and detector itself) is usually measured in units of I(>R) = #N/m²*min, where N is the number of particles registered by detector. Count rate of particle detector when corrected to atmospheric effects is rather stable, however, a violent explosions on the sun can send additional high energy protons and ions to the Earth thus enlarging secondary particle intensities. Estimation of the intensity of SCR above atmosphere is very important for the research of the solar accelerators and for forewarning on upcoming radiation and geomagnetic storms.

Space born detectors also measure fluxes of SCR of lower energies. Space-born spectrometers can measure also differential fluxes in the unit of energy and solid angle; differential fluxes, presenting differential flux in the units of D(E,Ω) = #N /cm²*sec*ster*MeV, where Ω is the solid angle. For instance, differential and integral fluxes of the GOES (Geostationary Operational Environmental Satellite) spectrometers measure different energy spectra in the intervals: 4 – 9 MeV, 9 – 15 MeV… etc, and integral spectra in intervals >10MeV, >30MeV… etc. Intensities presented as function of energy called energy spectra: differential and integral energy spectra. If we integrate also over the time when SCR were detected we obtained so called fluence spectra. Most of particle monitors do not measure particle energy, they poses several difficulties on estimation of the energy spectra of SCRs. By spectrometers on board GOES it is possible to measure proton energy spectra up to 700MeV. Facilities of the Pamella satellite (Sparvoli, 2008) can prolong maximal energy up to several units of GeV. To extend the spectrum to tens of GeV one should use surface particle detector data as well.

To obtain the differential fluence (to be comparabele with GOES measured fluxes) one should take into account the zenith angle < dependence of the intensity in the form ~cos⁶. Total flux is obtained by integrating over zenith angle ~ 0-90^o and azimuth 0-360^o (azimuth dependence of intensity is uniform). Therefore to obtain differential fluence in units 1/m²*ster we should divide total monitor flux to coefficient k:

To connect obtained surface abundance with one existent above atmosphere we have to perform Monte-Carlo simulations of particle interactions and development of the particle cascades in terrestrial atmosphere. By implementing CORSIKA simulation code with fixed primary proton energies we obtain the efficiencies of primary protons of different energies to produce nmuons with energies greater than 5 GeV (see Table 1).

Table 1. Expected number of muons and efficiencies to yield a muon with energy greater than 5 GeV by protons with definite energies incident on the earth atmosphere.

However, to calculate the total efficiency and to connect secondary and primary fluxes we need to make an assumption on the spectral shape of the primary spectra. Overall understanding is that these spectra can be approximated with broken power law (power low with several spectral “knees”). The place of the spectral brake is event specific, and if it encounters on considerably high energies (several hundreds of MeV) this hard spectra event is extremely dangerous for spacecraft and people onboard of over-polar flights. The estimate of the spectral index value in GeV region can be made by comparing the enhancement of neutron and muon fluxes; or by comparing neutron fluxes measured at same geographical coordinates, but at different altitudes.

4.2 Estimation of the Power Index of

GLE N 69 on January 20, 2005

A traditional method for determining energy spectra is to employ GLE observations from the world-wide network of neutron monitors with different cutoff rigidities. An example of such a model is the NM-BANGLE model which couples primary solar cosmic rays at the top of the Earth’s atmosphere with the secondary ones detected at ground level by the world-wide network of neutron monitors, characterized by the rigidity range from 0.5 until 12 GeV (Plainaki et al, 2008). However, the usage of the model function separable in energy and anisotropy for the GLE fitting can introduce a bias in the recovered spectra (see discussion in Abassi et al., 2008) and it is difficult to follow the time-history of spectral indices. ASEC monitors access wide range of primary energies and allow recovering of the energy spectra by the particle data measured at one and the same location. Sure, only from ASEC data we cannot measure the anisotropy of the event; however, the observations from the growing SEVAN network (Chilingarian et al., 2008) along with existent particle detector networks will allow accessing also information of the anisotropy of the GLE event.

The largest GLE of the space era was detected by particle detectors worldwide on 20 January 2005 (Bieber et al, 2005, Buetikofer et al., 2006). All Aragats particle detectors registered significant intensity increases. The most important result was obtained with the Aragats Multichannel Muon Monitor (AMMM, Chilingarian et. al., 2005), establishing flux of >20 GeV muons at 7:01-7:03 UT, 20 January 2005 (Bostanjyan et al, 2007, Chilingarian, 2009). In addition, neutron monitors located at Aragats detected significant enhancement of neutron intensity, several minutes later at ~7:15 UT.

The analysis presented in this paper is based on the Aragats and Nor-Amberd neutron monitors count rates. These two neutron monitors are located on different altitudes, but at the same geographical coordinates.

The idea to deduce the spectra of solar flare protons using two neutron monitors located close by at the same vertical cutoff rigidity, but at different altitudes above sea level was proposed by J.A. Lockwood et al. (2002).

Our method is based on the modeling of the responses of Aragats and Nor-Amberd neutrons monitors to solar proton flux (Zazyan, Chilingarian, 2005). We use some trial spectrum of solar protons for CORSIKA simulation. Based on data from ACE, SAMPEX and GOES11 spacecraft (ACE News #87) the intensity of protons with kinetic energy E_k<1GeV was found to be

I(E_k)~4.07x10⁵E_k^-2.15part/(m²·sr·s·GeV) (1)

Taking into account that ground-based instruments observed much softer spectra and assuming that there is a knee around ~1GeV, a trial spectrum at higher energy was adopted in the form:

I(E_k)~4.07x10⁵E_k^-γpart/(m²·sr·s·GeV) (2)

The total number of solar protons of kinetic energy corresponding to rigidity cut-off of the location was calculated according to equation (1) for different spectral indexes. Particle fluxes at ground level were simulated, and the count rates were determined for Aragats and Nor-Amberd neutron monitors.

The expected increases in the count rates, calculated for possible spectral indices, as well as detected increases of Aragats and Nor-Amberd neutron monitors are presented in Table 2. Table 2 data supports hypothesis that the spectral index g ~ 6.

Table 2. Simulated and experimental count rate relative increases of the Aragats and Nor-Amberd neutron monitors at 7:15UT on 20 January 2005

However, we realize that the results of simulation depends also on the value of the second spectral parameter, the constant A in the power-law energy spectrum I(E_k)=AE_k^-g. To avoid this dependence, we consider the ratio of count rate increases of two monitors:

R(ArNM/NANM) = (DN/N)_ArNM/(DN/N)_NANM, (6)

which is a function on spectral index only.

The ratios of the count rate relative increases for Aragats and Nor-Amberd neutron monitors simulated for different spectral indexes and the calculated from measured count rates are presented in Table 3.

Table 3. Simulated and experimental ratios of count rate relative increases of Aragats and Nor-Amberd neutron monitors at 7:15UT

From the comparison of the computed and observed ratios we estimate that at 7:15 the spectral index of the primary solar proton flux was equal or greater than 5. Thus, based on our analysis (see Tables 2 and Table 3) we conclude that γ ~ 6 is a reasonable choice for the spectral index at the time 7:15 UT.

References

• Abassi R., Ackermann M., Adams J., et al. Solar Energetic particle spectrum on 2006 December 13 determined by IceTop. ApJ Letters, 689, L65-68, 2008.
• Agostinelli, S., Allison, J., Amako, K. GEANT4 — a simulation toolkit. Nucl. Instr. Meth. A 506, 250-303, 2003.
• ACE News #87 - Feb 23, 2005.“Space Weather Aspects of the January 20, 2005 Solar Energetic Particle Event”.
• www.srl.caltech.edu/ACE/ACENews/ACENews87.html
• Bieber, J.W., Clem, J.M., Duldig, M.L. et al. Latitude survey observations of neutron monitor multiplicity. J. Geophys. Res., 109, A12106, 2004
• Bostanjyan, N.K. et al. On the production of highest energy solar protons at 20 January 2005, J. Adv. Space Res. 39, 1456-1459, 2007
• Buetikofer, R., Flueckiger, E.O., Moser, M.R., and Desorgher, L. The extreme cosmic ray ground level enhancement of January 20, 2005, Proc. 2nd International Symposium on Solar Extreme Events, Nor-Amberd, Armenia, 1, 214-217, 2006.
• Chilingarian, A. Avakyan K. Babayan V., et al. Aragats space-environmental centre: status and SEP forecasting possibilities. J. Phys. G: Nucl. Part. Phys. 29, 939–951, 2003.
• Chilingarian A. and Reymers A. Investigations of the response of hybrid particle detectors for the Space Environmental Viewing and Analysis Network (SEVAN). Ann. Geophys., 26, 249-257, 2008.
• Chilingarian A. Statistical study of the detection of solar protons of highest energies at 20 January 2005. J. Adv. Space Res.,43,702-707,1009.
• Heck, D., and Knapp, J., A Monte Carlo Code to Simulate Extensive Air Showers, 1998, Forschungszentrum Karlsryhe, FZKA Report 6019.
• Lockwood J.A., Debrunner H., Flukiger E.O.and Ryan J.M. Solar proton rigidity spectra from 1 to 10 GV of selected flare event since 1960, Solar Physics, 208 (1) , pp 113-140 (2002)
• Plainaki C., Mavromichalaki H., Belov A., Eroshenko E. and Yanke V. Modeling the solar cosmic ray event of 13 December 2006 using ground level neutron monitor data. doi:10.1016/j.asr.2008.07.011.
• Sparvoli R. Direct measurements of cosmic rays, IL NUOVO CIMENTO Vol. 123 B, N. 6-7 Giugno-Luglio, 2008.
• Zazyan, M.Z., Chilingarian, A.A.. On the Possibility to Deduce Solar Proton Energy Spectrum of the 20 January 2005 GLE using Aragats and Nor-Amber Neutron Monitors Data. 2nd Int. Symp. on Solar Extreme Events, Fundamental Science and Applied Aspects, Nor-Amberd, Armenia, 200-202, 2005b.