<figure><img src="image_41.png" /><figcaption>**Fig. 4.5** Example using the inversion model (Agueda et al. 2008) to illustrate the importance of having directional information of particle intensities. Near-relativistic electron injection history profiles and $\lambda_r$ (left column), omnidirectional intensities (middle column) and directional intensities (right column) are shown for different scenarios. The model fits (black curves) reproduce the observations (colour curves) only in the second case. See text for details</figcaption></figure>

more information is needed to find the correct solution. In the right panel of Fig. 4.5 the corresponding directional intensities (colour curves) are shown. The model fits (black curves) only reproduce the directional intensities correctly in the second case; thus showing that directional intensities are crucial for inferring the correct parameters. Directional intensities or angular information of the particle distribution function is not always provided by instrumentation onboard spacecraft. It is usually available for near-relativistic electrons and low-energy protons, but not for high-energy protons for which measurement statistics are relatively low.

## 4.4 Concluding Remarks

In this chapter the key basic facts of the interplanetary scenario and of the main effects to consider when simulating the SEP transport in interplanetary space have been presented. The interested reader may follow the various references provided to deepen in the study of SEP transport. In summary, the main messages to take away are: the average interplanetary magnetic field can be described by an Archimedean spiral. Superposed on this average spiral field are small-scale random fluctuations. In the co-rotating frame, the motion of the guiding centre of SEPs travels along
the mean spiral direction and particles are scattered by small-scale fluctuations embedded in the solar wind. Interplanetary transport models help to infer the particle source function of SEP events.

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<figure><img src="image_42.png" /></figure>
# Chapter 5
## Cosmic Ray Particle Transport in the Earth's Magnetosphere

R. Bütikofer

**Abstract** The transport of the cosmic ray particles in the Earth's magnetic field must be considered for cosmic ray investigations based on cosmic ray measurements in the geomagnetosphere. The motion of charged particles in a magnetic field is defined by the Lorentz force. The trajectories of cosmic ray particles are curved by the Earth's magnetic field. In a first approximation the geomagnetic field can be described by a dipole magnetic field. For a more accurate description the geomagnetic magnetic field is divided into two parts: the inner part generated by an internal dynamo and the outer part induced by different current systems in the ionosphere and the magnetosphere. Models have been developed that describe the inner and the outer magnetic field. The computations of the propagation of the cosmic ray particles in the Earth's magnetosphere are made with computer programs based on numerical integration of the equation of motion. For the specification of geomagnetic effects on cosmic ray particles the concept of cutoff rigidities and of asymptotic directions have been introduced.

### 5.1 Introduction

Charged particles moving in a magnetic field are deflected. Investigations of cosmic ray observations based on ground-based and on space-based detectors inside the geomagnetosphere require therefore a detailed knowledge of the propagation of the cosmic ray particles in the Earth's magnetic field. The conditions under which a cosmic ray particle has access to a specific point of observation are defined by the Earth's magnetic field, the energy of the particle as well as the direction of incidence.

The implementation of the quantity “magnetic rigidity” is useful as particles with the same rigidity $R$, charge sign and initial conditions have identical trajectories in a

<footnote>R. Bütikofer (✉)</footnote>

<footnote>University of Bern, Physikalisches Institut, Sidlerstrasse 5, CH-3012 Bern, Switzerland</footnote>

<footnote>High Altitude Research Stations Jungfraujoch and Gornergrat, Sidlerstrasse 5, CH-3012 Bern, Switzerland</footnote>

<footnote>e-mail: rolf.buetikofer@space.unibe.ch</footnote>
static magnetic field. The rigidity $R$ is defined as $R = \frac{pc}{Ze}$, where $p$ is the momentum, $c$ is the speed of light and $Ze$ is the charge of the cosmic ray particle. The unit of the rigidity $R$ is volts. A convenient unit is GV ($10^9$ V).

History:

~~1st cent. AD~~ First known magnetic compass was invented in China

13th cent. AD First theories about geomagnetism

In early 1890s Hendrik Lorentz derived the equation that describes the forces on a charged particle in an electromagnetic field, the so-called Lorentz force

1912 Discovery of the cosmic ray by the Austrian Victor Hess

1930 First works were started by Störmer to understand the geomagnetic effects on cosmic rays (Störmer 1930)

1957/58 International Geophysical Year
Systematic investigations of the effects of the Earth's magnetic field on the cosmic rays as observed on the ground

For a more detailed historical overview, see e.g. Smart et al. (2000).

The forces that act on moving charged particles in an electromagnetic field and their effects on the particles' trajectories are described in Sect. 5.2. The Earth's magnetic field, i.e. the inner and the outer part of the Earth's magnetic field as well as the models describing these fields, is addressed in Sect. 5.3. In Sect. 5.4 the differential equations that describe the motion of the charged cosmic ray particles in the Earth's magnetic field and their numerical computation are summarised. The concepts of "cutoff rigidities" and of "asymptotic directions" that have been introduced to quantify the geomagnetic field effect are described in Sect. 5.5.

## 5.2 Motion of Charged Particles in a Magnetic Field: Lorentz Force

The combination of electric and magnetic forces on a charged particle due to electromagnetic fields is described by the Lorentz force $\mathbf{F}$:

$$ \mathbf{F} = Ze \mathbf{E} + Ze [\mathbf{v} \times \mathbf{B}] \quad (5.1) $$

where

$Ze$ charge of the moving particle, $e$ is the elementary charge

$\mathbf{E}$ electric field

$\mathbf{v}$ velocity of the particle

$\mathbf{B}$ magnetic field

The effect of electric fields can be neglected in the geomagnetosphere due to its high electric conductivity.
The force equation becomes:

$$ \mathbf{F} = m \cdot \frac{dv}{dt} = Ze [\mathbf{v} \times \mathbf{B}] \qquad (5.2) $$

A charged particle is accelerated perpendicularly to the speed $v$, it follows that the absolute value of the momentum $|m \cdot v|$ and its kinetic energy are conserved. For relativistic particles with mass $m = \gamma m_0$, where $\gamma$ is the Lorentz factor ($\gamma = (1 - v^2/c^2)^{-1/2}$) and $m_0$ is the rest mass of the particle, it follows:

$$ \frac{dv}{dt} = -\frac{Ze}{\gamma m_0} [\mathbf{v} \times \mathbf{B}] \qquad (5.3) $$

For a moving charged particle in a uniform magnetic field, the speed vector $v$ can be split into a component parallel $v_\parallel$ and perpendicular $v_\perp$ to the magnetic field $B$. The motion of the particle is then described by a movement with constant speed along the magnetic field $v_\parallel$ and a circular motion around the magnetic field lines. The centripetal acceleration is

$$ \frac{v_\perp^2}{r_c} = \frac{Ze}{\gamma m_0} \cdot v_\perp \cdot |\mathbf{B}| \qquad (5.4) $$

where $r_c$ is the cyclotron radius or gyroradius. For the cyclotron radius $r_c$ follows:

$$ r_c = \frac{\gamma m_0 \cdot v_\perp}{Ze \cdot |\mathbf{B}|} \qquad (5.5) $$

The above formula for the cyclotron radius can be rearranged to give a more practical expression for an estimation of the cosmic ray trajectory characteristic:

$$ r_c [\text{meter}] = 3.3 \times \frac{(\gamma m_0 c^2 [\text{GeV}]) \cdot (v_\perp / c)}{(Z \cdot |\mathbf{B}| [\text{Tesla}])} \qquad (5.6) $$

where GeV is the unit of Giga-electron Volts.

A proton with kinetic energy $E_{kin} = 10$ GeV in the Earth's magnetic field close to the Earth where $|\mathbf{B}| \approx 30,000$ nT (Sect. 5.3.1) and $\mathbf{v} \perp \mathbf{B}$, i.e. $v_\perp = 0.99 c$, has a gyroradius in the order of $10^6$ m or 0.15 Earth radii.

## 5.3 Earth's Magnetic Field

The geomagnetosphere is the region close to the Earth where the motion of charged particles is mainly determined by the Earth's magnetic field. The size, the shape and the inner structure of the geomagnetosphere is configured by the
interaction of the solar wind with the Earth's magnetic field. The extension of the geomagnetosphere in space is therefore determined by the equilibrium between the pressure of the streaming solar wind plasma and the magnetic pressure of the magnetosphere. The front end of the magnetopause is at a standoff distance of 10–12 Earth's radii (Re) from the Earth's centre during quiescent solar wind conditions. The magnetotail has a length of at least 100 Re. During times of disturbed solar wind conditions the characteristics of the geomagnetosphere are changed and are defined by the solar wind speed, the particle density in the solar wind, the strength and the direction of the interplanetary magnetic field. In addition, the relative position of the magnetic dipole inside the Earth defines the characteristics of the geomagnetic field. In the models of the inner Earth's magnetic field these effects must be considered.

The magnetosheath, the space between the magnetopause and the bow shock, is the consequence of the fact that the solar wind can not penetrate the Earth's magnetic field because of its high electric conductivity and that therefore the magnetic field of the solar wind must be swept around the magnetopause. The magnetic field strength in the magnetosheath may be in the order of a few 10 nT (Kobel and Fluckiger 1994). The geomagnetic field line topology in the geomagnetosphere is illustrated in Fig. 5.1.

<figure><img src="image_43.png" /><figcaption>**Fig. 5.1** Illustration of the Earth's magnetic field line topology. From Bütikofer et al. (1995)</figcaption></figure>
Close to the Earth the magnetic field can be described in a first approximation by a geocentric dipole (Sect. 5.3.1). In a more accurate description the Earth's magnetic field is divided into an inner and an outer part. The inner magnetic field is produced by sources in the interior of the Earth. It is described by the IGRF model which is based on magnetic field measurements at the Earth's surface (Sect. 5.3.2). The external magnetic field is produced by the different electric current systems in the ionosphere and the inner magnetosphere. There exist different field models that describe the external Earth's magnetic field. The models by Tsyganenko—the models that are mainly used for cosmic ray trajectory computations within the geomagnetosphere—are presented in Sect. 5.3.4.

### 5.3.1 The Magnetic Field of the Earth as a Dipole Field

In a first approximation the Earth's magnetic field can be described by a geocentric magnetic dipole.

The magnetic moment **m** of a circular current is:

$$|\mathbf{m}| = I \cdot S \qquad (5.7)$$

where

* *I* electric current

* *S* area that is spanned by the circular current

For the Earth dipole: $|\mathbf{m}| = 8.1 \cdot 10^{22} \text{ A m}^2$

The geomagnetic moment is defined as:

$$\mathbf{M} = \frac{\mu_0}{4\pi} \mathbf{m} \qquad (5.8)$$

where the vacuum permeability $\mu_0 = 4\pi \cdot 10^{-7} \text{ V s / Am}$

$$|\mathbf{M}| = 8.1 \cdot 10^{25} \text{ Gauss cm}^3$$

$$= 8.1 \cdot 10^{15} \text{ V s m}$$

In polar coordinates the components of the magnetic field $\mathbf{B}(r, \lambda, \varphi)$ are:

$$B_r = -\frac{2 |\mathbf{M}| \sin \lambda}{r^3} \\ B_{\lambda} = -\frac{|\mathbf{M}| \cos \lambda}{r^3} \qquad (5.9)$$

$$B_{\varphi} = 0$$
where

$r$ distance from Earth's center

$\lambda$ geomagnetic latitude

$\varphi$ geomagnetic longitude

Magnetic field strength at the geomagnetic equator: $B_{\lambda} = \frac{M}{r^3}$, $B_{r} = 0$, i.e. at Earth's surface ($r = 6.4 \cdot 10^6$ m) $B_{\lambda} \approx 30,000$ nT.

Magnetic field strength at the poles: $B_{\lambda} = 0$, $B_{r} = \frac{2M}{r^3}$, i.e. at Earth's surface $B_{r} \approx 60,000$ nT.

The magnetic strength as function of $\lambda$ and $r$ is:

$$|\mathbf{B}| = \frac{|\mathbf{M}|}{r^3} \sqrt{1 + 3 \sin^2 \lambda} \sim \frac{1}{r^3} \qquad (5.10)$$

Units:

$$1 \text{ Gauss } (G) = 10^{-4} \text{ V s/m}^2 = 10^{-4} \text{ Tesla (T)}$$

$$1 \text{ Gamma } (\gamma) = 1 \text{ nT}$$

### 5.3.2 Magnetic Field Model Due to Internal Sources: IGRF

The main geomagnetic field is generated primarily by a hydrodynamic geodynamo in the Earth's fluid outer core which varies slowly with time. The geodynamo has an underlying offset dipolar configuration which is currently tilted at an angle of about 10° with respect to the Earth's rotational axis. The time dependence in the magnetic field models is usually approached by a sequence of static configurations. For a static magnetic field the equations of the magnetostatics must be fulfilled as a special case of the Maxwell's equations:

$$\nabla \cdot \mathbf{B} = 0$$

$$\nabla \times \mathbf{B} = \mu_0 \mathbf{j} \qquad \mathbf{j}: \text{current density}$$

There are no currents to the center of the Earth:

$$\mathbf{j} = 0, \text{ i.e. } \nabla \times \mathbf{B} = 0$$

From this it follows that there exists a potential $V$, so that

$$\mathbf{B} = -\nabla V$$
Since the magnetic field **B** is divergence-free (Gauss's law for magnetism) it follows for $r \ge$ Re:

$$ \nabla^2 V = 0 \text{ or } \Delta V = 0 \quad (\text{Laplace's equation}) $$

Assumption for the solution of the Laplace equation: only sources from the Earth's interior are considered.

The geomagnetic main field is usually described by spherical harmonics (Chapman and Bartels 1940). Here, the representation of the geomagnetic main field with spherical harmonics according to the method by Gauss with the Schmidt normalization (Chapman and Bartels 1940) is used. In geographic spherical coordinates $(r, \theta, \phi)$ the corresponding geomagnetic potential $V$ can be expressed:

$$ V(r, \theta, \phi) = a \sum_{n=1}^{\infty} \sum_{m=0}^{n} \left(\frac{a}{r}\right)^{n+1} P_n^m(\cos \theta) \left\{g_n^m \cos(m\phi) + h_n^m \sin(m\phi)\right\} \quad (5.11) $$

where

$a$ mean Earth's radius, $a = 6371.2$ km

$P_n^m$ Schmidt normalized (Chapman and Bartels 1940) associated Legendre functions of degree $n$ and of order $m$

$g_n^m, h_n^m$ Gauss coefficients

As a consequence of the secular variations in the geomagnetic field, the Gauss coefficients must be determined periodically. The variation of the declination is ~0.13°/year, the westward drift of the non-dipolar terms has a time period of ~2000 years, and the change in the dipole moment a period of some 1000 years (Merrill and McElhinny 1983). The International Union of Geodesy and Geophysics (IUGG) and the International Association of Geomagnetism and Aeronomy (IAGA) determine from measurements of the magnetic field **B** on the ground and publish every 5 years the Gauss coefficients $g_n^m$ and $h_n^m$ (Thébault et al. 2015). Before the year 2000, the parameters until degree $n = m = 10$ were determined and since the year 2000 until degree $n = m = 13$, see https://www.ngdc.noaa.gov/IAGA/vmod/igrf.html.

The components of $\mathbf{B}(r, \theta, \phi)$ in spherical coordinates are:

$$ \mathbf{B}_r(r, \theta, \phi) = -\frac{\partial V(r, \theta, \phi)}{\partial r} \\ \mathbf{B}_{\theta\theta}(r, \theta, \phi) = -\frac{1}{r} \frac{\partial V(r, \theta, \phi)}{\partial \theta} \quad (5.12) $$

$$ \mathbf{B}_{\text{ffl}}(r, \theta, \phi) = -\frac{1}{r \sin\theta} \frac{\partial V(r, \theta, \phi)}{\partial \Phi} $$
where

$r$ distance from Earth's center

$\theta$ geographic co-latitude, $\theta = 90^\circ - \Lambda$

$\Lambda$ geographic latitude

$\phi$ geographic length

The strength of the magnetic field at the Earth's surface ranges from less than 30,000 nT or 0.3 Gauss in South America (South Atlantic Anomaly) to over 60,000 nT around the magnetic poles (northern Canada, Siberia and coast of Antarctica, south of Australia). For comparison, the strength of the interplanetary magnetic field near Earth is typically 5 nT, i.e. the Earth's magnetic field at the Earth surface is about four orders of magnitude larger.

### 5.3.3 Contributions to the Earth's Magnetic Field by Magnetospheric Electric Currents

In addition to the internal sources of the Earth's magnetic field, there is also a contribution of external origin: the electrical current systems in the ionosphere and the magnetosphere. Figure 5.2 shows a schematic view of the different current

<figure><img src="image_44.png" /><figcaption>**Fig. 5.2** Schematic view of the different current systems which contribute to the Earth's magnetic field.</figcaption></figure>

(From Stern 1994, reproduced with permission from publisher John Wiley and Sons for electronic and press publishing, license number: 4118701268653, license date: May 30, 2017)
systems in the magnetosphere of the Earth. These current systems may vary rapidly, depending on the solar activity. During quiet periods the amplitudes of these external contributions are ~20 nT at mid-latitudes and may increase to more than the ten-fold during geomagnetic storms. The most important current systems are: the ring current in the radiation belts, the Chapman-Ferraro current on the magnetopause (magnetopause current), the field aligned (Birkeland) currents along geomagnetic field lines connecting the Earth's magnetosphere to the Earth's high latitude ionosphere, and the tail currents in the tail of the magnetosphere. The intensities of these currents reach millions of amperes and are related to the solar activity. During times of low solar activity, the standoff distance of the magnetopause currents is at ~10.5 Earth radii and the generated magnetic field close to the Earth is ~25 nT. The ring current, i.e. the longitudinal drift of energetic (10–200 keV) particles that are bouncing along the magnetic field lines between North and South polar regions, has a radius of ~6 R_E during quiet times and its contribution to the magnetic field at the Earth is about ~40 nT.

### 5.3.4 Magnetic Field Models of the External Sources

Since the 1970s efforts were made to improve the quantitative quality of the magnetospheric magnetic field models, see e.g. the review paper by Walker (1979). Most of the models include currents in the inner magnetosphere in addition to the boundary currents and the magnetotail current system. All the models include the tilt angle of the internal magnetic dipole as an input parameter. With the advent of the space era it became possible to extend the models from low to high altitudes, eventually including even the entire magnetosphere. However, the modeling of the magnetic field in that region is much more difficult, mostly because the magnetic field from external sources (currents in the geomagnetosphere) predominates the magnetic field with growing distance from the Earth. Vector measurements of the magnetic field should be made throughout the entire space where the field should be modeled, i.e. it is necessary to accumulate large amounts of space magnetometer data taken in a wide range of the geomagnetosphere. In contrast to the main geomagnetic field (variations on a timescale of thousands of years), the magnetic field in the outer regions of the geomagnetosphere is a very dynamical system on short time scales and depends on different factors. The first factor is the orientation of the Earth's magnetic axis with respect to the direction of the incoming solar wind flow, which varies with time because of the Earth's diurnal rotation and its yearly orbital motion around the Sun, and the frequent variations of the solar wind characteristics. Another important factor is the state of the solar wind, in particular, the orientation and strength of the interplanetary magnetic field. The interaction between the terrestrial and the interplanetary magnetic fields becomes strongly effective when the interplanetary magnetic field is antiparallel to the Earth's field on the dayside boundary of the magnetosphere. In this case, the geomagnetic and the interplanetary field lines connect across the magnetospheric boundary, which
strongly enhances the transfer of the solar wind mass, energy, and electric field inside the magnetosphere.

Different models have been developed to describe the magnetic field in the whole geomagnetosphere (Mead and Fairfield 1975; Olson and Pfitzer 1988; Tsyganenko 1987, 1989, 1996; Ostapenko and Maltsev 1997; Tsyganenko 2002a,b; Tsyganenko and Sitnov 2005). For the determination of cosmic ray particle trajectories mainly the magnetic field models by Tsyganenko (1989, 1996, 2002a,b), Ostapenko and Maltsev (1997) and Tsyganenko and Sitnov (2005) are used.

The Tsyganenko models are semi-empirical best-fit representations for the magnetic field, based on a large number of satellite observations (IMP, HEOS, ISEE, POLAR, Geotail, etc.). The models include the contributions from external magnetospheric sources: ring current, magnetotail current system, magnetopause currents and large-scale system of field-aligned currents.

Tsyganenko model T89 (Tsyganenko 1989) was primarily developed as a tail model. It is based on satellite measurements at distances from the Earth less than 70 $R_E$, therefore its domain of validity is limited to this region in space. It provides seven different states of the geomagnetosphere corresponding to different levels of the geomagnetic activity represented by the $Kp$-index<fnref n="1" /> 0, 1, ..., ≥6. The model does not consider the continuous variation of the structure of the magnetosphere as a function of geomagnetic indices like $Dst$ and of solar wind parameters. The consideration of these parameters to describe the evolution of the magnetosphere is in particular important during a magnetic storm. Therefore the use of T89 is not reasonable during times when the geomagnetic field is strongly disturbed.

Tsyganenko model T96 (Tsyganenko 1996) considers in contrast to the T89 model the continuous variation of the structure of the magnetosphere as a function of the geomagnetic indices like $Dst$ and of the solar wind parameters. In this model the external magnetospheric magnetic field is generated by different current systems where the shape and the strength depend on the dipole tilt angle, on the solar wind dynamic pressure, on the $Dst$ index and on the interplanetary magnetic field components $B_y^{GSM}$ and $B_z^{GSM}$ in geocentric solar magnetospheric coordinates (GSM). This model has an explicitly defined realistic magnetopause which is represented by a semi ellipsoid of rotation towards the Sun and by a cylindrical surface in the far tail for $x^{GSM} \le -60R_E$.

Tsyganenko model T01 (Tsyganenko 2002a,b) is based on the same principles as the model T96 but has essential improvements. The T01 model considers the variable configuration of the inner and near magnetosphere for different interplanetary conditions and ground disturbance levels.

<footnote n="1">¹The $Kp$-index is a quasi-logarithmic quantity for the variation of the magnetic field intensity at the Earth's surface as function of time. The range of the $Kp$-index is 0° (for quite conditions) over 0+, 1-, 1+ to 9° (for extreme disturbed magnetic field (geomagnetic storm)). It is derived from the maximum fluctuations of the horizontal components of the Earth's magnetic field observed by observation stations around the world and is published every 3 h.</footnote>
Tsyganenko model T04 (Tsyganenko and Sitnov 2005) is a dynamical model of the storm-time geomagnetic field in the inner magnetosphere, using space magnetometer data taken during 37 major events in 1996–2000 and concurrent observations of the solar wind and the interplanetary magnetic field. Therefore, this model is only applicable for times with strong disturbances of the geomagnetic field.

The Tsyganenko model T89 is usually used to compute cosmic ray trajectories in the geomagnetosphere due to the much simpler utilisation with only a few input parameters (date, time, Kp-index) and the much less time-consuming computation effort compared to the other Tsyganenko models.

The magnetic field of the magnetosheath is usually not considered in the computation of cosmic ray particle trajectories, although the change in the direction of approach at the border of the geomagnetosphere due to the effect of the magnetosheath may be a few 10° at low rigidities ($R \sim 1$GV) (Bütikofer et al. 1997).

## 5.4 Computation of the Propagation of Cosmic Ray Particles in the Earth's Magnetosphere

There exists no solution of the equation of motion of a charged particle in the geomagnetosphere magnetic field in a closed form. Therefore the determination of cosmic ray trajectories in the geomagnetosphere is almost exclusively made by numerical integration on computer by using a model of the magnetic field in the geomagnetosphere. The cosmic ray particle trajectories are computed backward, i.e. starting at the location of observation and compute the trajectory away from the Earth. Thereby the effect is used that the path of a negatively charged particle with mass, m, charge, Ze, and speed, v, in a static magnetic field, B, is identical to that of an identical but positively charged particle with reverse sign of the velocity vector. For observation locations at ground the computations start at an altitude of typically 20 km above sea level as the interactions of primary cosmic ray particles with atoms and atomic nuclei in the atmosphere become important below this altitude (Smart et al. 2000).

The equations of motion of charged particles in a known magnetic field $B(r, \theta, \phi)$ in a spherical coordinate system $(r, \theta, \phi)$ are:

$$ 
\begin{aligned}
\frac{dv_r}{dt} &= \frac{Ze}{m}(v_\theta B_\phi - v_\phi B_\theta) + \frac{v_\theta^2}{r} + \frac{v_\phi^2}{r} \\
\frac{dv_\theta}{dt} &= \frac{Ze}{m}(v_\phi B_r - v_r B_\phi) - \frac{v_r v_\theta}{r} + \frac{v_\phi^2}{r \tan \theta} \\
\frac{dv_\phi}{dt} &= \frac{Ze}{m}(v_r B_\theta - v_\theta B_r) - \frac{v_r v_\phi}{r} - \frac{v_\theta v_\phi}{r \tan \theta}
\end{aligned}
\qquad (5.13) $$
$$ 
\begin{aligned}
\frac{dx}{dt} &= v_r \\
\frac{d\theta}{dt} &= \frac{v_\theta}{r} \\
\frac{d\phi}{dt} &= \frac{v_\phi}{r \sin \theta}
\end{aligned}
 $$

where $B_r, B_\theta, B_\phi$ are the known magnetic field components, $v_r, v_\theta, v_\phi$ are the particle velocity components, $c$ is the speed of light, $Ze$ and $m$ are respectively the charge and the mass of the particle, and $r$ is the radial distance of the location of the particle from the center of the Earth.

The statement of the problem of the particle trajectory computation belongs to the category of initial value problems. They start at a selected time $t_0$ and with a set of known variables $r_0, \theta_0, \phi_0, v_{r0}, v_{\theta0}, v_{\phi0}$. From this set of initial values the corresponding values after a short time interval $\Delta t$, i.e. at time $t_0 + \Delta t$, can be computed.

There exist different types of numerical methods to solve the initial value problems e.g. Runge-Kutta or Bulirsch-Stoer method (Press et al. 1986). These methods optimize in different ways the step size of the numerical integration, i.e. the interval size $\Delta t$, on the one hand to prevent that the error per step exceeds a preset maximum value and on the other hand to reduce the computation time. Different computer codes for the cosmic ray trajectory computations in the Earth's magnetic field have been developed (see e.g. Shea and Smart 1975; Flueckiger and Kobel 1990; Desorgher et al. 2006).

Figure 5.3 shows an illustration of charged particle trajectories with different rigidities entering the Earth at the same location from zenith direction. The cosmic

<figure><img src="image_45.png" /><figcaption>**Fig. 5.3** Charged particle trajectories with different rigidities in the Earth's magnetic field. (From Smart et al. 2000, reproduced with permission from publisher Springer for electronic and press publishing, license number: 4118710609018, license date: May 30, 2017)</figcaption></figure>
ray particle trajectories labeled 1–3 have high rigidities and are therefore less bent compared to the trajectories labeled with values >3. The trajectories 4 and 5 show loops, but both can escape the geomagnetosphere, i.e. cosmic ray particles with these rigidities can reach the specified location on Earth from zenith direction (“allowed trajectories”). Particles with even lower rigidities are more bent and the trajectories of these particles penetrate the Earth (re-entrant trajectories), i.e. particles with these rigidities can not reach the location of observation from zenith direction from outside of the geomagnetosphere (“forbidden trajectories”).

## 5.5 The Concept of Cutoff Rigidities and Asymptotic Directions

The “cutoff rigidities” and the “asymptotic directions” have been introduced to specify the geomagnetic effects on cosmic ray particles and to determine the cosmic ray particle spectral characteristics and the anisotropy near Earth but outside the geomagnetosphere from cosmic ray measurements at ground (neutron monitors, muon detectors) or by space based detectors within the geomagnetosphere.

The cutoff rigidity at a selected location and with a specific direction of incidence is defined as the rigidity below which the cosmic ray particles have no access to this location from the given direction of incidence, i.e. trajectories with rigidities larger than the cutoff are “allowed trajectories” whereas trajectories with rigidities below the cutoff rigidity are “forbidden trajectories”. The asymptotic direction of cosmic ray particles is used as the particle’s trajectory direction of approach at the boundary of the geomagnetosphere.

The cutoff rigidities are determined by trajectory calculations at discrete rigidity intervals starting from a value above the highest possible cutoff rigidity down below the lowest possible allowed trajectory. The trajectories over this rigidity range show different features: first discontinuity in asymptotic direction, first forbidden trajectory, then usually a range of allowed and forbidden trajectories (co-called cosmic ray penumbra), lowest allowed trajectory.

The following parameters are used to describe the cutoff rigidity (Cooke et al. 1991):

* main cutoff rigidity $R_M$ or upper cutoff $R_{ul}$: rigidity of the last allowed trajectory before the first forbidden. This cutoff rigidity is close to the first discontinuity rigidity $R_1$, $R_M \approx R_1$

* Störmer cutoff $R_S$ or lower cutoff $R_l$: rigidity of the last allowed trajectory, i.e. trajectories of particles with rigidities $< R_S$ are forbidden

* $R_c$: effective cutoff rigidity which is between $R_{ul}$ and $R_l$ taking into account the penumbra, see Eq. (5.15).
<figure><img src="image_46.png" /><figcaption>Fig. 5.4 Function $\alpha(R)$ for the station Jungfraujoch for vertical direction of incidence and corresponding cutoff rigidity values: $R_S$ (Störmer cutoff), $R_M$ (main cutoff), and $R_1$ (first-discontinuity rigidity)</figcaption></figure>

For a location of observation and for a selected direction of incidence the effect of the Earth's magnetic field on the accessibility of cosmic ray particles is described by the filter function $\alpha(R)$:

$$ \alpha(R) = \begin{cases} 0 & : \text{if trajectory is forbidden for rigidity } R \\ 1 & : \text{if trajectory is allowed for } R \end{cases} \qquad (5.14) $$

Figure 5.4 shows the function $\alpha(R)$ for the station Jungfraujoch for vertical direction of incidence.

The effective cutoff rigidity $R_c$ is given by

$$ R_c = R_S + \int_{R_S}^{R_M} \alpha(R) dR \qquad (5.15) $$

The effective geomagnetic cutoff rigidity $R_c$ depends on the location of the observer, the direction of incidence into the atmosphere, the date and time, and the degree of disturbance of the geomagnetic field. The cutoff rigidities for ground-based cosmic ray stations and for vertical incidence range from $R_c \approx 0$ GV at the magnetic poles to $R_c \approx 15$ GV at the geomagnetic equator.

If one follows the cosmic ray particle's trajectory away from the Earth, the amount of bending per path length caused by the magnetic field is decreasing, i.e. the direction of the particle's trajectory approaches asymptotically its direction with no magnetic field. In the field of cosmic rays the expression asymptotic direction is used for the direction of the cosmic ray particle trajectory when it penetrates the border of the geomagnetosphere (magnetopause). The asymptotic direction of a cosmic ray particle that reaches the location of observation from a selected direction depends on the geographic coordinates of the observer and of the cosmic ray particle's rigidity. Figure 5.5 shows the trajectory of a cosmic ray particle reaching a location on the Earth from a selected direction and its puncture through the magnetopause. The arrow gives the direction of the trajectory at the puncture: the asymptotic direction.
<figure><img src="image_47.png" /><figcaption>**Fig. 5.5** Illustration of a cosmic ray particle's trajectory through the geomagnetosphere reaching a selected location on the Earth from a selected direction and of its related direction of approach at the magnetopause (asymptotic direction)</figcaption></figure>

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<figure><img src="image_48.png" /></figure>
Chapter 6

Ground-Based Measurements of Energetic
Particles by Neutron Monitors

R. Bütikofer

**Abstract** Since the International Geophysical Year (IGY) in 1957/58, the world-
wide network of neutron monitors is the standard instrument to investigate the
variations of the cosmic ray flux near Earth (11-year modulation of the galactic
cosmic rays, Forbush decreases, solar cosmic ray events) in the GeV range.
The ensemble of neutron monitors together with the geomagnetic field acts as a
giant spectrometer and enables to deduce information about the primary cosmic
ray spectrum near Earth in the energy range ~500 MeV to ~15 GeV. For the
interpretation of the ground-based neutron monitor measurements, the transport of
the cosmic rays in the Earth's magnetic field as well as the transport in the Earth's
atmosphere and the detection efficiency of the secondary nucleons by the neutron
monitors must be known. The Neutron Monitor Data Base (NMDB) developed in
2008/09 enables a rapid accessibility to the data of the worldwide neutron monitor
network. A considerable number of neutron monitor stations send their data to
NMDB in real-time which enables the operation of space weather applications based
on neutron monitor data.

**6.1 Introduction**

The ground-based neutron monitors are relatively simple instruments in respect to
technology and electronics. They are ideally suited to measure the intensity of the
nucleonic component of the secondary cosmic radiation in the Earth’s atmosphere
and respond to primary cosmic ray particles in the GeV-range. Even after 60
years of operation the neutron monitors remain the state-of-the-art instrument for
measuring the intensity variations of the primary cosmic rays in the energy range
from ~500 MeV to ~30 GeV. This energy region complements the range above the
energies covered by space-based cosmic ray detectors. The worldwide network of

<footnote>R. Bütikofer (✉)
University of Bern, Physikalisches Institut, Sidlerstrasse 5, CH-3012 Bern, Switzerland</footnote>

<footnote>High Altitude Research Stations Jungfraujoch and Gornergrat, Sidlerstrasse 5, CH-3012 Bern,
Switzerland</footnote>

<footnote>e-mail: rolf.buetikofer@space.unibe.ch</footnote>
neutron monitors is an excellent tool to investigate variations of the primary cosmic ray flux near Earth such as 11-year modulation and the sudden transient effects as Forbush decreases<fnref n="1" /> and solar cosmic ray events. Since recently, neutron monitor measurements are also an important input for space weather applications.

In the International Geophysical Year 1957/58 the worldwide network of standardised neutron monitors was developed to investigate the variations of the cosmic ray intensity near Earth. There are two types of standardised neutron monitors in operation. The IGY (for International Geophysical Year) type was designed by Simpson (1955) in the early 1950s. About 10 years later Carmichael (1968) designed the larger NM64 monitor with an increased counting rate. Figure 6.1 shows the 18-IGY neutron monitor at Jungfraujoch, Switzerland (left) and the 6-NM64 monitor of Athens, Greece (right). The digits 18 respectively 6 give the number of the counter tubes deployed in the respective neutron monitor.

The ensemble of neutron monitors together with the geomagnetic field acts as a giant spectrometer and enables the determination of the spectral variations of the galactic cosmic rays near Earth and the spectral characteristics of the sporadic solar cosmic rays. In addition, the simultaneous detection of relativistic particles with the entire global network of neutron monitors provides information about the anisotropy of the cosmic ray flux near Earth as the viewing directions of each neutron monitor station at the border of the geomagnetosphere depends on the neutron monitor's location, on the cosmic ray particle's rigidity, and on the direction of incidence above the neutron monitor station.

To deduce the variation of the primary cosmic rays near Earth but outside the geomagnetosphere from neutron monitor measurements, the relationship between the neutron monitor count rate and the primary cosmic ray flux must be known.

<figure><img src="image_49.png" /><figcaption>**Fig. 6.1** 18-IGY neutron monitor Jungfraujoch, Switzerland, (left) and 6-NM64 neutron monitor Athens, Greece (right). The digits 18 respectively 6 give the number of the counter tubes of the corresponding neutron monitor station</figcaption></figure>

<footnote n="1">¹Decrease within hours in the galactic cosmic ray intensity near Earth caused by the passage of a coronal mass ejection (CME) and slow recovery within days, named after the American cosmic ray physicist Scott E. Forbush.</footnote>
When primary cosmic ray particles approach the Earth, they enter first the geomag-
netosphere, where the cosmic ray particles are deviated by the Earth's magnetic field
(Lorentz force) and then penetrate into the Earth's atmosphere, where the cosmic ray
particles make electromagnetic interactions with the atoms and molecules as well
as hadronic processes with the nuclei of the atmospheric constituents. A cascade of
various secondary particles is produced.

In Sect. 6.2 a short overview of the history of the neutron monitors is given. The transport of cosmic rays in the Earth's magnetic field is described in more detail in Chap. 5. The transport of cosmic ray particles through the Earth's atmosphere is addressed in Sect. 6.3. The neutron monitor, i.e. its structure, layout, the functions of the different parts of the detector, the response of the neutron monitor to primary cosmic rays, and environmental effects on the measurements are described in Sect. 6.4. As a single neutron monitor does not give information about the energy spectrum and the direction of the flux of the primary cosmic rays, a network of neutron monitors at different latitudes and longitudes is needed to retrieve this information. Today this network contains about 50 operating stations. Section 6.5 gives an overview about the worldwide network of neutron monitor stations. The neutron monitor database NMDB initiated in 2008/09 as an European FP7 project is presented in Sect. 6.6.

6.2 History

After the discovery of the cosmic rays in 1912 by Victor Hess, mainly ionisation
chambers on ground were used to investigate the variations of the cosmic ray
intensities. The basic ideas for the development of neutron monitors as a continuous
recorder of the cosmic ray intensity originated from the measurements by Simpson
(1948). He found that the latitude dependences of the intensities of the energetic
nucleonic component and of the evaporation neutrons from the secondary cosmic
rays in the atmosphere are several times larger than those of the ionising component
(ionisation chambers) and the hard component (muon counters). In addition, the
measurement of the nucleonic component allows to study the time variations of the
primary cosmic rays at lower energies than this is possible with ionisation chambers
or muon counters. These facts stimulated the development of new detectors that
measure the secondary neutrons in the atmosphere.

The neutron monitor designed by Simpson (1955) was adopted as the standard
detector during the International Geophysical Year (IGY) 1957/58 and was called
IGY neutron monitor. It became evident soon that better statistical accuracy was
required, in particular for the study of short-term events as e.g. solar cosmic ray
events, so-called GLEs (Ground Level Enhancements or Ground Level Events). In
1959 large sized proportional counter tubes were constructed and produced at the
Chalk River Nuclear Laboratories, Ontario, Canada. This led to the design and the
construction of the supermonitor or NM64 monitor for the International Quiet Sun
Year (IQSY) (Carmichael 1968). The counting rate of the NM64 monitor per unit
area of lead producer is about three times that of the IGY neutron monitor. Today mainly NM64 monitors are in operation.

The different neutron monitor stations are mostly operated by research institutions that are located near the stations. For the data exchange in the days of the advent of neutron monitors the operators of the stations sent their hourly data in the form of tables on paper by mail to the World Data Centers (WDCs) (Pyle 2000), later on magnetic tapes and afterward on floppy disks. With the internet the data exchange became much easier.

## 6.3 Transport of Cosmic Ray Particles in the Earth's Atmosphere

Primary cosmic ray particles that penetrate the atmosphere undergo multiple interactions resulting in showers of secondary particles. If the secondary nucleons (neutrons or protons) reach the ground, they can be detected by neutron monitors.

To deduce the cosmic ray characteristics at the top of the atmosphere from neutron monitor measurements, the transport in the atmosphere, i.e. the interactions of energetic particles with matter, and the detection efficiency of the neutron monitor must be known. The physics of the interactions in the atmosphere when cosmic ray particles enter the atmosphere are today usually simulated with Monte Carlo methods.

The Earth's atmosphere, i.e. the medium in which the interactions take place, is described by a model (Sect. 6.3.1). The essential nuclear interactions of the cosmic ray particles when entering into the atmosphere, which are relevant for ground-based neutron monitor measurements, are addressed in Sect. 6.3.2.

### 6.3.1 Model of the Earth's Atmosphere

There exist several models that describe the properties (pressure, temperature, density, chemical composition) of the Earth's atmosphere primarily as a function of altitude (US Standard Atmosphere, International Standard Atmosphere, NRLMSISE-00).

Within the Geant4 (Agostinelli et al. 2003) software PLANETOCOSMICS (Desorgher et al. 2006), which is often used to simulate the transport of cosmic ray particles in the atmosphere, it is possible to select between the MSISE-90 model and its upgraded version NRLMSISE-00 (Labitzke et al. 1985; Hedin 1991; Picone et al. 2002). MSIS stands for Mass Spectrometer and Incoherent Scatter Radar, E indicates that the model extends from the ground through the exosphere and the number at the end of the short name is the year of release. NRL stands for the US Naval Research Laboratory. Both models provide temperature, density and
concentration profiles vs. altitude from the ground to the exobase (~450–500 km) as function of geographic latitude, longitude, date and time in UT, $F_{10.7}$ index (10.7 cm solar radio flux used as solar UV proxy), $F_{10.7\text{A}}$ index (3 month average of $F_{10.7}$) and the geomagnetic index $A_p$. The dependence of the model on $F_{10.7}$, $F_{10.7\text{A}}$, and $A_p$ is neglectable below 80 km. The Earth's atmosphere is divided into superposed homogeneous layers above a solid Earth. The density and composition of the layers are computed according to the altitude or atmospheric depth from the atmospheric model and are constant throughout each layer. The thickness of the layers may be selected by the user. The models may take different geometries: flat or concentric spherical geometry. In the case of the spherical geometry the Earth is modeled by a sphere of 6371.2 km radius and overlying curved layers.

### 6.3.2 Particle Cascade in the Atmosphere

When primary cosmic ray particles enter the Earth's atmosphere, they make electromagnetic interactions with the atoms and molecules of the atmospheric gases and hadronic interactions with the nuclei of the atmospheric matter. Thereby the cosmic ray particles rapidly lose energy and produce various secondary particles. The mean free path for nuclear interactions of a cosmic ray particle (proton) with nitrogen or oxygen nucleus is ~75 g/cm².

For the interpretation of neutron monitor measurements the nucleonic or hadron component in the atmosphere is relevant. The products of the nucleonic interactions are secondary nucleons and pions ($\pi^+, \pi^-$, and $\pi^0$). The secondary protons lose their energy mainly by ionisation. When the secondary nucleons have sufficient energy, they continue to multiply in successive generations of nuclear collisions until the energy of the particles drops below the energy that is required for multiple pion production, i.e. about 1 GeV. Secondary protons and ions with energies $\le 100$ MeV no longer undergo hadronic interactions, they are rapidly decelerated to rest by ionisation. On the other hand the neutrons still make nuclear interactions at these energies as well as elastic collisions with nuclei in the atmosphere. Below 10 MeV the neutrons lose their energy continuously by elastic collisions with atmospheric nuclei before they are captured by nucleons at thermal energies.

The neutral pions $\pi^0$ have a very short mean lifetime $\tau = 1.78 \times 10^{-16}$ s. The $\pi^0$ decays immediately into two $\gamma$-rays which initiate an electromagnetic cascade. The charged pions $\pi^+$ and $\pi^-$ decay into muons $\mu^+ \to \mu^+ + v_\mu$ and $\pi^- \to \mu^- + \bar{v}_\mu$ with a mean lifetime of $2.55 \times 10^{-8}$ s. The muons are slowed down mainly by ionisation. The low energy muons have time to decay ($\tau = 2.2 \times 10^{-6}$ s) before they reach the ground. The reactions are $\mu^+ \to e^+ + v_e + \bar{\nu}_\mu$ and $\mu^- \to e^- + \bar{\nu}_e + v_\mu$. However, many of the muons are produced with very high energies in the uppermost layers of the atmosphere and as these muons lose only little energy they have a large path length and survive (time dilatation according to the theory of relativity) and reach the surface of the Earth. The muons deep in the atmosphere and at sea level
are the most dominant component of the secondary cosmic rays and are therefore the dominant source of ionisation in this altitude range.

The primary particles at the top of the atmosphere must have an energy of roughly 500 MeV per nucleon to produce a cascade of secondary nucleons that can reach the ground at sea level. In high latitude regions, where the shielding effect of the Earth's magnetic field for incident cosmic rays is low, the lower threshold of the neutron monitor response is controlled therefore by the atmospheric mass which is ~1030 g cm⁻² at sea level. For high latitude neutron monitors at sea level this atmospheric cutoff for primary cosmic rays is ~450 MeV/nucleon. In regions like Central Antarctica, at an elevation of ~3 km above sea level (asl), the reduced atmospheric mass lowers the threshold to ~300 MeV/nucleon (Mishev et al. 2014).

## 6.4 Neutron Monitor Detector

Neutron monitors cover the energy range of primary cosmic ray particles from ~0.5 to ≳100 GeV per nucleon. This energy range includes the solar modulation of the galactic cosmic rays, Forbush decreases, sporadic GLEs or relativistic SEP (Solar Energetic Particle) events, and geomagnetic effects. The longterm stability of neutron monitors is generally excellent so that the cosmic ray effects of the 11-year solar activity cycle can be investigated over several solar cycles. The longest time series of single neutron monitor stations are available over a period of ~60 years, i.e. during a time range over more than five solar activity cycles. The comparison of the measurements of different neutron monitor stations have however shown that some neutron monitors may show a degrading of the detector efficiency (Bieber et al. 2007).

As the name suggests, neutron monitors record predominantly the secondary neutrons from the atmospheric cascades. The contribution to the total neutron monitor counting rate of an NM64 are neutrons ~85%, protons ~7%, µs ~6%, πs ~1% (Hatton 1971).

The functionality, construction and other properties of a neutron monitor are described in Sect. 6.4.1. The response of the neutron monitor to primary cosmic ray particles at the top of the Earth's atmosphere is explained in Sect. 6.4.2. The influence of the atmospheric effects on the neutron monitor measurements are addressed in Sect. 6.4.3.

### 6.4.1 Components of a Neutron Monitor

Both neutron monitor types IGY (Simpson 1955) and NM64 (Carmichael 1964) employ the same measurement strategy, i.e. the difference in the way high and low energy neutrons interact with different nuclei. As a particle with no electric charge, the neutron makes only interactions with nuclei and can therefore penetrate
large layers of material without interactions because of the small range of the strong nuclear force. Energetic neutrons can make three different kinds of interactions with nuclei: elastic and inelastic collisions as well as nuclear reactions. After a hadronic interaction of an energetic neutron with a nucleus, the excited target nucleus emits so-called evaporation neutrons. The production of these evaporation neutrons is proportional to $A^{2/3}$ according to the nuclear physics theory, where A is the atomic weight of the target nucleus. In a material containing nuclei with low atomic mass, the neutrons are effectively slowed down (moderated) in elastic collisions.

These facts led Simpson to the neutron monitor detector concept: production of fast neutrons in a target with high atomic weight, braking of the fast neutrons in a hydrogenous material, and finally detection of the thermic neutrons indirectly by ionising particles that are produced in a neutron induced nuclear reaction.

Figure 6.2 shows a schematic diagram of the NM64 neutron monitor. A standard NM64 neutron monitor with six counter tubes (6-NM64) has the following dimensions: width: ~315 cm, depth: ~220 cm, and height: ~50 cm. The lead producer with ~9650 kg is by weight the major component of an 6-NM64 monitor.

The different components of a neutron monitor detector are described in the following. The given specifications are valid for the NM64 neutron monitor (Carmichael 1964):

**Reflector** The whole assembly of the detector is enclosed by polyethylene (proton-rich material) of an average thickness of 7.5 cm. The task of the reflector is to reflect and to moderate the evaporation neutrons that are produced in the lead producer. The polyethylene (moderator material) contains a significant fraction of hydrogen, i.e. the energy loss per elastic collision of a neutron with the moderator material is maximal as the mass of the projectile and of the hydrogen nuclei in the target material are almost equal (conservation of momentum and energy). The neutron elastic interaction pathlength with hydrogen in polyethylene is roughly 1 cm for

<figure><img src="image_50.png" /><figcaption>Fig. 6.2 Schematic view of a 6-NM64 neutron monitor</figcaption></figure>
neutrons with energies $\leq 1$ MeV and in each collision the incident neutron reduces its kinetic energy on average by a factor of 2, i.e. the evaporation neutrons are very effectively slowed down in the reflector.

In addition, this neutron monitor component has the function to reflect and to absorb the low energy neutrons that are produced by high energy nucleons in interactions with the ambient material of the neutron monitor, e.g. detector housing.

In contrast, this reflector is largely transparent to the energetic neutrons that are produced in the cosmic ray induced cascade in the atmosphere, i.e. these energetic neutrons can easily reach and enter the lead producer.

**Producer** The core of the neutron monitor consists of a lead producer, a target with high atomic mass (A), to produce secondary neutrons. The average depth of 13.8 cm (156 g/cm²) corresponds to about 75% of the inelastic mean-free path of nucleons in lead. Thus ~50% of the nucleons, that cross the reflector and enter the lead, make at least one interaction in the producer. The production rate of neutrons per inelastic nucleon-nucleus interaction is roughly proportional to $A^{0.7}$ in the energy range 100-700 MeV of the interacting nucleon and slowly decreases with increasing energy (Shen 1968). The average number of produced neutrons (multiplicity) depends weakly on the incident nucleon energy, i.e. a neutron monitor can be used as an energy spectrometer by measuring the multiplicity only limited. On average about 15 evaporation neutrons with mean energy ~2.5 MeV are produced per nuclear reaction (Hatton 1971). These neutrons amplify the cosmic ray signal and can not easily escape the reflector. The lead producer is interspersed with a moderator and the BF₃ proportional counter tubes.

**Moderator** Each counter tube is surrounded by a polyethylene tube with a thickness of 2 cm acting as a moderator for the evaporation neutrons that are generated in the lead producer.

**Proportional Counter** The proportional counter tubes are filled with BF₃ (boron trifluoride) as counter gas. The BF₃ has been 90% enriched with the ¹⁰B isotope. When the very slow neutrons (thermal neutrons, $E = \frac{3}{2} k T = \sim 0.04$ eV) encounter a ¹⁰B₅ nucleus in the proportional counter, the following favoured reaction may take place:

$$ ^{10}\text{B}_5 + n \rightarrow ^{7}\text{Li}_3 + \alpha \qquad (6.1) $$

The cross-section for this reaction is inversely proportional to the neutron speed and has a value of about $3.0 \cdot 10^{-25} \text{m}^2$ or 3000 barns at neutron energy 0.04 eV and only roughly 0.2 barns at 1 MeV (Clem and Dorman 2000). The produced $\alpha$-particle and the Li-nucleus are accelerated by the applied high voltage within the counter tube, ionize the counter gas and the produced electrons cause an electric signal. The electric signal is amplified, discriminated and counted by a counter electronic. The detection probability of the evaporation neutrons is ~5.7% (Hatton 1971).

Later proportional counter tubes were filled with ³He as an alternative to the standard BF₃ counters, as BF₃ is highly toxic. The He counters require a higher
pressure to have an efficiency close to the BF₃ counters and they have a much higher temperature sensitivity and therefore require better environmental temperature stability. Currently, new neutron monitor counter tubes use again BF₃ because of the very high price for ³He.

As an incident neutron or proton into the neutron monitor may produce more than one evaporation neutron in the lead producer, it can be expected that a group of count signals is observed (multiplicity). However, the efficiency for detecting these evaporation neutrons is low. Therefore, the average detected multiplicity is typically not much larger than one. Due to the multiplicity effect in the neutron monitor the count impulses are not equally distributed. Therefore the variance of the counting rate σ(N) is not Poisson distributed. One has σ(N) > √N. The variance of the counting rate σ(N) is given by:

$$ \sigma(N) = k \cdot \sqrt{N} \qquad (6.2) $$

where k is around 1.5 for an NM64 monitor (Hatton 1971).

The average count rate of an 6-NM64 monitor at high latitude and at sea level is ~4200 counts per minute. Due to the multiplicity effect in the neutron monitor the relative random error for 1-min values is therefore ~2.5%. The count rate of an equatorial sea-level 6-NM64 monitor is ~0.7 times the count rate of an identical neutron monitor at high latitudes. Neutron monitors at high altitudes have higher counting rates because of the smaller atmospheric attenuation. The count rate of a neutron monitor at high latitudes and at an altitude of ~3000 m asl is about a factor of ten higher than at sea level.

## 6.4.2 Neutron Monitor Yield Function

The transport of cosmic ray particles through the Earth's atmosphere and the detection of the nucleonic component of the secondary cosmic rays by the neutron monitors are combined in the so-called neutron monitor yield function. The neutron monitor yield function can therefore directly be used to determine the cosmic ray flux at the top of the Earth's atmosphere from the measurements of the worldwide neutron monitors. Essentially, two methods are used to determine the neutron monitor response function:

* parameterisation of latitude survey observations (neutron monitor measurements e.g. on a ship cruise along a large range of geomagnetic latitudes)

* Monte Carlo simulations of the cosmic ray transport through the Earth's atmosphere and of the detection efficiency for the different secondary particles in the neutron monitor

The most commonly used response function based on latitude surveys is the Dorman function (Dorman and Yanke 1981). The Dorman function represents most latitude surveys fairly well, however the trend of the response function at low rigidities
can not be retrieved from latitude surveys. Belov and Struminsky (1987) made modifications to the Dorman function for rigidities <2.78 GV.

Different authors have determined the neutron monitor yield function with Monte Carlo simulations. In 1982 Debrunner et al. calculated the specific yield function for sea level neutron monitors. Clem and Dorman (2000) applied the FLUKA Monte-Carlo package (Fassò et al. 1993) for the simulations. In recent years different groups (Flückiger et al. 2008; Matthiä 2009; Mishev et al. 2013) used the Geant4 software package (Agostinelli et al. 2003) to compute the neutron monitor yield function. For the transport in the atmosphere the Geant4 software suite PLANETOCOSMICS (Desorgher et al. 2006) has been mostly used. Some of the determined yield functions are valid only for neutron monitors at sea level. This requires pressure corrections of the neutron monitor count rates to sea level. Mainly for high altitude neutron monitor stations these corrections may be inaccurate as the parameter for the barometric corrections depends on the cosmic ray spectrum, see Sect. 6.4.3. The yield function by Flückiger et al. (2008) is valid for different altitudes, i.e. the atmospheric depth of the neutron monitor station is a parameter of this yield function.

The relation between the counting rate $N_x$ of the neutron monitor station x and the differential fluxes of the different components k of the primary cosmic rays at the border of the geomagnetic field, $\psi_k$, can be described by the following formula:

$$N_x(h, \Lambda, \chi, t) = \sum_k \int_0^{2\pi} \int_0^{\pi/2} \int_0^{\infty} \alpha(R, \theta, \phi, \Lambda, \chi, t) \cdot \psi_k(R, \theta, \phi, \Lambda, \chi, t) \cdot \sin\theta \cdot S_x^k(h, R, \theta) \cdot A_x \cdot \cos\theta \cdot dR \, d\theta \, d\phi \quad (6.3)$$

where

* $\alpha$ filter function which is 1 for allowed cosmic ray particle trajectories and 0 for forbidden trajectories (Chap. 5).

* $R$ rigidity of the primary cosmic ray particle. $R = \frac{p \cdot c}{Z \cdot e}$ where p is the momentum of the particle, Ze is its charge and c is the speed of light.

* $\theta, \phi$ zenith and azimuth angle of the primary cosmic rays at the top of the atmosphere.

* $\Lambda, \chi$ geographic latitude and longitude of the neutron monitor station location.

* $t$ date and time in UT.

* $S_x^k$ yield function. It gives the number of count events produced by a primary particle of type k in the neutron monitor station x. The yield function depends on the rigidity, on the zenith angle, $\theta$, of the incident particle, and on the atmospheric depth, $h$, of the neutron monitor station.

* h atmospheric depth of the neutron monitor station.

* $A_x$ area of the neutron monitor station, x.
### 6.4.3 Atmospheric Effects

Because of the interactions of the primary and secondary cosmic ray particles with the matter of the Earth's atmosphere, the neutron monitor count rate depends also on meteorological conditions (Carmichael et al. 1968). With constant cosmic ray intensity at the top of the Earth's atmosphere the counting rate of a neutron monitor depends mainly on the atmospheric mass above the detector and in much lower degree on the temperature profile and on the water content in the atmosphere. Because of the relative small effects and because of the large complexity to determine the temperature profile and the water content in the atmosphere, only the change in the atmospheric mass is considered for neutron monitor measurements. In practice, the barometric pressure is used as a proxy for the air mass to correct the neutron monitor data to a constant atmospheric depth.

The dependence of the neutron monitor count rate upon atmospheric pressure is usually described by an exponential function:

$$N(p(t)) = N(\bar{p}) \cdot \exp\left(\frac{\bar{p} - p(t)}{\lambda}\right) \qquad (6.4)$$

where

$N(p(t))$ measured count rate at atmospheric pressure $p$ and at time $t$.

$N(\bar{p})$ neutron monitor count rate at some standard pressure $\bar{p}$.

$\lambda$ attenuation length of the nucleonic component of the cosmic radiation in the Earth's atmosphere.

The attenuation length $\lambda$ depends on the altitude, the geomagnetic latitude and on the primary cosmic ray spectrum. The attenuation length is larger for harder primary rigidity spectra and vice versa.

During a solar cosmic ray event measured by neutron monitors, the cosmic ray near Earth includes a galactic and a solar component. The solar particles show a softer rigidity spectrum compared to the spectrum of the galactic cosmic rays. The attenuation length for galactic cosmic rays $\lambda_g$ is about 140 g/cm², whereas the value for the solar cosmic rays $\lambda_s$ is typically around 100 g/cm². The two-attenuation length method by McCracken (1962) considers this fact.

The pressure corrected neutron monitor counting rate to the selected standard pressure $\bar{p}$ during a solar cosmic ray event can be written as follows by assuming that the galactic cosmic ray intensity during the solar cosmic ray event does not change:

$$N(t, \bar{p}) = N_0(p_0) \cdot \exp\left(\frac{p_0 - \bar{p}}{\lambda_g}\right) + \left[N(t, p(t)) - N_0(p_0) \cdot \exp\left(\frac{p_0 - p(t)}{\lambda_g}\right)\right] \cdot \exp\left(\frac{p(t) - \bar{p}}{\lambda_s}\right) \qquad (6.5)$$
where

$N(t, \bar{p})$ pressure corrected count rate to the standard pressure $\bar{p}$ of the neutron monitor station during a solar cosmic ray event.

$N_0(p_0)$ average measured count rate with an average atmospheric pressure $p_0$ during the reference time interval (typically the full hour before the onset of the solar cosmic ray event).

$\lambda_g$ attenuation length for the nucleonic component of the galactic cosmic rays in the Earth's atmosphere.

$N(t, p(t))$ measured count rate at time $t$ and atmospheric pressure $p(t)$.

$\lambda_s$ attenuation length for the nucleonic component of the solar cosmic rays in the Earth's atmosphere.

The first summand of equation (6.5) is the contribution to the count rate by the galactic cosmic ray corrected to the standard pressure $\bar{p}$. The second summand is the pressure corrected count rate caused by the solar cosmic rays. The expression between square brackets is the measured part to the counting rate caused by the solar cosmic ray at time $t$. For the determination of this portion the measured counting rate during the reference time interval $N_0(p_0)$ has to be corrected to the current atmospheric pressure $p(t)$ and has to be subtracted from the measured count rate $N(t, p(t))$ during the GLE.

The barometric pressure coefficient for galactic cosmic rays $\alpha = \lambda^{-1}$ for a neutron monitor has a value in the order of 1%/mmHg (or $0.0072 \text{ mbar}^{-1}$), i.e. the change in the air mass above a neutron monitor station has a large effect upon the count rate. Therefore, the barometric pressure at a neutron monitor station must be determined very accurately, as an error in the pressure measurement of 1 mmHg causes a change in the count rate of ~1%. As the spectrum of the galactic cosmic ray changes during the 11-year solar activity cycle, the barometric coefficient $\alpha$ shows a variation as well and should therefore be determined periodically.

Neutron monitor stations at exposed locations (e.g. high altitudes) may considerably be affected by environmental effects. These neutron monitor stations are heavily exposed to high wind speeds and gusty winds which may strongly affect the atmospheric pressure measurements. Consequently, the correction of the neutron monitor count rates for the effects of changes in the air mass above the detector using raw barometer data may lead to erroneous results (Bütikofer and Flückiger 1999). In addition, there are other environmental effects on the neutron monitor counting rate, e.g. the accumulation of snow on the roof and around the detector housing. This effect must usually not be taken into account during a solar cosmic ray event. However, when investigating long time data series, the use of neutron monitor stations, where possible changes of snow accumulations may occur on the roof and around of the detector housing, must be considered with care. These effects must be considered especially for the NM64 type as the thickness of the reflector is only 7.5 cm compared to 28 cm in the IGY neutron monitor. In the NM64 monitor the evaporation neutrons, that are produced in the surrounding material of the neutron
monitor, contribute to the counting rate with ~5% (Hatton 1971) and changes of this matter in the immediate environment therefore affect the counting rate.

## 6.5 Worldwide Network of Neutron Monitor Stations as a Giant Spectrometer

The ‘Simpson’ neutron monitor (Simpson 1955) was the standard cosmic ray detector for the International Geophysical Year (IGY) 1957/58, and it was called the ‘IGY’ neutron monitor. During the years 1957–1959 a worldwide network of 51 monitors was established. After the International Geophysical Year 1957/58 some of the IGY neutron monitors stopped, however most stations continued operating. With the launch of the NM64 or ‘supermonitor’ in the 1960s by Carmichael (1968) many of the IGY neutron monitors were replaced by the new detector type. During this transition time most principal investigators operated both neutron monitor types in parallel for some months to determine a normalization factor for long term studies. Today the majority of the worldwide network comprises NM64 monitors, however there are still a few IGY neutron monitors in operation. Figure 6.3 shows a world map with the locations of the neutron monitor stations that have been in operation in 2017 or only recently been closed. In 2017 about 50 neutron monitor stations have been in operation.

The Earth’s magnetic field establishes the worldwide network of neutron monitors to a huge spectrometer. The rigidity range of this spectrometer is determined by the atmospheric cutoff at the lower rigidity border and by the highest magnetic cutoff rigidity at the other end. Although the magnetic cutoff rigidity near the geomagnetic

<figure><img src="image_51.png" /><figcaption>**Fig. 6.3** World map with the locations of neutron monitors which have been in operation in 2017 or only recently been closed</figcaption></figure>
poles is 0 GV as the magnetic field lines enter vertically into the Earth, the primary cosmic ray particles penetrating the top of the atmosphere must have a minimal energy that the secondary nucleons can reach the ground. This atmospheric cutoff energy for a sea level detector is ~450 MeV, i.e. a rigidity of ~1 GV for protons. The maximum vertical magnetic cutoff rigidity is ~15 GV. The measurements of the worldwide network of neutron monitors enable therefore to determine spectral variations of the galactic cosmic rays near Earth and the spectral characteristics of GLEs in the energy range from ~500 MeV to ~15 GeV.

When working with neutron monitor data it is important to realise that the neutron monitor stations of the worldwide network are operated by different institutes, i.e. the measurements (e.g. obvious outliers in the count rate, data gaps etc.) are handled differently. The neutron monitor stations are located at very different locations (sea level, high altitude, polar regions), therefore e.g. the stability of the temperature inside the detector housing, of the humidity as well as the behaviour of the electronic devices may differ and cause different qualities of the measurements. In earlier days there were also problems with the accuracy of the used clocks.

## 6.6 Neutron Monitor Database: NMDB

In the early days of neutron monitors, the cosmic ray scientists exchanged their data with data tables and books (mostly on a monthly/half-year basis and only with a resolution of one hour). Later the operators of neutron monitor stations wrote the measured data on storage media like magnetic tapes or floppy disks and sent these media to the World Data Centers (WDC) in the USA, USSR, and Japan (Pyle 2000). For neutron monitor data analysis the scientists ordered the data either directly from the PIs or from the WDCs and received the data on magnetic tape and later on compact discs. The advent of the internet made the data exchange much easier. The different groups published their measurements on their own webpage. More and more the cosmic ray scientists have the demand to have the measurements of the worldwide network available in real-time. There were also some initiatives to develop a data base for neutron monitor data, however only the project "NMDB – Real-Time database for high resolution Neutron Monitor measurements" (http:\www.nmdb.eu) funded by the Commission of the European Communities as an FP7 project in the years 2008/09 was successful. A number of 12 institutions were involved in the project. First only the data of the institutions involved in the project were brought into NMDB. However, since then the number of neutron monitor stations that send their data to the NMDB has increased and in 2017 a total of about 40 neutron monitor stations transmit their data regularly to NMDB, about 30 neutron monitor stations in real-time or near real-time. The neutron monitor measurements are stored in NMDB as 1-min and hourly data.
<figure><img src="image_52.png" /><figcaption>**Fig. 6.4** Relative increase of pressure corrected 2-min data of the neutron monitor stations Oulu, Apatity, Kiel and Rome during GLE#70 (13 December 2006) plotted with NEST</figcaption></figure>

In addition to the database there are different applications available from the NMDB webpage www.nmdb.eu (Mavromichalaki et al. 2011). NMDB provides e.g. the application NEST (http://www.nmdb.eu/nest/) to generate plots of the count rate of selected neutron monitor stations with different time resolutions. It is also possible to plot neutron monitor data together with the sunspot number (smoothed or monthly), geomagnetic *Kp*-index (3-hourly), or GOES data (channels >10 MeV, >50 MeV, >100 MeV). The plots can be modified by different style adjustments. The generation of plots during GLEs and Forbush decreases from the past can be selected with one click. Figure 6.4 shows as an example the measured relative increase in the count rate of a selection of neutron monitors during GLE#70 on 13 December 2006 as plotted with the NMDB NEST application. In addition to the graphic output it is also possible to extract ASCII data from NMDB with NEST. Other NMDB applications are e.g. GLE alarm systems or GLE characteristics determination.

In addition to NMDB the Cosmic Ray Station of the University of Oulu reactivated and operates the GLE database http://gle.oulu.fi/ where the neutron monitor data of the worldwide network during GLEs are stored and are made available for plotting and for downloading.
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<figure><img src="image_53.png" /></figure>
Chapter 7

HESPERIA Forecasting Tools: Real-Time
and Post-Event

Marlon Núñez, Karl-Ludwig Klein, Bernd Heber, Olga E. Malandraki, Pietro Zucca, Johannes Labrens, Pedro Reyes-Santiago, Patrick Kuehl, and Evgenios Pavlos

**Abstract** Within the HESPERIA Horizon 2020 project, two novel real-time tools to predict Solar Energetic Particle (SEP) events were developed. The HESPERIA UMASEP-500 tool makes real-time predictions using a lag-correlation between the soft X-ray (SXR) flux and high-energy differential proton fluxes of the GOES satellite network. We found that the use of proton data alone allowed this tool to make predictions before any Neutron Monitor (NM) station's alert. The performance of this tool for predicting Ground Level Enhancement (GLE) events for the period 2000–2016 may be summarized as follows: the probability of detection (POD) was 53.8%, the false alarm ratio (FAR) was 30%, and the average warning time (AWT) to the first NM station's alert was 8 min. The developed HESPERIA REleASE tool makes real-time predictions of the proton flux-time profiles of 30–50 MeV protons at L1 and is based on electron intensity measurements of energies from 0.25 to 1 MeV and their intensity changes. The performance was tested by using all historic ACE/EPAM and SOHO/EPHIN data from 2009 until 2016 and has shown that the forecast tools have a low FAR (~30%) and a high POD (63%). Furthermore, two methods using historical data were explored for predicting SEP events and

<footnote>M. Núñez (✉) • P. Reyes-Santiago
Universidad de Málaga, Málaga, Spain
e-mail: mnunez@uma.es</footnote>

<footnote>K.-L. Klein • P. Zucca
Observatoire de Paris, Meudon, France
e-mail: ludwig.klein@obspm.fr</footnote>

<footnote>B. Heber • J. Labrens • P. Kuehl
Christian-Albrechts – University of Kiel, Kiel, Germany
e-mail: heber@physik.uni-kiel.de</footnote>

<footnote>O.E. Malandraki • E. Pavlos
National Observatory of Athens, IAASARS, Athens, Greece
e-mail: omaland@astro.noa.gr</footnote>
compared. The UMASEP-10mw tool was developed for predicting >10 MeV SEP events using microwave data. The time derivative of the soft X-rays (SXR) was replaced by the microwave flux density. It was found that the use of SXRs and microwave data produced the same POD (~78%) with the most notable difference being that the use of microwave data does not yield any false alarm. Furthermore, a study was carried out on the possibility for the microwave emissions to be used to predict the spectral hardness of the SEP event and important results were deduced.

## 7.1 Introduction

Forecasting solar energetic particle (SEP) events is of potential interest for spacecraft and launching operations, and for the assessment of radio wave propagation conditions in the polar ionosphere of the Earth. It will be mandatory for human spaceflight beyond low-Earth orbit, especially outside the Earth's magnetosphere. Besides predicting SEP events in general, the prediction of particularly energetic SEPs is a second aim of forecasting, because they penetrate deeper into the terrestrial atmosphere and contribute to the radiation dose aboard aircraft.

Operational real-time SEP forecasts are currently supported by empirical models which rely on observations of associated solar phenomena, including electromagnetic signatures of SEP acceleration/escape near the Sun and observations at the near-Earth environment (L1 or 1 AU) of energetic particles. In this chapter the two novel real-time SEP forecasting tools developed and operating within the HESPERIA project are presented, based on the University of MAlaga Solar particle Event Predictor (UMASEP) (Núñez 2011, 2015) and Relativistic Electron Alert System for Exploration (REleASE) schemes (Posner 2007).

The developed and operational HESPERIA UMASEP-500 tool makes real-time predictions of the occurrence of Ground Level Enhancement (GLE) events, from the analysis of soft X-ray (SXR) and differential proton flux measured by the Geostationary Operational Environmental Satellites (GOES) satellite network. Using near-relativistic as well as relativistic electrons as precursors for the arrival of energetic protons, the developed HESPERIA REleASE tools make real-time predictions of the proton flux-time profiles of 30–50 MeV protons at L1. Furthermore, two methods using historical data explored under the HESPERIA project for predicting SEP events are presented and compared. We have tested if the UMASEP scheme can be improved using microwave observations and also studied if the microwave emissions can be used to predict the spectral hardness of the SEP event and important results are deduced.

The first two sections of the chapter are dedicated to the investigations of whether historical microwave emissions can be used in the forecasting of SEP events (Sect. 7.2 and 7.3), whereas the two following sections describe the real-time HESPERIA SEP forecasting tools, using the REleASE and UMASEP proven concepts (Sect. 7.4 and 7.5). Concluding remarks as well as future possibilities are given in Sect. 7.6.
## 7.2 Predicting SEP Event Onsets from Historical Microwave Data by Using the UMASEP Scheme

Within the HESPERIA project we tested whether microwave emission could be used in the forecasting of SEP events. This is not possible in real time, because no real-time microwave data are presently provided. However, we attempted a proof-of-concept by using historical SEP events.

The UMASEP forecasting scheme (Núñez 2011, 2015) uses the positive time derivative of the observed SXR flux as an indicator of energy release at the Sun. The SXR burst shows the heating of the corona during a flare. The UMASEP scheme considers that a common positive derivative with the particle flux near Earth, with a suitable time delay, indicates a magnetic connection between the Earth and a site of particle acceleration near the Sun. It is well known (Neupert 1968; Dennis and Zarro 1993; Holman et al. 2011) that hard X-ray (HXR) or microwave bursts, produced by non-thermal electrons in the solar atmosphere through bremsstrahlung and gyrosynchrotron emission (see Chap. 2), have time profiles that mimic the time derivative of the SXR. The reason is a common time evolution of the energy release that goes to the electron acceleration on the one hand and to the heating of the plasma during the related flare on the other. While non-thermal electrons lose their energy rapidly through interactions with the solar atmosphere, the heated coronal plasma cools on much slower time scales, and its time evolution is therefore the integral over the distinct episodes of energy release traced by the non-thermal signatures. So as long as the microwave emission is due to gyrosynchrotron radiation of non-thermal electrons, its time profile can be considered as being close to the time derivative of the SXR profile in the impulsive flare phase.

Patrol observations of the whole Sun at microwaves can be conducted with ground-based antennas. The US Air Force operates the Radio Solar Telescope Network (RSTN) consisting of four stations around the world. These stations observe independently from each other, but with identical equipment at selected frequencies.

The most interesting frequencies for our purpose are 4.995 (henceforth referred to as 5 GHz), 8.8 and 15.4 GHz. The data are publicly available after about 1 year via the National Geophysical Data Center (NGDC).<fnref n="1" /> Data from the Nobeyama Radio Polarimeters<fnref n="2" /> (NoRP), (Torii et al. 1979; Nakajima et al. 1985), operated by the National Astronomical Observatory of Japan, were used for checking purposes and to replace RSTN when necessary.

In order to test to which extent microwave data can support the UMASEP scheme, we constructed a continuous time series of RSTN observations during a 13-month long period from December 2011 to December 2012. The observations

<footnote n="1">¹http://www.ngdc.noaa.gov/stp/space-weather/solar-data/solar-features/solar-radio/rstn-1-second/</footnote>

<footnote n="2">²http://solar.nro.nao.ac.jp/norp/html/event/</footnote>
<figure><img src="image_54.png" /><figcaption>**Fig. 7.1** The combined time history of the microwave flux density at two frequencies during the 13 months from 2011 Dec 01 to 2012 Dec 31, constructed from observations of the four RSTN stations</figcaption></figure>

of the individual RSTN stations have a number of problems that needed a careful consideration. We applied a series of standard treatments to remove spikes, data gaps, baseline drifts due to wrong antenna pointing. Then the corrected daily records of the individual stations were combined into the 13-month long time series. A uniform average background was added at each frequency, and smaller flux densities were set to the background value. 5-min integration further smoothes out short-term irregularities that remain after the data cleaning procedure.

Figure 7.1 shows the resulting flux density calculated for the 13 months interval from December 2011 to December 2012. At both frequencies numerous bursts are seen. During this period, nine SEP events were considered as well-connected events and four were considered as poorly connected. An SEP event in the sense used here is an event where the proton intensity at energies above 10 MeV exceeds 10 pfu.

Based on the UMASEP scheme the UMASEP-10mw tool was developed for predicting >10 MeV SEP events using microwave data, the time derivative of the SXR was replaced by the microwave flux density. The UMASEP thresholds were recalibrated. The tool UMASEP-10mw has been developed to be used for calculating the correlation between the solar microwave flux densities at 5 GHz and 8.8 GHz, which are monitored by patrol instruments, and the time derivatives of the near-earth differential proton fluxes measured in different energy channels (i.e. using the GOES satellites).
<figure><img src="image_55.png" /><figcaption>**Fig. 7.2** UMASEP-10mw output after processing microwave data at 5 GHz from 2012 July 12 and GOES proton fluxes of >10 MeV energies. The *yellow/orange* band in the proton intensity plots gives the predicted range, with the colour scale shown by the *vertical bar*.</figcaption></figure>

We illustrate the forecast of the UMASEP-10mw tool using microwave data at 5 GHz for predicting the >10 MeV SEP event.

Figure 7.2 shows the forecast graphical output that an operator would have seen if the UMASEP-10mw tool had processed real-time microwave data on 2012 July 12. The upper time series in both images shows the observed integral proton flux with energies greater than 10 MeV. The current flux is indicated below the label “now” at each image. To the right of this label, the forecast integral proton flux is presented as a yellow/orange-coloured band. The central curve in each panel displays the microwave flux density time profile, and the lower time series shows the magnetic connectivity estimation with the best-connected coronal mass ejection (CME)/flare process zone.

Figure 7.2 also shows the prediction at 18:05 (2012 July 12). This forecast is that an event will start during the following 2 h and reach a peak intensity of 36 pfu 9 (see white section “Automatic forecast”). Below the forecast section, the system also presents the model inference section, which shows that the Earth is well-connected with the solar region 11520. The system also shows that the associated X1.4 flare
took place at S15W01. As time passes, the integral proton flux also rises. At 18:35 UT, the flux exceeds the 10-pfu threshold, which indicates that a proton event is occurring. Note that the well-connected SEP event was successfully forecast 30 min earlier, when the enhancement of the integral proton flux was still weak (1.24 pfu).

To measure the overall performance of this tool, we run the UMASEP forecasting schemes using on the one hand the SXR observations, on the other hand the microwave observations at the two frequencies considered for the aforementioned period. We evaluated two quantities: the probability of detection (POD) is the number of the predicted SEP events divided by that of the SEP events that actually occurred, i.e. nine events in the considered time interval. The false-alarm ratio (FAR) is the number of false predictions over the number of predictions. Seven predictions were triggered when microwaves were used, and eight with SXR. We found that the use of SXR and microwave data produced the same POD = 77.8% (7/9). The most notable difference is that the use of microwave data does not yield any false alarm. The average warning time (AWT) is slightly higher when microwave observations are used 30.7 min as compared to 26.4 min.

The probabilities of detection used above are adequate to compare the performance of SXR and microwaves within the UMASEP scheme, but overestimate the expected ones: SEP events originating behind the solar limb are undetectable to the UMASEP Well-Connected Prediction model (WCP), because it uses electromagnetic observations from a terrestrial vantage point. This bias affects SXR from GOES and radio observations from ground alike.

A more detailed account of this work is given in Zucca et al. (2017).

## 7.3 Predicting SEP Energy Spectra from Historical Microwave Data

Depending on their peak intensity and spectral hardness, SEP events constitute different kinds of space weather hazard. Protons and heavy ions at energies between several MeV and several tens of MeV may interact with spacecraft and human beings above low-Earth orbit, and ionize the high polar atmosphere of the Earth. GeV protons create atmospheric cascades down to the Earth and enhanced radiation doses at aircraft altitudes. High intensities in the two energy ranges are not necessarily observed in the same events (Mewaldt et al. 2007). Besides the occurrence, spectral hardness is therefore a space-weather relevant information, and a second goal in SEP forecasting.

It was shown in Grechnev et al. (2015 and references therein) that SEP events above 100 MeV are often accompanied by strong microwave emission well above the average peak frequency of 10 GHz. On the other hand the peak flux density or peak fluence of microwave bursts also show some correlation with the peak intensity of SEPs at tens of MeV (Kahler 1982; Trottet et al. 2015). Chertok et al. (2009) went one step further and suggested that SEP events with hard proton
<figure><img src="image_56.png" /><figcaption>Fig. 7.3 Scatter plots of the spectral hardness of the proton spectrum $\delta$, versus the peak microwave flux density ratio at 8.8 and 15.4 GHz, labelled S9/S15. (a) Study by Chertok et al. (2009). (b) Present work based on data from GOES integral intensities above 10 MeV and above 100 MeV taken during solar cycles 23 and 24</figcaption></figure>

spectra in space in the 10–100 MeV range tend to be accompanied by microwave bursts where the flux density at the highest frequency continually monitored from ground, which is 15.4 GHz, exceeds the flux density at 9 GHz. The ratio of flux densities at the two frequencies, which is an easily observable parameter, seems to correlate significantly ($r = 0.55$) with the proton spectral hardness during solar cycles 22–23.

We re-examined the relationship during cycles 23 and 24, using the integral proton intensities measured by the GOES. We consider integral intensities above 10 MeV (designated by $J_{10}$ in the following) and 100 MeV ($J_{100}$) for events associated with activity in the western solar hemisphere, and calculated the ratio

$$ \delta = \log_{10} \left( \frac{J_{10}}{J_{100}} \right) \qquad (7.1) $$

In Fig. 7.3 the scatter plot between the proton spectral hardness $\delta$ and the ratio of peak flux densities at 8.8 and 15.4 GHz derived by Chertok et al. (2009) (a) is compared with our work (b). Both plots suggest a slight trend that SEP events with hard proton spectra are associated with microwave bursts that are stronger at 15.4 than at 8.8 GHz. But the correlation is questionable in cycles 23–24: the linear correlation coefficient of the sample in Fig. 7.3b is $0.26 \pm 0.20$ in solar cycle 23, and still weaker in solar cycle 24. So we find no convincing correlation that could support a forecasting procedure of spectral hardness of SEPs. We also tested a correlation between spectral hardness and the speed of the associated CME. This was also inconclusive, with a correlation coefficient of $0.15 \pm 0.16$ in solar cycle 23.

There is a number of reasons why a relationship between the microwave peak frequency and the SEP spectral hardness in the range (10–100) MeV could be masked. One is the likely contribution of different acceleration processes to the SEP
populations (Trottet et al. 2015) and the variation of their contribution with particle
energy (Dierckxsens et al. 2015). If the SEPs above 10 MeV were predominantly
accelerated by CME shocks, and those above 100 MeV by flares or similar processes
lower in the corona, no direct correlation would be expected. The other reason is
that the microwave flux density spectrum depends strongly on the magnetic field
strength and orientation in the radio source, which is also not expected to have an
effect on the SEPs. Finally there is an interesting hint that radio bursts with relatively
high flux density at 15.4 GHz (and flat SEP spectra) were lacking in solar cycle 24.
Forecasting schemes can of course use empirical correlations independently of our
understanding of the physical relationships. But this does not seem convincing in
the present case.

## 7.4 Predicting 30–50 MeV SEP Events by Using the RELEASE Scheme

The fact that near relativistic electrons (1 MeV electrons have 95% of the speed of light) travel faster than ions (30 MeV protons have 25% of the speed of light) and are always present in SEP events, a forecast of the arrival of protons from SEP events can be based on real-time measurements of near relativistic electrons. The faster electrons arrive 30–90 min before the slower protons at Lagrangian point 1. The Relativistic Electron Alert System for Exploration (RELEASE) forecasting scheme uses this effect to predict the proton flux by utilizing the actual electron flux and the increase of the electron flux in the last 60 min. A detailed description of the RELEASE scheme can be found in (Posner 2007). The original RELEASE code uses real-time electron flux measurements from the Electron Proton Helium Instrument (EPHIN) (Müller-Mellin 1995) on board the Solar and Heliospheric Observatory (SOHO) to forecast the expected proton flux.

RELEASE is based on electron intensity measurements of energies from 0.25 to 1 MeV and their intensity changes. It utilizes an empirical matrix in order to predict the proton intensity 30, 60 or 90 min ahead. Figure 7.4b displays the forecast matrix for one proton channel and the 60-min interval. EPHIN provides realtime data which are used with the RELEASE scheme. One disadvantage of EPHIN data is the limited time coverage in the realtime data of less than 4 h per day. If no realtime data are available as input for the RELEASE scheme, no forecast can be produced. The Electron Proton Alpha Monitor (EPAM) onboard the Advanced Composition Explorer (ACE) was selected to be a good candidate to deliver continuously input for RELEASE because of the nearly full time coverage. EPAM provides realtime electron intensities in a comparable energy range (0.175–0.315 MeV vs. 0.25–1.0 MeV) but in a time resolution of 5 min instead of 1 min.

The forecast depends on the measured electron intensities and their increase. Hence we decided to determine a correlation between the intensities and the increase parameter. Figure 7.4a shows the time profile of EPAM (red) and EPHIN
<figure><img src="image_57.png" /><figcaption>**Fig. 7.4** The left panel (a) shows the time series of EPHIN (black) and EPAM (red) electron intensities. The electron intensity measured by EPAM is divided by 10. The right panel (b) displays an example of one forecast matrix used within the REleASE scheme. This Matrix shows the predicted intensity of protons in 1 h as function of the measured absolute electron intensities and the intensity rise parameter</figcaption></figure>

<figure><img src="image_58.png" /><figcaption>**Fig. 7.5** The left panel (a) displays 5 min electron intensities of EPAM (x-axis) and EPHIN (y-axis) plotted against each other. The right panel (b) shows the same plot for background subtracted data</figcaption></figure>

(black) electron intensities of 2014. Despite the high background of the EPAM measurements there seems to be a good correlation. If there is an increase in EPHIN electron intensity there is also one in EPAM.

To quantify this correlation Fig. 7.5a shows the EPHIN electron intensity on the y-axis plotted against the corresponding EPAM intensities on the x-axis. The higher background level of EPAM reflects itself by the nearly vertical line at low EPAM intensities. In order to correct for that we subtracted a background intensity of 18 (cm² s sr MeV)⁻¹ from the EPAM data. The result of this procedure is shown in Fig. 7.5b in the right panel. Despite these differences the EPAM electron intensity is roughly ten times higher as the one determined by EPHIN. This is indicated by the black line showing the function where EPAM intensity is ten times higher than EPHIN intensities.
<figure><img src="image_59.png" /><figcaption>**Fig. 7.6** Rise parameter of 5 min electron intensities measured by EPAM (x-axis) and EPHIN (y-axis). The EPAM intensity was background subtracted. The right panel displays all data from 2012 while the left panel shows only rise-parameters for strong enhanced electron fluxes</figcaption></figure>

From our investigation, we conclude that there is a good correlation for intensities higher than 20 (cm² s sr MeV)⁻¹. Due to the large background the correlation breaks down for EPAM intensities below 20 particles (cm² s sr MeV)⁻¹. Since the goal of the REleASE system is to forecast SEP events with high particle fluxes the background uncertainties play a negligible role here. The EPAM intensity in addition was raised to the power of 1.02 to correct for different correlation at very high intensities.

The second parameter used in the REleASE forecast matrices (x-axis) is the intensity rise parameter. This parameter is calculated by linear fits through the logarithmic electron intensities of the last 5–60 min. The maximum of these parameters is transferred to the rise parameter position in the forecast matrices. A comparison of the rise parameters from EPHIN and EPAM is shown in Fig. 7.6. One can see that most of the data points are close to the bisecting line, but do not show a correlation between the rise parameters. If we only take electron fluxes higher than 102 into account, the correlation gets stronger. Due to this and the fact that the forecast matrix in Fig. 7.4 shows a much stronger dependence on the electron intensity we decided to use the uncorrected EPAM rise parameter as input to the REleASE scheme. Figure 7.7 shows an example of an SEP event where the EPHIN based and EPAM based forecasts predicted the real proton flux very accurately.

Since forecasts are made for different time offsets (30, 60, 90 min) and different overlapping energy channels (16–40 and 28–50 MeV), we investigated a suitable forecast condition in combining the different forecasts. We tested different combination of forecasts for different time offsets and found that the following condition delivered the best performance of the forecast systems:

* Alarm: if any forecast > $10^{-1}$ (cm² s sr MeV)⁻¹ and one 30 min forecast > $10^{-2}$ (cm² s sr MeV)⁻¹.

* Event: if real proton flux > $10^{-1}$ (cm² s sr MeV)⁻¹.
<figure><img src="image_60.png" /><figcaption>**Fig. 7.7** An example of an SEP event where the EPHIN and EPAM based forecasts predicted the real proton flux accurately</figcaption></figure>

<table><caption>**Table 7.1** Results of REleASE implementation utilizing either SOHO/EPHIN or ACE/EPAM</caption><thead><tr><th></th><th>T</th><th>M</th><th>F</th><th>POD (%)</th><th>FAR (%)</th><th>AWT (min)</th></tr></thead><tbody><tr><td>EPHIN</td><td>24</td><td>14</td><td>10</td><td>63</td><td>29</td><td>107</td></tr><tr><td>EPAM</td><td>24</td><td>14</td><td>13</td><td>63</td><td>35</td><td>123</td></tr></tbody></table>

The performance was tested by using all historic EPAM and EPHIN data from 2009 until 2016. All SEP events of this time period were investigated. The following results for events are possible:

* True forecast (Alarm and Event): T

* Missed event (No/late Alarm and Event): M

* False alarm (Alarm and no Event): F

By using the total number of true forecasts, missed events and false alarms of the analysed time period, it is possible to calculate the Probability of Detection (POD) and False Alarm Ratio (FAR):

* False Alarm Ratio: $FAR = \frac{F}{T+F}$

* Probability Of Detection: $POD = \frac{T}{T+M}$

The results of the described analysis are summarized in Table 7.1.

The described forecast tools have low FARs and sufficient PODs. The tools are publicly available via the HESPERIA project web site. On this web site we provide an e-mail alert system. Interested users are welcome to sign in for this alert system.
## 7.5 Predicting >500 MeV SEP Events by Using the UMASEP Scheme

Solar energetic particles (SEPs) are sometimes energetic enough and the flux is high enough to cause air showers in the stratosphere and in the troposphere, which are an important ionization source in the atmosphere. >500 MeV solar protons are so energetic that they usually have effects on the ground, producing what is called a Ground Level Enhancement (GLE). One of the goals of the HESPERIA project was the development of a predictor of >500 SEP events at the near-earth (e.g. at geostationary orbit). The implemented predictor, called HESPERIA UMASEP-500, makes a lag-correlation between the SXR flux and high-energy differential proton fluxes of the GOES satellites. When the correlation estimation surpasses a threshold, and the associated flare is greater than a specific SXR peak flux, a >500 MeV SEP forecast is issued.

The lag-correlation is carried out using the High-Energy UMASEP approach explained in Núñez (2015). In this project, this approach uses 1-min SXR and proton data. Firstly, it generates a bit-based time series from the SXR time-derivatives and three bit-based time series from the time-derivatives of each of the P9-P11 channels of the GOES6-GOES15 satellites. The “1s” in each bit-based time series are set when its positive time derivative surpasses a percentage *p* of the maximum value of the time derivative in the present sequence of size *L* (beyond which no influence is assumed in the SEP event to be predicted); otherwise, the flux level is transformed into a “0”. To avoid false alarms due to relatively strong fluctuations during periods of low solar activity, a threshold *d* is necessary, which is the minimum value to consider it as positive fluctuation (i.e., a “1”). This forecasting approach creates a list of *cause-consequence pairs* as follows: it takes the first “1” of the SXR-based time series, and the first “1” of the proton-based time series, to create a *pair*; it then takes the second pair of “1s” in each time series, and thus successively, until all the “1s” of the SXR-based time series are inspected. After following this procedure, if a “1” does belong to any pair, it is classified as an “odd”. For each pair, the *pair separation* between the SXR-based “1” and the proton-based “1” is calculated.

An ideal magnetic connection is detected when a sequence of SXR-based “1s” in a row is followed by a sequence of proton-based “1s” in a row. In an ideal magnetically connected event, all pairs have the same temporal separation, and no odd “1” has been found; in other words, an ideal magnetic connection is detected when all recently-measured strongest rises in the SXR flux are followed, some minutes later (i.e. the lag), by all recently-measured strongest rises in a proton channel. We say that this ideal magnetic connection would have a *Fluctuation Correlation* of 1. In general, we need a formula, described in Núñez (2015), that calculates the Fluctuation Correlation between the bit-valued SXR-based time series and a proton-based time series. A >500 MeV SEP event is triggered when the lag-correlation is greater than a threshold *r*; and the SXR intensity of the associated flare is greater than a threshold *f*.
It is important to mention that a >500 MeV SEP event is detected when the integral proton flux surpasses a certain threshold *pfu*500. To calculate this threshold, firstly we had to use the geometrical factors of P9, P10 and P11 proton channels provided by the National Oceanic and Atmospheric Administration (NOAA). Then, we manually varied this threshold to match each >500 MeV SEP event with each GLE event. The study ended with a threshold of 0.8 pfu, which yielded a one-to-one correspondence in 26 of the events of all 32 GLE events within the analyzed period (1986–2016). In 8 cases, a GLE was observed at Earth; however, the enhancement in >500 MeV integral proton flux did not surpass 0.8 pfu. In only one case (see Event 44.5 in Table 7.2) a >500 MeV SEP event took place, which was not observed at the ground.

The UMASEP-500 model’s parameter calibration from historical data was an optimization process whose purpose was to obtain a high POD and Advance Warning Time (AWT), and a low FAR. We found that the same thresholds and parameters found for predicting >500 MeV SEP events were also very appropriate to predict GLE events; for this reason, this section also presents a summary of the GLE forecast results. For more information about the GLE forecast results, please consult Núñez et al. 2017.

The original purpose of the HESPERIA UMASEP-500 tool was to correlate SXR with neutron and proton data. We found that the use of proton data alone allowed this tool to make predictions before any Neutron Monitor (NM) station’s alert. This satisfactory result became our operational criterion for classifying a GLE forecast as successful. We found that the correlation of SXR and neutron counter data did not trigger any hit additional to those generated using proton data alone. We also found that the use of neutron data provoked the generation of many false alarms due to some quality data problems (mainly spikes) caused by technical issues, such as problems in the neutron sensor tubes and power supplies, among others (Souvatzoglou et al. 2014). Since the use of neutron data did not increment the POD, but did increment the FAR, we decided not to use neutron data for making predictions.

Figure 7.8 presents the forecast output for the >500 MeV and GLE event on October 28, 2003. The upper time series shows the recent >500 MeV proton flux; the predicted flux is presented with a colored curve. The middle time series shows the recent SXR flux. The plot at the bottom of the forecast output presents the empirically-estimated level of magnetic connectivity. The Automatic Prediction section (on the right) presents in red the prediction of the occurrence of the GLE event. Below, the tool presents the details of the associated flare, and the proton channels for which the SXR correlation was found. The small image at the top-right shows the real evolution of the integral proton flux after this prediction. The 1-min real-time forecast outputs of this tool are shown on the website of the HESPERIA project (i.e. https://www.hesperia.astro.noa.gr/index.php/results/real-time-prediction-tools/umasep).

The overall prediction performance of event occurrences for the analyzed period (1986–2016) was calculated in terms of POD, FAR and AWT. Table 7.2 presents the list of GLEs, >500 MeV SEP events, and the HESPERIA UMASEP-500’s
<table><caption>**Table 7.2** HESPERIA UMASEP-500's forecast results of the GLE and >500 MeV SEP events that took place during the analyzed period (1986–2016)</caption><thead><tr><th>Solar event<br>Event ID</th><th>GLE Onset<br>(UTC)</th><th>Time</th><th>GLE Forecast<br>Result<sup>a</sup></th><th>GLE Forecast<br>Warning Time<br>(min)<sup>a</sup></th><th>&gt;500 SEP Event<br>Onset Time (UTC)</th><th>&gt;500 SEP<br>Forecast Result</th><th>&gt;500 SEP<br>Forecast Result<br>Warning Time (min)</th></tr></thead><tbody><tr><td>GLE-40</td><td>25/07/1989</td><td>8:50</td><td>Miss</td><td></td><td>9:13</td><td>Miss</td><td></td></tr><tr><td>GLE-41</td><td>16/08/1989</td><td>1:25</td><td>Hit</td><td>20</td><td>1:37</td><td>Hit</td><td>32</td></tr><tr><td>GLE-42</td><td>29/09/1989</td><td>11:40</td><td>Hit</td><td>6</td><td>11:51</td><td>Hit</td><td>17</td></tr><tr><td>GLE-43</td><td>19/10/1989</td><td>13:00</td><td>Hit</td><td>8</td><td>13:03</td><td>Hit</td><td>11</td></tr><tr><td>GLE-44</td><td>22/10/1989</td><td>17:55</td><td>Miss</td><td></td><td>17:57</td><td>Miss</td><td></td></tr><tr><td>Ev-44.5</td><td>23/10/1989</td><td></td><td></td><td></td><td>12:42</td><td>Miss</td><td></td></tr><tr><td>GLE-45</td><td>24/10/1989</td><td>18:18</td><td>Miss</td><td></td><td>18:24</td><td>Miss</td><td></td></tr><tr><td>GLE-46</td><td>15/11/1989</td><td>7:00</td><td>Miss</td><td></td><td></td><td></td><td></td></tr><tr><td>GLE-47</td><td>21/05/1990</td><td>22:29</td><td>Miss</td><td></td><td>23:02</td><td>Miss</td><td></td></tr><tr><td>GLE-48</td><td>24/05/1990</td><td>20:49</td><td>Miss</td><td></td><td>21:06</td><td>Miss</td><td></td></tr><tr><td>GLE-49</td><td>26/05/1990</td><td>20:55</td><td>Miss</td><td></td><td>21:10</td><td>Miss</td><td></td></tr><tr><td>GLE-50</td><td>28/05/1990</td><td>5:34</td><td>Miss</td><td></td><td></td><td></td><td></td></tr><tr><td>GLE-51</td><td>11/06/1991</td><td>2:30</td><td>Hit</td><td>24</td><td>3:18</td><td>Hit</td><td>72</td></tr><tr><td>GLE-52</td><td>15/06/1991</td><td>8:35</td><td>Hit</td><td>2</td><td>8:40</td><td>Hit</td><td>7</td></tr><tr><td>GLE-53</td><td>25/06/1992</td><td>20:15</td><td>Miss</td><td></td><td>20:18</td><td>Miss</td><td></td></tr><tr><td>GLE-54</td><td>02/11/1992</td><td>3:50</td><td>Hit</td><td>20</td><td>3:24</td><td>Hit</td><td>28</td></tr><tr><td>GLE-55</td><td>06/11/1997</td><td>12:10</td><td>Miss</td><td></td><td>12:27</td><td>Miss</td><td></td></tr><tr><td>GLE-56</td><td>02/05/1998</td><td>13:55</td><td>Miss</td><td></td><td></td><td></td><td></td></tr><tr><td>GLE-57</td><td>06/05/1998</td><td>8:25</td><td>Miss</td><td></td><td></td><td></td><td></td></tr><tr><td>GLE-58</td><td>24/08/1998</td><td>22:50</td><td>Miss</td><td></td><td></td><td></td><td></td></tr><tr><td>GLE-59</td><td>14/07/2000</td><td>10:34</td><td>Hit</td><td>12</td><td>10:36</td><td>Hit</td><td>14</td></tr><tr><td>GLE-60</td><td>15/04/2001</td><td>13:57</td><td>Hit</td><td>1</td><td>13:57</td><td>Hit</td><td>1</td></tr></tbody></table>
<table><tr><td>GLE-61</td><td>18/04/2001</td><td>2:33</td><td>Miss</td><td></td><td></td><td></td></tr><tr><td>GLE-62</td><td>04/11/2001</td><td>16:55</td><td>Miss</td><td></td><td>16:44</td><td>Miss</td></tr><tr><td>GLE-63</td><td>26/12/2001</td><td>5:39</td><td>Miss</td><td></td><td>6:08</td><td>Miss</td></tr><tr><td>GLE-64</td><td>24/08/2002</td><td>1:23</td><td>Hit</td><td>13</td><td>1:30</td><td>Hit</td><td>20</td></tr><tr><td>GLE-65</td><td>28/10/2003</td><td>11:17</td><td>Hit</td><td>9</td><td>11:31</td><td>Hit</td><td>23</td></tr><tr><td>GLE-66</td><td>29/10/2003</td><td>21:02</td><td>Hit</td><td>3</td><td>21:19</td><td>Hit</td><td>20</td></tr><tr><td>GLE-67</td><td>02/11/2003</td><td>17:27</td><td>Hit</td><td>3</td><td>17:35</td><td>Hit</td><td>11</td></tr><tr><td>GLE-68</td><td>17/01/2005</td><td>9:52</td><td>Miss</td><td></td><td></td><td></td></tr><tr><td>GLE-69</td><td>20/01/2005</td><td>6:47</td><td>Miss</td><td></td><td>6:46</td><td>Miss</td></tr><tr><td>GLE-70</td><td>13/12/2006</td><td>2:50</td><td>Hit</td><td>15</td><td>2:59</td><td>Hit</td><td>24</td></tr><tr><td>GLE-71</td><td>17/05/2012</td><td>1:55</td><td>Miss</td><td></td><td>2:07</td><td>Miss</td></tr></table>

<footnote>a Hits are predictions that are triggered before the first NM station's GLE alert</footnote>
<figure><img src="image_61.png" /><figcaption>**Fig. 7.8** This figure shows the forecast output of HESPERIA UMASEP-500 for the event occurred on October 28, 2003. This prediction, issued at 11:08, was successful because it was issued before the >500 MeV integral proton flux surpassed 0.8 pfu (at 11:31), and before the first NM station's alert, issued at 11:17</figcaption></figure>

prediction results for the events of the analyzed period. Column 1 presents the GLE event ID; column 2 lists the time of the first detection of the event of an NM station; column 3 presents the HESPERIA UMASEP-500 GLE prediction results (hits are those events successfully predicted, and misses are those notsuccessfully predicted); column 4 lists the warning times (i.e. the temporal difference between the time at which the forecast was triggered by this tool and the time of the first NM station's alert); column 5 lists the time the occurrence of the SEP event (i.e. the time when the >500 MeV proton flux surpassed 0.8 pfu); column 6 presents the SEP prediction results; and, column 7 lists the warning times.

Regarding the prediction of >500 MeV SEP event, the forecast performance results of this tool for the period 1986–2016 may be summarized as follows: the POD was 50% (13/26), the FAR was 31.6% (6/19), and the average warning time to the first NM’s alert was 13 min.

Regarding the prediction of GLE events, the forecasting results for the most recent half of the evaluation period (i.e. 2000–2016) may be used to compare UMASEP-500 with those of the GLE Alert Plus. These results may be summarized as follows: the POD was 53.8% (7 of 13 GLE events); the FAR was 30.0% (3/10);
the AWT to the first NM's alert was 8 min; and, the AWT to the GLE Alert Plus's warning was 15 min. The GLE forecasting results for the first half of the evaluation period (i.e. 1986-1999) are summarized as follows: the POD was 31.6% (6 of 19 GLE events); the FAR was 33.3% (3/9); and, the AWT to the first NM's alert was 13.3 min. There are no forecasting results of the GLE Alert Plus for this period.

For the whole evaluation period, the GLE forecasting performance may be summarized as follows: the POD was 40.6% (13 of 32); the FAR was 31.6% (6 of 19); and, the AWT to the first NM's alert was 10.5 min. Note that the FAR of the most recent period is similar to that of the oldest period (30.0% vs. 33.3%); however, the POD of the most recent period (i.e. 53.8%) is better than the POD of the oldest period (i.e. 31.6%). We do not know the reason for the better POD performance in the most recent period; nevertheless, we think that the use of a more recent and refined instrument technology and/or more experienced calibration procedures yields better forecasting performance.

## 7.6 Concluding Remarks

We experimented the use of microwave time histories in the UMASEP prediction scheme of the occurrence of SEP events. The test run over 13 months shows that microwaves provide a comparable probability of detection, but a reduced false-alarm ratio as compared to the time derivative of the SXR flux, which is used in the traditional UMASEP scheme.

The reduction of false alarms is due to the fact that microwave bursts are signature of non-thermal particle acceleration and are less frequent than the ubiquitous thermal soft X-ray brightenings. This reduces the probability to interpret the chance coincidence between a rise of the radiative signature and the rise of the particle intensity at the spacecraft as an indication of a magnetic connection. The forecasting scheme using microwaves fails when the microwave emission is thermal and slowly rising. This is especially the case when SEP events are related to the eruption of quiescent filaments.

A second test of microwave patrol observations in SEP forecasting was conducted with the aim to predict the hardness of proton spectra using the ratio of peak flux densities at 15.4 and 8.8 GHz: the expectation was to find a preferential association of hard proton spectra with microwave bursts that are particularly strong at 15.4 GHz, as had been shown in previous activity cycles (Chertok et al. 2009). We were unable to confirm this expectation: we found no significant correlation between the proton spectral hardness and the microwave flux density ratio. The intrinsic variations from event to event are much stronger than any underlying trend that might exist.

The radio patrol observations used by our study are carried out with rather simple patrol instruments, which monitor the whole Sun flux density using parabolic antennas with a typical size of ~1 m. Such data are presently not provided in real time, but there is no technical obstacle to do so. But the results of our test run for the
prediction of well-connected SEP events show that microwave observations have the potential to improve SEP forecasting. An interesting perspective could be the combination of the REleASE and UMASEP forecasting schemes, because, on one hand they could correlate rises between microwaves at the Sun and electrons, and on the other hand, forecasts may be provided for those SEPs whose parent solar event is behind the limb. This combination of schemes could bring a major gain in advance warning time.

The HESPERIA REleASE tools make real-time predictions of the proton flux (30–50 MeV) at Lagrangian point 1 and are available via the HESPERIA web site.<fnref n="3" /> An analysis of historic data from 2009 to 2016 has shown that the forecast tools have a low FAR (~30%) and a high POD (63%).

The HESPERIA UMASEP-500 model makes real-time predictions of the occurrence of >500 MeV SEP and GLE events from the analysis of SXR and differential proton flux measured by the GOES satellite network. Real-time predictions are available in the HESPERIA web site.<fnref n="4" /> We assume that a prediction is successful when it is reported before the first GLE alert is issued by any NM station. Regarding the prediction of GLE events for the period 2000–2016, this tool had a POD of 53.8%, and a FAR of 30.0%. For this period, the tool obtained an AWT of 8 min taking as reference the alert time from the first NM station; taking as reference the time of the warnings issued by the GLE Alert Plus for the aforementioned period, the HESPERIA UMASEP-500 tool obtained an AWT of 15 min.

In summary, the goal of the presented tools has been to improve mitigation of adverse effects both in space and in the air from a significant solar radiation storm, providing valuable added minutes of forewarning to space weather users.

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Núñez, M.: Predicting solar energetic proton events (E>10 MeV). Space Weather. **9**, S07003 (2011)

Núñez, M.: Real-time prediction of the occurrence and intensity of the first hours of >100 MeV solar energetic proton events. Space Weather. **13**(11), 807–819 (2015)

Núñez, M., Reyes-Santiago, P., Malandraki, O.E.: Real-time prediction of the occurrence of GLE events. Space Weather 15 (2017). doi:10.1002/2017SW001605

Posner, A.: Up to 1-hour forecasting of radiation hazards from solar energetic ion events with relativistic electrons. Space Weather. **5**, S05001 (2007)

Souvatzoglou, G., Papaioannou, A., Mavromichalaki, H., Dimitroulakos, J., Sarlanis, C.: Optimizing the real-time ground level enhancement alert system based on neutron monitor measurements: introducing GLE Alert Plus. Space Weather. **12**(11), 633–649 (2014)

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**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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<figure><img src="image_62.png" /></figure>
Chapter 8

X-Ray, Radio and SEP Observations
of Relativistic Gamma-Ray Events

Karl-Ludwig Klein, Kostas Tziotziou, Pietro Zucca, Eino Valtonen, Nicole Vilmer, Olga E. Malandraki, Clarisse Hamadache, Bernd Heber, and Jürgen Kiener

**Abstract** The rather frequent occurrence, and sometimes long duration, of γ-
ray events at photon energies above 100 MeV challenges our understanding of
particle acceleration processes at the Sun. The emission is ascribed to pion-decay
photons due to protons with energies above 300 MeV. We study the X-ray and radio
emissions and the solar energetic particles (SEPs) in space for a set of 25 *Fermi*
γ-ray events. They are accompanied by strong SEP events, including, in most cases
where the parent activity is well-connected, protons above 300 MeV. Signatures of
energetic electron acceleration in the corona accompany the impulsive and early
post-impulsive γ-ray emission. γ-ray emission lasting several hours accompanies
in general the decay phase of long-lasting soft X-ray bursts and decametric-to-
kilometric type II bursts. We discuss the impact of these results on the origin of
the γ-ray events.

K.-L. Klein (✉) • N. Vilmer • P. Zucca
LESIA-Observatoire de Paris, CNRS, 92190 Meudon, France

PSL Research University, Universités P & M. Curie, Paris-Diderot, Meudon, France
e-mail: ludwig.klein@obspm.fr; pietro.zucca@obspm.fr; nicole.vilmer@obspm.fr

K. Tziotziou • O.E. Malandraki
National Observatory of Athens, IAASARS, Athens, Greece
e-mail: kostas@noa.gr; omaland@astro.noa.gr

E. Valtonen
Department of Physics and Astronomy, Space Research Laboratory, University of Turku, Turku,
Finland
e-mail: eino.valtonen@utu.fi

C. Hamadache • J. Kiener
CSNSM, IN2P3-CNRS, Univ. Paris-Sud, 91405 Orsay Cedex, France
e-mail: clarisse.hamadache@csnsm.in2p3.fr; Jurgen.kiener@csnsm.in2p3.fr

B. Heber
Christian-Albrechts-Universität zu Kiel, Kiel, Germany
e-mail: heber@physik.uni-kiel.de
## 8.1 Introduction

The advent of the *Fermi* mission showed that the Sun is an occasional, but unexpectedly frequent, emitter of γ-ray photons above 100 MeV. These are understood to be produced by pion decays in nuclear interactions involving protons or He-nuclei at energies above 300 MeV/nucleon. One did not expect that the Sun was able to accelerate relativistic protons and nuclei even in seemingly modest flares. These particles are rarely detected in space (<1 event per year). Furthermore, the duration, several hours, of some γ-ray events is much longer than that of hard X-ray signatures of electron acceleration in the impulsive flare phase.

The question of how the γ-ray emission is related to other signatures of particle acceleration and energy release in the corona is crucial to understanding the origin of the high-energy protons. It might also be expected that such high-energy populations interacting at the Sun are accompanied by particularly energetic solar energetic particle (SEP) events. This chapter is based on 25 events. The *Fermi/LAT* temporal data were made available to the HESPERIA project by G. Share prior to their publication in a comprehensive paper (Share et al. 2017). The present chapter introduces the relevant process of emission and pre-*Fermi* observations of pion-decay γ-rays (Sect. 8.2), and gives an overview of the *Fermi/LAT* observations (Sect. 8.3). Section 8.3 was prepared by Gerald Share and Ron Murphy. Related X-ray and radio observations and associated SEP events are presented in Sects. 8.4 and 8.5, respectively. Preliminary conclusions on the interpretation of the γ-ray events are in Sect. 8.6.

## 8.2 Theory and Early Observations of Gamma-Ray Emission at Photon Energies >60 MeV

On 1982 Jun 3 the gamma-ray spectrometer on the *Solar Maximum Mission* satellite observed emission from 0.3 to 100 MeV from a X8.0 GOES-class flare (Forrest et al. 1986). The impulsive flare lasted about 1 min and was followed by a distinct harder emission phase that peaked in about 1 min and lasted for over 15 min. The energy spectrum of this sustained emission displayed a characteristic hump at photon energies above 60 MeV (Fig. 8.1a), which appeared to be consistent with that from pion-decays produced by the interaction of >300 MeV protons in the solar atmosphere (Forrest et al. 1985, see below); the authors speculated whether the emission might be associated with the acceleration of solar energetic particles. There were several more of these events in the ensuing years, all associated with intense X-class flares, that were summarized in a paper entitled “Long-Duration Solar Gamma-Ray Flares” (LDGRFs) (Ryan 2000). Various origins were suggested, and a
<figure><img src="image_63.png" /><figcaption>**Fig. 8.1** (a) The γ-ray spectrum showing the pion-decay bump of the 1982 Jun 3 event, observed by SMM (Forrest et al. 1985). Credit: Forrest et al., Internat. Cosmic Ray Conf. 4, 146, 1985, courtesy W.T. Vestrand. (b) Time profile of the first sustained γ-ray event detected by the Compton Gamma-Ray Telescope (adapted from Kanbach et al. (1993); credit: Kanbach et al., A&A Suppl. 97, 349, 1993, reproduced with permission ©ESO)</figcaption></figure>

key question was whether such emission would be observed when the accompanying flare was weaker and did not produce impulsive gamma radiation.

Detection of such events continued with observations from GAMMA-1 (Akimov et al. 1992), the Compton Gamma-Ray Observatory (CGRO) (Mandzhavidze and Ramaty 1992; Kanbach et al. 1993; Dunphy et al. 1999), GRANAT (Debrunner et al. 1997; Vilmer et al. 2003), CORONAS-F (Kuznetsov et al. 2011; Kuznetsov et al. 2014). Around 20 events had been observed then with significant emission above 60 MeV from pion decay radiation (see Lockwood et al. 1997; Chupp and Ryan 2009; Vilmer et al. 2011 for reviews). For some of the events, pion decay radiation is observed during the impulsive phase of the event as defined by the production of hard X-rays above 100 keV. In some events, high energy emissions had also been observed for hours after the impulsive phase of the flare, revealing that high energy ions are present on time scales of several hours (e.g. Kanbach et al. 1993; Ryan et al. 1994; Ryan 2000; Rank et al. 2001).

### 8.2.1 Pion-Decay γ-Ray Emission

High-energy (>60 MeV) emission in solar flares results from nuclear interactions of mildly relativistic ions (above a few hundred MeV/nucleon) with the ambient solar atmosphere (most probably the dense chromosphere). These nuclear reactions result in the production of pions. Charged pions decay to electrons and positrons, which produce γ-ray emissions through bremsstrahlung radiation. Energetic positrons also
contribute to the γ-ray continuum by annihilating in flight. The neutral pions decay in two photons, one being emitted at high energies. The result is a very flat spectrum with a broad-bump feature with a maximum at 67 MeV (Murphy et al. 1987). In a magnetized region, synchrotron losses of electrons and positrons may be important and reduce their contributions with respect to the radiation from neutral-pion decay (Murphy et al. 1987; Vilmer et al. 2003). When energetic electrons are present at energies above 10 MeV, they produce bremsstrahlung emission above 10 MeV (Chap. 2), which may mask pion-decay radiation.

Early work on the modelling of pion decay radiation and γ-ray emission (produced by >10 MeV ions) (Murphy et al. 1997) gave a first determination of the high energy spectrum of ions in flares. Assuming a spectral shape for the energetic ions (either a Bessel function or a power law), number and spectra of energetic protons were estimated for both the impulsive and the extended phase of the first detected event (1980 Jun 21) and showed that the proton spectrum was steeper in the impulsive phase than in the later, so-called 'extended' phase. This evolution of the ion spectrum in the extended phase was confirmed by further observations such as the ones of the 1991 Jun 11 event by CGRO/EGRET (Dunphy et al. 1999).

Quantitative analysis of several events with significant pion production has been performed providing information on the ion energy spectrum above 300 MeV/nucleon and allowing a comparison of this spectrum with the one deduced at lower energies from γ-ray line spectroscopy (see, e.g., Alexander et al. 1994; Dunphy et al. 1999; Kocharov et al. 1994, 1998; Vilmer et al. 2003). These comparisons have shown that the ion energy distribution does not have a simple power-law form from the γ-ray line producing energy domain (1–10 MeV) to the pion-producing energy domain (>300 MeV/nucleon).

### 8.2.2 Long-Duration γ-Ray Events

Even before the Fermi era, a few events had been observed where enhanced pion-decay radiation lasted several hours, and the question of the origin of these long duration events had been examined. On 1991 Jun 11 (Fig. 8.1b) emission above 50 MeV was detected for almost 8 h after the flare by COMPTON/EGRET. Several interpretations had been proposed to explain these long duration emissions, either the continuous acceleration of protons above 300 MeV (e.g., Ryan and Lee 1991) or the trapping of protons on very long time-scales. In particular, Mandzhavidze and Ramaty (1992) showed that the long duration phase could be explained by the injection of energetic protons in the impulsive phase and subsequent trapping. An efficient trapping on such long timescales required a strong mirror ratio in the trapping region (>10) as well as a coronal density less than $5 \cdot 10^{11} \text{ cm}^{-3}$. The question of how trapped particle populations could remain stable over hours was, however, not explained satisfactorily. An observational justification of continuous time-extended acceleration came from the discovery of sustained γ-ray events of moderate duration (1–2 h), which were accompanied by non-thermal microwave emission (Kocharov et al. 1994; Trottet et al. 1994; Akimov et al. 1996).
## 8.3 New Insights of Sustained Emission Events from *Fermi* Observations

With the launch of the sensitive *Fermi* Large Area Telescope (LAT) (Atwood et al. 2009), it became possible to observe weak $\gamma$-ray emission from the Sun due to its large effective area and aperture, and excellent background rejection. This permitted detection of quiescent $\gamma$-ray emission from cosmic-ray protons interacting in the solar atmosphere and cosmic-ray electrons interacting with sunlight (Abdo et al. 2011) with fluxes of 5 and $7 \times 10^{-7} \gamma$ cm$^{-2}$ s$^{-1}$, respectively. LAT first detected transient $>100$ MeV solar $\gamma$-rays on 2010 Jun 12 from the impulsive M2 class flare (Ackermann et al. 2012a,b) during an $\sim$50 s period. The emission was delayed about 10 s from the associated hard X-ray and nuclear-line emission and there was no evidence for any $>100$ MeV $\gamma$-ray emission in the hours after the flare. The *Fermi*/LAT team reported the detection of 18 $>100$ MeV events associated with solar flares covering the time period from 2008 August to 2012 August (Ackermann et al. 2014) which they classified as being impulsive, sustained, or delayed. In some cases they categorized the events as having both impulsive and sustained characteristics. Only three of the events were classified as only having an impulsive component. We prefer to use the name “sustained” to categorize all emission that is distinct from the impulsive flare independent of its duration.

Details of the 2011 Mar 7 and 2011 Jun 7 $\gamma$-ray observations and related solar measurements were also presented in Ackermann et al. (2014). The March 7 event was reported as having both impulsive and sustained emission components, while the June 7 event was classified as only having sustained emission because $\gamma$-rays were detected in only one LAT exposure about 1 h after the flare and there was no exposure to the flare. The $\gamma$-ray spectra were fit by two empirical models, a power law and a power law with exponential cutoff; and a physical pion-decay spectrum based on Murphy et al. (1987). Only heuristic arguments were presented to justify that the observed spectrum was from pion decay and not from electron bremsstrahlung. There was clear evidence for spectral softening over the 13 h period that the March 7 event was observed. As LAT’s instrumental point spread function is about 1°, even above 1 GeV, only the location of the centroid of the $\gamma$-ray source could be deduced. The centroids of both sources were consistent with the active regions with uncertainties on the scale of a solar quadrant.

Ajello et al. (2014) reported detection on 2012 Mar 7 by LAT of what appeared to be distinct impulsive and sustained-emission phases associated with X5.4 and X1.3 (actually about M7 when the tail of the X5 flare is subtracted) flares, CMEs with speeds of about 2700 and 1800 km s$^{-1}$, and a strong solar energetic particle event. The $\gamma$-ray flux was one of the brightest observed by LAT; it lasted close to 20 h and the fitted spectrum again softened with time. The time integrated centroid of the emission was consistent with the location of the flares with a $1 \sigma$ uncertainty of $\sim$10°. There is evidence that the source of the emission moved from the eastern to the western hemisphere about 7 h following the flares. Once again there was no information on the spatial extent of the emission.
With detection of >100 MeV γ-ray emission associated with two behind-the-limb solar flares, it has become clear that emission can extend as much as 40° from the flare site (Pesce-Rollins et al. 2015; Ackermann et al. 2017). The events occurred on 2013 Oct 11 and 2014 Sep 1 and were associated with fast CMEs and strong solar energetic particle events. The centroids of the γ-ray emission for both events were close to the solar limb. The centroid for the October 11 event was consistent with the N21 latitude of the active region, located about 13° behind the East limb, and its 1 σ uncertainty extended to about 50° East. In contrast, the centroid of the September 1 event was significantly north (~15°) of the flare site that was located about 35° behind the East limb.

More information on the characteristics and origin of these solar γ-ray events became available with the completion of a comprehensive study of 29 sustained emission events observed by LAT between 2008 and 2016 (Share et al. 2017). This study indicates that the emission is not spatially distributed globally on the Sun but is probably distributed over a few tens of degrees around the centroid location. From this study it is also clear that the sustained >100 MeV emission is temporally distinct from the impulsive flare phase, which often emits hard X-rays extending only to hundreds of keV. The time profile of the first event observed by LAT on 2011 Mar 7, discussed above and plotted in Fig. 8.2, provides an example of such a distinct sustained-emission phase. While the analysis done by Share et al. (2017) is different from that of Ackermann et al. (2014), it uses the same source-class data and yields comparable fluxes and spectral results. It is simply a 'light-bucket' in which photons arriving with directions <10° of the Sun are accumulated, as long as the Sun is far from the Earth's horizon. The main plot in Fig. 8.2 shows the hours-long time profile of this 13 h event with LAT solar exposures every 3 h. The background level contains roughly equal contributions from the quiescent Sun, and Galactic and extra-galactic γ rays. The emission began during the time of the GOES flare and rose to peak about 6 h later.

The inset in Fig. 8.2 shows >100 MeV fluxes plotted at 4 min resolution after the hard X-ray peak of the March 7 flare. For comparison, the dotted line follows the high-energy time profile observed in the 1991 June 11 event which exhibited both impulsive emission and sustained emission lasting 8 h. The >100 MeV emission on March 7 appears to increase during the observations after the impulsive phase. There is also no evidence for nuclear line emission during the impulsive flare, suggesting that >1 MeV protons were not present in significant numbers. A limit on the 2.223 MeV neutron capture line during the flare suggests that the flare had at most only 20% of the number of >500 MeV protons observed in the sustained emission phase (Share et al. 2017). This indicates that only sustained >100 MeV emission was observed by LAT on March 7, in contrast to what was reported by Ackermann et al. (2014). The same conclusion can be reached about other events reported by Ackermann et al. (2012b) to have impulsive >100 MeV phases. Specifically, Share et al. (2017) find that the first >100 MeV outburst on 2012 Mar 7 described in detail by Ackermann et al. (2014) was distinct sustained emission and not directly associated with the X5.4 flare.
<figure><img src="image_64.png" /><figcaption>**Fig. 8.2** Time history of the >100 MeV flux from $\le 10^8$ of the Sun revealing the 2011 Mar 7 LAT event (data points and $\pm 1\sigma$ statistical uncertainties). *Vertical dashed lines* show the GOES start and end times. The inset shows 4-min accumulation LAT data points and the merged and arbitrarily scaled >100 keV count rates observed by *RHESSI* and *Fermi*/GBM during the impulsive flare. The *dashed curve* shows the GOES 1–8Å profile (scale on right ordinate) and the < – > symbol shows the range in CME onset times in the CDAW catalog derived for linear and quadratic extrapolations. The *vertical solid arrow* depicts our estimate of the CME onset from inspection of SDO/AIA images and the *vertical dashed arrow* shows the estimated onset of Type II radio emission</figcaption></figure>

Share et al. (2017) also find that 19 of the 29 sustained-emission events had time profiles distinct from the impulsive phase and most of these had onset times after the hard X-ray peaks. For the remaining events, there were not enough data to determine whether the sustained emission was distinct from or primarily associated with the impulsive phase, but in no case is there clear evidence that the sustained emission is the tail of the impulsive flare.

Pion-decay spectra from protons having different power-law spectral indices fit the spectra from the 2011 Mar 7 event and the other 28 events (Share et al. 2017). In general the results are consistent with those obtained by Ackermann et al. (2014, 2017) and Ajello et al. (2014). In addition, Share et al. (2017) demonstrated that only pion-decay spectra are consistent with the brightest sustained emission events and that any plausible electron bremsstrahlung spectra are not. Using nuclear line observations during these same bright sustained emission events, it was also possible to demonstrate that the proton spectra from 10 to 300 MeV were flatter than the spectra at higher energies. In addition to the two events found to have spectra that softened with time, Share et al. (2017) found two more that softened in time and two that hardened in time.
Detailed spectroscopic studies of many of the events observed by LAT revealed that the number of >500 MeV protons producing the sustained emission was typically at least a factor ten more than found in the accompanying impulsive flare. This is consistent with the distinctly different nature of the time profiles of the impulsive flares and the sustained emission discussed above. As Share et al. (2017) discuss, it is now clear that another energy source is necessary to accelerate protons to energies >300 MeV in order to produce the pion-decay emission observed in the sustained events. These energetic considerations and the rise in sustained γ-ray emission following the impulsive phases in many events suggests the likely source of the energy is the accompanying fast CME, possibly through its shock that is thought to produce gradual SEPs. The authors (Share et al. 2017) find that the number of >500 MeV SEP protons is on average about 100 times the number returning to the Sun to produce the sustained γ-ray emission. This is consistent with what shock wave models estimate (Kocharov et al. 2015).

The 2013 Oct 13 and 2014 Sep 1 behind-the-limb events (Ackermann et al. 2017) were also studied by Share et al. (2017). The time profile of the latter event, which lasted at least 2 h, is plotted in Fig. 8.3. Both >100 MeV γ-ray and >100 keV electron bremsstrahlung rose about 7 min following the impulsive hard X-ray flare, as inferred from SAX observations on MESSENGER (Schlemm et al. 2007). The bremsstrahlung extended up to at least 10 MeV and is consistent with production by

<figure><img src="image_65.png" /></figure>

**Fig. 8.3** Time history of the >100 MeV flux of the Sun revealing the 2014 Sep 1 LAT event (data points and ±1σ statistical uncertainties). Vertical dashed lines show the soft X-ray start and end times from MESSENGER/SAX. The inset shows 1-min accumulation >100 MeV data points (±1σ statistical uncertainties) and the arbitrarily scaled 100–300 keV count rates observed by GBM. The dashed curve shows the soft X-ray profile from SAX and the thin solid curve its derivative. The vertical solid arrow depicts our estimate of the CME onset from inspection of SDO/AIA images
electrons interacting in a thick target, indicating the electrons were produced by the same CME shock that accelerated the protons producing the sustained γ radiation (Share et al. 2017). This conclusion is consistent with the finding that a direct magnetic connection exists between the shock wave and the low solar atmosphere at the onset of the hard X-rays and γ-rays in both behind the limb events (Plotnikov et al. 2017).

The conclusion reached by Share et al. (2017) is that the sustained emission events are likely due to shock-accelerated particles, associated with those in SEPs, that are imparted to field lines that return to the Sun and those that return to the Sun on open field lines from an SEP reservoir. This interpretation will be discussed in Sect. 8.4.

## 8.4 Multiwavelength Observations of Fermi/LAT γ-Ray Events

In this section we examine the relationship between the γ-ray events and other manifestations of energy release in the corona, namely heating as revealed by soft X-ray bursts, and electron acceleration traced by hard X-ray and radio emission. We use especially hard X-ray observations from RHESSI (Lin et al. 2002) and INTEGRAL/ACS (Rodríguez-Gasén et al. 2014), whole-Sun radio fluxes from the RSTN and Nobeyama Observatories (Torii et al. 1979; Nakajima et al. 1985) on ground, and from the radio spectrographs aboard Wind (Bougeret et al. 1995) and STEREO (Bougeret et al. 2008).

At decametric and longer waves (referred to as DH in the following) all 25 γ-ray events were accompanied by type III bursts, and 23/25 by type II bursts. The type III bursts show that electrons (particles) had access to open field lines during all γ-ray events. The bursts occurred in general during the impulsive and early post-impulsive phase of the parent flare, as commonly observed in SEP events. They were not found later on during long-duration γ-ray events. The presence of type II bursts shows that shock waves in the high corona are a common counterpart of γ-ray events. Metric continuum emission (type IV bursts) is observed in some events.

### 8.4.1 Impulsive and Early Post-impulsive γ-Ray Emission

A rare Fermi/LAT observation showing a γ-ray event during and after the impulsive flare phase is illustrated in Fig. 8.4. Hard X-rays (INTEGRAL/ACS, photon energies >80 keV; Rodríguez-Gasén et al. 2014) rise and decline during the rise of the soft X-ray flux, as do the radio flux densities at 15,400 and 8800 MHz. The γ-ray emission, which is observed with much poorer time coverage, shows a similar rise and initial decay, but then stays on an enhanced level until the end of
<figure><img src="image_66.png" /><figcaption>**Fig. 8.4** Time evolution of the high-energy γ-ray, X-ray and radio emission in the impulsive and early post-impulsive phase of a flare</figcaption></figure>

the observations. This long persistence is the key feature of the sustained events introduced in Sect. 8.3. While the microwaves $\ge 8800$ MHz show no counterpart, emissions at 2695 and 245 MHz have a prolonged tail that accompanies the observed part of the post-impulsive γ-ray emission. Renewed energy release after the impulsive phase is also suggested by the bump in the decaying soft X-ray profile. The continued emission of both pion-decay γ-rays and microwaves in the early post-impulsive phase is consistent with the earlier observations by GAMMA1 (Kocharov et al. 1994; Akimov et al. 1996) and SMM (Trottet et al. 1994).

## 8.4.2 Long-Duration γ-Ray Events

As shown in Fig. 8.2, γ-ray emission may rise again well after the impulsive phase. Among the 25 γ-ray events studied, a total of twelve had duration longer than 2 h. Long-duration γ-ray emission occurs most often during the decay of the associated soft X-ray burst, as illustrated in Fig. 8.5. In EUV images taken by AIA/SDO or SWAP/Proba2 the decay of the soft X-ray bursts is accompanied by the formation of post-flare loop arcades.

Although there is still some microwave burst activity at low frequencies (2.695 MHz) in Fig. 8.5, the long-duration γ-rays are in general not accompanied by time-extended or recurrent hard X-ray or microwave burst activity. On 2011 Mar 7 the long-duration γ-rays are accompanied by several flares, rather than the decay of a single soft X-ray burst. But the microwave or hard X-ray emissions are weak, and in any case are only observed during a short fraction of the γ-ray event. In
<figure><img src="image_67.png" /><figcaption>**Fig. 8.5** Time evolution of the high-energy γ-ray, soft and hard X-ray and radio emission from the impulsive phase throughout the rise and decay of sustained γ-ray emission</figcaption></figure>

summary, we find no evidence of repeated efficient electron acceleration in the low corona during most parts of this or any other long-duration γ-ray event.

### 8.4.3 Soft X-Ray Bursts and γ-Ray Events

The close relationship between the durations of γ-ray and soft X-ray emissions is confirmed by the quantitative analysis of the decay profiles of soft X-ray bursts associated with γ-ray events: short duration γ-ray bursts (<2 h; the exact duration is difficult to determine because of gaps in the solar observations of Fermi/LAT) are found to have relatively short soft X-ray decay phases, while the long γ-ray events accompany comparatively long soft X-ray decay phases. There are some intermediate events, showing the distribution of burst durations is not bimodal. But it is clear from this observational analysis that long-duration γ-ray events tend to be associated with long-duration energy release in the solar corona.

Although the long-duration γ-ray emission may start more than an hour after the peak of the associated soft X-ray burst, the logarithms of the peak fluxes of the two emissions correlate, with a linear correlation coefficient 0.72, and a probability that the same or a higher value is obtained from two unrelated samples of 0.8%. The corresponding values for the CME speed and the logarithm of the γ-ray peak flux are 0.61 and 3.7%, respectively. These are rough evaluations, because the γ-ray time profile is not densely covered by the Fermi/LAT observations, and the peak fluxes are only lower limits.
<figure><img src="image_68.png" /><figcaption>**Fig. 8.6** Time history of high-energy γ-rays and the decametric-hectometric radio emission, showing a type II burst accompanies the γ-rays. The *grey vertical stripes* in the *bottom panel* show time intervals of unfavourable solar observing conditions for *Fermi/LAT*</figcaption></figure>

### 8.4.4 Coronal Shock Waves and γ-Ray Events

The only signature of electron acceleration that we found to accompany long-lasting γ-ray emission are DH type II bursts, which are ascribed to CME-driven shocks (Reiner et al. 2007). The type II burst in Fig. 8.6 mostly shows up as a sequence of patches after ~7 UT that gradually drift from higher to lower frequencies. The noticeable fact is that this emission persists throughout the several hours duration of the γ-ray emission.

It is tempting to interpret the association between sustained γ-ray events and DH type II bursts as evidence that the CME shock accelerates protons to relativistic energies, which then stream back from the downstream region of the shock to the low solar atmosphere, where they create pions (see Sect. 8.3 and Chap. 9). We consider in the following the implication of this interpretation on the number of particles that must be present in the downstream region of the shock in order to account for the observed γ-ray emission. To this end we analyze the events with a long duration sustained emission that occurred on 2011 Mar 7, 2012 Jan 23, Mar 5 and May 17.

All four events were accompanied by CMEs well-observed by the LASCO coronagraphs. The quasi-parallel shock often invoked as the site of SEP acceleration is expected to be located around the summit of the CME, following the trajectory
shown by the height-time curves given in the LASCO CME catalogue.<fnref n="1" /> The type II source is usually believed to be located in the quasi-perpendicular region of the shock (Pulupa and Bale 2008), hence on the flank of the CME rather than near its summit. We therefore considered separately the heights of the CME estimated by the LASCO catalogue and of the type II source, inferred from the electron density model of Leblanc et al. (1999), both at the peak of the long-duration γ-ray emission. The heliocentric distances of the CME apices range from 11 $R_⊙$ to 26 $R_⊙$, those of type II sources from 7 $R_⊙$ to 18 $R_⊙$.

Particles accelerated at the shock must hence stream to the solar chromosphere over a distance of many solar radii without being mirrored by the magnetic field before. This implies that they are injected into coronal magnetic field lines near the shock with a pitch angle smaller than some limiting value $α_0$ such that $sin^2 α_0 = B(r)/B(R_⊙)$. The magnetic field decreases outward from the low corona with some power of the heliocentric distance r. If we just extrapolate the radial component of the solar wind magnetic field back to the photosphere, hence assuming that $B(r) \sim r^{-2}$, the maximum pitch angles allowed for protons that reach the low solar atmosphere are 2°–5° when the particles start from the CME apex, and 3°–8° when they start from the type II source. Hence only protons injected nearly parallel to the coronal magnetic field lines near the shock can reach a sufficiently dense part of the solar atmosphere to undergo nuclear reactions. If we suppose that the protons are isotropically distributed at the shock, only a fraction $1 - \cos α_0$ is expected to achieve this. This fraction is 1% of the initial population for $α_0 = 8°$ ($6 \cdot 10^{-4}$ for $α_0 = 2°$). It will be further reduced by the expected stronger decrease of the magnetic field within the solar wind source surface.

## 8.5 Solar Energetic Particle Events Associated with Fermi/LAT Gamma-Ray Events

All *Fermi*/LAT γ-ray events discussed in Sect. 8.3 are associated with SEP events observed at 1 AU from the Sun, by instruments at L1 or by the twin STEREO spacecraft, or both. Proton and/or electron enhancements are observed with SoHO/ERNE (Torsti et al. 1995), STEREO/LET (Mewaldt et al. 2008), STEREO/HET (von Rosenvinge et al. 2008), STEREO/SEPT (Müller-Mellin et al. 2008), and ACE/EPAM (Gold et al. 1998) over a wide range of energy (55 keV to 4 MeV for electrons and 1.6 to 130 MeV for protons). Higher energy protons are available from SoHO/EPHIN (penetrating protons at 100–1000 MeV energies) as well as from GOES/HEPAD (only for 9 of the 25 investigated *Fermi*/LAT events, see Fig. 8.7 for an example) in three differential energy channels ranging from 330 to 700 MeV and an integral channel >700 MeV.

<footnote n="1">¹https://cdaw.gsfc.nasa.gov/CME_list/.</footnote>
<figure><img src="image_69.png" /><figcaption>**Fig. 8.7** GOES 15/HEPAD proton fluxes on 2012 May 17. The *vertical purple dashed* and the *red dotted lines* indicate respectively the flare onset and the derived SEP onset with the sigma-method (see text)</figcaption></figure>

## 8.5.1 SEP Characteristics and Association with Fermi/LAT

Most of the SEP events show a slow rise phase, but some show a fast rise phase in all observed energy ranges (see Reames 1999 for a review on general SEP characteristics). This distinction is somewhat subjective, but we mean by “fast” a rise in 2–3 h, and by “slow” a rise within several hours, sometimes one day. Onset times for all observed SEP events can be derived either by implementing a threshold to be exceeded by the flux as described in Malandraki et al. (2012) or a Poisson-CUSUM analysis (Huttunen-Heikinmaa et al. 2005). For SEP events with a fast rise a velocity dispersion analysis (VDA) can be used (Krucker et al. 1999; Malandraki et al. 2012) to estimate both the release time at the Sun and the apparent path length of the particles: the solar release time of the first particles seen at the spacecraft is obtained from a linear fit of the derived onset times of electrons and protons at different energies as a function of their respective inverse velocity. Such an analysis could only be performed for 11 of the 25 *Fermi/LAT* events. For a comparison of derived release times with photon arrival times measured at the observer’s distance (1 AU) we add 8 min.

Hereafter, we will discuss the events of 2011 Mar 7, 2012 Mar 7, 2013 Apr 11 and 2014 Feb 25, for which a VDA analysis could be performed at L1 and/or STEREO, as well as the events of 2012 Jan 23 and May 17 that are of particular interest for numerical transport simulations discussed in Chap. 9. Table 8.1 gives the date and location, soft X-ray class, start and peak time, start and end of the decametric-to-hectometric type III bursts and CME speed from the LASCO/CME catalogue. SEP parameters are given for STEREO A and B (STA, STB), for SoHO/ERNE or ACE/EPAM at L1, and for GOES/HEPAD (HEP) such as the characterization of the
<table><caption>**Table 8.1** Characteristics of the 6 SEP event cases discussed in this section (see text for further information)</caption><thead><tr><th rowspan="2">Date</th><th colspan="2">Soft X-rays</th><th rowspan="2">DH III</th><th rowspan="2">CME [km s<sup>-1</sup>]</th><th rowspan="2">SEP (s/c, rise, energy)</th><th rowspan="2">SRT + 8 min [min]</th></tr><tr><th>Class Location</th><th>Start Peak</th></tr></thead><tbody><tr><td rowspan="3">2011 Mar 7</td><td>M3.7</td><td>19:43</td><td rowspan="3">19:50–20:10</td><td rowspan="3">2125</td><td>STA (s) ~60 MeV</td><td>–</td></tr><tr><td rowspan="2">N30W47</td><td rowspan="2">20:58</td><td>L1 (f) ~ 80 MeV</td><td>20:26±00:04</td></tr><tr><td>HEP no detection</td><td>–</td></tr><tr><td rowspan="5">23 Jan 2012</td><td>M8.7</td><td>03:38</td><td rowspan="5">03:40–04:20</td><td rowspan="5">2175</td><td>STB (f) ~60 MeV</td><td>–</td></tr><tr><td rowspan="4">N33W21</td><td rowspan="4">04:34</td><td>STA (s) ~100 MeV</td><td>–</td></tr><tr><td>L1 (f) ~100 MeV</td><td>–</td></tr><tr><td>HEP (s) ~ 600 MeV weak</td><td>–</td></tr><tr><td>STB (s) ~100 MeV</td><td>–</td></tr><tr><td rowspan="4">2012 Mar 7</td><td>X5.4</td><td>00:02</td><td rowspan="4">00:15–01:00</td><td rowspan="4">2864</td><td>STA (s) > 130 MeV</td><td>–</td></tr><tr><td rowspan="2">N17E27</td><td rowspan="2">00:40</td><td>L1 (s) >100 MeV</td><td>23:21±00:51</td></tr><tr><td>X1.2</td><td>01:05</td><td>01:15–01:30</td><td>1825</td></tr><tr><td rowspan="3">N17E27</td><td rowspan="3">01:23</td><td>HEP (s) >700 MeV</td><td>–</td></tr><tr><td>STB (f) >100 MeV</td><td>00:37±00:01</td></tr><tr><td>M5.1</td><td>01:25</td><td>01:30–01:40</td><td>1582</td></tr><tr><td rowspan="5">2012 May 17</td><td rowspan="5">N07W88</td><td rowspan="5">02:14</td><td rowspan="5"></td><td rowspan="5"></td><td>STA (s) ~100 MeV</td><td>–</td></tr><tr><td>L1 (f) ~ 130 MeV</td><td>–</td></tr><tr><td>HEP (f) >700 MeV</td><td>–</td></tr><tr><td>STB (s) ~100 MeV</td><td>–</td></tr><tr><td>M6.5</td><td>06:55</td><td>07:00–07:30</td><td>861</td></tr><tr><td rowspan="4">2013 Apr 11</td><td rowspan="4">N07E13</td><td rowspan="4">07:29</td><td rowspan="4"></td><td rowspan="4"></td><td>STA (s) weak</td><td>–</td></tr><tr><td>L1 (f) ~ 130 MeV</td><td>07:24±00:08</td></tr><tr><td>HEP very weak ~600 MeV</td><td>–</td></tr><tr><td>STB (f) ~100 MeV</td><td>07:10±00:01</td></tr><tr><td rowspan="4">25 Feb 2014</td><td>X4.9</td><td>00:39</td><td rowspan="4">00:45–01:15</td><td rowspan="4">2147</td><td>STA (f) ~100 MeV</td><td>01:06±00:01</td></tr><tr><td rowspan="3">N00E78</td><td rowspan="3">01:03</td><td>L1 (s) ~ 130 MeV</td><td>01:22±00:20</td></tr><tr><td>HEP very weak</td><td>–</td></tr><tr><td>STB (f) ~100 MeV</td><td>00:56±00:01</td></tr></tbody></table>

SEP flux rise as “fast” (f) or “slow” (s), the approximate energy up to which the SEPs are observed and the derived solar release time (SRT) from VDA.

**2011 Mar 7:** The event had moderate SEP flux. The *Fermi/LAT* sustained emission (Fig. 8.2) was observed ~15 min after the CME onset (defined from inspection of SDO/AIA images) and peaked several hours later (~7 h). The derived SRT from the L1 observations is ~20 min later than the *Fermi/LAT* emission onset and the particle path length of ~1.9 AU does not indicate substantial scattering.

**2012 Jan 23:** An intense SEP event was observed by ACE/EPAM at L1. VDA could not produce reliable SRT results, while GOES/HEPAD indicates a very weak event with a poorly determined onset (~7 h after the flare). The weak event was preceded by a slow rise right after the flare. The interaction between the parent CME and a preceding much slower one (1400 km s⁻¹), associated with an earlier
M1.1 class flare, may be responsible for both the observed high SEP flux and the significant changes in the SEP intensity profile (Joshi et al. 2013). Sustained *Fermi/LAT* emission was observed ~15 min after the hard X-ray flare peak, lasting for many hours while the delayed observed GOES/HEPAD onset with respect to the *Fermi/LAT* onset could be related to this several-hours lasting sustained γ-ray emission.

**2012 Mar 7:** For the double solar event with considerable SEP flux, GOES/HEPAD saw a steep rise ~6 h after the first flare. It was, however, preceded by a continuous slow rise starting immediately after the flare, as often observed in eastern SEP events. According to Kouloumvakos et al. (2016) (a) the first flare/CME was responsible for the SEP event observed at different spacecraft, (b) the proton SRT observed by STEREO B is consistent with the arrival of an observed EUV wave on the Sun at the STEREO-B footpoint, and (c) the considerably delayed SRT at L1 compared to STEREO B suggests a release of particles further away from the Sun consistent with the timing and location of the shock's western flank. No plausible explanations could be derived from the observed behaviour at STEREO A. Our L1 VDA analysis is not reliable as the derived apparent particle path length is ~8 AU. The observed large *Fermi/LAT* sustained fluxes, peaking after the first flare and lasting for several hours, have a derived first onset near the first flare peak time, while the second *Fermi/LAT* onset is estimated ~45 min after the second flare onset. The derived STEREO B release time is co-temporal, within errors, with the first *Fermi/LAT* onset.

**2012 May 17:** The strong SEP event was associated with the first Ground Level Enhancement (GLE) of solar cycle 24. VDA could not produce reliable SRTs. GOES/HEPAD registered a fast rising intense event starting right after the flare (see Fig. 8.7). The expansion of the shock forming in the corona was studied using a new technique based on coronal magnetic field reconstructions, full magneto-hydrodynamic simulations and multi-point imaging inversion techniques (Rouillard et al. 2016). This analysis concluded that GeV particles were released when this shock became super-critical (Mach numbers >3). The magnetic connectivity between the shock and L1 was established via a magnetic cloud that erupted from the same active region 5 days earlier. *Fermi/LAT* observations (Fig. 8.5) indicate significant sustained emission starting after the flare and lasting several hours, while the GOES/HEPAD flux onset coincides with the *Fermi/LAT* emission onset.

**2013 Apr 11:** A fast-rising strong SEP event was observed at L1 and STEREO B, but only a small slowly rising one at STEREO A. GOES/HEPAD recorded a very weak event with a poorly-determined onset 3 h after the flare. By determining the angular extent of the observed EUV wave and CME, Lario et al. (2014) concluded that while the particle SRT from STEREO B is within uncertainties consistent with the arrival of the EUV wave and CME-driven shock at the footpoint of the spacecraft, the EUV wave did not reach the footpoint of the field lines connecting to L1; the observed intense SEPs at L1 were most likely originating from the western flank of the CME-driven shock as it was propagating higher in the corona. Our analysis indicates (a) a particle release time to L1 that coincides within errors with the peak of the flare and is at least 15 min later than the SRT from STEREO B and
<figure><img src="image_70.png" /><figcaption>**Fig. 8.8** *Fermi/LAT* observations for the 2014 Feb 25 event. Vertical light and dark green lines indicate respectively the derived STEREO A and B onsets, while purple and orange vertical lines indicate the respective L1 and *Fermi/LAT* onsets. Horizontal lines indicate the derived error ranges</figcaption></figure>

(b) an apparent path length of ~2.1 AU, consistent with the picture emerging from Lario et al. (2014). The derived STEREO B SRT coincides precisely with the onset of the *Fermi/LAT* sustained emission that lasts for ~20 min and peaks a few minutes after the soft X-ray flux.

**25 Feb 2014** (Fig. 8.8): The SEPs rose fast to high fluxes at STEREO A and B, while a weak slowly-rising event was recorded at L1. GOES/HEPAD showed a very weak SEP event with a poorly-determined onset >5 h after the flare. According to Lario et al. (2016), despite the considerable distance between the footpoints of the field lines connecting the Sun with STEREO A, B and L1 and the small extent of the observed EUV wave, the expansion of the extended shock, accompanying the CME, to higher latitudes into the corona determined the release of particles and the observed intense SEP event. Our analysis indicates a SRT at both STEREO satellites and L1 well after the flare in accordance to these findings. However, the VDA at L1 and the respective SRT are not reliable as the particle path length is ~5.2 AU. Due to gaps in the observing time, sustained γ-ray emission is only observed for a short time, starting ~15 min after the onset of the flare, then peaking and dropping quite rapidly within ~20 min. The STEREO B SRT coincides with the *Fermi* onset, while the STEREO A SRT is 10 min later.

## 8.5.2 SEP Spectra

Event-integrated energy spectra of oxygen, neon, and iron+nickel as a group, and the abundance ratios Ne/O, (Fe+Ni)/O, and (Fe+Ni)/Ne were investigated by using
SOHO/ERNE measurements. Heavy ion signatures were searched for in all 25 γ-ray events, and were observed above the quiet-time background in twelve of them. For events occurring in a close sequence of time it was not possible to distinguish possible multiple injections of heavy ions that could have been associated with each individual γ-ray event. This was the case, e.g., for the four events during the time period of 2012 Mar 7–10. The heavy ions observed were associated with the first γ-ray event of this period. Continuous data coverage over an entire event was also required, and this limited the investigation to eight of the 25 γ-ray events.

The event-integrated intensities of O, Ne and Fe+Ni were calculated for 10 energy channels between ~3.2–160 MeV/nucleon of each ion species by integrating from the event onset in each energy channel till the time when the background-detrended cumulative intensity at that energy reached 95% of the maximum. Thus, individual integration times were used for each ion at each energy channel. The energy spectra were fitted by using double power-law functions by Band et al. (1993). The fitting procedure gave the low and high-energy spectral indices ($\gamma_a$ and $\gamma_b$), the break energy ($E_B$), and the normalization constant for the spectra. These quantities for oxygen and iron+nickel are given in Table 8.2 for the events of 2012 Mar 7 and 2013 Apr 11. The measured abundance ratios Ne/O and (Fe+Ni)/O as function of energy are shown in Fig. 8.9. The γ-ray events were characterized by the peak fluxes of ~94×10⁻⁵ cm⁻² s⁻¹ (2012 Mar 7) and ~3.9×10⁻⁵ cm⁻² s⁻¹ (2013 Apr 11) with event durations of 9.9 h and 1.2 h, respectively. Both were eastern events (Table 8.1).

Figure 8.9 shows that the Ne/O ratios in these two events are similar and roughly constant (~0.2) up to ~30 MeV/nucleon, but differ at higher energies with the ratio decreasing with energy in the 2013 Apr 11 event. On the other hand, the (Fe+Ni)/O ratios are quite strongly increasing with energy. The ratio is significantly higher in the event of 2013 Apr 11 than on 2012 Mar 7 reaching the maximum of ~0.7 in the 8–20 MeV/nucleon energy range and then decreasing with energy. The changes with energy in the abundance ratios and the differences between the two studied events can be explained by the differences in the energy where the high-energy spectral index is predominant. The high-energy spectral indices are believed to be dependent on the contribution of suprathermal flare material in the seed population. The high (Fe+Ni)/O ratio in the 2013 Apr 11 event indicates a more impulsive nature and larger flare material contribution in this smaller γ-ray event. It should be noted, however, that both of these events were large proton events lasting for several days. The abundance ratios can be compared with the average values of Ne/O = 0.157 and Fe/O = 0.131 in gradual solar energetic particle events at energies 2–15

<table><caption>**Table 8.2** Heavy ion spectral parameters for the events of 2012 Mar 7 and 2013 Apr 11</caption><thead><tr><th rowspan="2">Event</th><th colspan="3">Oxygen</th><th colspan="3">Iron+Nickel</th></tr><tr><th>γ<sub>a</sub></th><th>γ<sub>b</sub></th><th>E<sub>B</sub> (MeV)</th><th>γ<sub>a</sub></th><th>γ<sub>b</sub></th><th>E<sub>B</sub> (MeV)</th></tr></thead><tbody><tr><td>2012 Mar 7</td><td>1.03</td><td>5.22</td><td>9.8</td><td>0.3</td><td>4.9</td><td>6.4</td></tr><tr><td>2013 Apr 11</td><td>1.53</td><td>4.01</td><td>18</td><td>-0.2</td><td>3.1</td><td>3</td></tr></tbody></table>
<figure><img src="image_71.png" /><figcaption>Fig. 8.9 Abundance ratios Ne/O and (Fe+Ni)/O for the events of 2012 Mar 7 and 2013 Apr 11</figcaption></figure>

MeV/nucleon (Reames 2014) and Ne/O = 0.478 and Fe/O = 1.17 on the average in impulsive SEP events (Reames et al. 2014).

## 8.6 Summary and Discussion

This overview on electromagnetic and SEP signatures that accompany sustained γ-ray emission of 25 events detected by Fermi/LAT is summarized as follows:

* High-energy γ-ray emission during the impulsive and early post-impulsive phase is accompanied by hard X-ray and radio signatures of energetic electron acceleration in the solar atmosphere. This is similar to the earlier findings for pion-decay γ-ray events (Kocharov et al. 1994; Trottet et al. 1994; Akimov et al. 1996) and GLEs (e.g., Klein et al. 2014). The manifestations in the early post-impulsive phase are visible at lower microwave frequencies than those of the impulsive phase, and at dm-to-m wavelengths (type IV bursts).

* γ-ray emission lasting several hours is not accompanied by similarly extended emissions in hard X-rays or radio waves. In all cases (but 2011 Mar 7) these long-duration events accompany the gradual decay of the soft X-ray flux. Although the parent soft X-ray burst starts sometimes more than an hour before the long-lasting γ-ray enhancement, there are statistical relationships between (1) the importance of the parent soft X-ray burst and the peak flux of the long-duration γ-ray emission, and (2) the duration of the decay phase of the soft X-ray burst and the duration of the long-duration γ-ray emission.

* The 2011 Mar 7 γ-ray event was accompanied by several distinct flares. But only the first of them showed conspicuous hard X-ray and radio emission. There is no indication that the long-lasting γ-ray emission could be understood as the superposition of several successive acceleration episodes in independent flares.

* Besides decaying soft X-ray emission and the related post-flare loop arcades, the only other electromagnetic counterpart of long-duration γ-rays are decametric-to-hectometric type II bursts. They accompany the γ-ray emission of all long-duration events.
* SEP events are associated with all high-energy γ-ray events. In most well-connected γ-ray events with long duration GOES/HEPAD detected protons above 300 MeV, and in several cases above 700 MeV. The 2011 Mar 7 γ-ray event is again an exception.

* At energies of several MeV to about 100 MeV the SEP events are strong, but we found no characteristic feature that distinguishes them from strong SEP events in general. All are associated with DH type III bursts, as are SEP events in general (Cane et al. 2010; Vainio et al. 2013). When the solar release time of the first SEPs could be inferred from velocity dispersion analysis, it was found close to the interval of the type III bursts. A temporal relationship with the rise of the late long-duration γ-ray emission could not be excluded, but definite evidence for such a relationship could not be established either.

* The event-integrated abundances of O, Ne, Fe+Ni, and $ ^{3}\text{He} $ in the analysed SEP events show no unambiguous classification with respect to the conventional impulsive or gradual SEP values. There are, however, significant event-to-event variations in the $ ^{3}\text{He} $ and heavy ion abundance ratios and in their energy dependence. The sources of these variations and their possible relationships to the characteristics of the γ-ray emission need further analysis.

We conclude from the observations that pion-decay γ-rays during the impulsive and early post-impulsive phase are a manifestation of common particle acceleration with electrons, seen through hard X-ray and radio emissions. In the post-impulsive phase the signatures are mostly seen at long-centimetric to metric waves.

The association of γ-ray events with soft X-ray emission from the thermal plasma is not a direct clue to the origin of the mildly relativistic protons. Particle acceleration at the CME-driven shock in the high corona appears as an attractive interpretation, because it can explain that γ-rays are observed from flares behind the solar limb (Sect. 8.3) and because type II bursts are the unique systematic radio counterpart of long-duration γ-ray emissions (Sect. 8.4). Stereoscopic CME observations and sophisticated modelling allow one to estimate Mach numbers. Modelling of the shock acceleration (Chap. 9) shows that the highest Mach numbers, observed in restricted regions on the CME surface (Rouillard et al. 2016), may explain shock-accelerated protons up to GeV energies. This modelling shows furthermore that magnetic connections exist between the CME shock and the solar surface (Plotnikov et al. 2017). The interpretation faces two challenges from our present analysis: First, only a small fraction of the particles at the shock, less than 1% as estimated by a simple model, can reach the low solar atmosphere where nuclear interactions can take place. This may still be consistent with the estimation of proton numbers in space and the low solar atmosphere mentioned in Sect. 8.3. The second challenge is to explain why SEPs were only observed up to about 80 MeV during the long-duration γ-ray event on 2011 Mar 7.

The HESPERIA sample of 25 events is too small to draw firm general conclusions on the origin of high-energy events and their relationship with SEPs. But it is rich enough to provide constraints on the processes of acceleration and coronal transport of mildly relativistic protons.
**Acknowledgements** The authors are grateful to Gerald Share and Ron Murphy for preparing the text of Sect. 8.3.

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<figure><img src="image_72.png" /></figure>
Chapter 9
# Modelling of Shock-Accelerated Gamma-Ray Events

Alexandr Afanasiev, Angels Aran, Rami Vainio, Alexis Rouillard, Pietro Zucca, David Lario, Suvi Barcewicz, Robert Siipola, Jens Pomoell, Blai Sanahuja, and Olga E. Malandraki

**Abstract** Solar γ-ray events recently detected by the Fermi/LAT instrument at energies above 100 MeV have presented a puzzle for solar physicists as many of such events were observed lasting for many hours after the associated flare/coronal mass ejection (CME) eruption. Data analyses suggest the γ-ray emission originate from decay of pions produced mainly by interactions of high-energy protons deep in the chromosphere. Whether those protons are accelerated in the associated flare or in the CME-driven shock has been under active discussion. In this chapter, we present some modelling efforts aimed at testing the shock acceleration hypothesis.

A. Afanasiev (✉) • R. Vainio • S. Barcewicz • R. Siipola
Department of Physics and Astronomy, University of Turku, 20014 Turku, Finland
e-mail: alexandr.afanasiev@utu.fi; rami.vainio@utu.fi; t09susaa@utu.fi; roamsi@utu.fi

A. Aran • B. Sanahuja
Departament de Física Quàntica i Astrofísica, Institut de Ciències del Cosmos (ICCUB),
Universitat de Barcelona, Barcelona, Spain
e-mail: angels.aran@fqa.ub.edu; blai.sanahuja@ub.edu

A. Rouillard
Institut de Recherche en Astrophysique et Planétologie, Université de Toulouse, Toulouse, France
e-mail: arouillard@irap.omp.eu

P. Zucca
LESIA - Observatoire de Paris, CNRS, 92190 Meudon, France
e-mail: pietro.zucca@obspm.fr

D. Lario
Applied Physics Laboratory, Johns Hopkins University, Laurel, MD 20723, USA
e-mail: david.lario@jhuapl.edu

J. Pomoell
Department of Physics, University of Helsinki, 00014 Helsinki, Finland
e-mail: jens.pomoell@helsinki.fi

O.E. Malandraki
National Observatory of Athens, IAASARS, Athens, Greece
e-mail: omaland@astro.noa.gr