The Calculation of Solar Gamma-Rays by TALYS

ELSEVIER

CHINESE ASTRONOMY AND ASTROPHYSICS Chinese Astronomy and Astrophysics 36 (2012) 49–62

The Calculation of Solar Gamma-Rays by TALYS†  CHEN Wei

GAN Wei-qun

Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210008

Abstract Solar gamma-ray lines, produced from nuclear reactions of accelerated particles interacting with the solar atmospheric medium, are the most direct diagnosis for the acceleration and transportation of energetic electrons and ions in solar flares. Much information about composition, spectrum, and angular distribution of the accelerated ions, as well as the elemental abundances of the ambient solar atmosphere can be derived from solar gamma-ray line spectra. A new gamma-ray calculation program has been developed by using an efficient nuclear code − TALYS. The theory of gamma-ray production in solar flares is treated in detail. The characteristics of gamma-ray spectrum are also presented. Key words: sun: flares, sun: gamma rays

1. INTRODUCTION A wealth of particles (electrons and ions) are accelerated in solar flares. The bremsstrahlung of high-energy electrons produces hard X-ray emission. And the interactions of energetic ions (e.g. protons, α-particles, and heavier nuclei) with ambient matter produce gammaray lines and a variety of secondary products, such as positrons, neutrons, π-mesons, and other residual nuclei[1] . Lines resulting from elastic collisions of accelerated light-weight ions (protons and α-particles) with ambient nuclei heavier than He are narrow (with fractional widths of about 2% the line-center energy). This is because the relatively low recoil velocity of the heavy nuclei results in moderate Doppler shifting of the photons. These reactions †

Supported by National Natural Science Foundation and MSTC Received 2009–10–15; revised version 2010–12–17  A translation of Acta Astron. Sin. Vol. 52, No. 3, pp. 219–232, 2011 � [email protected]

0275-1062/11/$-see front matter 2012 Elsevier B.V. All rights reserved. c 2011 0275-1062/01/$-see front©matter  Elsevier Science B. V. All rights reserved. doi:10.1016/j.chinastron.2011.12.002 PII:

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are referred as direct reactions. On the other hand, lines resulting from inelastic collisions of accelerated heavy ions with ambient Hydrogen and Helium are broad (with fractional widths of about 20% the line-center energy). This is because the heavy nuclei retain a large fraction of their initial velocities resulting in significant Doppler shifting. These reactions are referred as inverse reactions. Based on some measured cross sections in laboratory, Ramaty et al.[2] (hereafter RKL) calculated the solar gamma-ray spectrum for the first time. Kozlovsky et al.[3] updated the cross sections for the explicit lines using the extensive and systematic laboratory measurements that became available after RKL was published. However, due to the limitation of the cross sections by measurements, the calculation of the complete solar gamma-ray spectrum was restrained. Moreover, the calculations about nuclear continuum in these work were based on some empirical assumptions. TALYS is a versatile tool to analyze basic microscopic experiments and to generate nuclear data for applications. It is a user-friendly, efficient code to compute the nuclear cross sections. We apply this code into the calculation of solar gamma-ray lines. It makes the calculation be more complete than ever. The evaluation of nuclear continuum is also provided by TALYS. In Section 2 we demonstrate the validity of TALYS. In Section 3, we describe in detail the calculation method and calculate the properties of explicit lines and nuclear continua, as well as their dependence on various physical conditions in solar flares. We also discuss how the results can be used in the study of solar gamma-ray spectra. The conclusions are presented in Section 4.

2. TALYS CODE TALYS (http://www.talys.eu/) is a software for the simulation of nuclear reactions of 1 keV to 250 MeV projectiles (e.g. proton, α-particle, 3 He, neutron, and photon). Many stateof-the-art nuclear models are included to cover all main reaction mechanisms encountered in light particle-induced nuclear reactions. TALYS provides a complete description of all reaction channels and observables, and is user-friendly. By setting the input parameters of TALYS, the user can obtain details of the nuclear reaction process, such as the reaction cross section, angular distribution of emitted particles, the residual nuclei components, etc. TALYS has been used in astrophysical calculations of nuclear reaction rates[4,5], and gammaray line yields in solar flares[6,7] . The authors of TALYS and others have verified its accuracy by comparing calculated results with experimental data for a variety of nuclear reactions[8,9]. However, most of these tests and comparisons dealt with the particle emitting reactions. For solar flares, we are interested in gamma-ray-producing reactions. Referring to the book of “Table of Isotope”[10] , we have therefore made some amendments to the source code of TALYS. Compared with the cross sections obtained by measurements in laboratory, TALYS has its advantages to calculate more complete set of cross sections of solar gamma-ray production. For determining the unresolved-line component, TALYS provides the best approach to describe the complex behavior and structure of the radiation resulting from thousands of lines. Since this component comes from such a large number of transitions, it is impossible to obtain each cross section in laboratory measurements. The state-of-the-art nuclear models



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used by TALYS do contain parameters which are empirically determined by measurements. These parameters are stored in TALYS and then used in the calculations for other different reactions, such as for the other gamma-ray line production unavailable in measurements. Therefore, TALYS is indispensable for evaluation of the unresolved-line component. 3. SOLAR GAMMA-RAY LINE PRODUCTION Gamma-ray emission is actually the electromagnetic radiation caused by the nuclear transition from an excited state to a state of lower levels. The principal mechanisms of gamma-ray production are the decay of a radioactive nucleus and the nuclear reaction. Radioactive decay results in the nucleus in a different state, or a different nucleus, either of which is named the daughter nuclide. The daughter nuclide transits from an excited state to the lower level, emitting a high-energy photon. On the other hand, the nucleus could also be excitated by the bombardment of the energetic ions, producing the gamma-rays through the decay reaction or direct transitions to the low-level states. For solar flares this is the principal mechanism of gamma-ray production. The most abundant elements in the solar atmosphere are Hydrogen and Helium. Due to lack of the excited state in these nuclei, the proton-proton and proton-α reactions cannot produce explicit lines. However, these nuclear reactions can produce π-meson, which results in the emission of gamma-rays contributing mainly to the continuum spectrum. In addition, since the abundances of heavy nuclei are very low in the solar atmosphere, we ignore the nuclear reactions between nuclei heavier than He in our calculation, although some authors thought that these reactions are important to the gamma-ray spectrum[11] . Therefore, we consider only the nuclear reactions of light nuclear particles like protons and α particles with heavier nuclei in our solar gamma-ray production. In the projectile energy range between 1 MeV and several hundreds of MeV, the importance of a particular nuclear reaction mechanism appears or disappears upon varying the incident energy. Starting from the low-energy side, if the energy of projectile is below the excitation energy of the first excited state, the first possible mechanism of gamma-ray production is radiative capture, i.e., the projectile a is captured by the target nucleus b, forming a compound nucleus c with emission of a gamma-ray at the same time a+b→c+γ.

However, the cross section for this reaction is relatively small in the case of charged particles like protons, α particles, and become smaller as the energy of projectile increased. For instance, the production of neutron capture line (n+p → 2 H+γ) occurs in solar flares mainly for thermalized neutrons, because the cross section of this reaction is inversely proportional to the projectile velocity. At somewhat higher projectile energies, the inelastic channels open up, and the radiative capture reactions are completely negligible with respect to inelastic scattering reactions. The projectile particles collide with target nuclei, and transfer energy to target in excited states. The gamma-ray is emitted through the transition to a low-level state. a + b → a + b∗ → a + b + γ .

Generally, the threshold energy for these reactions is not far above the excitation energy of the first excited state in the target nucleus. For solar flares, several strongest lines are from

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transitions of the first few excited levels in the abundant target nuclei (i.e., 12 C, 14 N, 16 O, 20 Ne, 24 Mg, 28 Si, 32 S, and 56 Fe). These reactions constitute the main gamma-ray producing process for <100 MeV projectile energies in solar flares. At still higher projectile energies, above several tens of MeV, more and more residual nucleus formed in reactions may decay and produce more gamma-rays.

Fig. 1

Flowchart of solar gamma-ray calculation

Fig.1 is the flowchart of our solar gamma-ray calculation. The total de-excitation line spectrum consists of narrow lines and continua. The narrow lines are resulted from accelerated protons and α-particles interacting with ambient heavy elements. And continua contain broad lines which are generated from accelerated heavy elements interacting with ambient H and He. Some other unresolved-line continua include a mass of weak lines, compound continuum and pre-equilibrium continuum. The exact number of possible transitions is impossible to be determined due to incomplete nuclear structure information and too much transitions. TALYS uses the keyword Ns to divide the nuclear levels into two categories. The first category is for the energy levels which are less than Ns . In this category, TALYS considers the transitions between these levels as discrete emission process. Some transitions of high probability will produce strong emission lines. These lines are referred as explicit lines. While there are more transitions to generate low-intensity lines which mainly contribute to the continuum. These lines are referred as weak lines. The second category is for the energy levels which are greater than Ns . For heavier nuclei, because the number of excited energy levels is very large, the transitions among these levels would produce a huge number of gamma-ray lines. For simplification, the mutual transitions between these higher levels or the transitions between higher levels and lower discrete levels are considered as continuous emission process (see TALYS user manual in detail). 3.1 The Explicit Line Calculation As mentioned above, when nuclei are excitated, some of nuclei produce new residual nuclei, and some of nuclei produce gamma-rays through transitions directly. Those transitions which have lower threshold energies and larger cross sections would produce stronger emission lines (for example, the 12 C 4.438 MeV line). Taking the abundances of solar at-



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mosphere into consideration, we just calculate explicit lines via the nuclear reactions of the accelerated protons and α-particles with ambient heavy nuclei. In our calculation, first we obtain the cross sections from TALYS calculations. Take the 4.438 MeV line from 12 C as example, there are several nuclear reactions contributing to this line, like P + 12 C → P + 12 C; P + 14 N → X + 12 C; P + 16 O → X + 12 C, here P is proton or α-particle, X stands for other possible residual nuclei. The cross sections of these reactions can be seen in Fig.2. At projectile energies above 250 MeV, the cross sections of nuclear reactions are calculated by extrapolations based on the trend established at 250 MeV.

Fig. 2

Cross sections for the production of 4.438 MeV line by interactions of proton (a) and α (b) projectiles with C, N, O as calculated by TALYS

Since almost all gamma-ray lines are emitted promptly after collisions (typically ∼10−12 s), the line broadening depends on the recoil velocity of the excited heavy nucleus. We assume that the inelastic scattering process is a simple binary collision, and then calculate the line profiles by using Monte Carlo method. A particular line can be produced by reactions between different projectiles and target nuclei, like the 4.438 MeV line, which is mainly produced in inelastic scattering reactions of light projectiles (protons and α-particles) with 12 C and by spallation of 16 O. Line shape calculations require precise nuclear reaction data and information for projectiles, like angular distribution, energy distribution, etc. Under assumptions of isotropic injection of projectiles and Carbon-to-Oxygen abundance ratio ([C]/[O]) of 0.5, we calculate the shape of 4.438 MeV line for various spectral indexes of accelerated ions and α/p ratios. Fig.3 illustrates how the line shape depends on these parameters. First, we compare the results with the same spectrum of accelerated ions and different α/p ratios, and find that the shape of this line is mainly contributed by p+C and p+O reactions for α/p of 0.1 (Fig.3(a)); while the α/p ratio increases to 0.5, the contribution from α+C reaction is increased significantly. The line profile also widens as the α/p increases because the Doppler broadening results from α-particle projectile reactions (see Fig.3(b)). On the other hand, under the same condition of α/p ratio, the line profile changes obviously for the different ion spectra. For a harder ion spectrum, due to involving

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more energetic ions (protons and heavies) and more interactions with Oxygen nuclei, the contribution of Oxygen to the line becomes significant (see Fig.3(c)). As the ion spectrum softens (Figs.3(d)∼(e)), the α-particle projectile reactions become more and more important due to the lower threshold energies for these reactions. Downward-isotropic angular distribution of accelerated ions makes the line profile depend on the flare location. To illustrate this, in Fig.4 we present the line shapes for two flare locations: solar disk and limb. For a disk flare (Fig.4(a)), because all the recoil nuclei are downward, resulting in a red shift of the line shape. On the other hand, if the flare occurred at the solar limb (Fig.4(b)), the recoil nuclei moving towards the observer are equal to those moving backwards the observer in number, so the line center would not changed, but the Doppler broadening is obvious. The line broadening is a complex problem which depends on many factors, like α/p ratio, ambient abundances, nuclear cross sections, and the angular distribution and spectral index of accelerated ions. In our solar gamma-ray code, we calculate the inelastic interactions of accelerated protons, α-particles, and 3 He particles with heavy elements (i.e., C, N, O, Ne, Na, Mg, Al, Si, S, Ca, Fe, Ar, Cr, Ni, Ti, and Zn), and the inverse reactions of these interactions, and α − α reactions. The overall reactions are more than 5000 in quantity. We extract the 430 intense lines as explicit lines in our calculation. Most energies of these lines range from 300 keV to 8 MeV. Table 1 lists the information of some explicit lines. The first column is the line-center energy, and the second and third columns represent the transition and emission mechanism of the line, respectively; the last two columns are the mean life time and branch ratio of the emission, respectively. 3.2 Nuclear Continuum Calculation The solar gamma-ray continuum spectrum comes from the contributions of many mechanisms, like bremsstrahlung emission of accelerated electrons, 3-photon process of positronelectron annihilation[12] , Compton scattering of neutron capture line, π-meson decay[13] , and nuclear reactions. Here we focus on the continuum production from nuclear reactions. As shown in Fig.1, the nuclear continuum contains the unresolved-line spectra and broad lines. The unresolved-line spectrum includes numbers of weak lines, and emissions from compound reactions and pre-equilibrium reactions. While the broad lines are resulted from inverse reactions. All of these continuum components range mainly from 1 to 8 MeV. 3.2.1 Quasi-continuum of weak lines This component consists of the radiation from discrete transitions treated by TALYS. When all possible residual nuclei are considered, the number of these lines is very large (for Fe, the number of levels can be greater than 50, resulting more than thousand lines). With the increase of projectile energy, the target nuclei would be excited to higher levels, especially for heavy nuclei that have a lot of excited levels, and then emit gamma-rays through discrete transition reactions or disintegration reactions. Generally, these reactions have smaller cross sections than that of explicit lines, and also require a higher energy threshold. Therefore, these numerous weak lines are always submerged in the emission of explicit lines.



Fig. 3

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The line profiles of the 4.438 MeV from different reactions with isotropic energetic particle

distribution (full line). Four reactions are also shown (dotted line: p + 12 C → p + 12 C* + γ; dashed line: p + 16 O → X + 12 C* + γ; dot-dashed line: α + 12 C → α + 12 C* + γ; dot-dot-dashed line: α + 16 O → X+

12 C*

+ γ. We made the assumption that the abundance [C]/[O] ratio is 0.5 in the calculation.

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Fig. 4 The 4.438 MeV line profile changes with the location of flares, and the accelerated particles are assumed to have a downward-isotropic (DI) distribution.

Let us take the 100 MeV proton projectiles interacting with 56 Fe and 24 Mg as an example. In Fig.5, we show the cross sections for these productions. We have combined the discrete lines into 1 keV bins. As shown in the figure, the lines of proton interacting with 56 Fe are very large (more than 2000), and all the energies are below ∼4 MeV. This is a computational artifact of TALYS. For 56 Fe, the energy of the 25 (Ns )-th level is about 4 MeV, and so 4 MeV is the largest photon energy in this case. Due to the Doppler effect, these numerous weak lines often overlap and blend with each other. We refer to this component as the quasi-continuum of weak lines.

Fig. 5 Cross sections for weak lines from 100 MeV proton projectiles interacting with

56 Fe

(a) and

24 Mg

(b) as calculated by TALYS

3.2.2 Compound Continuum and Pre-equilibrium Continuum As discussed above, TALYS treats the transitions initiated in the bins (i.e., from levels > Ns ) as a continuum. This radiation includes transitions between the bins themselves and transitions from the bins to lower discrete levels. We refer to emission from these transitions as the compound continuum. Given the known nuclear-level density functions, TALYS can calculate the shape and intensity of the compound continuum.



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Table 1

Line center energy, nuclear reaction, mean life and branch ratio of excited level of explicit gamma-ray lines from solar flare

Energy(MeV) 0.429 0.440 0.478 0.718

Transition → g.s. 23 Na∗0.440 → g.s. 7 Li∗0.478 → g.s. 10 B∗0.718 → g.s. 7 Be∗0.429

0.844 0.847

27 Al∗0.844 56 Fe∗0.847

→ g.s. → g.s.

1.369

24 Mg∗1.369

→ g.s.

1.634

20 Ne∗1.634

→ g.s.

1.779

28 Si∗1.779

→ g.s.

2.000 2.230

11 C∗2.000

→ g.s. → g.s.

3.737

40 Ca∗3.737

4.438

12 C∗4.439

→ g.s.

4.444

11 B∗4.445

→ g.s.

5.105

14 N∗5.106

→ g.s.

5.240

15 O∗5.241

→ g.s.

5.269

15 N∗5.270

→ g.s.

6.129

16 O∗6.129

→ g.s.

7.115

16 O∗7.117

→ g.s.

32 S∗2.230

→ g.s.

Reaction x)7 Be 24 Mg(p, x)23 Na 4 He(α, x)7 Li 12 C(p, x)10 B 16 O(p, x)10 B 28 Si(p, x)27 Al 56 Fe(p, x)56 Fe 56 Fe(α, x)56 Fe 24 Mg(p, x)24 Mg 24 Mg(α, x)24 Mg 20 Ne(p, x)20 Ne 20 Ne(α, x)20 Ne 24 Mg(p, x)20 Ne 28 Si(p, x)28 Si 28 Si(α, x)28 Si 32 S(p, x)28 Si 12 C(p, x)11 C 32 S(p, x)32 S 32 S(α, x)32 S 40 Ca(p, x)40 Ca 40 Ca(α, x)40 Ca 12 C(p, x)12 C 12 C(α, x)12 C 14 N(p, x)12 C 14 N(α, x)12 C 16 O(p, x)12 C 16 O(α, x)12 C 12 C(p, x)11 B 12 C(α, x)11 B 14 N(p, x)14 N 14 N(α, x)14 N 16 O(p, x)14 N 16 O(α, x)14 N 16 O(p, x)15 O 16 O(α, x)15 O 16 O(p, x)15 N 16 O(α, x)15 N 16 O(p, x)16 O 16 O(α, x)16 O 20 Ne(p, x)16 O 20 Ne(α, x)16 O 16 O(p, x)16 O 16 O(α, x)16 O 4 He(α,

Mean life(10−12 s) 0.133 1.11 0.073 707

Branch ratio 100 100 100 100

35 6.07

100 100

1.35

100

0.73

100

0.48

100

0.007 0.17

100 100

42

100

0.061

100

100 4.35

100

2.25

100

1.79

100

0.018

100

0.008

99.9

Note: g.s. stands for ground state.

Besides the radiation from transitions between well-defined quantum states (bound or unbound), the nuclear reactions can also produce emission before the statistical equilibrium of the compound nucleus is reached. This emission cannot simply be described with a given energy. We refer to this component as the pre-equilibrium continuum which can be calculated with TALYS. We show in Fig.6 the total unresolved-line continuum produced by 100 MeV protons interacting with 56 Fe and 24 Mg, including the weak line quasi-continuum, compound continuum, and pre-equilibrium continuum. To better describe the total unresolved-line continuum, we redraw Fig.6 with more

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Fig. 6 Cross sections for total unresolved-line continuum (solid line), including weak lines, the compound continuum (dashed line) and the pre-equilibrium continuum (dotted line) from 100 MeV proton projectiles interacting with

56 Fe

(a) and

24 Mg

(b), respectively

smoothed curves through changing the energy bins (combined into 100 keV bins) in Fig.7. We see structures in both spectra, and it seems to have more structures for the 24 Mg. The reason is that the number of states for the lighter 24 Mg nucleus is less than that of 56 Fe and the energy of the 25th level is higher (for 24 Mg it is ∼9.3 MeV). Moreover, the structure of unresolved-line continuum depends also on projectile energy. In Fig.8 we show the results for interactions of 10, 50, and 100 MeV protons with 56 Fe. We see that a smoother spectrum presents with higher projectile energies, because more higher-lying levels are accessed, resulting in a large number of weak lines.

Fig. 7 Cross sections for total unresolved-line continuum (solid line) from 100 MeV proton projectiles interacting with

56 Fe

(a) and

24 Mg

(b), respectively. Dashed lines represent the contribution from compound continuum

3.2.3 Broad-lines continuum The nuclear broad lines are caused by interactions of heavy energetic nuclei with ambient Hydrogen and Helium. Because the heavy nuclei retain a large fraction of their initial velocities after nuclear collisions, resulting in a significant Doppler broadening. For solar gamma-ray spectrum, a large number of nuclear broad lines blend into a continuum spec-



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Fig. 8 Cross sections for total unresolved-line continuum from 10 MeV, 50 MeV and 100 MeV proton projectiles interacting with 56 Fe

trum. The calculation of the nuclear broad line component is similar to that of explicit line, and its strength depends on the compositions and the energy spectra of heavy accelerated nuclei. 3.3 Total solar gamma-ray spectrum calculation In solar flares, both ions and electrons are accelerated to high energies. These energetic particles are injected into a magnetic loop and transport down to the chromospheric and photospheric portions of the solar atmosphere. These energetic particles ultimately lose their energy by collisions with ambient medium in these two dense layers. Under the thick-target model, the yield of gamma-rays emitted in a reaction of projectile i with target j is given by[14]  Emax  Emax   σij (Ep ) dEp × N γ = nj Ni (Ep )dEp , (1) dE/dx ETh Ep

where ET h is the threshold energy for the reaction, nj is abundance of target nucleus j in the ambient medium, and σij is the cross section of interaction of projectile i with target j, which is calculated by TALYS; dE/dx is the stopping power for particle i in the solar atmosphere. In our calculation, both ambient element abundances and accelerated ion compositions are adjustable parameters. Ni (E) is the instantaneous number of accelerated particles in the interaction region per unit energy at E. We use the power-law distribution for this value Ni (E) = N0 E −s .

(2)

Where i denotes the species of the particles; N0 is a constant determined by normalizing the particle number to 1 proton of energy greater than 30 MeV; and s is the power-law spectral index assumed to be the same for all charged particle components. In passing through matter, energetic charged particles gradually lose their energy. Stopping power (dE/dx) is defined as the average energy loss of the particle per unit path length, measured in MeV mg−1 cm−2 (see Fig.9). The stopping power depends on the species and energy of the particle and on the properties of the ambient medium. It consists mainly of two parts[15] : electronic stopping and nuclear stopping. SRIM[16] is a group of computer

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programs which calculate interaction of ions with matter. It is based on a Monte Carlo simulation method, namely the binary collision approximation with a random selection of the impact parameter of the next colliding ion. We use this code to calculate the stopping power for ions in solar atmosphere, whose composition may be well approximated by a mixture of 90% Hydrogen and 10% Helium. To illustrate how the stopping power depend on ion energy and species, in Fig.9 we show the stopping power for interactions of protons and carbon nuclei with solar atmosphere. In the beginning of the slowing down process at high energies, both of ions are slowed down mainly by electronic stopping, and it moves almost in a straight path. When the ion has slowed down sufficiently, the nuclear stopping become more and more probable, finally dominating the slowing down.

Fig. 9 SRIM calculation of the stopping power for ions in the solar atmosphere, which is composed by a mixture of 90% H and 10% He. Dotted and dashed lines represent the contributions from electronic stopping and nuclear stopping, respectively

In solar gamma-ray production, the typically energy of ions are greater than 1 MeV nucleon−1 for nuclear reactions. As shown in Fig.9, the electronic stopping is dominant and the nuclear stopping can be ignored at these energies. The stopping power is simply linearly proportional to the ion energy. Here we use the Bethe[17] formula to describe the energy loss of charged ions per unit pathlength −

4π nz 2 e2 2 2me c2 β 2 dE = ) − β2] . ( ) [ln( dx me c2 β 2 4πε0 I(1 − β 2 )

(3)

4πnz 2 e2 2 2me υ 2 dE = ). ( ) ln( dx me υ 2 4πε0 I

(4)

Where β is velocity of the particle, I is the mean excitation potential of the target. Ze and ε0 represent the particle charge and vacuum permittivity, respectively. From Eq.(3), we can see that the stopping power is proportional to square of charge number. Therefore, the higher particle charge number is, the faster the energy losses. At low energy, i.e., for small velocities of the particle (β � 1 ), the Bethe formula reduces to −

According to Eqs.(1∼4), we calculate the yield and the shape of each line by using Monte Carlo simulation. Then we obtain the whole gamma-ray spectrum of solar flare. We show in Fig.10 the broad lines (dashed line) and also total gamma-ray spectrum (solid line)



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for various spectral indexes of accelerated ions and α/p ratios. For these calculations, we have assumed a coronal composition[18] for both the ambient medium and the accelerated ions (except with He/H = 0.1 and α/p = 0.1 or 0.5) and an isotropic ion angular distribution. We see that the shape of gamma-ray spectrum changes with the spectrum of accelerated ions For the harder spectrum (s = 2.5), more high-energy ions involve in reactions, resulting in a relatively smooth continuum. For a softer spectrum (s = 4.5), in contrast, the structure of the spectrum is noticeable. In addition, the α/p ratio would affect the intensity of the 0.45 MeV line which results from α − α nuclear reaction, and also affect the shape of gamma-ray spectrum. Because a higher α/p ratio involves more α-particles, and therefore results in a larger Doppler broadening of the radiation.

Fig. 10 Total solar gamma-ray spectra (solid line) from isotropic accelerated ions interacting with solar atmosphere. The abundances of both accelerated particles and ambient elements are coronal (Reames 1995). Dashed line represents the broad line component

4. SUMMARY Solar gamma-ray spectrum is the most direct window to study the accelerated ions in solar flares. Through analyzing solar flare gamma-ray data such as RHESSI data and the GBM on Fermi, we can obtain the information about the energy spectrum, angular distribution, total number, and total energy of accelerated ions, as well as the knowledge of physical condition, such as the α/p ratio, ambient medium abundance, and the composition of accelerated ions. Therefore, improving the theoretical calculation of solar gamma-ray spectrum is an important topic.

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By using TALYS, we obtain a more complete cross sections of nuclear reactions, and thus a more accurate solar gamma-ray spectrum. In our production code, we calculate the interactions of protons and α-particles with such C, N, O, Ne, Mg, Al, Si, S, Ca, Fe as the heavy elements, and the inverse reactions of these interactions. Although TALYS gives us a more complete nuclear cross section data, it cannot be used to calculate the cross sections for the interactions between light nuclei, and cannot let us study the decay of high-energy π-meson. We are trying to obtain the gamma-ray energy spectrum at higher energies by other means. We also calculate the unresolved-line continuum in detail, including a large number of weak lines, the compound continuum, and the pre-equilibrium continuum. Considering the lack of laboratory measurements of these spectra, TALYS is indispensable for evaluation of this component. In addition, we have also analyzed the effects of accelerated particle energy spectrum, α/p ratio and location of solar flares to the shape of gamma-ray lines. The results show that the line shape would become unpredictable with changing these three parameters. In more precise study, all the composition of accelerated ions, the solar ambient abundances, angular distribution of accelerated ions, pitch angle scattering and the structure of the magnetic field would determine the line shape of the calculation. So many parameters combined together make the line shape distinctly elusive. However, with the improvement of theoretical calculation and technique development of future high-energy telescope, we would obtain much more information of solar physics. For this reason, studying solar gamma rays will be a dynamic and challenging scientific task. References 1

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