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The window on heavy charged dark matter was never open

Daniele Perri, Glennys Farrar

TL;DR

The paper readdresses the proposed CHAMP window in the mass range $m_X$ between $100 (q_{ m X}/e)^2$ TeV and $10^8 (q_{ m X}/e)$ TeV, arguing that the conclusion depends crucially on the assumed GMF geometry. Using CRPropa, it simulates heavy charged dark matter trajectories in three physically motivated GMF models (toroidal, JF12, and finite-size uniform) and demonstrates that CHAMPs can reach the Earth from outside the disk when the GMF is finite and divergence-free. The results contradict the prior claim that such CHAMPs are excluded from entering the Galactic disk, showing that that window is not generic but model-dependent. This work underscores the importance of using physically realistic GMF configurations when assessing direct-detection prospects for charged dark matter and clarifies how magnetic-field geometry and gyroradius affect particle ingress and angular distributions.

Abstract

There is a claim in the literature that charged dark matter particles in the mass range $100 (q_{\rm X}/e)^2~\mathrm{TeV} \leq m_{\rm X} \leq 10^8 (q_{\rm X}/e)~\mathrm{TeV}$ are allowed, based on arguing that heavy charged particles cannot reach the Earth from outside the magnetized region of the Milky Way (Chuzhoy-Kolb, 2009). We point out that this claim fails for physical models for the Galactic magnetic field. We explicitly confirm our argument by simulating with the software CRPropa the trajectories of heavy charged dark matter in models of the Galactic magnetic field.

The window on heavy charged dark matter was never open

TL;DR

The paper readdresses the proposed CHAMP window in the mass range between TeV and TeV, arguing that the conclusion depends crucially on the assumed GMF geometry. Using CRPropa, it simulates heavy charged dark matter trajectories in three physically motivated GMF models (toroidal, JF12, and finite-size uniform) and demonstrates that CHAMPs can reach the Earth from outside the disk when the GMF is finite and divergence-free. The results contradict the prior claim that such CHAMPs are excluded from entering the Galactic disk, showing that that window is not generic but model-dependent. This work underscores the importance of using physically realistic GMF configurations when assessing direct-detection prospects for charged dark matter and clarifies how magnetic-field geometry and gyroradius affect particle ingress and angular distributions.

Abstract

There is a claim in the literature that charged dark matter particles in the mass range are allowed, based on arguing that heavy charged particles cannot reach the Earth from outside the magnetized region of the Milky Way (Chuzhoy-Kolb, 2009). We point out that this claim fails for physical models for the Galactic magnetic field. We explicitly confirm our argument by simulating with the software CRPropa the trajectories of heavy charged dark matter in models of the Galactic magnetic field.
Paper Structure (10 sections, 8 equations, 5 figures)

This paper contains 10 sections, 8 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Charged dark matter in the Galactic disk
  3. Models of the Galactic Magnetic Field
  4. Gyromagnetic radius of CHAMPs
  5. Simulation of the trajectories with CRPropa
  6. Back-tracking uniform distributions at the Earth surface
  7. Angular distribution of CHAMPs at the Earth
  8. Discussion of the results
  9. Conclusion
  10. Estimate of the number of particle reaching an observer from an incoming Lambert distribution

Figures (5)

  • Figure 1: Models of the Galactic magnetic field in the $xy$-plane. (a): toroidal magnetic field as in Eq. \ref{['eq:toroidal']} with $R_1 = 5~\mathrm{kpc}$ and $R_2 = 8~\mathrm{kpc}$; (b): disk component of the solenoidal JF12 model as in Kleimann_2019; (c): finite version of the uniform magnetic field model adopted in Chuzhoy:2008zy as in Eq. \ref{['eq:uniform']} with $R = 5~\mathrm{kpc}$ and $R' = 10~\mathrm{kpc}$.
  • Figure 2: Trajectories of CHAMPs with mass $10^7$ TeV and velocity $10^{-3} c$ that reach the Earth with an isotropic distribution. Here we show the simulation of 9 particles for three different models of the Galactic magnetic field: (a) toroidal solenoid in Eq. \ref{['eq:toroidal']} with $B_{\rm toro} = 2 \times 10^{-6}~\mathrm{G}$, $R_1 = 5~\mathrm{kpc}$, $R_2 = 8.5~\mathrm{kpc}$, (b) JF12 model Jansson_2012Kleimann_2019, (c) finite uniform model in \ref{['eq:uniform_finite']} with $B_{\rm homo} = 2 \times 10^{-6}~\mathrm{G}$, $R = 5~\mathrm{kpc}$, $R' = 10~\mathrm{kpc}$.
  • Figure 3: Trajectories of heavy charged particles with mass $10^7$ TeV and velocity $10^{-1} c$ that reach the Earth with an isotropic distribution. Here we show the simulation of 9 particles for three different models of the Galactic magnetic field: (a) toroidal solenoid in Eq. \ref{['eq:toroidal']} with $B_{\rm toro} = 2 \times 10^{-6}~\mathrm{G}$, $R_1 = 5~\mathrm{kpc}$, $R_2 = 8.5~\mathrm{kpc}$, (b) finite uniform model in \ref{['eq:uniform_finite']} with $B_{\rm homo} = 2 \times 10^{-6}~\mathrm{G}$, $R = 5~\mathrm{kpc}$, $R' = 10~\mathrm{kpc}$.
  • Figure 4: Angular distribution of the incoming particles on Earth, assuming a Lambert distribution on the surface of a sphere of radius $20~\mathrm{kpc}$ and propagating through the fully divergence-free version of the JF12 magnetic field model of Kleimann_2019 with an initial sample of $10^8$ particles. The light blue line shows the same, for an isotropic distribution with the same number of events. A particle mass of $m_{\rm X} = 10^7$ TeV and velocity $v = 10^{-3} c$ are assumed. The results of the simulation clearly show the presence of two different populations of particles. See the main text for a discussion of the anisotropies in the simulated distribution.
  • Figure 5: Angular distribution of the incoming particles on Earth, assuming Lambert's distribution on the surface of a sphere with radius $20~\mathrm{kpc}$ and the toroidal solenoid magnetic field model for the Milky Way. Here we consider an initial number of particles of $10^6$. We also show the result for an isotropic distribution with the same number of events. We assume for the particles a mass $m_{\rm X} = 10^7$ TeV and a velocity $v = 10^{-1}~c$. The results of the simulation are compatible with an isotropic distribution, see the main text for more details.