New solutions, for the stationary and temporary states, are derived for the 1D diffusion of cosmic rays in the presence of losses. The new results are applied to the latitude profile of radiation emitted above the galactic plane. Percolation theory for a spiral galaxy coupled with the evolution of the super-bubbles allows building a model for the radiation of a spiral galaxy as seen face on. The annulus of radiation of our galaxy is also simulated and the excess of radiation observed at the centre of our galaxy is explained by the sine law which arises in the theory of the image.
References
[1]
Streimatter, R.E., Balasubrahmanyan, V.K., Protheroe, R.J. and Ormes, J.F. (1985) Cosmic Ray Propagation in the Local Superbubble. Astronomy & Astrophysics, 143, 249-255.
[2]
Higdon, J.C., Lingenfelter, R.E. and Ramaty, R. (1998) Cosmic-Ray Acceleration from Supernova Ejecta in Superbubbles. The Astrophysical Journal, 509, L33-L36. https://doi.org/10.1086/311757
[3]
Alibés, A., Labay, J. and Canal, R. (2002) Galactic Cosmic Rays from Superbubbles and the Abundances of Lithium, Beryllium, and Boron. The Astrophysical Journal, 571, 326-333. (Preprint) https://doi.org/10.1086/339937
[4]
Higdon, J.C. and Lingenfelter, R.E. (2003) The Superbubble Origin of 22Ne in Cosmic Rays. The Astrophysical Journal, 590, 822-832. https://doi.org/10.1086/375192
[5]
Higdon, J.C. and Lingenfelter, R.E. (2005) OB Associations, Supernova-Generated Superbubbles, and the Source of Cosmic Rays. The Astrophysical Journal, 628, 738-749. https://doi.org/10.1086/430814
[6]
Lingenfelter, R.E. and Higdon, J.C. (2007) Cosmic Rays, Dust, and the Mixing of Supernova Ejecta into the Interstellar Medium in Superbubbles. The Astrophysical Journal, 660, 330-335. https://doi.org/10.1086/513420
[7]
Butt, Y.M. and Bykov, A.M. (2008) A Cosmic-Ray Resolution to the Superbubble Energy Crisis. The Astrophysical Journal, 677, L21-L22. (Preprint) https://doi.org/10.1086/587875
[8]
Ferrand, G. and Marcowith, A. (2010) On the Shape of the Spectrum of Cosmic Rays Accelerated Inside Superbubbles. Astronomy & Astrophysics, 510, Article No. A101. (Preprint) https://doi.org/10.1051/0004-6361/200913520
[9]
Barghouty, A.F. and Schnee, D.A. (2012) Anomalous Transport of High-energy Cosmic Rays in Galactic Superbubbles. I. Numerical Simulations. The Astrophysical Journal, 749, 178-188. https://doi.org/10.1088/0004-637X/749/2/178
[10]
Heesen, V., Brinks, E., Krause, M.G.H., Harwood, J.J., Rau, U., Rupen, M.P., Hunter, D.A., Chyży, K.T. and Kitchener, G. (2015) The Non-Thermal Superbubble in IC 10: The Generation of Cosmic Ray Electrons Caught in the Act. Monthly Notices of the Royal Astronomical Society: Letters, 447, L1-L5. (Preprint) https://doi.org/10.1093/mnrasl/slu168
[11]
Gupta, S., Nath, B.B., Sharma, P. and Eichler, D. (2018) Lack of Thermal Energy in Superbubbles: Hint of Cosmic Rays? Monthly Notices of the Royal Astronomical Society: Letters, 473, 1537-1553. (Preprint) https://doi.org/10.1093/mnras/stx2427
[12]
Lingenfelter, R.E. (2018) Cosmic Rays from Supernova Remnants and Superbubbles. Advances in Space Research, 62, 2750-2763. (Preprint) https://doi.org/10.1016/j.asr.2017.04.006
[13]
Tolksdorf, T., Grenier, I.A., Joubaud, T. and Schlickeiser, R. (2019) Cosmic Rays in Superbubbles. The Astrophysical Journal, 879, 66-76. https://doi.org/10.3847/1538-4357/ab24c6
[14]
Zhang, Z., Murase, K. and Mészáros, P. (2020) Cosmic Rays Escaping from Galactic Starburst-Driven Superbubbles. Monthly Notices of the Royal Astronomical Society: Letters, 492, 2250-2260. (Preprint) https://doi.org/10.1093/mnras/staa022
[15]
Joubaud, T., Grenier, I.A., Casandjian, J.M., Tolksdorf, T. and Schlickeiser, R. (2020) The Cosmic-Ray Content of the Orion-Eridanus Superbubble. Astronomy & Astrophysics, 635, Article No. A96. (Preprint) https://doi.org/10.1051/0004-6361/201937205
[16]
Vieu, T., Gabici, S., Tatischeff, V. and Ravikularaman, S. (2022) Cosmic Ray Production in Superbubbles. Monthly Notices of the Royal Astronomical Society: Letters, 512, 1275-12293. (Preprint) https://doi.org/10.1093/mnras/stac543
[17]
Murgia, S. (2020) The Fermi-LAT Galactic Center Excess: Evidence of Annihilating Dark Matter? Annual Review of Nuclear and Particle Science, 70, 455-483. https://doi.org/10.1146/annurev-nucl-101916-123029
[18]
Gould, H. and Tobochnik, J. (1988) An Introduction to Computer Simulation Methods. Addison-Wesley, Reading, MA.
[19]
Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P. (1992) Numerical Recipes in Fortran 77. The Art of Scientific Computing. Cambridge University Press, Cambridge.
[20]
Abdo, A.A., Allen, B., Aune, T., et al. (2008) A Measurement of the Spatial Distribution of Diffuse TeV Gamma-Ray Emission from the Galactic Plane with Milagro. The Astrophysical Journal, 688, 1078-1083. (Preprint)
[21]
Bartoli, B., Bernardini, P., Bi, X.J., et al. (2015) Study of the Diffuse Gamma-Ray Emission from the Galactic Plane with ARGO-YBJ. The Astrophysical Journal, 806, 20-31. (Preprint)
[22]
Planck Collaboration, P.A.R.A., Aghanim, N., Alves, M.I.R., et al. (2015) Planck Intermediate Results. XXIII. Galactic Plane Emission Components Derived from Planck with Ancillary Data. Astronomy & Astrophysics, 580, A13-A41. (Preprint)
[23]
Seiden, P.E. and Gerola, H. (1979) Properties of Spiral Galaxies from a Stochastic Star Formation Model. The Astrophysical Journal, 233, 56-66. https://doi.org/10.1086/157366
[24]
Seiden, P.E. (1983) The Role of the Gas in Propagating Star Formation. The Astrophysical Journal, 266, 555-561. https://doi.org/10.1086/157366
[25]
Schulman, L.S. and Seiden, P.E. (1986) Percolation and Galaxies Science, 233, 425-431. https://doi.org/10.1126/science.233.4762.425
[26]
Zaninetti, L. (1988) Percolation and Synchrotron Emission. I—The Case of Spiral Galaxies. Astronomy & Astrophysics, 190, 17-20.
[27]
Seiden, P.E. and Schulman, L.S. (1990) Percolation Model of Galactic Structure. Advances in Physics, 39, 1-54. https://doi.org/10.1080/00018739000101461
[28]
Zaninetti, L. (2017) The Milky Way as Modeled by Percolation and Superbubbles. (Preprint)
[29]
Jungwiert, B. and Palouš, J. (1994) Stochastic Self-Propagating Star Formation with Anisotropic Probability Distribution. Astronomy & Astrophysics, 287, 55-67.
[30]
Vallée, J.P. (2022) Superposing the Magnetic Spiral Structure of the Milky Way, on the Stellar Spiral Arms—Matching the Unique Galactic Magnetic Field Reversal Zone with Two Galactic Spiral Arm Segments. International Journal of Astronomy and Astrophysics, 12, 281-300. https://doi.org/10.4236/ijaa.2022.124017
[31]
Bisnovatyi-Kogan, G.S. and Silich, S.A. (1995) Shock-Wave Propagation in the Nonuniform Interstellar Medium. Reviews of Modern Physics, 67, 661-712. https://doi.org/10.1103/RevModPhys.67.661
[32]
Dickey, J.M. and Lockman, F.J. (1990) H I in the Galaxy. Annual Review of Astronomy and Astrophysics, 28, 215-259. https://doi.org/10.1146/annurev.aa.28.090190.001243
[33]
Lockman, F.J. (1984) The H I Halo in the Inner Galaxy. The Astrophysical Journal, 283, 90-97. https://doi.org/10.1086/162277
[34]
Rybicki, G. and Lightman, A. (1991) Radiative Processes in Astrophysics. Wiley-Interscience, New York.
[35]
Hjellming, R.M. (1988) Radio Stars. In: Verschuur, G.L. and Kellermann, K.I., Eds., Galactic and Extragalactic Radio Astronomy, Astronomy and Astrophysics Library, Springer-Verlag, Berlin, 381-438. https://doi.org/10.1007/978-1-4612-3936-9_9
[36]
Zaninetti, L. (2009) Scaling for the Intensity of Radiation in Spherical and Aspherical Planetary Nebulae. Monthly Notices of the Royal Astronomical Society: Letters, 395, 667-697. https://doi.org/10.1111/j.1365-2966.2009.14551.x
[37]
Zyla, P., et al. (Particle Data Group) (2020) Review of Particle Physics. PTEP: Progress of Theoretical and Experimental Physics, 2020, 083C01.
[38]
Roth, M.A., Krumholz, M.R., Crocker, R.M. and Celli, S. (2021) The Diffuse γ-Ray Background Is Dominated by Star-Forming Galaxies. Nature, 597, 341-344. (Preprint) https://doi.org/10.1038/s41586-021-03802-x
