We employ the theory of gravitational repulsion in the Schwarzschild field to show that neither Active Galactic Nuclei (AGN) nor main sequence stars are the sources of ultra high energy cosmic ray protons. Instead the theory leads to the conclusion that the sources of these particles are brown dwarfs except for protons with energies >1.887×10 20 eV, which are produced by planetary mass bodies. The theory predicts that brown dwarfs and main sequence stars are the sources of very high energy cosmic ray protons.
KeywordsCosmic Ray ProtonsGeneral RelativityGravitational RepulsionSchwarzschild Field
de la Fuente Marcos, R. and de la Fuente Marcos, C. (2015) On the Angular Distribution of IceCube High-Energy Events. Astronomische Nachrichten , 336, 657-664. https://doi.org/10.1002/asna.201512210
Abbasi, R., Ackermann, M., Adams, J., Agarwalla, S.K., Aguilar, J.A., Ahlers, M., et al . (2025) Constraints on the Correlation of IceCube Neutrinos with Tracers of Large-scale Structure. arXiv: 2510.18119.
Guevel, D., Fang, K., (2023) IceCube Collaboration: Cross Correlation of IceCube Neutrinos with Tracers of Large Scale Structure. arXiv: 2308.03978.
Fang, K., Banerjee, A., Charles, E. and Omori, Y. (2020) A Cross-Correlation Study of High-Energy Neutrinos and Tracers of Large-Scale Structure. The Astrophysical Journal , 894, Article 112. https://doi.org/10.3847/1538-4357/ab8561
The IceCube, Auger, P. and Telescope Array Collaborations (2016) Search for Correlations between the Arrival Directions of IceCube Neutrino Events and Ultrahigh-Energy Cosmic Rays Detected by the Pierre Auger Observatory and the Telescope Array. Journal of Cosmology and Astroparticle Physics , 2016, Article 37. https://doi.org/10.1088/1475-7516/2016/01/037
Bellenghi, C., Glauch, T., Haack, C., Kontrimas, T., Niederhausen, H., Reimann, R., Wolf, M. and IceCube Collaboration (2021) A New Search for Neutrino Point Sources with IceCube. arXiv: 2107.08700.
Globus, N. and Blandford, R.D. (2025) Ultrahigh-Energy Cosmic Rays. Annual Review of Astronomy and Astrophysics , 63, 339-377. https://doi.org/10.1146/annurev-astro-052622-033150
Globus, N. and Blandford, R. (2023) Ultra High Energy Cosmic Ray Source Models: Successes, Challenges and General Predictions. EPJ Web of Conferences , 283, Article ID: 04001. https://doi.org/10.1051/epjconf/202328304001
Bister, T. (2025) Probing the Sources of Ultra-High-Energy Cosmic Rays—Constraints from Cosmic-Ray Measurements. Universe , 11, Article 331. https://doi.org/10.3390/universe11100331
Alves Batista, R., Biteau, J., Bustamante, M., Dolag, K., Engel, R., Fang, K., et al . (2019) Open Questions in Cosmic-Ray Research at Ultrahigh Energies. Frontiers in Astronomy and Space Sciences , 6, Article 23. https://doi.org/10.3389/fspas.2019.00023
Letessier-Selvon, A. and Stanev, T. (2011) Ultrahigh Energy Cosmic Rays. Reviews of Modern Physics , 83, 907-942. https://doi.org/10.1103/revmodphys.83.907
Uryson, A.V. (2006) Ultra High Energy Cosmic Rays: Identification of Possible Sources, Energy Spectra, and Propagation. Physics of Particles and Nuclei , 37, 347-367. https://doi.org/10.1134/s106377960603004x
McGruder III, C.H. (2026) The Cosmic Origin of High Energy Neutrinos, Ultra High Energy Neutrinos and the Mass of the Muon Neutrino. Journal of Modern Physics , 17, 179-198. https://doi.org/10.4236/jmp.2026.172013
McGruder, C.H. (2017) Acceleration of Particles to High Energy via Gravitational Repulsion in the Schwarzschild Field. Astroparticle Physics , 86, 18-20. https://doi.org/10.1016/j.astropartphys.2016.10.003
Rieger, F.M. (2022) Active Galactic Nuclei as Potential Sources of Ultra-High Energy Cosmic Rays. Universe , 8, Article 607. https://doi.org/10.3390/universe8110607
Kotera, K. and Olinto, A.V. (2011) The Astrophysics of Ultrahigh-Energy Cosmic Rays. Annual Review of Astronomy and Astrophysics , 49, 119-153. https://doi.org/10.1146/annurev-astro-081710-102620
Hillas, A.M. (1984) The Origin of Ultra-High-Energy Cosmic Rays. Annual Review of Astronomy and Astrophysics , 22, 425-444. https://doi.org/10.1146/annurev.aa.22.090184.002233
Watson, L.J., Mortlock, D.J. and Jaffe, A.H. (2011) A Bayesian Analysis of the 27 Highest Energy Cosmic Rays Detected by the Pierre Auger Observatory: The Highest Energy Cosmic Rays. Monthly Notices of the Royal Astronomical Society , 418, 206-213. https://doi.org/10.1111/j.1365-2966.2011.19476.x
Terrano, W.A., Zaw, I. and Farrar, G.R. (2012) CHANDRA Observations and Classification of Active Galactic Nucleus Candidates Correlated with Auger Uhecrs. The Astrophysical Journal , 754, Article 142. https://doi.org/10.1088/0004-637x/754/2/142
Gureev, S. and Troitsky, S. (2010) Physical Conditions in Nearby Active Galaxies Correlated with Ultra-High-Energy Cosmic Rays Detected by the Pierre Auger Observatory. International Journal of Modern Physics A , 25, 2917-2932. https://doi.org/10.1142/s0217751x10048512
Aloisio, R. and Boncioli, D. (2011) Ultra High Energy Cosmic Rays: Anisotropies and Spectrum. Astroparticle Physics , 35, 152-160. https://doi.org/10.1016/j.astropartphys.2011.05.006
Aab, A., Abreu, P., Aglietta, M., Albuquerque, I.F.M., Allekotte, I., Almela, A., et al . (2018) An Indication of Anisotropy in Arrival Directions of Ultra-High-Energy Cosmic Rays through Comparison to the Flux Pattern of Extragalactic Gamma-Ray Sources. The Astrophysical Journal Letters , 853, L29. https://doi.org/10.3847/2041-8213/aaa66d
Abbasi, R.U., Abe, M., Abu-Zayyad, T., Allen, M., Azuma, R., Barcikowski, E., et al . (2018) Testing a Reported Correlation between Arrival Directions of Ultra-High-Energy Cosmic Rays and a Flux Pattern from nearby Starburst Galaxies Using Telescope Array Data. The Astrophysical Journal Letters , 867, L27.
Anchordoqui, L.A. (2018) Acceleration of Ultrahigh-Energy Cosmic Rays in Starburst Superwinds. Physical Review D , 97, Article ID: 063010. https://doi.org/10.1103/physrevd.97.063010
Abdul Halim, A., Abreu, P., Aglietta, M., Allekotte, I., Almeida Cheminant, K., Al-mela, A., et al . (2024) Constraining Models for the Origin of Ultra-High-Energy Cos-Mic Rays with a Novel Combined Analysis of Arrival Directions, Spectrum, and Composition Data Measured at the Pierre Auger Observatory. Journal of Cosmology and Astroparticle Physics , 2024, Article 22.
Doghmane, R. and Attallah, R. (2022) Probing Cosmic-Ray Anisotropy at Ultra-High Energy. Journal of Astrophysics and Astronomy , 43, Article No. 89. https://doi.org/10.1007/s12036-022-09887-8
Vietri, M., De Marco, D. and Guetta, D. (2003) On the Generation of Ultra-High-Energy Cosmic Rays in γ -Ray Bursts: A Reappraisal. The Astrophysical Journal , 592, 378-389. https://doi.org/10.1086/375719
Dermer, C.D., McEnery, J.E., Racusin, J.L. and Gehrels, N. (2011) Are γ -Ray Bursts the Sources of the Ultra-High Energy Cosmic Rays? AIP Conference Proceedings , 1358, 355-360. https://doi.org/10.1063/1.3621804
Baerwald, P., Bustamante, M. and Winter, W. (2015) Are γ -Ray Bursts the Sources of Ultra-High Energy Cosmic Rays? Astroparticle Physics , 62, 66-91. https://doi.org/10.1016/j.astropartphys.2014.07.007
Zhang, B.T., Murase, K., Kimura, S.S., Horiuchi, S. and Mészáros, P. (2018) Low-luminosity γ -Ray Bursts as the Sources of Ultrahigh-Energy Cosmic Ray Nuclei. Physical Review D , 97, Article ID: 083010. https://doi.org/10.1103/physrevd.97.083010
Wang, X., Razzaque, S. and Mészáros, P. (2008) On the Origin and Survival of Ultra‐High-Energy Cosmic-Ray Nuclei in γ -Ray Bursts and Hypernovae. The Astrophysical Journal , 677, 432-440. https://doi.org/10.1086/529018
He, H., Zhang, B.T. and Fan, Y. (2024) A Detectable Ultra-High-Energy Cosmic-Ray Outburst from GRB 221009A. The Astrophysical Journal , 963, Article 109. https://doi.org/10.3847/1538-4357/ad2352
Ryu, D., Kang, H., Hallman, E. and Jones, T.W. (2003) Cosmological Shock Waves and Their Role in the Large-Scale Structure of the Universe. The Astrophysical Journal , 593, 599-610. https://doi.org/10.1086/376723
Norman, C.A., Melrose, D.B. and Achterberg, A. (1995) The Origin of Cosmic Rays above 10 18.5 eV. The Astrophysical Journal , 454, 60. https://doi.org/10.1086/176465
Kang, H. and Ryu, D. (2013) Diffusive Shock Acceleration at Cosmological Shock Waves. The Astrophysical Journal , 764, Article 95. https://doi.org/10.1088/0004-637x/764/1/95
Gabici, S. (2003) γ -Ray Emission from Clusters of Galaxies. arXiv: astro-ph/0307499.
Vazza, F., Brunetti, G. and Gheller, C. (2009) Shock Waves in Eulerian Cosmological Simulations: Main Properties and Acceleration of Cosmic Rays. Monthly Notices of the Royal Astronomical Society , 395, 1333-1354. https://doi.org/10.1111/j.1365-2966.2009.14691.x
Blasi, P. (2013) The Origin of Galactic Cosmic Rays. The Astronomy and Astrophysics Review , 21, Article No. 70. https://doi.org/10.1007/s00159-013-0070-7
Blasi, P., Epstein, R.I. and Olinto, A.V. (2000) Ultra-High-Energy Cosmic Rays from Young Neutron Star Winds. The Astrophysical Journal , 533, L123-L126. https://doi.org/10.1086/312626
Arons, J. (2003) Magnetars in the Metagalaxy: An Origin for Ultra-High-Energy Cosmic Rays in the Nearby Universe. The Astrophysical Journal , 589, 871-892. https://doi.org/10.1086/374776
Kotera, K. and Amato, E. (2015) Engines of Radio Transients: Neutron Star Birth and Cosmic Rays. Annual Review of Nuclear and Particle Science , 65, 449-472.
Fang, K., Kotera, K. and Olinto, A.V. (2014) Newly Born Pulsars as Sources of Ultrahigh Energy Cosmic Rays. arXiv: 1201.5197.
Fang, K. and Olinto, A.V. (2016) High-Energy Neutrinos from Sources in Clusters of Galaxies. The Astrophysical Journal , 828, 37. https://doi.org/10.3847/0004-637X/828/1/37
Murase, K., Kashiyama, K. and Mészáros, P. (2014) A New Class of High-Energy Transients from Crustal Failure of Neutron Stars during Binary Mergers. Monthly Notices of the Royal Astronomical Society , 442, 60-64.
Farrar, G.R. (2025) Binary Neutron Star Mergers as the Source of the Highest Energy Cosmic Rays. Physical Review Letters , 134, Article ID: 081003. https://doi.org/10.1103/physrevlett.134.081003
Rodrigues, X., Biehl, D., Boncioli, D. and Taylor, A.M. (2019) Binary Neutron Star Merger Remnants as Sources of Cosmic Rays Below the “Ankle”. Astroparticle Physics , 106, 10-17. https://doi.org/10.1016/j.astropartphys.2018.10.007
Guo, G., Qian, Y. and Wu, M. (2025) Binary Neutron Star Mergers as Potential Sources for Ultrahigh-Energy Cosmic Rays and High-Energy Neutrinos. Physical Review D , 112, Article ID: 063022. https://doi.org/10.1103/zfp3-y9yw
Zhang, B.T., Murase, K., Oikonomou, F. and Li, Z. (2017) High-Energy Cosmic Ray Nuclei from Tidal Disruption Events: Origin, Survival, and Implications. Physical Review D , 96, Article ID: 063007. https://doi.org/10.1103/physrevd.96.063007
Biehl, D., Boncioli, D., Lunardini, C. and Winter, W. (2018) Tidally Disrupted Stars as a Possible Origin of Both Cosmic Rays and Neutrinos at the Highest Energies. Scientific Reports , 8, Article No. 10828. https://doi.org/10.1038/s41598-018-29022-4
Pfeffer, D.N., Kovetz, E.D. and Kamionkowski, M. (2016) Ultrahigh-Energy Cosmic Ray Hotspots from Tidal Disruption Events. Monthly Notices of the Royal Astronomical Society , 466, 2922-2926. https://doi.org/10.1093/mnras/stw3337
Guépin, C., Kotera, K., Barausse, E., Fang, K. and Murase, K. (2018) Ultra-High-Energy Cosmic Rays and Neutrinos from Tidal Disruptions by Massive Black Holes. Astronomy & Astrophysics , 616, A179. https://doi.org/10.1051/0004-6361/201732392
Reames, D.V. (1999) Particle Acceleration at the Sun and in the Heliosphere. Space Science Reviews , 90, 413-491. https://doi.org/10.1023/a:1005105831781
Giacalone, J. and Kóta, J. (2006) Acceleration of Solar-Energetic Particles by Shocks. Space Science Reviews , 124, 277-288. https://doi.org/10.1007/s11214-006-9110-1
Lee, M.A., Mewaldt, R.A. and Giacalone, J. (2012) Shock Acceleration of Ions in the Heliosphere. Space Science Reviews , 173, 247-281. https://doi.org/10.1007/s11214-012-9932-y
Desai, M. and Giacalone, J. (2016) Large Gradual Solar Energetic Particle Events. Living Reviews in Solar Physics , 13, Article No. 3. https://doi.org/10.1007/s41116-016-0002-5
Li, G., Zank, G.P. and Rice, W.K.M. (2003) Energetic Particle Acceleration and Transport at Coronal Mass Ejection-Driven Shocks. Journal of Geophysical Research : Space Physics , 108, Article 1082. https://doi.org/10.1029/2002ja009666
Afanasiev, A., Vainio, R., Rouillard, A.P., Battarbee, M., Aran, A. and Zucca, P. (2018) Modelling of Proton Acceleration in Application to a Ground Level Enhancement. Astronomy & Astrophysics , 614, A4. https://doi.org/10.1051/0004-6361/201731343
Gopalswamy, N., Xie, H., Yashiro, S., Akiyama, S., Mäkelä, P. and Usoskin, I.G. (2010) Ground Level Enhancement Events of Solar Cycle 23. International Journal of Remote Sensing and Space Physics , 39, 240-248.
Krymskii, G.F. (1977) A Regular Mechanism for the Acceleration of Charged Particles on the Front of a Shock Wave. Akademiia Nauk SSSR Doklady , 234, 1306-1308.
Bell, A.R. (1978) The Acceleration of Cosmic Rays in Shock Fronts—I. Monthly Notices of the Royal Astronomical Society , 182, 147-156. https://doi.org/10.1093/mnras/182.2.147
Bell, A.R. (1978) The Acceleration of Cosmic Rays in Shock Fronts—II. Monthly Notices of the Royal Astronomical Society , 182, 443-455. https://doi.org/10.1093/mnras/182.3.443
Drury, L.O. (1983) An Introduction to the Theory of Diffusive Shock Acceleration of Energetic Particles in Tenuous Plasmas. Reports on Progress in Physics , 46, 973-1027. https://doi.org/10.1088/0034-4885/46/8/002
Blandford, R. and Eichler, D. (1987) Particle Acceleration at Astrophysical Shocks: A Theory of Cosmic Ray Origin. Physics Reports , 154, 1-75. https://doi.org/10.1016/0370-1573(87)90134-7
Baring, M.G. (2004) Diffusive Shock Acceleration of High Energy Cosmic Rays. Nuclear Physics B — Proceedings Supplements , 136, 198-207. https://doi.org/10.1016/j.nuclphysbps.2004.10.008
Peretti, E., Lamastra, A., Saturni, F.G., Ahlers, M., Blasi, P., Morlino, G., et al . (2023) Diffusive Shock Acceleration at EeV and Associated Multimessenger Flux from Ultra-Fast Outflows Driven by Active Galactic Nuclei. Monthly Notices of the Royal Astronomical Society , 526, 181-192. https://doi.org/10.1093/mnras/stad2740
Longair, M.S. (2011) Cosmic Ray Astrophysics. Cambridge University Press.
Berezinsky, V.S., Bulanov, S.V., Dogiel, V.A. and Ginzburg, V.L. (1990) Astrophysics of Cosmic Rays. North-Holland Publisher.
Droste, J. (1915) On the Field of a Single Centre in Einstein’s Theory of Gravitation. Koninklijke Nederlandse Akademie van Wetenschappen Proceedings Series B Physical Sciences , 17, 998-1011.
Droste, J. (1916) Het zwaartekrachtsveld van een of meer lichamen volgens de theorie van Einstein. Ph.D. Thesis, Leiden University.
Hilbert, D. (1915) Die Grundlagen der Physik. (Erste Mitteilung). Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen , Mathematisch-Physikalische Klasse , 395-407.
Hilbert, D. (1916) Die Feldgleichungen der Gravitation. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen , Mathematisch-Physikalische Klasse , 48, 844-847.
Hilbert, D. (1917) Die Grundlagen der Physik (Zweite Mitteilung). Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen , Mathematisch-Physikalische Klasse , 53-76.
McGruder III, C.H. and Van Der Meer, B.W. (2018) The 1916 PhD Thesis of Johannes Droste and the Discovery of Gravitational Repulsion. arXiv: 1801.07592.
McGruder, C.H. (1982) Gravitational Repulsion in the Schwarzschild Field. Physical Review D , 25, 3191-3194. https://doi.org/10.1103/physrevd.25.3191
Aiello, S., Albert, A., Alhebsi, A.R., Alshamsi, M., Alves Garre, S., Ambrosone, A., et al . (2025) Observation of an Ultra-High-Energy Cosmic Neutrino with KM3NeT. Nature , 638, 376-382. https://doi.org/10.1038/s41586-024-08543-1
Krori, K.D., Sarmah, J.C. and Goswami, D. (1984) Gravitational Repulsion in the Einstein-Zero-Mass Scalar Theory. Canadian Journal of Physics , 62, 629-631. https://doi.org/10.1139/p84-085
P L Bragança, D. (2024) Gravitational Repulsion in an Expanding Ball of Dust. Classical and Quantum Gravity , 41, Article ID: 075008. https://doi.org/10.1088/1361-6382/ad2d70
Polo, C.L. and Singh, H.S. (2024) Hilbert Repulsion in the Kerr-Newman Anti-De Sitter Spacetime. Astrophysics and Space Science , 369, Article No. 41. https://doi.org/10.1007/s10509-024-04304-8
Célérier, M.N., Santos, N.O. and Satheeshkumar, V.H. (2017) Hilbert Repulsion in the Reissner-Nordström and Schwarzschild spacetimes. arXiv: 1707.06994.
Gorkavyi, N. and Vasilkov, A. (2016) A Repulsive Force in the Einstein Theory. Monthly Notices of the Royal Astronomical Society , 461, 2929-2933. https://doi.org/10.1093/mnras/stw1517
Kutschera, M. and Zajiczek, W. (2009) Shapiro Effect for for Relativistic Particles-Testing General Relativity in a New Window. arXiv: 0906.5088.
Herrera, L. (2005) Geodesics in a Quash-Spherical Spacetime: A Case of Gravitational Repulsion. Foundations of Physics Letters , 18, 21-36. https://doi.org/10.1007/s10702-005-2467-7
Ponce de Leon, J. (1988) Gravitational Repulsion in Sources of the Reissner-Nordström Field. Journal of Mathematical Physics , 29, 197-206. https://doi.org/10.1063/1.528172
Krori, K.D. and Barua, M. (1985) Gravitational Repulsion by Kerr and Kerr-Newman Black Holes. Physical Review D , 31, 3135-3139. https://doi.org/10.1103/physrevd.31.3135
Greene, J.E. and Ho, L.C. (2007) The Mass Function of Active Black Holes in the Local Universe. The Astrophysical Journal , 667, 131-148.
Blandford, R.D. and McKee, C.F. (1982) Reverberation Mapping of the Emission Line Regions of Seyfert Galaxies and Quasars. The Astrophysical Journal , 255, 419-439. https://doi.org/10.1086/159843
Peterson, B.M., Ferrarese, L., Gilbert, K.M., Kaspi, S., Malkan, M.A., Maoz, D., et al . (2004) Central Masses and Broad‐line Region Sizes of Active Galactic Nuclei. II. A Homogeneous Analysis of a Large Reverberation‐mapping Database. The Astrophysical Journal , 613, 682-699. https://doi.org/10.1086/423269
Bentz, M.C. and Katz, S. (2015) The AGN Black Hole Mass Database. Publications of the Astronomical Society of the Pacific , 127, 67-73. https://doi.org/10.1086/679601
Vestergaard, M. and Peterson, B.M. (2006) Determining Central Black Hole Masses in Distant Active Galaxies and Quasars. II. Improved Optical and UV Scaling Relationships. The Astrophysical Journal , 641, 689-709. https://doi.org/10.1086/500572
Shen, Y., Richards, G.T., Strauss, M.A., Hall, P.B., Schneider, D.P., Snedden, S., et al . (2011) A Catalog of Quasar Properties from Sloan Digital Sky Survey Data Release 7. The Astrophysical Journal Supplement Series , 194, Article 45. https://doi.org/10.1088/0067-0049/194/2/45
Shen, Y., Strauss, M.A., Oguri, M., Hennawi, J.F., Fan, X., Richards, G.T., et al . (2007) Clustering of High-Redshift ( z ≥ 2.9) Quasars from the Sloan Digital Sky Survey. The Astronomical Journal , 133, 2222-2241. https://doi.org/10.1086/513517
McConnell, N.J., Ma, C., Gebhardt, K., Wright, S.A., Murphy, J.D., Lauer, T.R., et al . (2011) Two Ten-Billion-Solar-Mass Black Holes at the Centres of Giant Elliptical Galaxies. Nature , 480, 215-218. https://doi.org/10.1038/nature10636
van den Bosch, R.C.E., Gebhardt, K., Gültekin, K., van de Ven, G., van der Wel, A. and Walsh, J.L. (2012) An Over-Massive Black Hole in the Compact Lenticular Galaxy NGC 1277. Nature , 491, 729-731. https://doi.org/10.1038/nature11592
McConnell, N.J. and Ma, C. (2013) Revisiting the Scaling Relations of Black Hole Masses and Host Galaxy Properties. The Astrophysical Journal , 764, Article 184. https://doi.org/10.1088/0004-637x/764/2/184
Kormendy, J. and Ho, L.C. (2013) Coevolution (or Not) of Supermassive Black Holes and Host Galaxies. Annual Review of Astronomy and Astrophysics , 51, 511-653. https://doi.org/10.1146/annurev-astro-082708-101811
Kachelriess, M. and Serpico, P.D. (2007) The GZK Horizon of Ultra-High Energy Cosmic Rays. arXiv: 0711.3635.
Berezinsky, V., Gazizov, A. and Grigorieva, S. (2006) On Astrophysical Solution to Ultrahigh Energy Cosmic Rays. Physical Review D , 74, Article ID: 043005. https://doi.org/10.1103/physrevd.74.043005
Greisen, K. (1966) End to the Cosmic-Ray Spectrum? Physical Review Letters , 16, 748-750. https://doi.org/10.1103/physrevlett.16.748
Zatsepin, G.T. AND Kuzmin, V.A. (1966) Upper Limit of the Spectrum of Cosmic Rays. JETP Letters , 4, 78-80.
Abbasi, R.U., Abu-Zayyad, T., Allen, M., et al . (2008) First Observation of the Greisen-Zatsepin-Kuzmin Suppression. Physical Review Letters , 100, Article ID: 101101.
Abraham, J., Abreu, P., Aglietta, M., et al . (2008) Observation of the Suppression of the Flux of Cosmic Rays above 4 1019 ev. Physical Review Letters , 101, Article ID: 061101.
Watson, A.A. (2014) High-Energy Cosmic Rays and the Greisen-Zatsepin-Kuz’min Effect. Reports on Progress in Physics , 77, Article ID: 036901. https://doi.org/10.1088/0034-4885/77/3/036901
Kowalski, A.F. (2024) Stellar Flares. Living Reviews in Solar Physics , 21, Article No. 1. https://doi.org/10.1007/s41116-024-00039-4
Segura, A., Walkowicz, L.M., Meadows, V., Kasting, J. and Hawley, S. (2010) The Effect of a Strong Stellar Flare on the Atmospheric Chemistry of an Earth-Like Planet Orbiting an M Dwarf. Astrobiology , 10, 751-771. https://doi.org/10.1089/ast.2009.0376
Althukair, A. and Tsiklauri, D. (2022) Statistical Properties of Stellar Superflares from f-to m-Type Stars Observed by Kepler. Astrophysical Journal , 926, Article 196.
Bai, T. (1989) Particle Acceleration in Solar Flares. Annual Review of Astronomy and Astrophysics , 27, 421-474.
Burrows, A., Marley, M., Hubbard, W.B., Lunine, J.I., Guillot, T., Saumon, D., et al . (1997) A Nongray Theory of Extrasolar Giant Planets and Brown Dwarfs. The Astrophysical Journal , 491, 856-875. https://doi.org/10.1086/305002
Chabrier, G. and Baraffe, I. (1997) Structure and Evolution of Low-Mass Stars. Astronomy & Astrophysics , 327, 1039-1053.
Baraffe, I., Chabrier, G., Allard, F. and Hauschildt, P.H. (1998) Evolutionary Models for Solar Metallicity Low-Mass Stars: Mass-Magnitude Relationships and Color-Magnitude Diagrams. Astronomy & Astrophysics , 337, 403-412.
Kippenhahn, R., Weigert, A. and Weiss, A. (2012) Stellar Structure and Evolution. 2nd Edition, Springer.
Burrows, A., Hubbard, W.B., Lunine, J.I. and Liebert, J. (2001) The Theory of Brown Dwarfs and Extrasolar Giant Planets. Reviews of Modern Physics , 73, 719-765. https://doi.org/10.1103/revmodphys.73.719
Chabrier, G., Phillips, M.W., Baraffe, I., Borysow, A. and Jørgensen, U.G. (2023) New Determination of the Hydrogen Burning Limit. Astronomy & Astrophysics , 671, Article No. A119.
Spiegel, D.S., Burrows, A. and Milsom, J.A. (2011) The Deuterium-Burning Mass Limit for Brown Dwarfs and Giant Planets. The Astrophysical Journal , 727, Article 57. https://doi.org/10.1088/0004-637x/727/1/57
Zuckerman, B. (2000) Brown Dwarfs: At Last Filling the Gap between Stars and Planets. Proceedings of the National Academy of Sciences of the United States of America , 97, 963-966. https://doi.org/10.1073/pnas.97.3.963
Liu, B., Lambrechts, M., Johansen, A., Pascucci, I. and Henning, T. (2020) Pebble-driven Planet Formation around Very Low-Mass Stars and Brown Dwarfs. Astronomy & Astrophysics , 638, A88. https://doi.org/10.1051/0004-6361/202037720
Basri, G. and Brown, M.E. (2006) Planetesimals to Brown Dwarfs: What Is a Planet? Annual Review of Earth and Planetary Sciences , 34, 193-216. https://doi.org/10.1146/annurev.earth.34.031405.125058
Berger, E., Ball, S., Becker, K.M., Clarke, M., Frail, D.A., Fukuda, T.A., et al . (2001) Discovery of Radio Emission from the Brown Dwarf LP944-20. Nature , 410, 338-340. https://doi.org/10.1038/35066514
Rodríguez-Barrera, M.I., Helling, C. and Wood, K. (2018) Environmental Effects on the Ionisation of Brown Dwarf Atmospheres. Astronomy & Astrophysics , 618, A107. https://doi.org/10.1051/0004-6361/201832685
Saur, J., Willmes, C., Fischer, C., et al . (2021) Brown Dwarfs as Candidates for Detecting UV Aurora Outside the Solar System: Hubble Space Telescope Observations of 2MASS J1237+6526. Astronomy & Astrophysics, 655, Article ID: A75.
Hallinan, G., Littlefair, S.P., Cotter, G., Bourke, S., Harding, L.K., Pineda, J.S., et al . (2015) Magnetospherically Driven Optical and Radio Aurorae at the End of the Stellar Main Sequence. Nature , 523, 568-571. https://doi.org/10.1038/nature14619
Gizis, J.E., et al . (2017) The White Light Flare Rate of Young Brown Dwarfs. arXiv: 1703.08745.
Reiners, A. and Basri, G. (2007) The First Direct Measurements of Surface Magnetic Fields on Very Low Mass Stars. The Astrophysical Journal , 656, 1121-1135. https://doi.org/10.1086/510304
Reiners, A. and Basri, G. (2009) On the Magnetic Topology of Partially and Fully Convective Stars. Astronomy & Astrophysics , 496, 787-790. https://doi.org/10.1051/0004-6361:200811450
Johns-Krull, C.M. and Valenti, J.A. (1996) Detection of Strong Magnetic Fields on M Dwarfs. The Astrophysical Journal , 459, L95. https://doi.org/10.1086/309954
Saar, S.H. (1996) Recent Measurements of Stellar Magnetic Fields. Symposium — International Astronomical Union , 176, 237-244. https://doi.org/10.1017/s0074180900083261
Donati, J., Morin, J., Petit, P., Delfosse, X., Forveille, T., Aurière, M., et al . (2008) Large-Scale Magnetic Topologies of Early M Dwarfs. Monthly Notices of the Royal Astronomical Society , 390, 545-560. https://doi.org/10.1111/j.1365-2966.2008.13799.x
Shulyak, D., Reiners, A., Engeln, A., et al . (2017) Strong Dipole Magnetic Fields in Fast Rotating Fully Convective Stars. Nature Astronomy , 1, Article 184.
Reiners, A. and Christensen, U.R. (2010) A Magnetic Field Evolution Scenario for Brown Dwarfs and Giant Planets. Astronomy & Astrophysics , 522, A13. https://doi.org/10.1051/0004-6361/201014251
Berdyugina, S.V., Harrington, D.M., Kuzmychov, O., Kuhn, J.R., Hallinan, G., Kowalski, A.F., et al . (2017) First Detection of a Strong Magnetic Field on a Bursty Brown Dwarf: Puzzle Solved. The Astrophysical Journal , 847, Article 61. https://doi.org/10.3847/1538-4357/aa866b
Bailer-Jones, C.A.L. and Mundt, R. (2001) Variability in Ultra Cool Dwarfs: Evidence for the Evolution of Surface Features. Astr onomy & Astrophysics , 367, 218-235. https://doi.org/10.1051/0004-6361:20000416
Mohanty, S. and Basri, G. (2003) Rotation & Activity in Mid-M to L Dwarfs. The Astrophysical Journal , 583, 451-472.
Reiners, A. and Basri, G. (2008) Chromospheric Activity, Rotation, and Rotational Braking in M and L Dwarfs. The Astrophysical Journal , 684, 1390-1403. https://doi.org/10.1086/590073
Metchev, S.A., Heinze, A., Apai, D., Flateau, D., Radigan, J., Burgasser, A., et al . (2015) Weather on Other Worlds. II. Survey Results: Spots Are Ubiquitous on L and T Dwarfs. The Astrophysical Journal , 799, Article 154. https://doi.org/10.1088/0004-637x/799/2/154
Zapatero Osorio, M.R., Martin, E.L., Bouy, H., Tata, R., Deshpande, R. and Wainscoat, R.J. (2006) Spectroscopic Rotational Velocities of Brown Dwarfs. The Astrophysical Journal , 647, 1405-1412. https://doi.org/10.1086/505484
Waxman, E. (1995) Cosmological Gamma-Ray Bursts and the Highest Energy Cosmic Rays. Physical Review Letters , 75, 386-389. https://doi.org/10.1103/physrevlett.75.386
Ahlers, M. and Anchordoqui, L.A. (2012) High-Energy Cosmic Rays from Astrophysical Sources: An Overview. Physical Review D , 85, Article ID: 063010.
Kirkpatrick, J.D., Marocco, F., Gelino, C.R., Raghu, Y., Faherty, J.K., Bardalez Gagliuffi, D.C., et al . (2024) The Backyard Worlds: Planet 9 Collaboration: The Initial Mass Function Based on the Full-Sky 20 pc Census of 3600 Stars and Brown Dwarfs. arXiv: 2312.03639.
Karachentsev, I.D. and Telikova, K.N. (2018) Stellar and Dark Matter Density in the Local Universe. Astronomische Nachrichten , 339, 615-622. https://doi.org/10.1002/asna.201813520
Luhman, K.L. (2012) The Formation and Early Evolution of Low-Mass Stars and Brown Dwarfs. Annual Review of Astronomy and Astrophysics , 50, 65-106. https://doi.org/10.1146/annurev-astro-081811-125528
Sorahana, S., Yamamura, I. and Murakami, H. (2013) On the Radii of Brown Dwarfs Measured with Akari Near-Infrared Spectroscopy. The Astrophysical Journal , 767, Article 77. https://doi.org/10.1088/0004-637x/767/1/77
Carmichael, T.W. (2022) Improved Radius Determinations for the Transiting Brown Dwarf Population in the Era of GAIA and TESS . Monthly Notices of the Royal Astronomical Society , 519, 5177-5190. https://doi.org/10.1093/mnras/stac3720
Chabrier, G. and Baraffe, I. (2000) Theory of Low-Mass Stars and Substellar Objects. Annual Review of Astronomy and Astrophysics , 38, 337-377. https://doi.org/10.1146/annurev.astro.38.1.337
Baraffe, I., Chabrier, G., Allard, F. and Hauschildt, P. (2003) Evolutionary Models for Low Mass Stars and Brown Dwarfs at Young Ages. Symposium — International Astronomical Union , 211, 41-50. https://doi.org/10.1017/s0074180900210243
Zapolsky, H.S. and Salpeter, E.E. (1969) The Mass-Radius Relation for Cold Spheres of Low Mass. The Astrophysical Journal , 158, 809. https://doi.org/10.1086/150240
Blasi, P. and De Marco, D. (2004) The Small Scale Anisotropies, the Spectrum and the Sources of Ultra-High Energy Cosmic Rays. Astroparticle Physics , 20, 559-577. https://doi.org/10.1016/j.astropartphys.2003.07.002
Takami, H., Nishimichi, T., Yahata, K. and Sato, K. (2009) Cross-Correlation between UHECR Arrival Distribution and Large-Scale Structure. Journal of Cosmology and Astroparticle Physics , 2009, Article 31. https://doi.org/10.1088/1475-7516/2009/06/031
Pierre Auger Collaboration, Abreu, P., Aglietta, M., Ahlers, M., Ahn, E.J., Albuquerque, I.F.M., Allard, D., et al . (2013) Constraints on the Origin of Cosmic Rays above 10 18 eV from Large-Scale Anisotropy Searches in Data of the Pierre Auger Observatory. The Astrophysical Journal Letters , 762, L13.
Aab, A., Abreu, P., Aglietta, M., et al . (2017) Observation of a Large-Scale Anisotropy in the Arrival Directions of Cosmic Rays above 8 Times 10 18 eV. Science , 357, 1266-1270.
Aab, A., et al . (2020) Large-Scale Cosmic-Ray Anisotropies above 4 EeV Measured by the Pierre Auger Observatory. arXiv: 1808.03579.
Abbasi, R.U., Abe, M., Abu-Zayyad, T., Allen, M., Anderson, R., Azuma, R., et al . (2014) Indications of Intermediate-Scale Anisotropy of Cosmic Rays with Energy Greater Than 57 EeV in the Northern Sky Measured with the Surface Detector of the Telescope Array Experiment. arXiv: 1404.5890.
Collaboration, P.A. and Collaboration, T.A. (2014) Full-Sky Search for Large-Scale Anisotropies in the Arrival Directions of Cosmic Rays Detected Above 1019 eV. The Astrophysical Journal , 794, 172.
Allard, D. (2012) Extragalactic Propagation of Ultrahigh Energy Cosmic-Rays. Astroparticle Physics , 39, 33-43. https://doi.org/10.1016/j.astropartphys.2011.10.011
Aloisio, R., Berezinsky, V. and Blasi, P. (2017) Ultra-High Energy Cosmic Rays: Implications of Auger Data for Source Spectra and Chemical Composition. Journal of Cosmology and Astroparticle Physics , 2017, Article 20.
Bird, D.J., Corbato, S.C., Dai, H.Y., Elbert, J.W., Green, K.D., Huang, M.A., et al . (1995) Detection of a Cosmic Ray with Measured Energy Well Beyond the Expected Spectral Cutoff Due to Cosmic Microwave Radiation. The Astrophysical Journal , 441, 144. https://doi.org/10.1086/175344
Bagheri, F., Lopez, R.E. and Shahmoradi, A. (2024) Infrared-Radio-Follow-Up Observations for Detection of the Magnetic Radio Emission of Extra Solar Planets: A New Window to Detect Exoplanets. Frontiers in Astronomy and Space Sciences , 11, Article 1400032. https://doi.org/10.3389/fspas.2024.1400032
Ohsawa, Y. (2014) Ultrarelativistic Particle Acceleration in Collisionless Shock Waves. Physics Reports , 536, 147-254. https://doi.org/10.1016/j.physrep.2013.11.004
Aab, A., Abreu, P., Aglietta, M., Albury, J.M., Allekotte, I., Almela, A., et al . (2020) Features of the Energy Spectrum of Cosmic Rays above 2.5 ×10 18 eV Using the Pierre Auger Observatory. Physical Review Letters , 125, Article ID: 121106.
Abraham, J., Abreu, P., Aglietta, M., Aguirre, C., Allard, D., Allekotte, I., et al . (2007) Correlation of the Highest-Energy Cosmic Rays with Nearby Extragalactic Objects. Science , 318, 938-943. https://doi.org/10.1126/science.1151124
Parizot, E. (2004) GZK Horizon and Magnetic Fields. Nuclear Physics B — Proceedings Supplements , 136, 169-178. https://doi.org/10.1016/j.nuclphysbps.2004.10.034
Mollerach, S. and Roulet, E. (2022) Anisotropies of Ultrahigh-Energy Cosmic Rays in a Scenario with Nearby Sources. Physical Review D , 105, Article ID: 063001. https://doi.org/10.1103/physrevd.105.063001
Deason, A.J., Belokurov, V., Koposov, S.E. and Rockosi, C.M. (2014) Touching the Void: A Striking Drop in Stellar Halo Density Beyond 50 kpc. The Astrophysical Journal , 787, Article 30. https://doi.org/10.1088/0004-637x/787/1/30
Hernitschek, N., Cohen, J.G., Rix, H., Sesar, B., Martin, N.F., Magnier, E., et al . (2018) The Profile of the Galactic Halo from Pan-STARRS1 3 π RR Lyrae. The Astrophysical Journal , 859, Article 31. https://doi.org/10.3847/1538-4357/aabfbb
Helmi, A. (2008) The Stellar Halo of the Galaxy. The Astronomy and Astrophysics Review , 15, 145-188. https://doi.org/10.1007/s00159-008-0009-6
Xue, X., Rix, H., Ma, Z., Morrison, H., Bovy, J., Sesar, B., et al . (2015) The Radial Profile and Flattening of the Milky Way’s Stellar Halo to 80 kpc from the Segue K-Giant Survey. The Astrophysical Journal , 809, Article 144. https://doi.org/10.1088/0004-637x/809/2/144
Slater, C.T., Nidever, D.L., Munn, J.A., Bell, E.F. and Majewski, S.R. (2016) The Stellar Density Profile of the Distant Galactic Halo. The A strophysical Journal , 832, Article 206. https://doi.org/10.3847/0004-637x/832/2/206