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 >1.887×1020 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.
References
[1]
de la Fuente Marcos, R. and de la Fuente Marcos, C. (2015) On the Angular Distribution of IceCube High-Energy Events. AstronomischeNachrichten, 336, 657-664. https://doi.org/10.1002/asna.201512210
[2]
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.
[3]
Guevel, D., Fang, K., (2023) IceCube Collaboration: Cross Correlation of IceCube Neutrinos with Tracers of Large Scale Structure. arXiv: 2308.03978.
[4]
Fang, K., Banerjee, A., Charles, E. and Omori, Y. (2020) A Cross-Correlation Study of High-Energy Neutrinos and Tracers of Large-Scale Structure. TheAstrophysicalJournal, 894, Article 112. https://doi.org/10.3847/1538-4357/ab8561
[5]
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. JournalofCosmologyandAstroparticlePhysics, 2016, Article 37. https://doi.org/10.1088/1475-7516/2016/01/037
[6]
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.
[7]
Globus, N. and Blandford, R.D. (2025) Ultrahigh-Energy Cosmic Rays. AnnualReviewofAstronomyandAstrophysics, 63, 339-377. https://doi.org/10.1146/annurev-astro-052622-033150
[8]
Globus, N. and Blandford, R. (2023) Ultra High Energy Cosmic Ray Source Models: Successes, Challenges and General Predictions. EPJWebofConferences, 283, Article ID: 04001. https://doi.org/10.1051/epjconf/202328304001
[9]
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
[10]
Alves Batista, R., Biteau, J., Bustamante, M., Dolag, K., Engel, R., Fang, K., etal. (2019) Open Questions in Cosmic-Ray Research at Ultrahigh Energies. FrontiersinAstronomyandSpaceSciences, 6, Article 23. https://doi.org/10.3389/fspas.2019.00023
[11]
Letessier-Selvon, A. and Stanev, T. (2011) Ultrahigh Energy Cosmic Rays. ReviewsofModernPhysics, 83, 907-942. https://doi.org/10.1103/revmodphys.83.907
[12]
Uryson, A.V. (2006) Ultra High Energy Cosmic Rays: Identification of Possible Sources, Energy Spectra, and Propagation. PhysicsofParticlesandNuclei, 37, 347-367. https://doi.org/10.1134/s106377960603004x
[13]
McGruder III, C.H. (2026) The Cosmic Origin of High Energy Neutrinos, Ultra High Energy Neutrinos and the Mass of the Muon Neutrino. JournalofModernPhysics, 17, 179-198. https://doi.org/10.4236/jmp.2026.172013
[14]
McGruder, C.H. (2017) Acceleration of Particles to High Energy via Gravitational Repulsion in the Schwarzschild Field. AstroparticlePhysics, 86, 18-20. https://doi.org/10.1016/j.astropartphys.2016.10.003
[15]
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
[16]
Kotera, K. and Olinto, A.V. (2011) The Astrophysics of Ultrahigh-Energy Cosmic Rays. AnnualReviewofAstronomyandAstrophysics, 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
[19]
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. MonthlyNoticesoftheRoyalAstronomicalSociety, 418, 206-213. https://doi.org/10.1111/j.1365-2966.2011.19476.x
[20]
Terrano, W.A., Zaw, I. and Farrar, G.R. (2012) CHANDRA Observations and Classification of Active Galactic Nucleus Candidates Correlated with Auger Uhecrs. TheAstrophysicalJournal, 754, Article 142. https://doi.org/10.1088/0004-637x/754/2/142
[21]
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. InternationalJournalofModernPhysicsA, 25, 2917-2932. https://doi.org/10.1142/s0217751x10048512
[22]
Aloisio, R. and Boncioli, D. (2011) Ultra High Energy Cosmic Rays: Anisotropies and Spectrum. AstroparticlePhysics, 35, 152-160. https://doi.org/10.1016/j.astropartphys.2011.05.006
[23]
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. TheAstrophysicalJournalLetters, 853, L29. https://doi.org/10.3847/2041-8213/aaa66d
[24]
Abbasi, R.U., Abe, M., Abu-Zayyad, T., Allen, M., Azuma, R., Barcikowski, E., etal. (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. TheAstrophysicalJournalLetters, 867, L27.
[25]
Anchordoqui, L.A. (2018) Acceleration of Ultrahigh-Energy Cosmic Rays in Starburst Superwinds. PhysicalReviewD, 97, Article ID: 063010. https://doi.org/10.1103/physrevd.97.063010
[26]
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. JournalofCosmologyandAstroparticlePhysics, 2024, Article 22.
[27]
Doghmane, R. and Attallah, R. (2022) Probing Cosmic-Ray Anisotropy at Ultra-High Energy. JournalofAstrophysicsandAstronomy, 43, Article No. 89. https://doi.org/10.1007/s12036-022-09887-8
[28]
Vietri, M., De Marco, D. and Guetta, D. (2003) On the Generation of Ultra-High-Energy Cosmic Rays in γ-Ray Bursts: A Reappraisal. TheAstrophysicalJournal, 592, 378-389. https://doi.org/10.1086/375719
[29]
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? AIPConferenceProceedings, 1358, 355-360. https://doi.org/10.1063/1.3621804
[30]
Baerwald, P., Bustamante, M. and Winter, W. (2015) Are γ-Ray Bursts the Sources of Ultra-High Energy Cosmic Rays? AstroparticlePhysics, 62, 66-91. https://doi.org/10.1016/j.astropartphys.2014.07.007
[31]
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. PhysicalReviewD, 97, Article ID: 083010. https://doi.org/10.1103/physrevd.97.083010
[32]
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. TheAstrophysicalJournal, 677, 432-440. https://doi.org/10.1086/529018
[33]
He, H., Zhang, B.T. and Fan, Y. (2024) A Detectable Ultra-High-Energy Cosmic-Ray Outburst from GRB 221009A. TheAstrophysicalJournal, 963, Article 109. https://doi.org/10.3847/1538-4357/ad2352
[34]
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. TheAstrophysicalJournal, 593, 599-610. https://doi.org/10.1086/376723
[35]
Norman, C.A., Melrose, D.B. and Achterberg, A. (1995) The Origin of Cosmic Rays above 10 18.5 eV. TheAstrophysicalJournal, 454, 60. https://doi.org/10.1086/176465
[36]
Kang, H. and Ryu, D. (2013) Diffusive Shock Acceleration at Cosmological Shock Waves. TheAstrophysicalJournal, 764, Article 95. https://doi.org/10.1088/0004-637x/764/1/95
[37]
Gabici, S. (2003) γ-Ray Emission from Clusters of Galaxies. arXiv: astro-ph/0307499.
[38]
Vazza, F., Brunetti, G. and Gheller, C. (2009) Shock Waves in Eulerian Cosmological Simulations: Main Properties and Acceleration of Cosmic Rays. MonthlyNoticesoftheRoyalAstronomicalSociety, 395, 1333-1354. https://doi.org/10.1111/j.1365-2966.2009.14691.x
[39]
Blasi, P. (2013) The Origin of Galactic Cosmic Rays. TheAstronomyandAstrophysicsReview, 21, Article No. 70. https://doi.org/10.1007/s00159-013-0070-7
[40]
Blasi, P., Epstein, R.I. and Olinto, A.V. (2000) Ultra-High-Energy Cosmic Rays from Young Neutron Star Winds. TheAstrophysicalJournal, 533, L123-L126. https://doi.org/10.1086/312626
[41]
Arons, J. (2003) Magnetars in the Metagalaxy: An Origin for Ultra-High-Energy Cosmic Rays in the Nearby Universe. TheAstrophysicalJournal, 589, 871-892. https://doi.org/10.1086/374776
[42]
Kotera, K. and Amato, E. (2015) Engines of Radio Transients: Neutron Star Birth and Cosmic Rays. AnnualReviewofNuclearandParticleScience, 65, 449-472.
[43]
Fang, K., Kotera, K. and Olinto, A.V. (2014) Newly Born Pulsars as Sources of Ultrahigh Energy Cosmic Rays. arXiv: 1201.5197.
[44]
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
[45]
Murase, K., Kashiyama, K. and Mészáros, P. (2014) A New Class of High-Energy Transients from Crustal Failure of Neutron Stars during Binary Mergers. MonthlyNoticesoftheRoyalAstronomicalSociety, 442, 60-64.
[46]
Farrar, G.R. (2025) Binary Neutron Star Mergers as the Source of the Highest Energy Cosmic Rays. PhysicalReviewLetters, 134, Article ID: 081003. https://doi.org/10.1103/physrevlett.134.081003
[47]
Rodrigues, X., Biehl, D., Boncioli, D. and Taylor, A.M. (2019) Binary Neutron Star Merger Remnants as Sources of Cosmic Rays Below the “Ankle”. AstroparticlePhysics, 106, 10-17. https://doi.org/10.1016/j.astropartphys.2018.10.007
[48]
Guo, G., Qian, Y. and Wu, M. (2025) Binary Neutron Star Mergers as Potential Sources for Ultrahigh-Energy Cosmic Rays and High-Energy Neutrinos. PhysicalReviewD, 112, Article ID: 063022. https://doi.org/10.1103/zfp3-y9yw
[49]
Zhang, B.T., Murase, K., Oikonomou, F. and Li, Z. (2017) High-Energy Cosmic Ray Nuclei from Tidal Disruption Events: Origin, Survival, and Implications. PhysicalReviewD, 96, Article ID: 063007. https://doi.org/10.1103/physrevd.96.063007
[50]
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. ScientificReports, 8, Article No. 10828. https://doi.org/10.1038/s41598-018-29022-4
[51]
Pfeffer, D.N., Kovetz, E.D. and Kamionkowski, M. (2016) Ultrahigh-Energy Cosmic Ray Hotspots from Tidal Disruption Events. MonthlyNoticesoftheRoyalAstronomicalSociety, 466, 2922-2926. https://doi.org/10.1093/mnras/stw3337
[52]
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
[53]
Reames, D.V. (1999) Particle Acceleration at the Sun and in the Heliosphere. SpaceScienceReviews, 90, 413-491. https://doi.org/10.1023/a:1005105831781
[54]
Giacalone, J. and Kóta, J. (2006) Acceleration of Solar-Energetic Particles by Shocks. SpaceScienceReviews, 124, 277-288. https://doi.org/10.1007/s11214-006-9110-1
[55]
Lee, M.A., Mewaldt, R.A. and Giacalone, J. (2012) Shock Acceleration of Ions in the Heliosphere. SpaceScienceReviews, 173, 247-281. https://doi.org/10.1007/s11214-012-9932-y
[56]
Desai, M. and Giacalone, J. (2016) Large Gradual Solar Energetic Particle Events. LivingReviewsinSolarPhysics, 13, Article No. 3. https://doi.org/10.1007/s41116-016-0002-5
[57]
Li, G., Zank, G.P. and Rice, W.K.M. (2003) Energetic Particle Acceleration and Transport at Coronal Mass Ejection-Driven Shocks. JournalofGeophysicalResearch: SpacePhysics, 108, Article 1082. https://doi.org/10.1029/2002ja009666
[58]
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
[59]
Gopalswamy, N., Xie, H., Yashiro, S., Akiyama, S., Mäkelä, P. and Usoskin, I.G. (2010) Ground Level Enhancement Events of Solar Cycle 23. InternationalJournalofRemoteSensingandSpacePhysics, 39, 240-248.
[60]
Krymskii, G.F. (1977) A Regular Mechanism for the Acceleration of Charged Particles on the Front of a Shock Wave. AkademiiaNaukSSSRDoklady, 234, 1306-1308.
[61]
Bell, A.R. (1978) The Acceleration of Cosmic Rays in Shock Fronts—I. MonthlyNoticesoftheRoyalAstronomicalSociety, 182, 147-156. https://doi.org/10.1093/mnras/182.2.147
[62]
Bell, A.R. (1978) The Acceleration of Cosmic Rays in Shock Fronts—II. MonthlyNoticesoftheRoyalAstronomicalSociety, 182, 443-455. https://doi.org/10.1093/mnras/182.3.443
[63]
Drury, L.O. (1983) An Introduction to the Theory of Diffusive Shock Acceleration of Energetic Particles in Tenuous Plasmas. ReportsonProgressinPhysics, 46, 973-1027. https://doi.org/10.1088/0034-4885/46/8/002
[64]
Blandford, R. and Eichler, D. (1987) Particle Acceleration at Astrophysical Shocks: A Theory of Cosmic Ray Origin. PhysicsReports, 154, 1-75. https://doi.org/10.1016/0370-1573(87)90134-7
[65]
Baring, M.G. (2004) Diffusive Shock Acceleration of High Energy Cosmic Rays. NuclearPhysicsB—ProceedingsSupplements, 136, 198-207. https://doi.org/10.1016/j.nuclphysbps.2004.10.008
[66]
Peretti, E., Lamastra, A., Saturni, F.G., Ahlers, M., Blasi, P., Morlino, G., etal. (2023) Diffusive Shock Acceleration at EeV and Associated Multimessenger Flux from Ultra-Fast Outflows Driven by Active Galactic Nuclei. MonthlyNoticesoftheRoyalAstronomicalSociety, 526, 181-192. https://doi.org/10.1093/mnras/stad2740
[67]
Longair, M.S. (2011) Cosmic Ray Astrophysics. Cambridge University Press.
[68]
Berezinsky, V.S., Bulanov, S.V., Dogiel, V.A. and Ginzburg, V.L. (1990) Astrophysics of Cosmic Rays. North-Holland Publisher.
[69]
Droste, J. (1915) On the Field of a Single Centre in Einstein’s Theory of Gravitation. KoninklijkeNederlandseAkademievanWetenschappenProceedingsSeriesBPhysicalSciences, 17, 998-1011.
[70]
Droste, J. (1916) Het zwaartekrachtsveld van een of meer lichamen volgens de theorie van Einstein. Ph.D. Thesis, Leiden University.
[71]
Hilbert, D. (1915) Die Grundlagen der Physik. (Erste Mitteilung). Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, 395-407.
[72]
Hilbert, D. (1916) Die Feldgleichungen der Gravitation. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, 48, 844-847.
[73]
Hilbert, D. (1917) Die Grundlagen der Physik (Zweite Mitteilung). Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, 53-76.
[74]
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.
[75]
McGruder, C.H. (1982) Gravitational Repulsion in the Schwarzschild Field. PhysicalReviewD, 25, 3191-3194. https://doi.org/10.1103/physrevd.25.3191
[76]
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
[77]
Krori, K.D., Sarmah, J.C. and Goswami, D. (1984) Gravitational Repulsion in the Einstein-Zero-Mass Scalar Theory. CanadianJournalofPhysics, 62, 629-631. https://doi.org/10.1139/p84-085
[78]
P L Bragança, D. (2024) Gravitational Repulsion in an Expanding Ball of Dust. ClassicalandQuantumGravity, 41, Article ID: 075008. https://doi.org/10.1088/1361-6382/ad2d70
[79]
Polo, C.L. and Singh, H.S. (2024) Hilbert Repulsion in the Kerr-Newman Anti-De Sitter Spacetime. AstrophysicsandSpaceScience, 369, Article No. 41. https://doi.org/10.1007/s10509-024-04304-8
[80]
Célérier, M.N., Santos, N.O. and Satheeshkumar, V.H. (2017) Hilbert Repulsion in the Reissner-Nordström and Schwarzschild spacetimes. arXiv: 1707.06994.
[81]
Gorkavyi, N. and Vasilkov, A. (2016) A Repulsive Force in the Einstein Theory. MonthlyNoticesoftheRoyalAstronomicalSociety, 461, 2929-2933. https://doi.org/10.1093/mnras/stw1517
[82]
Kutschera, M. and Zajiczek, W. (2009) Shapiro Effect for for Relativistic Particles-Testing General Relativity in a New Window. arXiv: 0906.5088.
[83]
Herrera, L. (2005) Geodesics in a Quash-Spherical Spacetime: A Case of Gravitational Repulsion. FoundationsofPhysicsLetters, 18, 21-36. https://doi.org/10.1007/s10702-005-2467-7
[84]
Ponce de Leon, J. (1988) Gravitational Repulsion in Sources of the Reissner-Nordström Field. JournalofMathematicalPhysics, 29, 197-206. https://doi.org/10.1063/1.528172
[85]
Krori, K.D. and Barua, M. (1985) Gravitational Repulsion by Kerr and Kerr-Newman Black Holes. PhysicalReviewD, 31, 3135-3139. https://doi.org/10.1103/physrevd.31.3135
[86]
Greene, J.E. and Ho, L.C. (2007) The Mass Function of Active Black Holes in the Local Universe. TheAstrophysicalJournal, 667, 131-148.
[87]
Blandford, R.D. and McKee, C.F. (1982) Reverberation Mapping of the Emission Line Regions of Seyfert Galaxies and Quasars. TheAstrophysicalJournal, 255, 419-439. https://doi.org/10.1086/159843
[88]
Peterson, B.M., Ferrarese, L., Gilbert, K.M., Kaspi, S., Malkan, M.A., Maoz, D., etal. (2004) Central Masses and Broad‐line Region Sizes of Active Galactic Nuclei. II. A Homogeneous Analysis of a Large Reverberation‐mapping Database. TheAstrophysicalJournal, 613, 682-699. https://doi.org/10.1086/423269
[89]
Bentz, M.C. and Katz, S. (2015) The AGN Black Hole Mass Database. PublicationsoftheAstronomicalSocietyofthePacific, 127, 67-73. https://doi.org/10.1086/679601
[90]
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. TheAstrophysicalJournal, 641, 689-709. https://doi.org/10.1086/500572
[91]
Shen, Y., Richards, G.T., Strauss, M.A., Hall, P.B., Schneider, D.P., Snedden, S., etal. (2011) A Catalog of Quasar Properties from Sloan Digital Sky Survey Data Release 7. TheAstrophysicalJournalSupplementSeries, 194, Article 45. https://doi.org/10.1088/0067-0049/194/2/45
[92]
Shen, Y., Strauss, M.A., Oguri, M., Hennawi, J.F., Fan, X., Richards, G.T., etal. (2007) Clustering of High-Redshift (z ≥ 2.9) Quasars from the Sloan Digital Sky Survey. TheAstronomicalJournal, 133, 2222-2241. https://doi.org/10.1086/513517
[93]
McConnell, N.J., Ma, C., Gebhardt, K., Wright, S.A., Murphy, J.D., Lauer, T.R., etal. (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
[94]
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
[95]
McConnell, N.J. and Ma, C. (2013) Revisiting the Scaling Relations of Black Hole Masses and Host Galaxy Properties. TheAstrophysicalJournal, 764, Article 184. https://doi.org/10.1088/0004-637x/764/2/184
[96]
Kormendy, J. and Ho, L.C. (2013) Coevolution (or Not) of Supermassive Black Holes and Host Galaxies. AnnualReviewofAstronomyandAstrophysics, 51, 511-653. https://doi.org/10.1146/annurev-astro-082708-101811
[97]
Kachelriess, M. and Serpico, P.D. (2007) The GZK Horizon of Ultra-High Energy Cosmic Rays. arXiv: 0711.3635.
[98]
Berezinsky, V., Gazizov, A. and Grigorieva, S. (2006) On Astrophysical Solution to Ultrahigh Energy Cosmic Rays. PhysicalReviewD, 74, Article ID: 043005. https://doi.org/10.1103/physrevd.74.043005
[99]
Greisen, K. (1966) End to the Cosmic-Ray Spectrum? PhysicalReviewLetters, 16, 748-750. https://doi.org/10.1103/physrevlett.16.748
[100]
Zatsepin, G.T. AND Kuzmin, V.A. (1966) Upper Limit of the Spectrum of Cosmic Rays. JETPLetters, 4, 78-80.
[101]
Abbasi, R.U., Abu-Zayyad, T., Allen, M., etal. (2008) First Observation of the Greisen-Zatsepin-Kuzmin Suppression. PhysicalReviewLetters, 100, Article ID: 101101.
[102]
Abraham, J., Abreu, P., Aglietta, M., etal. (2008) Observation of the Suppression of the Flux of Cosmic Rays above 4 1019 ev. PhysicalReviewLetters, 101, Article ID: 061101.
[103]
Watson, A.A. (2014) High-Energy Cosmic Rays and the Greisen-Zatsepin-Kuz’min Effect. ReportsonProgressinPhysics, 77, Article ID: 036901. https://doi.org/10.1088/0034-4885/77/3/036901
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
[106]
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.
[107]
Bai, T. (1989) Particle Acceleration in Solar Flares. Annual Review of Astronomy and Astrophysics, 27, 421-474.
[108]
Burrows, A., Marley, M., Hubbard, W.B., Lunine, J.I., Guillot, T., Saumon, D., etal. (1997) A Nongray Theory of Extrasolar Giant Planets and Brown Dwarfs. TheAstrophysicalJournal, 491, 856-875. https://doi.org/10.1086/305002
[109]
Chabrier, G. and Baraffe, I. (1997) Structure and Evolution of Low-Mass Stars. Astronomy&Astrophysics, 327, 1039-1053.
[110]
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.
[111]
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. ReviewsofModernPhysics, 73, 719-765. https://doi.org/10.1103/revmodphys.73.719
[114]
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.
[115]
Spiegel, D.S., Burrows, A. and Milsom, J.A. (2011) The Deuterium-Burning Mass Limit for Brown Dwarfs and Giant Planets. TheAstrophysicalJournal, 727, Article 57. https://doi.org/10.1088/0004-637x/727/1/57
[116]
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
[117]
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
[118]
Basri, G. and Brown, M.E. (2006) Planetesimals to Brown Dwarfs: What Is a Planet? AnnualReviewofEarthandPlanetarySciences, 34, 193-216. https://doi.org/10.1146/annurev.earth.34.031405.125058
[119]
Berger, E., Ball, S., Becker, K.M., Clarke, M., Frail, D.A., Fukuda, T.A., etal. (2001) Discovery of Radio Emission from the Brown Dwarf LP944-20. Nature, 410, 338-340. https://doi.org/10.1038/35066514
[120]
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
[121]
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.
[122]
Hallinan, G., Littlefair, S.P., Cotter, G., Bourke, S., Harding, L.K., Pineda, J.S., etal. (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
[123]
Gizis, J.E., et al. (2017) The White Light Flare Rate of Young Brown Dwarfs. arXiv: 1703.08745.
[124]
Reiners, A. and Basri, G. (2007) The First Direct Measurements of Surface Magnetic Fields on Very Low Mass Stars. TheAstrophysicalJournal, 656, 1121-1135. https://doi.org/10.1086/510304
[125]
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
[126]
Johns-Krull, C.M. and Valenti, J.A. (1996) Detection of Strong Magnetic Fields on M Dwarfs. TheAstrophysicalJournal, 459, L95. https://doi.org/10.1086/309954
[127]
Saar, S.H. (1996) Recent Measurements of Stellar Magnetic Fields. Symposium—InternationalAstronomicalUnion, 176, 237-244. https://doi.org/10.1017/s0074180900083261
[128]
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
[129]
Shulyak, D., Reiners, A., Engeln, A., et al. (2017) Strong Dipole Magnetic Fields in Fast Rotating Fully Convective Stars. Nature Astronomy, 1, Article 184.
[130]
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
[131]
Berdyugina, S.V., Harrington, D.M., Kuzmychov, O., Kuhn, J.R., Hallinan, G., Kowalski, A.F., etal. (2017) First Detection of a Strong Magnetic Field on a Bursty Brown Dwarf: Puzzle Solved. TheAstrophysicalJournal, 847, Article 61. https://doi.org/10.3847/1538-4357/aa866b
[132]
Bailer-Jones, C.A.L. and Mundt, R. (2001) Variability in Ultra Cool Dwarfs: Evidence for the Evolution of Surface Features. Astronomy&Astrophysics, 367, 218-235. https://doi.org/10.1051/0004-6361:20000416
[133]
Mohanty, S. and Basri, G. (2003) Rotation & Activity in Mid-M to L Dwarfs. The Astrophysical Journal, 583, 451-472.
[134]
Reiners, A. and Basri, G. (2008) Chromospheric Activity, Rotation, and Rotational Braking in M and L Dwarfs. TheAstrophysicalJournal, 684, 1390-1403. https://doi.org/10.1086/590073
[135]
Metchev, S.A., Heinze, A., Apai, D., Flateau, D., Radigan, J., Burgasser, A., etal. (2015) Weather on Other Worlds. II. Survey Results: Spots Are Ubiquitous on L and T Dwarfs. TheAstrophysicalJournal, 799, Article 154. https://doi.org/10.1088/0004-637x/799/2/154
[136]
Zapatero Osorio, M.R., Martin, E.L., Bouy, H., Tata, R., Deshpande, R. and Wainscoat, R.J. (2006) Spectroscopic Rotational Velocities of Brown Dwarfs. TheAstrophysicalJournal, 647, 1405-1412. https://doi.org/10.1086/505484
[137]
Waxman, E. (1995) Cosmological Gamma-Ray Bursts and the Highest Energy Cosmic Rays. PhysicalReviewLetters, 75, 386-389. https://doi.org/10.1103/physrevlett.75.386
[138]
Ahlers, M. and Anchordoqui, L.A. (2012) High-Energy Cosmic Rays from Astrophysical Sources: An Overview. PhysicalReviewD, 85, Article ID: 063010.
[139]
Kirkpatrick, J.D., Marocco, F., Gelino, C.R., Raghu, Y., Faherty, J.K., Bardalez Gagliuffi, D.C., etal. (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.
[140]
Karachentsev, I.D. and Telikova, K.N. (2018) Stellar and Dark Matter Density in the Local Universe. AstronomischeNachrichten, 339, 615-622. https://doi.org/10.1002/asna.201813520
[141]
Luhman, K.L. (2012) The Formation and Early Evolution of Low-Mass Stars and Brown Dwarfs. AnnualReviewofAstronomyandAstrophysics, 50, 65-106. https://doi.org/10.1146/annurev-astro-081811-125528
[142]
Sorahana, S., Yamamura, I. and Murakami, H. (2013) On the Radii of Brown Dwarfs Measured with Akari Near-Infrared Spectroscopy. TheAstrophysicalJournal, 767, Article 77. https://doi.org/10.1088/0004-637x/767/1/77
[143]
Carmichael, T.W. (2022) Improved Radius Determinations for the Transiting Brown Dwarf Population in the Era of GAIA and TESS. MonthlyNoticesoftheRoyalAstronomicalSociety, 519, 5177-5190. https://doi.org/10.1093/mnras/stac3720
[144]
Chabrier, G. and Baraffe, I. (2000) Theory of Low-Mass Stars and Substellar Objects. AnnualReviewofAstronomyandAstrophysics, 38, 337-377. https://doi.org/10.1146/annurev.astro.38.1.337
[145]
Baraffe, I., Chabrier, G., Allard, F. and Hauschildt, P. (2003) Evolutionary Models for Low Mass Stars and Brown Dwarfs at Young Ages. Symposium—InternationalAstronomicalUnion, 211, 41-50. https://doi.org/10.1017/s0074180900210243
[146]
Zapolsky, H.S. and Salpeter, E.E. (1969) The Mass-Radius Relation for Cold Spheres of Low Mass. TheAstrophysicalJournal, 158, 809. https://doi.org/10.1086/150240
[147]
Blasi, P. and De Marco, D. (2004) The Small Scale Anisotropies, the Spectrum and the Sources of Ultra-High Energy Cosmic Rays. AstroparticlePhysics, 20, 559-577. https://doi.org/10.1016/j.astropartphys.2003.07.002
[148]
Takami, H., Nishimichi, T., Yahata, K. and Sato, K. (2009) Cross-Correlation between UHECR Arrival Distribution and Large-Scale Structure. JournalofCosmologyandAstroparticlePhysics, 2009, Article 31. https://doi.org/10.1088/1475-7516/2009/06/031
[149]
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 1018 eV from Large-Scale Anisotropy Searches in Data of the Pierre Auger Observatory. The Astrophysical Journal Letters, 762, L13.
[150]
Aab, A., Abreu, P., Aglietta, M., etal. (2017) Observation of a Large-Scale Anisotropy in the Arrival Directions of Cosmic Rays above 8 Times 1018 eV. Science, 357, 1266-1270.
[151]
Aab, A., et al. (2020) Large-Scale Cosmic-Ray Anisotropies above 4 EeV Measured by the Pierre Auger Observatory. arXiv: 1808.03579.
[152]
Abbasi, R.U., Abe, M., Abu-Zayyad, T., Allen, M., Anderson, R., Azuma, R., etal. (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.
[153]
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.
[154]
Allard, D. (2012) Extragalactic Propagation of Ultrahigh Energy Cosmic-Rays. AstroparticlePhysics, 39, 33-43. https://doi.org/10.1016/j.astropartphys.2011.10.011
[155]
Aloisio, R., Berezinsky, V. and Blasi, P. (2017) Ultra-High Energy Cosmic Rays: Implications of Auger Data for Source Spectra and Chemical Composition. JournalofCosmologyandAstroparticlePhysics, 2017, Article 20.
[156]
Bird, D.J., Corbato, S.C., Dai, H.Y., Elbert, J.W., Green, K.D., Huang, M.A., etal. (1995) Detection of a Cosmic Ray with Measured Energy Well Beyond the Expected Spectral Cutoff Due to Cosmic Microwave Radiation. TheAstrophysicalJournal, 441, 144. https://doi.org/10.1086/175344
[157]
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. FrontiersinAstronomyandSpaceSciences, 11, Article 1400032. https://doi.org/10.3389/fspas.2024.1400032
[158]
Ohsawa, Y. (2014) Ultrarelativistic Particle Acceleration in Collisionless Shock Waves. PhysicsReports, 536, 147-254. https://doi.org/10.1016/j.physrep.2013.11.004
[159]
Aab, A., Abreu, P., Aglietta, M., Albury, J.M., Allekotte, I., Almela, A., etal. (2020) Features of the Energy Spectrum of Cosmic Rays above 2.5 ×1018 eV Using the Pierre Auger Observatory. Physical Review Letters, 125, Article ID: 121106.
[160]
Abraham, J., Abreu, P., Aglietta, M., Aguirre, C., Allard, D., Allekotte, I., etal. (2007) Correlation of the Highest-Energy Cosmic Rays with Nearby Extragalactic Objects. Science, 318, 938-943. https://doi.org/10.1126/science.1151124
[161]
Parizot, E. (2004) GZK Horizon and Magnetic Fields. NuclearPhysicsB—ProceedingsSupplements, 136, 169-178. https://doi.org/10.1016/j.nuclphysbps.2004.10.034
[162]
Mollerach, S. and Roulet, E. (2022) Anisotropies of Ultrahigh-Energy Cosmic Rays in a Scenario with Nearby Sources. PhysicalReviewD, 105, Article ID: 063001. https://doi.org/10.1103/physrevd.105.063001
[163]
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. TheAstrophysicalJournal, 787, Article 30. https://doi.org/10.1088/0004-637x/787/1/30
[164]
Hernitschek, N., Cohen, J.G., Rix, H., Sesar, B., Martin, N.F., Magnier, E., etal. (2018) The Profile of the Galactic Halo from Pan-STARRS1 3π RR Lyrae. TheAstrophysicalJournal, 859, Article 31. https://doi.org/10.3847/1538-4357/aabfbb
[165]
Helmi, A. (2008) The Stellar Halo of the Galaxy. TheAstronomyandAstrophysicsReview, 15, 145-188. https://doi.org/10.1007/s00159-008-0009-6
[166]
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
[167]
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 AstrophysicalJournal, 832, Article 206. https://doi.org/10.3847/0004-637x/832/2/206
