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Modeling a M class solar flare/CME with the Earth's atmosphere and extrapolating to an X class solar flare

Barrett Honors Thesis

Submitted 16 April 2021

Abstract

An X class solar flare has the potential to remove our satellites from orbit, permanently deactivate our main forms of communication and bring humanity into a technology-free age. By using Geant4, it is possible to simulate several layers of the Earth's atmosphere and send a simulated solar flare and coronal mass ejection. This thesis will show the interaction of photons and protons of various energies with several kilometers of atmosphere.

Introduction

There are two effects of a powerful solar flare interacting with the Earth. Initially, a solar flare occurs as a result of magnetic energy being built up in the Sun's atmosphere. The severity of the solar flare depends on the level of activity of the Sun. Several minutes later there is a possibility of a coronal mass ejection (CME), which is a release of plasma from the surface of the Sun. This plasma is primarily consisting of protons and electrons that move at the Alfvén speed, which is about 489 km/s on average. In 1859, the Carrington event (SOL1859-09-01) occurred. It was the highest recorded solar flare in human history with a flux of .0058 W/m2 and was categorized as class X58. The M2 class solar flare that will be simulated has a total flux of approximately 2e-4 W/m^2. Solar flare classes are shown in table 1. [3]

The Carrington event produced auroras as far south as Hawaii and set some telegraph systems on fire. The event allowed several individuals to communicate with telegraphs with no external power supply. This was a result of the aurora induced currents in the telegraph lines. Modern effects of a Carrington class event could include energy blackouts, crippled satellite communication, and potential permanent electronic or human harm due to hard X-rays.

Methodology

In Geant4, the atmosphere density was approximated by several concurrent layers at one-kilometer intervals within the file myDetectorConstruction.cc. The density at the first layer was found by choosing the average density between sea level and the altitude of one kilometer. This density was found to be 1.1685e-3 g/cm^3. [1] The composition of the atmosphere was approximated to be 70% nitrogen, and 30% oxygen with the atomic mass being 14.01 g/mole and 16.00 g/mole, respectively. The density changes based on the layer and this approximation is shown in figure 1.

Vacuum space must also be defined within Geant4, and this must be a non-zero number. The vacuum was defined with an atomic number 1, an atomic weight of 1.008 g/mole, a density of 1.0e-25 g/cm^3, a temperature of 2.73 kelvin, and a pressure of 3.0e-18 pascal. Following this definition of materials, we must define the size of the world that interactions are recorded in. The world is defined as a three-dimensional box with dimensions of 10,000 km in the X, Y, and Z direction. Within this world, everything is a vacuum except where there is another logical structure that has a different composition. The atmosphere is defined as a hemispherical shell with the first layer being defined with an inner radius of 6371 km and an outer radius of 6372 km, making it 1 km thick. Additionally, there is a 1 meter thick detector layer defined that is a hemispherical shell with an outer radius of 6371 km. Any particles that pass through this detector layer are recorded on a histogram with their energy and the number of particles at that energy bin. These energy bins are differentiated by 5 MeV bins. The detector layer is defined as a vacuum, See figure 2 for a visual diagram.

The particles launched are defined in myPrimaryGeneratorAction.cc where a proton or a photon can be defined by their particle number. A proton has a particle number of 14, and gamma has a particle number of 1. The particle number allows Geant4 to know which particle is being simulated and what characteristics it should have. The particle will then be shot from a particle gun towards the atmosphere in the negative z direction. We must define the energy of these particles. Initially, we define the fluence, or amount of particles at a certain energy bin. This is done by assigning every energy bin an arbitrary number that is then divided by the total of these numbers which gives a probability value. We then add these fractions for each higher energy and set an if function where if a random number generator makes a number less than the fraction, then this energy of particle will be shot through the particle gun.

Schematically, the code has the following structure:

double p1=2.5; //arbitrary probability value

double p2=5.3;

double pall=p1+p2;

double frac1=p1/pall;

double frac2=frac1+p2/pall;

G4double prand=G4UniformRand();

int binnumber=-1;

if (prand<=frac1){binnumber=1;}

else if(prand<=frac2){binnumber=2;}

if (binnumber==1) Ekin=MeV*(60+95)/2;

if (binnumber==2) Ekin=MeV*(95+150)/2;

After defining the energies from 60 to 95 MeV and 95 to 150 MeV as shown, we can define where these particles will be shot from. These particles will be shot from the cartesian coordinates (0m,0m,7000km), with the direction being (0,0,-1).

This is done by the following code:

particleGun->SetParticleMomentumDirection(G4ThreeVector(0,0,-1)); particleGun->SetParticlePosition(G4ThreeVector(0.0*m, 0.0*m, 7000.0*m);

We can then send any amount of these particles to be interacted with. After making the build directory, we can run the command ./crystalGrid -n1000000 which will send the defined particle in sets of 5000 until it reaches 1,000,000 particles. This computation takes a significant time as it is calculating the parent particles( the particles initially defined), as well as the interactions and movement of every secondary particle that is generated. The particles stop being simulated when they either stop moving or reach the world border. Geant4 has been set up to factor in Compton scattering, Rayleigh scattering, ionization, the photoelectric effect, pair creation and Bremsstrahlung radiation.

We achieve our output (the energy and the amount of particles that pass through the detector layer) by gathering data in root by setting this line of code in mySteppingAction.cc.

detector->SetRowColumnID(volume->GetName());

G4int crystalRowID = detector->GetRowID();

G4int crystalColID = detector->GetColID();

if (crystalRowID > -1 && crystalColID > -1) {myHistos.hEDep->Fill(prePos.x()/cm,prePos.y()/cm,edep);

eventaction->AddCrystalEnergy(edep,crystalRowID,crystalColID);}

G4double ke=p1track->GetKineticEnergy()/MeV;

eventaction->AddMyEnergyPaddle1(edep);

if (postPoint->GetStepStatus() == fGeomBoundary){

if (preVolumeName == "What0" && parentId == 0 ) { myHistos.hEout40->Fill(ke);}

if (preVolumeName == "Plate" && parentId != 0 && outParticle->GetParticleName() == "e-") {}}}

The first section of code pulls the particles 'thrown' at the atmosphere, which will show the mean, and the amount of particles at each energy bin. The second section of code only records the particles that pass through "What0" which is the logical name of the detector layer. This code will only record the particle energies of the initially defined particle (if parent Id==0), and will compile this data to a histogram. This will not consider secondary particles ,such as electrons, which are a consequence of the particle interaction. Only the parent particles, being a photon or proton, will be counted in this data.

A magnetic field has not been enforced for the proton simulation due to the cyclotron radius being extremely high for the energies tested. Using the formula

It was found that the cyclotron radius for the lowest proton energy (6.056MeV) was 7901 meters. This means that the magnetosphere does not significantly affect particle movement.

The energy bins and probability is from a M2.5 Solar flare from June 7th, 2011. [2] This was chosen due to the veracity of the data and this being a fair approximation for the energy bins of a M class solar flare.

Results

The first simulation was 100,000 photons interacting with 5 kilometers of atmosphere as shown in figure 3.

We see a transmittance of .35%, .33%, .27%, .27%, and .17%, for the energy bins 77.5, 122.5, 194.5, 308.5, and 489 MeV.

A similar experiment was conducted for a distance of 3 kilometers. When this simulation was done, a clear spike was seen at around 0MeV, and a more pronounced spike around 500MeV that is absent for the 5km simulation. This experiment was structured the same as the prior one, with a simulation of 1 million photons. The outcome is in figure 4.

The second simulation of 3 kilometers was chosen for data due to its larger sample size and better structured transmittance ratios. As a result of this second photon experiment, we achieve a transmittance of .79%, .55%, .40%, .31%, and .25% for energies 77.5, 122.5, 194.5, 308.5, and 489 MeV, respectfully. This is shown in Figure 5.

With our atmosphere approximation, we find that the ratio of the number of particles from 3 km to 50 km is 1:3.29. Meaning that over 50 kilometers of atmosphere you will pass through 3.29 times the number of particles as compared to 3 km. Thus, we have a transmittance of 1.20e-5%, 3.68e-6%, 1.29e-6%, 5.58e-7%, and 2.75e-7%, for the energy bins 77.5, 122.5, 194.5, 308.5, and 489 MeV, respectfully. This is graphically shown in figure 6.

Due to the power law, we can state that the flux of photons between 100MeV and 10GeV is 2.6 ± 0.2 ± 0.2 e-5 photons cm-2s-1. [2] The Earth has a radius of 6371km, so we must find the surface area of a circle with this radius. This surface area would be 1.3e8km^2 (1.3e18cm^2). As such, we can estimate that at the lowest energy bin we will see 3.3e13 photons hitting the Earth at this energy bin every second. When we account for the transmittance due to the atmosphere, we see that the number of photons hitting the surface of Earth is 4.1e6 photons per second. The most significant amount of flux from photons arrive within the initial 6 hours of a solar flare, making a total of 8.6e10, 2.6e10, 9.2e9, 4.0e9, 2.0e9 photons at their respective energies of 77.5, 122.5, 194.5, 308.5, and 489 MeV over a timeframe of 6 hours.

This can also be quantified in regards to the flux of the photons. Assuming the flux remains relatively constant at 2.60 ± 0.2 ± 0.2 e-5 photons cm^-2s^-1 for the various energies tested, then the flux changes to the following when accounting for the transmittance. 3.12e-12 photons cm^-2s^-1 for 77.5MeV, 9.57e-13 photons cm-2s-1 for 122.5MeV, 3.35e-13 photons cm^-2s^-1 for 194.5 MeV, 1.45e-13 photons cm^-2s^-1 for 308.5MeV, 7.15e-14 photons cm^-2s^-1 for 489 MeV.

As a result of the CME, within the span of hours or days, a barrage of high energy protons and electrons will reach the Earth. These particles, as previously mentioned, have a high cyclotron radius. Due to this, protons with energies larger than 1MeV are considered independent of the effects of the magnetic field. A similar simulation to the photons was performed for a M class CME. The energies of the protons sent and the output is shown in figure 7.

1 million particles were shot at 10 meters of atmosphere. The energy bins 7.39, 10.7, 15.48, 22.195, 32.075, 46.47, 67.23, 97.45, 140.38 MeV were used with 492214, 261858, 151512, 62559, 19076, 9010, 3082 ,594, 90 photons at each respective energy bin. We see a transmittance graphed in Figure 8.

It is important to notice how the transmittance increases at 40MeV as opposed to photons where it decreases. Protons with energies lower than approximately 20MeV have a transmittance rate of 0 as seen in figure 8. This simulation was additionally performed with an equal distribution of energies from 0 to 1000MeV. This was done to test the transmittance theory set previously that transmittance increases as energy increases for protons. This is seen in figure 9.

This data is intriguing as one can see that transmittance rate increases as energy increases, but it is not a uniform increase. It was seen in the data that every energy bin dropped on average of 20MeV which is why the initial two bins have a zero value.

For the proton simulation, much higher transmittance is seen at higher energies which is antithetical to the result found for photons. Therefore, the most concerning part of an X class solar flare is its CME, specifically the high energy protons. At higher energies, more protons travel through and these high energy protons will directly affect the earth's surface in greater quantities.

Discussion

An X class solar flare has the potential to cause great havoc here on Earth. Our atmosphere and magnetic field are successful at protecting us from the constant barrage of the solar wind, but is less helpful at higher energies. The data shows several important factors that must be considered.

One of the intriguing factors is the small energy decay of the particle as it passes through the atmosphere. For instance, a single proton with an initial energy of 780 MeV was found to have an energy of 767 MeV after passing through 100 meters of atmosphere. This is an energy retention of 98.3%. All of this energy was slowly lost via ionization of molecules in the atmosphere over 687 separation ionization events.

Another crucial point is the opposite transmittance results for the photon and proton simulation. It was confirmed in the 3 km and 5 km photon simulation that we see decreasing transmittance with higher energies of photons. This may be due to Compton scattering which is an additional factor that does not affect protons. Although, it must be considered that protons have a much lower transmittance which is the reason for why the simulation is for 10 meters as opposed to 3 kilometers.

Additionally, it should be noted that the dip in transmittance in figure 9 over 200 to 300 MeV is most likely due to an incorrect setting within Geant4, as there is no physics perspective on why this is occurring. This error does not change the conclusion made from the graph, but should be noted and the polynomial fit should be used more for interpretation of data.

Conclusion

From the data provided, we can see that transmittance increases for protons as energy increases and decreases for photons as energy increases. As such, high energy but lower probability photons are not as concerning for the energy bins tested. Protons are more interesting as they have a much lower transmittance when compared to photons. This is why simulations were run between 10 and 100 meters for protons compared to 3 to 5 kilometers for photons. However, in spite of this comparatively low transmittance, there is an increase in transmittance as energy increases. This makes low probability but very high energy protons a serious concern. According to reports from the Carrington event, we know that a significant amount of protons interacted with the surface of the earth meaning the overall proton flux was high. This, in addition to figure 9, shows the significance of the effect of protons on the earth.

Other exotic high energy solar particles are expected but were not simulated. These particles, depending on the energy, are also a concern but due to the exoticness should not be the primary concern.

There will be an increase in ionization radiation and aurora borealis, but the effect on humans on earth should be minimal according to the simulation. People and electronics in space will be the most affected with no shields from the proton or gamma radiation.

Acknowledgments

I would like to thank Dr. Igor Shovkovy and Mr. Brian Steinkamp. They were my thesis committee and were absolutely instrumental in directing my reasons, discovering solutions to issues and helping me pick this topic.

I would also like to thank Dr. Michael Dugger. He was incredibly helpful with running Geant4 simulations. He helped set up the atmosphere, the energy bins and enacted a magnetic field to test the interaction involved.

References

• [1] "U.S. Standard Atmosphere." Engineering ToolBox, www.engineeringtoolbox.com/standard-atmosphere-d_604.html.

• [2] M. Ackermann et al, High-energy Gamma-Ray Emission from Solar Flares: Summary of Fermi Large Area Telescope Detections and Analysis of Two M-class Flares, The Astrophysical Journal, Volume 787, Issue 1, article id. 15, 13 pp. (2014).

• [3] "What Are Solar Flares?" StackPath, www.spaceweatherlive.com/en/help/what-are-solar-flares.