A natural explanation of the Galactic Magnetic Fields from multistate Scalar Field Dark Matter

TL;DR

The paper investigates whether microgauss galactic magnetic fields can originate from a complex scalar-field dark matter (SFDM) halo endowed with a local $U(1)$ charge. By formulating a perturbative, coupled scalar–gauge-field framework on an expanding background and decomposing perturbations into spherical Bessel and harmonic modes, the authors show that the induced magnetic field inherits the same $j_k(l r)$ and $Y_k^m(\theta,\phi)$ structure that describes the multistate SFDM halo, while leaving the dark-matter density profile intact. They derive explicit expressions for the electric and magnetic fields in terms of mode amplitudes and time evolution $T_R(\eta)$, and they solve the background cosmology to ensure consistency with the standard thermal history. Applying the model to the Milky Way, Andromeda, and Centaurus A, they obtain $\mu$G-scale fields with dipolar features associated with the first excited SFDM state, and show that magnetic fields can arise without primordial seeds or dynamos. Overall, the work links the quantum structure of SFDM halos to large-scale galactic magnetism and VPOS-like anisotropies, offering a unified, testable dark-matter framework.

Abstract

In this article, we investigate the possibility that the large-scale magnetic fields observed in galaxies, of the order of microgauss, arise naturally from a complex Scalar Field Dark Matter (SFDM) halo charged under a local $U(1)$ symmetry. Extending our previous work, where multistate SFDM solutions were shown to form ``gravitational atoms'' capable of explaining the anisotropic distribution of satellite galaxies (VPOS), we analyze here the coupled dynamics of the scalar and a gauge field at the perturbative level. By solving the perturbed Klein-Gordon and gauge-field equations, we find the temporal evolution and show that the spatial structure of the induced electromagnetic fields is governed by the same spherical Bessel functions and spherical harmonics that characterize the ground and excited states of the multi-state SFDM halo. Remarkably, the presence of the gauge field does not modify the dark-matter density distribution, which preserves the multi-state configuration previously obtained. Our results demonstrate that a charged multi-state SFDM halo can generate coherent, large-scale magnetic fields whose morphology is determined by the excited modes of the scalar field, providing a unified framework in which both galactic magnetic fields and VPOS-like structures originate from the underlying quantum nature of dark matter.

Figures (5)

• Figure 1: Radial dependence of the first two spherical Bessel functions, $j_0(x)$ (left) and $j_1(x)$ (right). The function $j_0$ corresponds to the spherically symmetric ground state, while $j_1$ vanishes at the origin and describes the first excited, dipolar-like mode that plays a central role in the multistate SFDM halo and the associated gauge-field configurations.
• Figure 2: Evolution of the density parameters with respect to the scale factor, $a$. $\Omega_{\Phi}$ is the density parameter of the SFDM.
• Figure 3: Galactic magnetic field of the Milky Way generated by the charged multistate SFDM halo at the present epoch ($a=1$), shown on physical galactic scales. Upper left panel: The magnetic field is sampled on a Cartesian grid within a cubic domain of side $16$ kpc (a volume of 4096 kpc$^3$) and only points satisfying $5\leq r\leq10$ kpc are displayed. Upper right panel: magnetic field configuration at a fixed radius of $6$ kpc. Bottom left panel: magnetic field at a radius of $12$ kpc. Bottom right panel: magnetic field structure at different galactocentric radii. The field amplitude is expressed in microgauss units, allowing for direct comparison with observational estimates. The spatial coherence over kiloparsec scales reflects the underlying spherical Bessel modes of the scalar-field perturbations, while the angular structure follows from the spherical harmonic decomposition. In particular, the last panel exhibits a dipolar-like pattern, consistent with the two-lobed structure associated with the first excited state of the scalar field. For parameter values compatible with realistic halo sizes and rotation curves, the magnetic field naturally reaches amplitudes of the order of microgauss, without requiring additional amplification mechanisms.
• Figure 4: Galactic magnetic field of Andromeda generated by the charged multistate SFDM halo at the present epoch ($a=1$). Upper left side: The magnetic field is sampled on a Cartesian grid within a cubic domain of side $16$ kpc (a volume of 4096 kpc$^3$) and only points satisfying $5\leq r\leq10$ kpc are displayed. Upper right side: Galactic magnetic field at a radius of $6$ Kpc. Bottom left side: Magnetic field of Andromeda at a radius of $12$ kpc. Bottom right side: Magnetic field of Andromeda at different radii. This last panel exhibits a dipolar-like pattern, consistent with the two-lobed structure associated with the first excited state of the scalar field.
• Figure 5: Galactic magnetic field of Centaurus A generated by the charged multistate SFDM halo at the present epoch ($a=1$). Upper left side: The magnetic field is sampled on a Cartesian grid within a cubic domain of side $16$ kpc (a volume of 4096 kpc$^3$) and only points satisfying $5\leq r\leq10$ kpc are displayed. Upper right side: Galactic magnetic field at a radius of $6$ kpc. Bottom left side: Magnetic field of Centaurus A at a radius of $12$ kpc. Bottom right side: Magnetic field of Centaurus A at different radii. This last panel exhibits a dipolar-like pattern, consistent with the two-lobed structure associated with the first excited state of the scalar field.