On stellar activity cycle-related cosmic ray modulation effects in the astrosphere of Proxima Centauri | Journal of Space Weather and Space Climate

Topical Issue - Space Climate: Solar Extremes, Long-Term Variability, and Impacts on Earth’s System

Open Access

Issue		J. Space Weather Space Clim. Volume 16, 2026 Topical Issue - Space Climate: Solar Extremes, Long-Term Variability, and Impacts on Earth’s System


Article Number		13
Number of page(s)		18
DOI		https://doi.org/10.1051/swsc/2026012
Published online		07 May 2026

Adhikari L, Zank GP, Zhao L. 2021. The transport and evolution of MHD turbulence throughout the heliosphere: Models and observations. Fluids 6(10): 368. https://doi.org/10.3390/fluids6100368, https://www.mdpi.com/2311-5521/6/10/368. [Google Scholar]
Adriani O, Barbarino GC, Bazilevskaya GA, Bellotti R, Boezio M, et al. 2013. Measurement of the isotopic composition of Hydrogen and Helium nuclei in cosmic rays with the PAMELA experiment. Astrophys J 770(1): 2. https://doi.org/10.1088/0004-637X/770/1/2. [Google Scholar]
Agarwal R, Mishra RK. 2008. Solar cycle phenomena in cosmic ray intensity up to the recent solar cycle. Phys Lett B 664(1–2): 31–34. https://doi.org/10.1016/j.physletb.2008.04.057. [Google Scholar]
Ahluwalia HS. 2000. On galactic cosmic ray flux decrease near solar minima and IMF intensity. Geophys Res Lett 27(11): 1603–1606. https://doi.org/10.1029/2000GL003759, https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2000GL003759. [Google Scholar]
Airapetian VS, Glocer A, Gronoff G, Hébrard E, Danchi W. 2016. Prebiotic chemistry and atmospheric warming of early Earth by an active young Sun. Nat Geosci 9(6): 452–455. httpss://doi.org/10.1038/ngeo2719. [Google Scholar]
Alvarado-Gómez JD, Drake JJ, Garraffo C, Cohen O, Poppenhaeger K, et al. 2020. An Earth-like stellar wind environment for Proxima Centauri c. Astrophys J 902(1): L9. https://doi.org/10.3847/2041-8213/abb885. [Google Scholar]
Alvarado-Gómez JD, Drake JJ, Moschou SP, Garraffo C, Cohen O, et al. 2019. Coronal response to magnetically suppressed CME events in M-dwarf stars. Astrophys J 884(1): L13. https://doi.org/10.3847/2041-8213/ab44d0. [Google Scholar]
Alvarado-Gómez JD, Hussain GAJ, Amazo-Gómez EM, Xu Y, Poppenhäger K, et al. 2025. Far beyond the Sun: III. The magnetic cycle of ı Horologii. Astron Astrophys 704: A68. https://doi.org/10.1051/0004-6361/202555349. [Google Scholar]
Anglada-Escudé G, Amado PJ, Barnes J, Berdiñas ZM, Butler RP, et al. 2016. A terrestrial planet candidate in a temperate orbit around Proxima Centauri. Nature 536(7617): 437–440. https://doi.org/10.1038/nature19106. [Google Scholar]
Balogh A, Smith EJ. 2001. The heliospheric magnetic field at solar maximum: Ulysses observations. Space Sci Rev 97: 147–160. https://doi.org/10.1023/A:1011854901760. [Google Scholar]
Banjac S, Herbst K, Heber B. 2019. The Atmospheric Radiation Interaction Simulator (AtRIS): Description and validation. J Geophys Res: Space Phys 124(1): 50–67. https://doi.org/10.1029/2018JA026042, https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2018JA026042. [Google Scholar]
Bellotti S, Petit P, Jeffers SV, Marsden SC, Morin J, et al. 2025. A BCool survey of stellar magnetic cycles. Astron Astrophys 693: A269. https://doi.org/10.1051/0004-6361/202452378. [Google Scholar]
Bieber JW, Matthaeus WH, Smith CW, Wanner W, Kallenrode M-B, et al. 1994. Proton and electron mean free paths: The Palmer consensus revisited. Astrophys J 420: 294. https://doi.org/10.1086/173559. [CrossRef] [Google Scholar]
Bieber JW, Wanner W, Matthaeus WH. 1996. Dominant two-dimensional solar wind turbulence with implications for cosmic ray transport. J Geophys Res 101(A2): 2511–2522. https://doi.org/10.1029/95JA02588. [Google Scholar]
Boro Saikia S, Jeffers SV, Morin J, Petit P, Folsom CP, et al. 2016. A solar-like magnetic cycle on the mature K-dwarf 61 Cygni A (HD 201091). Astron Astrophys 594: A29. https://doi.org/10.1051/0004-6361/201628262. [Google Scholar]
Boro Saikia S, Lüftinger T, Folsom CP, Antonova A, Alecian E, et al. 2022. Time evolution of magnetic activity cycles in young suns: The curious case of κ Ceti. Astron Astrophys 658: A16. https://doi.org/10.1051/0004-6361/202141525. [Google Scholar]
Boschini MJ, Della Torre S, Gervasi M, Grandi D, Jóhannesson G, et al. 2020. Inference of the local interstellar spectra of cosmic-ray nuclei Z ≤ 28 with the GALPROP-HELMOD framework. Astrophys J Supp 250(2): 27. https://doi.org/10.3847/1538-4365/aba901. [Google Scholar]
Breech B, Matthaeus WH, Minnie J, Bieber JW, Oughton S, et al. 2008. Turbulence transport throughout the heliosphere. J Geophys Res Space Phys 113(A8): A08105. https://doi.org/10.1029/2007JA012711. [Google Scholar]
Burger RA. 2012. Modeling drift along the heliospheric wavy neutral sheet. Astrophys J 760(1): 60. https://doi.org/10.1088/0004-637X/760/1/60. [Google Scholar]
Burger RA, Krüger TPJ, Hitge M, Engelbrecht NE. 2008. A fisk-parker hybrid heliospheric magnetic field with a solar-cycle dependence. Astrophys J 674(1): 511–519. https://doi.org/10.1086/525039. [Google Scholar]
Burger RA, McKee SR. 2023. Evaluation and analysis of Voyager 1 48-s resolution magnetic field data. Adv Space Res 71(11): 4916–4922. https://doi.org/10.1016/j.asr.2023.01.033. [Google Scholar]
Burger RA, Nel AE, Engelbrecht NE. 2022. Spectral properties of the N component of the heliospheric magnetic field from IMP and ACE observations for 1973–2020. Astrophys J 926(2): 128. https://doi.org/10.3847/1538-4357/ac4741. [Google Scholar]
Burlaga LF. 1984. MHD processes in the outer heliosphere. Space Sci Rev 39: 255–316. [Google Scholar]
Burlaga LF, Ness NF. 2000. Merged interaction regions observed by Voyagers 1 and 2 during 1998. J Geophys Res 105(A3): 5141–5148. https://doi.org/10.1029/1999JA000379. [Google Scholar]
Burlaga LF, Wang C, Richardson JD, Ness NF. 2003. Large-scale magnetic field fluctuations and development of the 1999–2000 global merged interaction region: 1–60 AU. Astrophys J 585: 1158–1168. [Google Scholar]
Caballero-Lopez RA, Engelbrecht NE, Richardson JD. 2019. Correlation of long-term cosmic-ray modulation with solar activity parameters. Astrophys J: 883(1): 73. https://doi.org/10.3847/1538-4357/ab3c57. [Google Scholar]
Chahal D, Kamath D, de Grijs R, Montet BT, Chen X. 2025. Photometric activity cycles in fast-rotating stars: Revisiting the reality of stellar activity cycle branches. MNRAS 540(1): 668–687. https://doi.org/10.1093/mnras/staf754. [Google Scholar]
Cuesta ME, Parashar TN, Chhiber R, Matthaeus WH. 2022. Intermittency in the expanding solar wind: Observations from Parker Solar Probe (0.16 au), Helios 1 (0.3–1 au), and Voyager 1 (1–10 au). Astrophys J Supp, 259(1): 23. https://doi.org/10.3847/1538-4365/ac45fa. [Google Scholar]
Els PL, Engelbrecht NE, Lang JT, Strauss RD. 2024. The diffusion tensor of protons at 1 au: Comparing simulation, observation, and theory. Astrophys J 975(1): 134. https://doi.org/10.3847/1538-4357/ad7c44. [Google Scholar]
Engelbrecht NE, Burger RA. 2015a. A comparison of turbulence-reduced drift coefficients of importance for the modulation of galactic cosmic-ray protons in the supersonic solar wind. Adv Space Res 55(1): 390–400. https://doi.org/10.1016/j.asr.2014.09.019. [Google Scholar]
Engelbrecht NE, Burger RA. 2015b. Sensitivity of cosmic-ray proton spectra to the low-wavenumber behavior of the 2D turbulence power spectrum. Astrophys J 814(2): 152. https://doi.org/10.1088/0004-637X/814/2/152. [Google Scholar]
Engelbrecht NE, Di Felice V. 2020. Uncertainties implicit to the use of the force-field solutions to the Parker transport equation in analyses of observed cosmic ray antiproton intensities. Phys Rev D 102(10): 103007. https://doi.org/10.1103/PhysRevD.102.103007. [Google Scholar]
Engelbrecht NE, Effenberger F, Florinski V, Potgieter M, Ruffolo D, et al. 2022. Theory of cosmic ray transport in the heliosphere. Space Sci Rev 218: 33. https://doi.org/10.1007/s11214-022-00896-1. [Google Scholar]
Engelbrecht NE, Herbst K, Scherer K, Oughton S, Airapetian VS. 2026. Particle transport from first principles in the early heliosphere: κ¹ Ceti as a case study for the young sun. Astrophys J 998(1): 45. https://doi.org/10.3847/1538-4357/ae313e. [Google Scholar]
Engelbrecht NE, Herbst K, Strauss RDT, Scherer K, Light J, et al. 2024. On the comprehensive 3D modeling of the radiation environment of Proxima Centauri b: A new constraint on habitability? Astrophys J 964(1): 89. https://doi.org/10.3847/1538-4357/ad2ade. [Google Scholar]
Engelbrecht NE, Mohlolo ST, Ferreira SES. 2019. An improved treatment of neutral sheet drift in the inner heliosphere. Astrophys J 884(2): L54. https://doi.org/10.3847/2041-8213/ab4ad6. [Google Scholar]
Engelbrecht NE, Moloto KD. 2021. An Ab initio approach to antiproton modulation in the inner heliosphere. Astrophys J 908(2): 167. https://doi.org/10.3847/1538-4357/abd3a5. [Google Scholar]
Engelbrecht NE, Strauss RD, le Roux JA, Burger RA. 2017. Toward a greater understanding of the reduction of drift coefficients in the presence of turbulence. Astrophys J, 841(2): 107. https://doi.org/10.3847/1538-4357/aa7058. [Google Scholar]
Engelbrecht NE, Wolmarans CP. 2020. Towards a deeper understanding of historic cosmic ray modulation during solar cycle 20. Adv Space Res 66(11): 2722–2732. https://doi.org/10.1016/j.asr.2020.09.022. [Google Scholar]
Forbush SE. 1958. Cosmic-ray intensity variations during two solar cycles. J Geophys Res 63(4): 651–669. https://doi.org/10.1029/JZ063i004p00651, https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/JZ063i004p00651. [CrossRef] [Google Scholar]
Forman MA, Jokipii JR, Owens AJ. 1974. Cosmic-ray streaming perpendicular to the mean magnetic field. Astrophys J 192: 535–540. https://doi.org/10.1086/153087. [Google Scholar]
Fuhrmeister B, Lalitha S, Poppenhaeger K, Rudolf N, Liefke C, et al. 2011. Multi-wavelength observations of Proxima Centauri. Astron Astrophys 534: A133. https://doi.org/10.1051/0004-6361/201117447. [Google Scholar]
Gardner JP, Mather JC, Abbott R, Abell JS, Abernathy M, et al. 2023. The James Webb Space Telescope Mission. PASP 135(1048): 068001. https://doi.org/10.1088/1538-3873/acd1b5. [Google Scholar]
Gardner JP, Mather JC, Clampin M, Doyon R, Greenhouse MA, et al. 2006. The James Webb Space Telescope. Space Sci Rev 123(4): 485–606. https://doi.org/10.1007/s11214-006-8315-7. [Google Scholar]
Garraffo C, Alvarado-Gómez JD, Cohen O, Drake JJ. 2022. Revisiting the space weather environment of Proxima Centauri b. Astrophys J 941(1): L8. https://doi.org/10.3847/2041-8213/aca487. [Google Scholar]
Garraffo C, Drake JJ, Cohen O. 2016. The space weather of Proxima Centauri b. Astrophys J 833(1): L4. https://doi.org/10.3847/2041-8205/833/1/L4. [Google Scholar]
Gieseler J, Heber B, Herbst K. 2017. An empirical modification of the force field approach to describe the modulation of galactic cosmic rays close to Earth in a broad range of rigidities. J Geophys Res Space Phys 122(11): 10 964–10 979. https://doi.org/10.1002/2017JA024763. [Google Scholar]
Globus N, Blandford RD. 2020. The chiral puzzle of life. Astrophys J 895(1): L11. https://doi.org/10.3847/2041-8213/ab8dc6. [Google Scholar]
Grenfell JL, Grießmeier J-M, von Paris P, Patzer ABC, Lammer H, et al. 2012. Response of atmospheric biomarkers to NOx-induced photochemistry generated by stellar cosmic rays for Earth-like planets in the habitable zone of M Dwarf stars. Astrobiology 12(12): 1109–1122. https://doi.org/10.1089/ast.2011.0682. [NASA ADS] [CrossRef] [Google Scholar]
Guo J, Banjac S, Röstel L, Terasa JC, Herbst K, et al. 2019. Implementation and validation of the GEANT4/AtRIS code to model the radiation environment at Mars. J Space Weather Space Clim 9: A2. https://doi.org/10.1051/swsc/2018051. [Google Scholar]
Hathaway DH. 2015. The solar cycle. Liv Rev Sol Phys 12(1): 4. https://doi.org/10.1007/lrsp-2015-4. [Google Scholar]
Hedgecock PC. 1975. Measurements of the interplanetary magnetic field in relation to the modulation of cosmic rays. Sol Phys 42(2): 497–527. https://doi.org/10.1007/BF00149929. [Google Scholar]
Herbst K, Baalmann L, Bykov A, Engelbrecht N, Ferreira S, et al. 2022. Astrospheres of planet-hosting cool stars and beyond: When modeling meets observations. Space Sci Rev 218: 29. https://doi.org/10.1007/s11214-022-00894-3. [Google Scholar]
Herbst K, Banjac S, Atri D, Nordheim TA. 2020a. Revisiting the cosmic-ray induced Venusian radiation dose in the context of habitability. Astron Astrophys 633: A15. https://doi.org/10.1051/0004-6361/201936968. [Google Scholar]
Herbst K, Banjac S, Nordheim TA. 2019a. Revisiting the cosmic-ray induced Venusian ionization with the Atmospheric Radiation Interaction Simulator (AtRIS). Astron Astrophys 624: A124. https://doi.org/10.1051/0004-6361/201935152. [Google Scholar]
Herbst K, Bartenschlager A, Grenfell JL, Iro N, Sinnhuber M, et al. 2024. Impact of cosmic rays on atmospheric ion chemistry and spectral transmission features of TRAPPIST-1e. Astrophys J 961(2): 164. https://doi.org/10.3847/1538-4357/ad0895. [Google Scholar]
Herbst K, Grenfell JL, Sinnhuber M, Rauer H, Heber B, et al. 2019b. A new model suite to determine the influence of cosmic rays on (exo)planetary atmospheric biosignatures. Validation based on modern Earth. Astron Astrophys 631: A101. https://doi.org/10.1051/0004-6361/201935888. [Google Scholar]
Herbst K, Scherer K, Ferreira SES, Baalmann LR, Engelbrecht NE, et al. 2020b. On the diversity of M-star astrospheres and the role of galactic cosmic rays within. Astrophys J 897(2): L27. https://doi.org/10.3847/2041-8213/ab9df3. [Google Scholar]
Hessman FV, Dhillon VS, Winget DE, Schreiber MR, Horne K, et al. 2010. On the naming convention used for multiple star systems and extrasolar planets. arXiv e-prints [arXiv:1012.0707]. https://doi.org/10.48550/arXiv.1012.0707 [Google Scholar]
Hoeksema JT. 1995. The large-scale structure of the heliospheric current sheet during the ULYSSES epoch. Space Sci Rev 72(1–2): 137–148. https://doi.org/10.1007/BF00768770. [Google Scholar]
Ibañez Bustos RV, Buccino AP, Nardetto N, Mourard D, Flores M, et al. 2025. Characterisation of magnetic activity of M dwarfs: Possible impact on surface brightness. Astron Astrophys 696: A230. https://doi.org/10.1051/0004-6361/202450348. [Google Scholar]
Irving ZA, Saar SH, Wargelin BJ, do Nascimento J-D. 2023. Stellar cycles in fully convective stars and a new interpretation of dynamo evolution. Astrophys J 949(2): 51. https://doi.org/10.3847/1538-4357/acc468. [Google Scholar]
Isenberg PA, Jokipii JR. 1979. Gradient and curvature drifts in magnetic fields with arbitrary spatial variation. Astrophys J 234: 746–752. [Google Scholar]
Jeffers SV, Cameron RH, Marsden SC, Boro Saikia S, Folsom CP. et al., 2022. The crucial role of surface magnetic fields for stellar dynamos: Eridani, 61 Cygni A, and the Sun. Astron Astrophys 661: A152. https://doi.org/10.1051/0004-6361/202142202. [Google Scholar]
Jeffers SV, Kiefer R, Metcalfe TS. 2023. Stellar activity cycles. Space Sci Rev 219(7): 54. https://doi.org/10.1007/s11214-023-01000-x. [Google Scholar]
Jeffers SV, Petit P, Marsden SC, Morin J, Donati J-F, et al. 2014. Eridani: An active K dwarf and a planet hosting star? The variability of its large-scale magnetic field topology. Astron Astrophys 569: A79. https://doi.org/10.1051/0004-6361/201423725. [Google Scholar]
Jokipii JR. 1966. Cosmic-ray Propagation. I. Charged particles in a random magnetic field. Astrophys J 146: 480. https://doi.org/10.1086/148912. [CrossRef] [Google Scholar]
Jokipii JR, Thomas B. 1981. Effects of drift on the transport of cosmic rays. 4 – Modulation by a wavy interplanetary current sheet. Astrophys J 243: 1115–1122. [Google Scholar]
Kavanagh RD, Vidotto AA, Klein B, Jardine MM, Donati J-F, et al. 2021. Planet-induced radio emission from the coronae of M dwarfs: The case of Prox Cen and AU Mic. MNRAS 504(1): 1511–1518. https://doi.org/10.1093/mnras/stab929. [Google Scholar]
Kennedy AR. 2014. Biological effects of space radiation and development of effective countermeasures. Life Sci Space Res 1: 10–43. https://doi.org/10.1016/j.lssr.2014.02.004, https://www.sciencedirect.com/science/article/pii/S2214552414000108. [Google Scholar]
Khabarova O, Malandraki O, Malova H, Kislov R, Greco A, et al. 2021. Current sheets, plasmoids and flux ropes in the heliosphere. Part I. 2-D or not 2-D? General and observational aspects. Space Sci Rev 217(3): 38. https://doi.org/10.1007/s11214-021-00814-x. [Google Scholar]
Kharayat H, Prasad L, Mathpal R, Garia S, Bhatt B. 2016. Study of cosmic ray intensity in relation to the interplanetary magnetic field and geomagnetic storms for solar cycle 23. Sol Phys 291: 603–611. https://doi.org/10.1007/s11207-016-0852-y. [Google Scholar]
King JH, Papitashvili NE. 2005. Solar wind spatial scales in and comparisons of hourly Wind and ACE plasma and magnetic field data. J Geophys Res Space Phys 110(A2): A02104. https://doi.org/10.1029/2004JA010649. [Google Scholar]
Klein B, Donati J-F, Hébrard ÉM, Zaire B, Folsom CP, et al. 2021. The large-scale magnetic field of Proxima Centauri near activity maximum. MNRAS 500(2): 1844–1850. https://doi.org/10.1093/mnras/staa3396. [Google Scholar]
Kóta J. 2013. Theory and modeling of galactic cosmic rays: Trends and prospects. Space Sci Rev 176(1–4) 391–403. https://doi.org/10.1007/s11214-012-9870-8. [Google Scholar]
Kota J, Jokipii JR. 1983. Effects of drift on the transport of cosmic rays. 6–A Three-dimensional model including diffusion. Astrophys J 265: 573–581. [Google Scholar]
Lang JT, Strauss RD, Engelbrecht NE, van den Berg JP, Dresing N, et al. 2024. A detailed survey of the parallel mean free path of solar energetic particle protons and electrons. Astrophys J 971(1): 105. https://doi.org/10.3847/1538-4357/ad55c3. [Google Scholar]
le Roux J. 1999. Time-dependent cosmic-ray modulation and global merged interaction regions. Adv Space Res 23(3): 491–499. https://doi.org/10.1016/S0273-1177(99)00112-X, https://www.sciencedirect.com/science/article/pii/S027311779900112X. [Google Scholar]
le Roux JA, Fichtner H. 1999. Global merged interaction regions, the heliospheric termination shock, and time-dependent cosmic ray modulation. J Geophys Res 104(A3): 4709–4730. https://doi.org/10.1029/1998JA900089. [Google Scholar]
Lehmann LT, Donati JF, Fouqué P, Moutou C, Bellotti S, et al. 2024. SPIRou reveals unusually strong magnetic fields of slowly rotating M dwarfs. MNRAS 527(2): 4330–4352. https://doi.org/10.1093/mnras/stad3472. [Google Scholar]
Light J, Engelbrecht NE, Herbst K, Scherer KD. 2025. On the 3D transport of galactic cosmic rays in a selection of exoplanet-hosting astrospheres: the influence of stellar rotation. MNRAS 537(2): 2097–2111. https://doi.org/10.1093/mnras/staf164. [Google Scholar]
Lockwood JA, Webber WR. 2005. Intensities of galactic cosmic rays of 1.5 GV rigidity at Earth versus the heliospheric current sheet tilt. J Geophys Res: Space Phys 110(A4): A04102. https://doi.org/10.1029/2004JA010880, https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2004JA010880. [Google Scholar]
Manuel R, Ferreira SES, Potgieter MS, Strauss RD, Engelbrecht NE. 2011. Time-dependent cosmic ray modulation. Adv Space Res 47(9): 1529–1537. https://doi.org/10.1016/j.asr.2010.12.007. [Google Scholar]
Matthaeus WH, Goldstein ML, Roberts DA. 1990. Evidence for the presence of quasi-two-dimensional nearly incompressible fluctuations in the solar wind. J Geophys Res 95: 20 673–20 683. https://doi.org/10.1029/JA095iA12p20673. [Google Scholar]
Matthaeus WH, Qin G, Bieber JW, Zank GP. 2003. Nonlinear collisionless perpendicular diffusion of charged particles. Astrophys J 590: L53–L56. [Google Scholar]
Mavromichalaki H, Paouris E, Karalidi T. 2007. Cosmic-ray modulation: An empirical relation with solar and heliospheric parameters. Sol Phys 245: 369–390. https://doi.org/10.1007/s11207-007-9043-1. [Google Scholar]
McDonald FB. 1998. Cosmic-ray modulation in the heliosphere A phenomenological study. Space Sci Rev 83: 33–50. [Google Scholar]
McDonald FB, Moraal H, Reinecke JPL, Lal N, McGuire RE. 1992. The cosmic radiation in the heliosphere at successive solar minima. J Geophys Res 97(A2): 1557–1570. https://doi.org/10.1029/91JA02389. [Google Scholar]
McNair A. 1981. ICRU report 33 – Radiation quantities and units pub: International commission on radiation units and measurements, Washington D.C. USA issued 15 April 1980, pp.25. J Labelled Compd Radiopharm 18(9): 1398–1398. https://doi.org/10.1002/jlcr.2580180918. [Google Scholar]
Mesquita AL, Rodgers-Lee D, Vidotto AA. 2021. The Earth-like Galactic cosmic ray intensity in the habitable zone of the M dwarf GJ 436. MNRAS 505(2): 1817–1826. https://doi.org/10.1093/mnras/stab1483. [Google Scholar]
Mesquita AL, Rodgers-Lee D, Vidotto AA, Atri D, Wood BE. 2022. Galactic cosmic ray propagation through M dwarf planetary systems. MNRAS 509(2): 2091–2101. https://doi.org/10.1093/mnras/stab3131. [Google Scholar]
Minnie J, Bieber JW, Matthaeus WH, Burger RA. 2007. Suppression of particle drifts by turbulence. Astrophys J 670(2): 1149–1158. https://doi.org/10.1086/522026. [Google Scholar]
Mohlolo ST, Engelbrecht NE, Ferreira SES. 2022. A detailed comparison of techniques used to model drift in numerical cosmic ray modulation models. Adv Space Res 69(6): 2574–2588. https://doi.org/10.1016/j.asr.2021.12.035. [Google Scholar]
Moloto KD, Engelbrecht NE. 2020. A fully time-dependent Ab initio cosmic-ray modulation model applied to historical cosmic-ray modulation. Astrophys J 894(2): 121. https://doi.org/10.3847/1538-4357/ab87a2. [Google Scholar]
Moloto KD, Engelbrecht NE, Burger RA. 2018. A Simplified Ab initio cosmic-ray modulation model with simulated time dependence and predictive capability. Astrophys J 859(2): 107. https://doi.org/10.3847/1538-4357/aac174. [Google Scholar]
Moloto KD, Eugene Engelbrecht N, Strauss RD, Diedericks C. 2023. The Southern African neutron monitor program: A regional network to study global cosmic ray modulation. Adv Space Res 72(3): 830–843. https://doi.org/10.1016/j.asr.2022.05.044. [Google Scholar]
Moraal H. 1976. Observations of the eleven-year cosmic-ray modulation cycle. Space Sci Rev 19(6): 845–920. https://doi.org/10.1007/BF00173707. [Google Scholar]
Moraal H. 2013. Cosmic-ray modulation equations. Space Sci Rev 176(1–4): 299–319. https://doi.org/10.1007/s11214-011-9819-3. [Google Scholar]
Moschou S-P, Drake JJ, Cohen O, Alvarado-Gómez JD, Garraffo C, et al. 2019. The stellar CME-flare relation: What do historic observations reveal? Astrophys J 877(2): 105. https://doi.org/10.3847/1538-4357/ab1b37. [Google Scholar]
Nagashima K, Morishita I. 1980a. Long term modulation of cosmic rays and inferable electromagnetic state in solar modulating region. Planet Space Sci 28(2): 177–194. https://doi.org/10.1016/0032-0633(80)90094-X. [Google Scholar]
Nagashima K, Morishita L. 1980b. Twenty-two year modulation of cosmic rays associated with polarity reversal of polar magnetic field of the sun. Planet Space Sci 28(2): 195–205. https://doi.org/10.1016/0032-0633(80)90095-1. [Google Scholar]
Nigro G. 2022. An argument in favor of magnetic polarity reversals due to heat flux variations in fully convective stars and planets. Astrophys J 938(1): 22. https://doi.org/10.3847/1538-4357/ac8d57. [Google Scholar]
Oughton S, Engelbrecht NE. 2021. Solar wind turbulence: Connections with energetic particles. New Astron 83: 101507. https://doi.org/10.1016/j.newast.2020.101507. [Google Scholar]
Oughton S, Matthaeus WH, Smith CW, Breech B, Isenberg PA. 2011. Transport of solar wind fluctuations: A two-component model. J Geophys Res Space Phys 116(A8): A08105. https://doi.org/10.1029/2010JA016365. [Google Scholar]
Owens MJ, Forsyth RJ. 2013. The heliospheric magnetic field. Liv Rev Sol Phys 10(1): 5. https://doi.org/10.12942/lrsp-2013-5. [Google Scholar]
Padovani P, Cirasuolo M. 2023. The extremely large telescope. Contemp Phys 64(1): 47–64. https://doi.org/10.1080/00107514.2023.2266921. [Google Scholar]
Palmer ID. 1982. Transport coefficients of low-energy cosmic rays in interplanetary space. Rev Geophys Space Phys 20: 335–351. https://doi.org/10.1029/RG020i002p00335. [CrossRef] [Google Scholar]
Parker EN. 1958. Dynamics of the interplanetary gas and magnetic fields. Astrophys J 128: 664. https://doi.org/10.1086/146579. [CrossRef] [Google Scholar]
Parker EN. 1965. The passage of energetic charged particles through interplanetary space. Planet Space Sci 13(1): 9–49. https://doi.org/10.1016/0032-0633(65)90131-5. [Google Scholar]
Pei C, Bieber JW, Burger RA, Clem J. 2010. A general time-dependent stochastic method for solving Parker’s transport equation in spherical coordinates. J Geophys Res Space Phys 115(A12): A12107. https://doi.org/10.1029/2010JA015721. [Google Scholar]
Pine ZB, Smith CW, Hollick SJ, Argall MR, Vasquez BJ, et al. 2020. Solar wind turbulence from 1 to 45 au. II. Analysis of inertial-range fluctuations using voyager and ACE observations. Astrophys J 900(2): 92. https://doi.org/10.3847/1538-4357/abab0f. [Google Scholar]
Potgieter MS, Le Roux JA, Burlaga LF, McDonald FB. 1993. The role of merged interaction regions and drifts in the heliospheric modulation of cosmic rays beyond 20 AU: A computer simulation. Astrophys J 403: 760–768. [Google Scholar]
Quenby J. 1984. The theory of cosmic-ray modulation. Space Sci Rev 176: 201–267. [Google Scholar]
Reinecke JPL, Potgieter MS. 1994. An explanation for the difference in cosmic ray modulation at low and neutron monitor energies during consecutive solar minimum periods. J Geophys Res: Space Phys 99(A8): 14 761–14 767. https://doi.org/10.1029/94JA00792, https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/94JA00792. [Google Scholar]
Reiners A, Basri G. 2008. The moderate magnetic field of the flare star Proxima Centauri. Astron Astrophys 489(3): L45–L48. https://doi.org/10.1051/0004-6361:200810491. [Google Scholar]
Richardson JD, Paularena KI, Wang C, Burlaga LF. 2002. The life of a CME and the development of a MIR: From the Sun to 58 AU. J Geophys Res: Space Phys 107(A4): SSH 1–1–SSH 1–9. https://doi.org/10.1029/2001JA000175, https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2001JA000175. [Google Scholar]
Rimmer PB, Helling C, Bilger C. 2014. The influence of galactic cosmic rays on ion-neutral hydrocarbon chemistry in the upper atmospheres of free-floating exoplanets. Int J Astrobiol 13(2): 173–181. https://doi.org/10.1017/S1473550413000487. [Google Scholar]
Rodgers-Lee D, Rimmer PB, Vidotto AA, Louca AJ, Taylor AM, et al. 2023. The energetic particle environment of a GJ 436 b-like planet. MNRAS 521(4): 5880–5891. https://doi.org/10.1093/mnras/stad900. [Google Scholar]
Rodgers-Lee D, Taylor AM, Vidotto AA, Downes TP. 2021. Stellar versus Galactic: The intensity of cosmic rays at the evolving Earth and young exoplanets around Sun-like stars. MNRAS 504(1): 1519–1530. https://doi.org/10.1093/mnras/stab935. [Google Scholar]
Rosén L, Kochukhov O, Hackman T, Lehtinen J. 2016. Magnetic fields of young solar twins. Astron Astrophys 593: A35. https://doi.org/10.1051/0004-6361/201628443. [Google Scholar]
Sadovski AM, Struminsky AB, Belov A. 2018. Cosmic rays near Proxima Centauri b. Astron Lett 44(5): 324–330. https://doi.org/10.1134/S1063773718040072. [Google Scholar]
Scherer K, Herbst K, Engelbrecht NE, Ferreira SES, Kleimann J, et al. 2025. Modeling the astrosphere of LHS 1140: On the differences of 3D magnetohydrodynamic single- and multi-fluid simulations and the consequences for exoplanetary habitability. Astron Astrophys 694: A106. https://doi.org/10.1051/0004-6361/202450324. [Google Scholar]
Scheucher M, Herbst K, Schmidt V, Grenfell JL, Schreier F, et al. 2020. Proxima Centauri b: A strong case for including cosmic-ray-induced chemistry in atmospheric biosignature studies. Astrophys J 893(1): 12. https://doi.org/10.3847/1538-4357/ab7b74. [Google Scholar]
See V, Jardine M, Vidotto AA, Donati J-F, Boro Saikia S, et al. 2016. The connection between stellar activity cycles and magnetic field topology. MNRAS 462(4): 4442–4450. https://doi.org/10.1093/mnras/stw2010. [Google Scholar]
Shalchi A. 2009. Nonlinear cosmic ray diffusion theories, vol. 362 of Astrophysics and Space Science Library. Springer, Berlin. https://doi.org/10.1007/978-3-642-00309-7. [Google Scholar]
Shalchi A, Bieber JW, Matthaeus WH. 2004. Analytic forms of the perpendicular diffusion coefficient in magnetostatic turbulence. Astrophys J 604(2): 675–686. https://doi.org/10.1086/382128. [Google Scholar]
Shapley H. 1951. Proxima Centauri as a flare star. Proc Natl Acad Sci USA 37(1): 15–18. http://www.jstor.org/stable/88208. [Google Scholar]
Shea M, Smart D. 1981. Preliminary search for cosmic radiation and solar-terrestrial parameters correlated with the reversal of the solar magnetic field. Adv Space Res 1(3): 147–150. https://doi.org/10.1016/0273-1177(81)90036-3, http://www.sciencedirect.com/science/article/pii/0273117781900363. [Google Scholar]
Simon Wedlund C, Gronoff G, Lilensten J, Ménager H, Barthélemy M. 2011. Comprehensive cal culation of the energy per ion pair or W values for five major planetary upper atmospheres. Ann Geophys 29(1): 187–195. [Google Scholar]
Smith CW, Isenberg PA, Matthaeus WH, Richardson JD. 2006. Turbulent heating of the solar wind by newborn interstellar pickup protons. Astrophys J 638(1): 508–517. https://doi.org/10.1086/498671. [Google Scholar]
Smith CW, Matthaeus WH, Zank GP, Ness NF, Oughton S, et al. 2001. Heating of the low-latitude solar wind by dissipation of turbulent magnetic fluctuations. J Geophys Res 106(A5): 8253–8272. https://doi.org/10.1029/2000JA000366. [Google Scholar]
Smith EJ. 2001a. The heliospheric current sheet. J Geophys Res 106(A8): 15 819–15 832. [Google Scholar]
Smith EJ. 2001b. The heliospheric current sheet. J Geophys Res 106(A8): 15 819–15 832. https://doi.org/10.1029/2000JA000120. [Google Scholar]
Stone EC, Cummings AC, McDonald FB, Heikkila BC, Lal N, et al. 2013. Voyager 1 observes low-energy galactic cosmic rays in a region depleted of heliospheric ions. Science 341(6142): 150–153. https://doi.org/10.1126/science.1236408. [Google Scholar]
Strauss RD, le Roux JA, Engelbrecht NE, Ruffolo D, Dunzlaff P. 2016. Non-axisymmetric perpendicular diffusion of charged particles and their transport across tangential magnetic discontinuities. Astrophys J 825(1) 43. https://doi.org/10.3847/0004-637X/825/1/43. [Google Scholar]
Strauss RD, Potgieter MS, Büsching I, Kopp A. 2012. Modelling heliospheric current sheet drift in stochastic cosmic ray transport models. Astrophys Space Sci 339(2): 223–236. [CrossRef] [Google Scholar]
Strauss RD, Potgieter MS, Kopp A, Büsching I. 2011. On the propagation times and energy losses of cosmic rays in the heliosphere. J Geophys Res Space Phys 116(A12): A12105. https://doi.org/10.1029/2011JA016831. [Google Scholar]
Strauss RDT, Effenberger F. 2017. A Hitch-hiker’s guide to stochastic differential equations. Solution methods for energetic particle transport in space physics and astrophysics. Space Sci Rev 212(1–2): 151–192. https://doi.org/10.1007/s11214-017-0351-y. [Google Scholar]
Strong AW, Moskalenko IV. 1998. Propagation of cosmic-ray nucleons in the galaxy. Astrophys J 509(1): 212–228. https://doi.org/10.1086/306470. [Google Scholar]
Suárez Mascareño A, Rebolo R, González Hernández JI. 2016a. Magnetic cycles and rotation periods of late-type stars from photometric time series. Astron Astrophys 595: A12. https://doi.org/10.1051/0004-6361/201628586. [Google Scholar]
Suárez Mascareño A, Rebolo R, González Hernández JI. 2016b. Magnetic cycles and rotation periods of late-type stars from photometric time series. Astron Astrophys 595: A12. https://doi.org/10.1051/0004-6361/201628586. [Google Scholar]
Teufel A, Schlickeiser R. 2003. Analytic calculation of the parallel mean free path of heliospheric cosmic rays. II. Dynamical magnetic slab turbulence and random sweeping slab turbulence with finite wave power at small wavenumbers. Astron Astrophys 397: 15–25. https://doi.org/10.1051/0004-6361:20021471. [Google Scholar]
Tinetti G, Eccleston P, Lueftinger T, Salvignol J-C, Fahmy S, et al. 2022. Ariel: Enabling planetary science across light-years. In European Planetary Science Congress, EPSC 2022–1114. https://doi.org/10.5194/epsc2022-1114. [Google Scholar]
Troskie JS, Engelbrecht NE, Steyn PJ. 2024. Cosmic-ray transport in the presence of a fisk-type heliospheric magnetic field: Investigating the influence of drift. Astrophys J 970(2): 144. https://doi.org/10.3847/1538-4357/ad517e. [Google Scholar]
Usoskin IG. 2023. A history of solar activity over millennia. Liv Rev Sol Phys 20(1): 2. https://doi.org/10.1007/s41116-023-00036-z. [Google Scholar]
van den Berg JP, Engelbrecht NE, Wijsen N, Strauss RD. 2021. On the turbulent reduction of drifts for solar energetic particles. Astrophys J 922(2): 200. https://doi.org/10.3847/1538-4357/ac2736. [Google Scholar]
Vida K, Oláh K, Kővári Z, van Driel-Gesztelyi L, Moór A, et al. 2019. Flaring activity of Proxima Centauri from TESS observations: Quasiperiodic oscillations during flare decay and inferences on the habitability of Proxima b. Astrophys J 884(2): 160. https://doi.org/10.3847/1538-4357/ab41f5. [Google Scholar]
Wang B-B, Bi X-J, Fang K, Lin S-J, Yin P-F. 2019. Time-dependent solar modulation of cosmic rays from solar minimum to solar maximum. Phys Rev D 100(6): 063006. https://doi.org/10.1103/PhysRevD.100.063006. [Google Scholar]
Wargelin BJ, Saar SH, Pojmański G, Drake JJ, Kashyap VL. 2017. Optical, UV, and X-ray evidence for a 7-yr stellar cycle in Proxima Centauri. MNRAS 464(3): 3281–3296. https://doi.org/10.1093/mnras/stw2570. [Google Scholar]
Webb DF, Howard TA. 2012. Coronal mass ejections: Observations. Liv Rev Sol Phys 9(1): 3. https://doi.org/10.12942/lrsp-2012-3. [Google Scholar]
Weygand JM, Matthaeus WH, Dasso S, Kivelson MG. 2011. Correlation and Taylor scale variability in the interplanetary magnetic field fluctuations as a function of solar wind speed. J Geophys Res Space Phys 116(A8): A08102. https://doi.org/10.1029/2011JA016621. [Google Scholar]
Wiengarten T, Fichtner H, Kleimann J, Kissmann R. 2015. Implementing turbulence transport in the CRONOS framework and application to the propagation of CMEs. Astrophys J 805(2): 155. https://doi.org/10.1088/0004-637X/805/2/155. [Google Scholar]
Winant A, Pierrard V, Botek E, Herbst K. 2023. The atmospheric influence on cosmic-ray-induced ionization and absorbed dose rates. Universe 9(12): 502. https://doi.org/10.3390/universe9120502, https://www.mdpi.com/2218-1997/9/12/502. [Google Scholar]
Yadav RK, Christensen UR, Wolk SJ, Poppenhaeger K. 2016. Magnetic cycles in a dynamo simulation of fully convective M-star Proxima Centauri. Astrophys J 833(2): L28. https://doi.org/10.3847/2041-8213/833/2/L28. [Google Scholar]
Zank GP, Matthaeus WH, Smith CW. 1996. Evolution of turbulent magnetic fluctuation power with heliospheric distance. J Geophys Res 101(A8): 17 093–17 108. https://doi.org/10.1029/96JA01275. [Google Scholar]
Zhang M. 1999. A Markov stochastic process theory of cosmic-ray modulation. Astrophys J 513(1), 409–420. https://doi.org/10.1086/306857. [Google Scholar]
Zhao LL, Adhikari L, Zank GP, Hu Q, Feng XS. 2018. Influence of the solar cycle on turbulence properties and cosmic-ray diffusion. Astrophys J 856(2): 94. https://doi.org/10.3847/1538-4357/aab362. [Google Scholar]
Zic A, Murphy T, Lynch C, Heald G, Lenc E, et al. 2020. A flare-type IV burst event from Proxima Centauri and implications for space weather. Astrophys J 905(1): 23. https://doi.org/10.3847/1538-4357/abca90. [Google Scholar]

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