Structure Formation with Dark Magnetohydrodynamics

TL;DR

This work investigates structure formation in a secluded dark sector with a massless dark photon by coupling gravity to magnetohydrodynamics. The authors derive an anisotropic Jeans criterion induced by a background dark magnetic field, leading to direction-dependent sound speeds and a modified growth of density perturbations, which in turn alters the linear matter power spectrum. They formulate a two-fluid dark plasma model (dark electrons/positrons) with a Chew-Goldberger-Low closure, derive the dispersion relation, and map the impact onto the isotropic power spectrum using Legendre multipoles, performing a χ^2 analysis against current and forecasted data. They find current constraints from CMB tensor modes dominate over linear-power measurements but show that forthcoming probes (CMB-HD lensing, HERA, EDGES) can test a wide range of dark charge-to-mass ratios and dark magnetic field strengths, potentially revealing halo-triaxiality signatures as a smoking gun of plasma-mediated dark structure formation.

Abstract

Long-range interactions in the dark sector can give rise to collective plasma phenomena that are capable of modifying the evolution of dark matter halos. We present the first study of gravitational collapse in a secluded dark $U(1)_D$ model using a magnetohydrodynamic description of the dark matter. We show that dark magnetic fields generate an anisotropic pressure that alters the Jeans scale and suppresses small-scale power in a direction-dependent manner. For a range of primordial magnetic spectral indices, this effect produces distinctive modifications to the linear matter power spectrum. We find that current observations cannot yet constrain viable dark magnetic fields, as CMB tensor modes mostly provide more stringent constraints. Nevertheless, forthcoming high-resolution probes of the matter power spectrum (CMB-HD lensing, HERA, and EDGES) will be able to test these predictions and are sensitive to dark charge-to-mass ratios in the range $10^{-20}\,\text{GeV}^{-1}\lesssim q_χ/m_χ\lesssim 10^{-14}\,\text{GeV}^{-1}$.

Figures (5)

• Figure 1: Constraints on the magnetic field strength at different comoving scales: $\lambda = 0.1$ Mpc (dark blue), 1 Mpc (medium blue), and 10 Mpc (light blue) at redshift $z=30$ as a function of spectral tilt of the magnetic power spectrum, $n$, reproduced from Ref. PhysRevD.61.043001.
• Figure 2: In the plots above, we show the perpendicular group velocity as a function of wavenumber. We set our reference scale for the magnetic field spectrum to be $\lambda = 0.1 \, h^{-1} \, \rm Mpc$. Left: The charge-to-mass ratio has been fixed to $10^{-16}\, \rm GeV^{-1}$ and we vary over different strengths of the dark magnetic field. Right: Here, the dark magnetic field has been fixed to $B_\lambda = 10^{-6}$ G and we vary over different charge-to-mass ratios.
• Figure 3: Here we show the isotropic power spectrum for a fixed charge-to-mass ratio, $q_\chi/m_\chi = 10^{-18}~~\text{GeV}^{-1}$, and a fixed background dark magnetic field value of $B_{\lambda} = 5\times10^{-9}~\rm{Gauss}$ for different spectral indices against the current measurements as well as future/planned surveys (see text for details). We plot using different colored dotted lines to denote various scenarios of a background dark magnetic field, based on constraints derived in the previous section.
• Figure 4: Here we show the transfer function at a fixed charge-to-mass ratio, $q_\chi/m_\chi = 10^{-18}~~\text{GeV}^{-1}$, and a fixed background dark magnetic field value of $B_{\lambda} = 5\times10^{-9}~\rm{Gauss}$ for different spectral indices. We have overlaid current measurements and future/planned surveys (see text for details).
• Figure 5: Here we show the resultant parameter space for scans using our effective group velocity Eq. \ref{['eq:cs-final']} to grow the linear density modes via Eq. \ref{['eq:lin-eq']} for current (shaded regions) and future (dashed lines) measurements of the linear matter power spectrum shown in Fig. \ref{['fig:power-spectrum-P0']} (see text for the data details). The region shown in pink is excluded at the $1\sigma$ level, the purple is excluded at the $2\sigma$ level, and the red region is excluded by a minimum of $3\sigma$. We also show constraint regions from the CMB PhysRevD.61.043001 (blue), Bullet Cluster Giffin (green), and the Weak Gravity Conjecture (yellow) Arkani_Hamed_2007.