Plasma Constraints on the Millicharged Dark Matter

Dark matter particles were suggested to have an electric charge smaller than the elementary charge unit $e$. The behavior of such a medium is similar to a collisionless plasma. In this paper, we set new stringent constraints on the charge and mass of the millicharged dark matter particle based on observational data on the Bullet X-ray Cluster.

💡 Research Summary

The paper investigates constraints on millicharged dark‑matter (DM) particles—those carrying an electric charge qχ = εe with ε < 1—by exploiting the unique astrophysical environment of the Bullet X‑ray Cluster (1E 0657‑56). The authors begin by reviewing existing laboratory and cosmological limits (ion‑trap experiments, collider searches, XENON100, Planck CMB data, BBN, SN 1987A, etc.) and note that a sizable region of the charge‑to‑mass parameter space remains viable. They then focus on the Bullet Cluster, a merging system where two sub‑clusters have collided at a relative velocity of roughly 4000 km s⁻¹, producing a clear separation of about 0.3 Mpc between the collisionless components (dark matter and galaxies) and the collisional hot intracluster gas. The intracluster magnetic field is of order a micro‑gauss and is largely turbulent.

Two independent physical arguments are used to derive new upper bounds on the millicharge. The first argument concerns the Larmor radius rL = v mχc/(qχB). For the dark‑matter particles to traverse the observed offset without being magnetically trapped, the Larmor radius must exceed the centroid separation d_c. This yields the inequality

 qχ/e ≲ 5 × 10⁻¹⁴ (mχ/GeV) (d_c/0.3 Mpc)⁻¹ (v/4000 km s⁻¹) (B/1 µG)⁻¹.

The second argument exploits the fact that a millicharged DM component behaves as a collisionless plasma. When two plasma blobs collide, kinetic instabilities (Weibel, Buneman, two‑stream) grow on the plasma skin depth λχ = c/ωp,χ, where ωp,χ ≈ √(4π qχ² nχ/mχ) and nχ is the DM number density within the cluster. The authors estimate nχ from the cluster overdensity δ_c ≈ 10⁴–2 × 10⁴, inferred from lensing mass maps. If λχ were smaller than the observed offset, the instabilities would generate density and magnetic‑field inhomogeneities that should be visible in high‑resolution lensing maps. Their absence therefore requires λχ ≳ d_c, leading to

 qχ/e ≲ 10⁻¹⁶ (mχ/GeV) (d_c/0.3 Mpc)⁻¹ δ_c⁻¹/².

Both constraints are plotted in Figure 1 and are labeled “Bullet Cluster, Larmor” and “Bullet Cluster, skin length”. They are independent of each other: the Larmor bound depends on the magnetic‑field strength, while the skin‑length bound depends only on the DM overdensity. Compared with existing limits, these new bounds are orders of magnitude stronger for DM masses above ∼1 GeV, tightening the allowed charge‑to‑mass ratio to qχ/mχ ≲ 10⁻¹⁴ e/GeV (Larmor) and qχ/mχ ≲ 10⁻¹⁶ e/GeV (skin length).

The authors also discuss the applicability of their results to particles with charges larger than the electron charge, such as multiply‑charged primordial black holes. For a black hole of mass ∼10¹⁷ g (≈10⁴¹ GeV), the charge acquired by immersion in the hot intracluster plasma is estimated to be q_bh ≈ 0.8 e · (T/10⁸·³ K)·(m_bh/10¹⁷ g)¹ᐟ², far below the Bullet‑Cluster limits, indicating that the constraints are not restrictive for such objects.

In the discussion, the authors emphasize that despite arising from different physics (magnetic deflection versus plasma instability), both constraints effectively bound the same combination qχ/mχ. They suggest that future high‑resolution magnetohydrodynamic and kinetic plasma simulations of cluster collisions could refine the estimates of instability growth and verify the robustness of the skin‑length argument. Overall, the paper provides a novel astrophysical probe that significantly narrows the viable parameter space for millicharged dark matter.