Spectrum of Accelerated Particles Derived from the 2.223 MeV Line Data in Some Solar Flares

1. Spectrum of Accelerated Particles Derived from the 2.223 MeV Line Data in Some Solar Flares Leonty I. Miroshnichenko (1, 2), Evgenia V. Troitskaia (3), and Wei Q. Gan (4) (1) Instituto de Geofísica, UNAM, MEXICO, leonty@geofisica.unam.mx(2) IZMIRAN, Troitsk, Moscow, RUSSIA, leonty@izmiran.troitsk.ru (3) SINP, Moscow State University, Moscow, RUSSIA (4) Purple Mountain Observatory (PMO), Nanjing, CHINA

2. Abstract • The 2.223 MeV line time profile for the flare of 16 December 1988 (for its third most intensive peak) is studied. The enhancement of plasma density in the deep photospheric layers below the flare region has been deduced. The energy spectrum of energetic solar particles (protons) is assumed to be formed by stochastic mechanism of acceleration. • To compare our model calculations with observations, we use two possible functions for spectrum presentation, the power-law and Bessel functions with spectral indices s and αT, respectively. The spectrum was shown to evolve with time, namely, the spectral index αT was found to increase from 0.005 to 0.1 during the decay phase of the burst, i.e., the proton spectrum has become harder. • The density enhancement found in the flare of 16 December 1988 is consistent with our previous results for two other gamma-ray flares, 6 November 1997 and 22 March 1991. • This conclusion seems do not depend on the function of spectrum presentation and on the model of secondary neutron production by accelerated solar particles in the solar atmosphere. It is suggested that density enhancement in the deep layers of the solar photosphere may be rather common feature of powerful solar flares.

3. Density models for the solar atmosphere Fig.1. Basic density model of the solar atmosphere (1) and four distorted models (2-5). Only fragments differing from the curve (1) are shown (Kuzhevskij et al., 2005). Parameter τ is the optical depth for a wavelength of 500 nm, the level τ = 0.005 corresponds to the top of the photosphere.

4. Results of Model Calculations (Power-Law Spectrum) Fig. 2.Observed 2.223 MeV line fluences of the 16 December 1988 flare (black diamonds) and the best density model 5 for the entire time profile of the third gamma-ray burst at S = 4.0.

5. Results of Model Calculations (Exponential Spectrum) Fig.3.Observed 2.223 MeV line fluences of the 16 December 1988 flare (black diamonds) and the best density model 5 for the entire time profile of the third gamma-ray burst. Model calculations have been made with a new neutron spectrum (Hua et al., 2002) at αT = 0.03.

6. Fig.4. Combined profile of the 2.223 MeV line burst on 16 December 1988 calculated at density models 2, 5 and S = 2, 4, 6 from Hua and Lingenfelter (1987)

7. Conclusions • The density enhancement found in the flare of 16 December 1988 is consistent with our previous results for two other gamma-ray flares, 6 November 1997 and 22 March 1991. • This conclusion seems do not depend on the function of spectrum presentation and on the model of secondary neutron production by accelerated solar particles in the solar atmosphere. • It is suggested that density enhancement in the deep layers of the solar photosphere may be rather common feature of powerful solar flares.

8. Implications and Prospects From above discussion it follows that implications and further prospects of suggested method are determined by involving new observational data on the flares registered during last years with high energy, time and angle resolutions, in particular, by RHESSI, CORONAS-F, and INTEGRAL spacecraft (23 July 2002, October-November 2003, and 20 January 2005).

9. Implications and Prospects • At this way a serious problem exists due to non-radiative neutron absorption on He-3. In this context, it would be very important to obtain independent measurements of the He-3 content by new methods of solar gamma-spectroscopy or by registration a weak line at 20.58 MeV from radiative absorption of neutrons by He-3 nuclei in solar flares. • Some other possibilities arise from the considerations of power-law spectra of solar protons accelerated by shock waves and from account for possible distribution of original neutrons on depth in the solar atmosphere.

10. ACKNOWLEDGEMENTS This work was supported partly by the CONACyT, Mexico (project 45822, PERPJ10332), Russian Foundation for Basic Research (RFBR, projects 02-02-39032, 03-02-96026, 05-02-39011), Federal Purpose Scientific and Technical Program, Section I, Project 4), and President’s Grant of Russian Federation (project 1445.2003.2). We also wish to thank S.A. Chaikin and G.A. Kuleshov for the help in calculations. The work by W. Gan was supported by NNSFC (China) via grants 10173027, 10221001, 10333040) and by grant G2000078402 from the Ministry of Science and Technology of China.

11. Acknowledgements • This work was greatly inspired by Prof. Boris M. Kuzhevskij who drastically passed away on 28 February 2005. His contribution to the investigation of different aspects of solar gamma rays remains very significant.

12. Important references • B.M. Kuzhevskij. Uspekhi Fizicheskikh Nauk, 137(2), 237-265 (1982). • X.-M. Hua, R.E. Lingenfelter. Solar Phys., 107, 351 (1987). • X.-M. Hua, B. Kozlovsky, R.E. Lingenfelter et al. (in all 5 authors). Ap. J. Suppl., 140, 563-579 (2002). • B.M. Kuzhevskij, L.I. Miroshnichenko, and E.V. Troitskaia. Russian Astronomy Reports, 49(7), 566-577 (2005).