Evolution of the magnetic field in spatially inhomogeneous axion structures

M. S. Dvornikov   ; P. M. Akhmet'ev

Teoretičeskaâ i matematičeskaâ fizika, Tome 218 (2024) no. 3, pp. 601-618

Résumé

We study the time evolution of magnetic fields in various configurations of spatially inhomogeneous pseudoscalar fields that are a coherent superposition of axions. For such systems, we derive a new induction equation for the magnetic field, which takes this inhomogeneity into account. Based on this equation, we study the evolution of a pair of Chern–Simons waves interacting with a linearly decreasing pseudoscalar field. The nonzero gradient of the pseudoscalar field leads to the mixing of these waves. We then consider the problem in a compact domain in the case where the initial Chern–Simons wave is mirror symmetric. The pseudoscalar field inhomogeneity then leads to an effective change in the $\alpha$ dynamo parameter. Thus, the influence of a spatially inhomogeneous pseudoscalar field on the magnetic field evolution bears a strong dependence on the system geometry.

Détail

Mots-clés : axion star
Keywords: dark matter, asymptotic ergodic Hopf invariant, magnetic hydrodynamics.

Bibliographie

[1] R. D. Peccei, H. R. Quinn, “CP conservation in the presence of pseudoparticles”, Phys. Rev. Lett., 38:25 (1977), 1440–1443 | DOI

[2] L. D. Duffy, K. van Bibber, “Axions as dark matter particles”, New J. Phys., 11:10 (2009), 105008, 21 pp., arXiv: 0904.3346 | DOI

[3] Y. K. Semertzidis, S. Youn, “Axions dark matter: how to see it?”, Sci. Adv., 8:8 (2022), eabm9928, 13 pp., arXiv: 2104.14831 | DOI

[4] G. Galanti, M. Roncadelli, “Axion-like particles implications for high-energy astrophysics”, Universe, 8:5 (2022), 253, 72 pp., arXiv: 2205.00940 | DOI

[5] D. J. E. Marsh, “Axion cosmology”, Phys. Rep., 643 (2016), 1–79, arXiv: 1510.07633 | DOI | MR

[6] J. Barranco, A. Bernal, “Self-gravitating system made of axions”, Phys. Rev. D, 83:4 (2011), 043525, 5 pp., arXiv: 1001.1769 | DOI

[7] E. W. Kolb, I. I. Tkachev, “Axion miniclusters and Bose stars”, Phys. Rev. Lett., 71:19 (1993), 3051–3054, arXiv: hep-ph/9303313 | DOI

[8] J. Enander, A. Pargner, T. Schwetz, “Axion minicluster power spectrum and mass function”, J. Cosmol. Astropart. Phys., 2017:12 (2017), 038, arXiv: 1708.04466 | DOI

[9] L. Visinelli, J. Redondo, “Axion miniclusters in modified cosmological histories”, Phys. Rev. D, 101:2 (2020), 023008, 28 pp., arXiv: 1808.01879 | DOI

[10] M. Yu. Khlopov, A. S. Sakharov, D. D. Sokoloff, “The nonlinear modulation of the density distribution in standard axionic CDM and its cosmological impact”, Nucl. Phys. B, Proc. Suppl., 72 (1999), 105–109, arXiv: hep-ph/9812286 | DOI

[11] A. V. Sokolov, A. Ringwald, Electromagnetic couplings of axions, arXiv: 2205.02605

[12] K. Choi, S. H. Im, C. S. Shin, “Recent progress in the physics of axions and axion-like particles”, Ann. Rev. Nucl. Part. Sci., 71 (2021), 225–252, arXiv: 2012.05029 | DOI

[13] A. Long, T. Vachaspati, “Implications of a primordial magnetic field for magnetic monopoles, axions, and Dirac neutrinos”, Phys. Rev. D, 91:10 (2015), 103522, 12 pp., arXiv: 1504.03319 | DOI

[14] M. Dvornikov, V. B. Semikoz, “Evolution of axions in the presence of primordial magnetic fields”, Phys. Rev. D, 102:12 (2020), 123526, 9 pp., arXiv: 2011.12712 | DOI | MR

[15] J.-C. Hwang, H. Noh, “Axion electrodynamics and magnetohydrodynamics”, Phys. Rev. D, 106:2 (2022), 023503, 8 pp., arXiv: 2203.03124 | DOI | MR

[16] M. Dvornikov, “Interaction of inhomogeneous axions with magnetic fields in the early universe”, Phys. Lett. B, 829 (2022), 137039, 7 pp., arXiv: 2201.10586 | DOI | MR

[17] F. Anzuini, J. A. Pons, A. Gómez-Bañón, P. D. Lasky, F. Bianchini, A. Melatos, “Magnetic dynamo caused by axions in neutron stars”, Phys. Rev. Lett., 130:7 (2023), 071001, 7 pp., arXiv: 2211.10863 | DOI | MR

[18] E. Braaten, H. Zhang, “Colloquium: The physics of axion stars”, Rev. Mod. Phys., 91:4 (2019), 041002, 22 pp., arXiv: 2211.10863 | DOI | MR

[19] V. I. Arnold, B. A. Khesin, Topological Methods in Hydrodynamics, Applied Mathematical Sciences, 125, Springer, New York, 2021 | DOI | MR

[20] P. M. Akhmet'ev, S. Candelaresi, A. Y. Smirnov, “Minimum quadratic helicity states”, J. Plasma Phys., 84:6 (2018), 775840601, 16 pp., arXiv: 1806.07428 | DOI

[21] A. M. Kamchatov, “Topologicheskie solitony v magnitogidrodinamike”, ZhETF, 82:1 (1982), 117–124 | MR

[22] G. Hornig, C. Mayer, “Towards a third-order topological invariant for magnetic fields”, J. Phys. A: Math. Gen., 35:17 (2002), 3945–3959, arXiv: physics/0203048 | DOI | MR

[23] P. M. Akhmet'ev, I. V. Vyugin, “Dispersion of the Arnold's asymptotic ergodic Hopf invariant and a formula for its calculation”, Arnold Math. J., 6:2 (2020), 199–211, arXiv: 1906.12131 | DOI | MR

[24] E. A. Kudryavtseva, “Spiralnost – edinstvennyi invariant neszhimaemykh techenii s nepreryvnoi v $C^1$-topologii proizvodnoi”, Matem. zametki, 99:4 (2016), 626–630, arXiv: 1511.03746 | DOI | DOI | MR

[25] V. Z. Grines, L. M. Lerman, “Neavtonomnaya dinamika: klassifikatsiya, invarianty, realizatsiya”, Differentsialnye i funktsionalno-differentsialnye uravneniya, SMFN, 68, no. 4, Rossiiskii universitet druzhby narodov, M., 2022, 596–620 | DOI | MR

[26] A. Brandenburg, K. Enqvist, P. Olesen, “Large-scale magnetic fields from hydromagnetic turbulence in the very early universe”, Phys. Rev. D, 54:2 (1996), 1291–1300, arXiv: astro-ph/9602031 | DOI

[27] L. Husdal, “On effective degrees of freedom in the early Universe”, Galaxies, 4:4 (2016), 78, 28 pp., arXiv: 1609.04979 | DOI

[28] L. Visinelli, “Boson stars and oscillatons: A review”, Internat. J. Modern Phys. D, 30:15 (2021), 2130006, 48 pp., arXiv: 2109.05481 | DOI | MR

[29] P. Charbonneau, “Dynamo models of the solar cycle”, Living Rev. Solar Phys., 17 (2020), 4, 104 pp. | DOI

[30] A. V. Gruzinov, P. H. Diamond, “Self-consistent theory of mean-field electrodynamics”, Phys. Rev. Lett., 72:11 (1994), 1651–1653 | DOI

[31] Y. Bai, Y. Hamada, “Detecting axion stars with radio telescopes”, Phys. Lett. B, 781 (2018), 187–194, arXiv: 1709.10516 | DOI

[32] M. Buschmann, C. Dessert, J. W. Foster, A. J. Long, B. R. Safdi, “Upper limit on the QCD axion mass from isolated neutron star cooling”, Phys. Rev. Lett., 128:9 (2022), 091102, 9 pp., arXiv: 2111.09892 | DOI

[33] F. Chadha-Day, J. Ellis, D. J. E. Marsh, “Axion dark matter: What is it and why now?”, Sci. Adv., 8:8 (2022), eabj3618, 20 pp., arXiv: 2105.01406 | DOI

[34] P. M. Akhmetev, “Potok magnitnoi spiralnosti dlya uravnenii srednego magnitnogo polya”, TMF, 204:1 (2020), 130–141 | DOI | DOI | MR

[35] P. M. Akhmet'ev, S. Candelaresi, A. Yu. Smirnov, “Calculations for the practical applications of quadratic helicity in MHD”, Phys. Plasmas, 24:10 (2017), 102128, 9 pp., arXiv: 1710.08833 | DOI

[36] D. G. Levkov, A. G. Panin, I. I. Tkachev, “Gravitational Bose–Einstein condensation in the kinetic regime”, Phys. Rev. Lett., 121:15 (2018), 151301, 5 pp., arXiv: 1804.05857 | DOI

[37] P. Jain, S. Panda, S. Sarala, “Electromagnetic polarization effects due to axion-photon mixing”, Phys. Rev. D, 66:8 (2002), 085007, 9 pp., arXiv: hep-ph/0206046 | DOI

[38] G. G. Raffelt, “Axion-photon oscillations. Mixing equations”, Stars as Laboratories for Fundamental Physics. Stars as Laboratories for Fundamental Physics: The Astrophysics of Neutrinos, Axions, and Other Weakly Interacting Particles, University of Chicago Press, Chicago, 1996, 179–181

[39] D. Harari, P. Sikivie, “Effects of a Nambu–Goldstone boson on the polarization of radio galaxies and the cosmic microwave background”, Phys. Lett. B, 289:1–2 (1992), 67–72 | DOI