Charged Dark Matter: Constraints & Phenomenology

• Charged dark matter is defined as particles with a small electric charge that interact electromagnetically, affecting early-universe density perturbations and the CMB.
• Astrophysical analyses leverage CMB anisotropies, BAO spectra, and galactic magnetic shielding to tightly bound the charge-to-mass ratio of these particles.
• Composite 'dark atom' models bind charged particles with ordinary nuclei, evading direct detection while offering distinct signatures through nuclear interactions.

Charged dark matter particles are hypothetical dark sector constituents that carry electric charge—often much smaller than the electron charge—allowing them to interact electromagnetically in addition to having gravitational interactions. These particles, also referred to as CHAMPs (Charged Massive Particles) or millicharged dark matter, are subject to stringent astrophysical, cosmological, and laboratory constraints due to their electromagnetic couplings. Theoretical models span a wide range: from fundamental particles acquiring a small electric charge through kinetic mixing, to composite states where stable charged species bind with baryonic or exotic nuclei to form neutral "dark atoms." Their phenomenology is governed by their charge-to-mass ratio, astrophysical environment, and possible late-universe dynamical processes.

1. Electromagnetic Charge Constraints from Structure Formation and the Cosmic Microwave Background

The presence of an electric charge on dark matter directly affects its coupling to the photon-baryon fluid in the early universe. This alters the evolution of cosmological density perturbations, especially during and prior to the epoch of recombination. Coulomb interactions between charged dark matter and baryons mediate momentum and energy exchange, leading to tight coupling that would erase dark matter density fluctuations via Silk damping. This effect produces observable modifications to cosmic microwave background (CMB) anisotropies and the baryon acoustic oscillation spectrum.

The coupling is quantitatively characterized by a momentum transfer rate $\Gamma_p$, which must satisfy the criterion $\Gamma_p^{-1}(T_R) > t_R$ at recombination ($t_R \simeq 3.8 \times 10^5$ years) to avoid excessive damping of small-scale perturbations. For dark matter mass $m_X$, the upper bound on the fractional electric charge $\epsilon$ is:

• $\epsilon \lesssim 10^{-6}$ for $m_X = 1\ \mathrm{GeV}$
• $\epsilon \lesssim 10^{-4}$ for $m_X = 10\ \mathrm{TeV}$

Heavier dark matter permits a larger charge to have equivalent plasma coupling, as the Coulomb scattering rate scales inversely with $m_X$ (McDermott et al., 2010). For CHAMPs or millicharged dark matter, this cosmological bound is general; for millicharged models, the constraint is typically stated as $$m_{\mathrm{Ch}} / \epsilon^2 \gtrsim 10^{11}\ \mathrm{GeV}$$ (Kamada et al., 2016).

2. Galactic Magnetic Fields, Supernovae, and Evacuation from the Galactic Disk

The local abundance of charged dark matter is governed by galactic and interstellar processes, notably the Milky Way's large-scale magnetic field and supernova shock waves. Charged particles gyrate in magnetic fields, with a characteristic radius:

$$R_g \simeq 5.4 \times 10^{-11}\ \mathrm{pc}\ \left(\frac{m_X}{1~\mathrm{GeV}}\right) \frac{1}{\epsilon} \left( \frac{v_X}{270~\mathrm{km/s}} \right) \left( \frac{5~\mu\mathrm{G}}{B} \right)$$

When $R_g \ll H_d$ (disk height, $H_d\simeq 100~\mathrm{pc}$), the Galactic disk acts as a magnetic barrier, making it difficult for charged dark matter from the halo to enter the disk. This leads to a magnetic shielding condition:

$$\epsilon > 5.4 \times 10^{-13} \left(\frac{m_X}{\mathrm{GeV}}\right)$$

which implies for typical masses that even minuscule charges exclude disk penetration (McDermott et al., 2010).

Supernova shock waves accelerate any remaining charged particles (via Fermi acceleration), expelling them unless they cool rapidly via interactions with ambient electrons. Efficient evacuation occurs if the cooling time is shorter than the acceleration time ($\tau_{\mathrm{cool}} < \tau_{\mathrm{acc}}$), imposing constraints as strong as:

$$\epsilon \lesssim 3.4 \times 10^{-4} \sqrt{m_X / \mathrm{GeV}}$$

for survival in the disk environment.

Table: Evacuation and Shielding Criteria

Constraint Type	Formula	Typical Effect
Magnetic shielding	$\epsilon > 5.4 \times 10^{-13} (m_X/\mathrm{GeV})$	No disk entry
Supernova shock blowout	$$\epsilon \lesssim 3.4\times 10^{-4} \sqrt{m_X/\mathrm{GeV}}$$	Efficient evacuation
Turbulent diffusion	$$\epsilon \lesssim 9\times 10^{-12} (m_X/\mathrm{GeV})$$	Poor disk replenishment

Even if magnetic turbulence is invoked to replenish charged dark matter in the disk, the threshold for meaningful replenishment typically yields $$\epsilon \lesssim 9\times 10^{-12} (m_X/\mathrm{GeV})$$—orders of magnitude too small for signals in current direct detection experiments.

3. Phenomenology in Direct Detection and Astrophysical Experiments

The differential cross section for non-relativistic Coulomb (Rutherford) scattering is highly velocity-enhanced:

$$\frac{d\sigma}{d\Omega} \propto \frac{\epsilon^2}{v_{\mathrm{rel}}^{4}\, \sin^4(\theta^*/2)}$$

The $v^{-4}$ enhancement implies, naively, that even millicharges far below the cosmological bound could generate large recoil signals in underground direct detection setups. However, due to the astrophysical evacuation of charged dark matter from the disk, the expected local number density is highly suppressed for all values of $\epsilon$ that would be detectable. This phenomenon precludes positive signals in standard direct detection tasks, and models invoking millicharged dark matter to explain signals such as DAMA or CoGeNT are robustly disfavored (McDermott et al., 2010).

4. Charged Composite Dark Matter and "Dark Atoms"

A class of models circumvents direct electromagnetic constraints by binding stable charged particles (typically with charge $-2e$) with ordinary helium nuclei to form neutral composite objects ("O-helium"), effectively hiding the charge inside a neutral atomic bound state (Khlopov, 2010, Khlopov, 2011, Khlopov, 2014, Khlopov, 2015). The generic binding energy and radius are:

• $$I_o = (Z_X^2 Z_{He}^2 \alpha^2 m_{\rm He})/2 \sim 1$$ MeV
• $$R_o = 1/(Z_X Z_{He} \alpha m_{He}) \sim 2 \times 10^{-13}$$ cm

These "dark atoms" are elusive to electromagnetic searches but can interact with ordinary matter via nuclear forces, potentially producing distinctive signals in detectors optimized for radiative capture rather than nuclear recoil, such as explaining the annual modulation seen by DAMA/LIBRA. Formation of anomalous isotopes is avoided by excluding stable $+1$ or $-1$ charged species.

Composite models require stable $-2$ charged constituents (from exotic leptons, technibaryons, or heavy quark clusters) and resolve many constraints through the neutralization mechanism, decoupling the predicted signatures from those of weakly or millicharged particles.

5. Large-Scale Astrophysical and Cosmological Constraints

Charged dark matter also induces cumulative effects on galactic dynamics. Charged particles traversing coherent, large-scale magnetic fields in spiral galaxies experience Lorentz forces, facilitating momentum transfer between the ISM and the dark halo. Over giga-year timescales, this results in torque on the galactic disk, potentially spinning down the ISM if the charge-to-mass ratio is too large. This yields an astrophysical upper bound:

$$\frac{q}{mc^2} \lesssim 3.5 \times 10^{-13 \pm 1} \frac{e}{\mathrm{GeV}}$$

for a dominant charged component (Stebbins et al., 2019). The limit weakens as the charged fraction $f_{\rm qdm}$ decreases, but for $f_{\rm qdm} \gtrsim 0.13$ the constraint remains significant.

Furthermore, charged dark matter is constrained by its possible effects on the cosmic microwave background, both through the kinetic re-coupling phenomenon that can affect acoustic oscillations at and after recombination, and through modification of the early integrated Sachs-Wolfe effect. For CHAMPs or millicharged particles, the precise bound is $$m_{\rm Ch}/\epsilon^2 \gtrsim 10^{11}\ \mathrm{GeV}$$, limiting the allowed parameter space for such models (Kamada et al., 2016).

6. Cosmic Ray and Laboratory Probes

Charged dark matter, especially in the context of millicharged particles, can be subject to acceleration in astrophysical shocks, generating "dark cosmic rays." These particles can be searched for as anomalous muon-like or neutrino-like events in Cherenkov detectors such as Super-Kamiokande and IceCube. The maximum energy, spectral properties, and detection signature scale with the millicharge parameter $\epsilon$ (Hu et al., 2016). Strong constraints on $\epsilon$ in the $10^{-2}$ to $10^{-5}$ range for masses spanning 1–100 GeV are obtained from non-observation of such signals.

Advanced laboratory setups have proposed searching for millicharged particles bound inside bulk matter by using optomechanical systems (levitated nanospheres in optical cavities under electrostatic fields). These setups can test for quantum effects such as output light squeezing and mechanical-optical entanglement, providing sensitivity to extremely small charges ($\epsilon \sim 10^{-5}$–$10^{-10}$) (Asjad et al., 2023).

7. Galactic Magnetic Shielding: Controversy and Clarification

It was previously hypothesized that the Galactic magnetic field could shield the Earth from heavy charged dark matter with insufficiently large gyroradius—creating a lower mass bound for detectability by Earth-based searches. However, this claim was shown to arise from oversimplified (infinite, uniform) magnetic field models. Realistic, finite, and divergence-free models such as the JF12 or toroidal field accurately implemented in trajectory simulations (e.g., using CRPropa) reveal that CHAMPs in the debated mass range ($100(q_X/e)^2$ TeV $\leq m_X \leq 10^8(q_X/e)$ TeV) can reach the Earth from the halo for all physically reasonable field configurations. Consequently, terrestrial direct detection experiments are sensitive to the full CHAMP parameter space, and the "blind window" does not exist (Perri et al., 19 Oct 2025).

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In summary, the parameter space for charged dark matter is strongly constrained by CMB anisotropies, structure formation damping, Galactic disk evacuation by electromagnetic processes, and cumulative galactic torque effects. For models based on composite "dark atoms" with shielded charge, these constraints are partially circumvented, motivating complementary collider and astrophysical searches. No strong claim for observable direct detection signals from electromagnetically charged dark matter (in the relevant range for direct detection) survives the combined cosmological and galactic constraints. The field continues to develop new experimental and observational strategies for probing subdominant charged relics, forbidden or hidden sectors, and exotic signatures beyond the neutral WIMP paradigm.