New Limits on Charged Dark Matter from Large-Scale Coherent Magnetic Fields

Albert Stebbins; Gordan Krnjaic

REVIEW 4 major objections 6 minor 2 cited by

New Limits on Charged Dark Matter from Large-Scale Coherent Magnetic Fields

T0 review · 4 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read This paper argues that charged dark matter crossing a spiral galaxy's magnetized gas disk would extract most of the disk's angular momentum within about 5 Gyr unless the charge-to-mass ratio is below roughly $3.5\times10^{-13}$ e/GeV (for…

desk verdict A genuinely new and strong bound on charged dark matter from galactic ISM spin-down, honestly caveated, but the exclusion claim rests on a load-bearing assumption about galaxy formation that the paper does not test. read the letter →

arxiv 1908.05275 v1 pith:ZA37JXF2 submitted 2019-08-14 astro-ph.CO astro-ph.GAhep-ph

Albert Stebbins , Gordan Krnjaic This is my paper · ORCID

classification astro-ph.COastro-ph.GAhep-ph

keywords chargeddarkmattermillichargedparticlesgalacticmagneticfieldsinterstellarmediumangularmomentumtransferspin-downfreeze-inproductionconstraints

topics Dark Matter

open problems Dark Matter

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Most of the dark matter could be neutral, but a small electrically charged component remains viable. This paper argues that such charged dark matter cannot merely orbit a spiral galaxy: each time it crosses the galaxy's gas disk, the disk's embedded magnetic field deflects it, and the reaction drags on the disk's rotation. Over the $\sim5$ Gyr that the Milky Way's gas disk and its $\sim\mu$G ordered field are thought to have persisted, this drag would remove an order-unity fraction of the disk's angular momentum unless the charge-to-mass ratio obeys $\sqrt{f_{\rm qdm}}\, q/(m c^2) \lesssim 3.5\times10^{-14}\, e/{\rm GeV}$, i.e. $q/(m c^2)\lesssim 3.5\times10^{-13}\, e/{\rm GeV}$ if all the dark matter is charged. This bound is strong enough to exclude freeze-in production of charged dark matter below about a TeV, making large-scale magnetic fields a new probe of dark matter's non-gravitational interactions.

What carries the argument

The load-bearing object is the line integral of the magnetic field along a qDM trajectory, $\Phi = \int \vec B\cdot d\vec\ell$, a quantity with dimensions of voltage; near the Sun the paper estimates $\Phi_{\rm eff}\approx 3.5\times10^{17}$ V. The argument runs through the second Born approximation: first-order kicks cancel between opposite charges and opposite directions, and the surviving momentum transfer is proportional to $(q\Phi/(m c \sigma))^2$, so the spin-down rate is set by the square of the ratio between the magnetic 'voltage' and the particle's charge-to-mass voltage $m c^2/q$. A four-particle reflection average isolates this surviving second-order term, and a logarithmic cutoff regulates low-inclination orbits that would otherwise be over-deflected. The machinery turns a purely electromagnetic interaction into an angular-momentum drag whose rate depends on $q/m$, the field voltage, the ISM surface density, and the qDM density and velocity dispersion.

What would settle it

Run a magnetohydrodynamic simulation of a Milky-Way-like galaxy from redshift $z\approx0.4$ to the present with $f_{\rm qdm}=1$ and $q/(m c^2)=3\times10^{-13}\,e/{\rm GeV}$; if the simulated gas disk retains more than half of its initial angular momentum while the ordered field stays near a microgauss, the paper's central bound would be refuted.

Watch

Extended reading notes

Core claim

The paper aims to establish that the ordered component of a spiral galaxy's magnetic field acts as a brake on the interstellar medium when charged dark matter passes through it. Because the field is embedded in the highly conducting, co-rotating ISM, the ideal MHD electric field $\vec E \approx -\vec V/c \times \vec B$ makes each qDM particle feel a force proportional to $(\vec v-\vec V)\times\vec B$. For any incoming velocity, opposite charges receive the same kick at leading order, so the first Born contribution to the momentum transfer cancels after averaging over charges and directions; the surviving effect is second order in the field. Averaging over four particles (opposite charges with velocities $\pm\vec v$) reduces the answer to two line integrals of $\vec B$ along the trajectory, and for planar fields the spin-down rate becomes proportional to $(q \Phi_{\rm eff} \sin\psi/m c \sigma)^2$, where $\Phi_{\rm eff}$ is the line integral of the ordered field, about $3.5\times10^{17}$ V in the solar neighborhood. Requiring the spin-down time to exceed $T_{\rm ism}=5$ Gyr yields the limit $\sqrt{f_{\rm qdm}}\, q/(m c^2) \lesssim 3.5\times10^{-14}\, e/{\rm GeV}$ for $f_{\rm qdm}\gtrsim 0.13$.

Load-bearing premise

The load-bearing premise is that a rotating gas disk with roughly today's magnetic field already existed for about five billion years before charged dark matter began dragging on it; if charged dark matter would have disrupted galaxy formation or magnetic-field growth earlier, the initial condition from which the spin-down bound is computed never holds.

Editorial extensions

If this is right

If all the dark matter is charged, the bound excludes the freeze-in production scenario for masses below roughly a TeV, since that mechanism requires $q/e\sim10^{-11}$, far above the limit.
For charged-dark-matter fractions below $f_{\rm qdm}\approx0.13$ there is not enough inertia in the dark matter to drag the disk; the prediction flips to qDM being spun up into co-rotation, altering its local velocity distribution rather than shrinking the gas disk.
The bound applies not only to directly charged particles but also to neutral dark matter coupled through an ultralight kinetically mixed dark photon, because the ISM plasma gives the photon an effective mass and the dark matter an effective charge.
At unit charge, the constraint reaches masses near $10^{13}$ GeV, cutting into the 'WIMPzilla' regime of supermassive dark matter.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A straightforward observational follow-up the paper does not carry out is to compare the radial sizes of gas disks versus stellar disks across a large sample of spiral galaxies; a systematic excess of small gas disks in galaxies with strong ordered fields would corroborate the spin-down picture.
The same second-order drag mechanism should operate in any magnetized plasma with a relative velocity to a charged halo, so merging galaxy clusters, whose fields can exceed 10 $\mu$G over tens of kpc, could set even tighter limits; the paper sketches this for the Bullet Cluster but leaves the calculation schematic.
The calculation regulates grazing trajectories with a cutoff rather than evolving the qDM distribution self-consistently; a particle-in-cell or MHD simulation would show whether the drag saturates as slow particles are captured into co-rotation, softening the sharpest part of the excluded region.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

You should know two things about this paper. First, it is a real contribution: the second-Born momentum-transfer calculation from ordered galactic magnetic fields is new, and the resulting bound on sqrt(f_qdm) q/m of about 1e-14 e/GeV lands squarely on freeze-in millicharge parameter space that is being actively pursued. Second, the central exclusion is not as solid as the abstract suggests, because the whole argument assumes a pre-existing, stable ISM disk and ordered field for ~5 Gyr, and the same qDM-B coupling could have altered galaxy formation and dynamo growth in the first place. The authors know this; they flag it explicitly as Assumption 6 and in the conclusion, but they do not resolve it.

The derivation itself is careful and mostly persuasive. I traced the logic from the Maxwell-Vlasov setup through the four-particle average, and the cancellation of first-Born terms with survival at second order is clean. The treatment of realistic field geometries via RM maps is a nice touch, and the authors are commendably honest about the lack of an observational spin-down test and the ad hoc two-order-of-magnitude uncertainty. The bound is a genuine first-principles estimate, not a fit.

The soft spots are real but not fatal. The formation-timeline assumption is the load-bearing one, and the stress-test concern is on target: if near-bound qDM prevents a normal disk from forming, then observing an unsHrunken disk does not exclude anything. That assumption is untested, and the paper's own admission that exploring it is beyond scope is not a substitute for doing so. The saturation regulator in Eq. (43) is heuristic, but the logarithmic divergence means the result is not sensitive to the exact choice, so I regard that as minor. The abstract's wording that the bound 'excludes' freeze-in production runs slightly ahead of the text's careful caveats, but this is a presentation issue, not a mathematical error.

Who is this for? Anyone working on millicharged dark matter, dark photons, or astrophysical signatures of charged relics. It is a useful paper to put on a reading group syllabus, and it deserves a serious referee. My recommendation: send it to review, but the referee should demand a clearer statement that the bound is conditional on standard galaxy formation, or better yet a short simulation section showing that qDM near the bound does not suppress disk assembly. With that revision, the paper would be a solid contribution rather than an overclaimed exclusion.

Referee Report

4 major / 6 minor

Summary. The paper derives an upper limit on the charge-to-mass ratio of a charged dark matter (qDM) population by considering angular momentum transfer between a rotating, magnetized interstellar medium (ISM) disk and a slowly rotating qDM halo. Working in the ballistic regime and using a second-Born perturbative expansion of the Lorentz force, the authors obtain a spin-down timescale for the ISM and show that, for local Milky Way parameters, avoiding order-unity ISM spin-down over T_ism ~ 5 Gyr requires q/(m c^2) below roughly 1e-14 e/GeV for f_qdm = 1, with an ad hoc two-order-of-magnitude uncertainty. The paper also discusses qDM spin-up for small f_qdm, compares the resulting exclusion with freeze-in production and other millicharged-particle bounds, and sketches possible applications to galaxy clusters and the Bullet Cluster.

Significance. If the result is correct, this is a novel and potentially very strong astrophysical bound: it is roughly two orders of magnitude stronger than the simple Larmor-radius coherence argument and would exclude much of the freeze-in millicharged parameter space below about a TeV. The analytic machinery for momentum transfer in the second Born approximation is original and carefully laid out, and the inputs are independently measured quantities rather than quantities fitted to the claimed bound. The paper is also unusually candid: it explicitly lists its assumptions, acknowledges the rough nature of the result, and admits that no observational spin-down test is specified. These strengths make the derivation worth publishing in some form, but the headline claim needs substantial revision before it can stand as a quantitative exclusion.

major comments (4)

[Eqs. (59), (65), and Abstract] The central value of the headline bound is internally inconsistent. Eq. (58) with tau_sd = 5 Gyr gives q/(m c^2) ~ 3.5e-14 e/GeV for f_qdm = 1, and Eq. (59) states this 3.5e-14 value. The Conclusion, however, restates the bound as 3.5e-13+/-1 e/GeV (Eq. (65)), and the Abstract says q/e ~ 1e-13+/-1 m c^2/GeV. These differ from Eq. (59) by a factor of ten in the central value. If Eqs. (58)-(59) are correct, the Abstract and Eq. (65) must be corrected; if the weaker value is intended, the derivation leading to Eq. (58) must be revisited. As written, the reader cannot tell which number is the claimed limit.
[Sec. III.1, Assumption 6; Fig. 2; Conclusion] The bound rests on the timeline in which the ISM disk and its ordered magnetic field already exist in roughly their current form for T_ism ~ 5 Gyr before qDM spin-down acts (Assumption 6 and Fig. 2). But a qDM population with q/m near the bound would have interacted with magnetic fields during protogalactic collapse, disk assembly, and dynamo growth. Those interactions could remove angular momentum from infalling gas, prevent the formation of a large rotation-supported disk, or suppress the ordered microgauss field, so the assumed initial state would never have formed. In that case the observation that present-day disks are not shrunken would not exclude the qDM parameters. The authors acknowledge this in Sec. III.1 and again in the Conclusion, but stating that the question is beyond the scope of the paper leaves the central exclusion unestablished. I request at least a quantitative estimate of the early-time effect, or an explicit reframing of the result as conditional on conventional galaxy formation, with the word 'limit' qualified accordingly.
[Sec. III.B.2, Eq. (43)] The logarithmic enhancement that enters the spin-down rate comes from the heuristic saturation regulator in Eq. (43), which replaces the divergent <1/|v_z|> average. The authors state that this cut-off could be implemented more rigorously but do not do so. Because this regulator controls the factor 1 - gamma_E - 2 ln(epsilon) in Eq. (49) and hence the magnitude of the dominant spin-down term, its systematic uncertainty propagates directly into the central bound. The ad hoc two-order-of-magnitude uncertainty is broad, but the derivation should still justify the regulator quantitatively or demonstrate explicitly that the bound is insensitive to the regulator's form.
[Sec. IV.4; Sec. VII] The exclusion regions in Figs. 3 and 4, and the phrase 'almost certainly ruled out' in the Fig. 3 caption, presuppose that a spun-down ISM would have been noticed, but the paper does not define a specific observable or a statistical criterion. Without an observational spin-down test, Eq. (59) is a theoretical estimate of when spin-down becomes large, not a measurement-driven upper limit. The authors are candid about this in Sec. VII, but the central claim of a new exclusion should either propose a concrete test or clearly label the result as an estimate pending such a test.

minor comments (6)

[Sec. II, after Eq. (4)] The sentence 'we set the criteria for no significant spin-down to be tau_sd < T_ism' has the inequality backwards; it should be tau_sd > T_ism.
[Sec. III.B.2, after Eq. (43)] The phrase '< vec v / |hat v| >' appears to be a typo; the non-divergent average is presumably < vec v / |v_z| > or similar.
[Sec. III.A.5, Eq. (32)] The superscript (1) on Delta vec p_{4+/-} in the momentum-transfer-rate equation is inconsistent with the second-Born definition in Eq. (22); the superscript should be (2).
[Sec. III.B.1, Eq. (40)] The statement that the pitch angle is 'hat v independent' should be phrased as psi(hat v) -> psi in the planar limit; as written it is confusing.
[References [32] and [50]] References [32] and [50] appear to be the same paper with the same arXiv number and should be consolidated or cross-referenced.
[Eqs. (59) and (65)] Once the central-value inconsistency is fixed, the notation for the uncertainty exponent should be made uniform: Eq. (59) uses -14 with 'minus-plus 1' while Eq. (65) uses -13 with 'plus-minus 1'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the qDM spin-down bound is derived from independently measured Galactic parameters and an analytic 2nd-Born momentum-transfer calculation, with no fitted input renamed as a prediction.

full rationale

The central derivation starts from the Lorentz force and MHD Ohm's law, computes momentum transfer in the 2nd Born approximation (Eqs. 9-33), specializes to a planar magnetic field and Maxwellian halo (Eqs. 40-49), and then imposes tau_sd > T_ism using locally measured quantities: rho_dm = 0.008 M_sun/pc^3, Sigma_ism = 17.2 M_sun/pc^2, sigma = 270 km/s, Phi_eff = 10^18 V extracted from rotation-measure maps, and T_ism = 5 Gyr motivated by the external observations of Mao et al. and simulations of Pakmor et al. The resulting bound in Eqs. (59) and (65) is a function of these inputs and q/m; no parameter is fitted to the target exclusion region. The only adjustable element is the explicit two-order-of-magnitude ad hoc uncertainty band, which does not feed back into the derivation of the central value. The paper explicitly lists its dubious assumptions in Sec. III.1, including Assumption 6 that the disk and magnetic field formed before qDM effects became important, and the Conclusion repeats that the bound assumes early qDM does not spoil galaxy formation; this is an acknowledged caveat about validity, not a circular definition of the bound. No load-bearing self-citation appears: prior work cited for T_ism, RM maps, and cluster constraints is external, and no uniqueness theorem or ansatz is imported from the authors' own earlier papers. The derivation is therefore self-contained against independently measured inputs.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

All inputs to the bound are independently measured astrophysical quantities; the hand-chosen scale height and spin-down duration set the central value, and the listed domain assumptions are flagged by the authors with varying levels of confidence.

free parameters (2)

magnetic field scale height h_B = h_e = 1 kpc
Adopted as a round number in Sec. IV.3; the inferred Phi_eff scales linearly with h_B, so this choice directly sets the central bound.
spin-down duration T_ism = 5 Gyr
Chosen from Mao et al. RM measurements and Pakmor et al. simulations (Sec. IV.1); the bound scales as T_ism^{-1/2}.

assumptions (6)

domain assumption The ISM and embedded magnetic fields are described by ideal MHD with E = -V x B / c (Eq. 7).
Used in Sec. III.2 to write the Lorentz force as (v - V) x B; standard for highly conducting ISM plasma.
domain assumption The qDM halo is non-rotating with a Maxwellian velocity distribution in the galaxy frame (Eq. 44).
Adopted in Sec. III.B.3; if the halo co-rotates significantly with the disk, the relative velocity and spin-down rate would be reduced.
ad hoc to paper The ordered galactic magnetic field has planar symmetry with B_z = 0 (Sec. III.B.1).
The authors state planar symmetry is a poor description of the actual B in the local disk but adopt it to compute Phi_eff; non-planar gradients would change the bound.
ad hoc to paper The 2nd Born approximation is valid (R_L >> Delta z) and the low-inclination divergence is regulated by the heuristic cut-off in Eq. (43).
The cut-off v_* is introduced without a rigorous treatment; the authors state it could be implemented more rigorously.
ad hoc to paper ISM disk and magnetic field configuration have not changed significantly over T_ism ~ 5 Gyr (assumptions 6 and 11).
This enables accumulating spin-down over the galaxy lifetime; the authors flag it as dubious and note qDM could modify field growth and galaxy formation.
standard math Classical non-relativistic single-particle dynamics and the Maxwell-Vlasov equation describe the qDM-ISM interaction (Sec. III.3).
Standard kinetic theory background for the derivation.

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Cite this review

Pith. "Pith review of New Limits on Charged Dark Matter from Large-Scale Coherent Magnetic Fields." pith.science (2026). https://pith.science/paper/ZA37JXF2

@misc{pith2026190805275,
  author       = {Pith},
  title        = {Pith review of: New Limits on Charged Dark Matter from Large-Scale Coherent Magnetic Fields},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZA37JXF2}},
  note         = {Machine review of arXiv:1908.05275}
}

abstract

We study the interaction of an electrically charged component of the dark matter with a magnetized galactic interstellar medium (ISM) of (rotating) spiral galaxies. For the observed ordered component of the field, $B\sim \mu$G, we find that the accumulated Lorentz interactions between the charged particles and the ISM will extract an order unity fraction of the disk angular momentum over the few Gyr Galactic lifetime unless $q/e \lesssim 10^{-13\pm 1}\,m\,c^2/$ GeV if all the dark matter is charged. The bound is weakened by factor $f_{\rm qdm}^{-1/2}$ if only a mass fraction $f_{\rm qdm}\gtrsim0.13$ of the dark matter is charged. Here $q$ and $m$ are the dark matter particle mass and charge. If $f_{\rm qdm}\approx1$ this bound excludes charged dark matter produced via the freeze-in mechanism for $m \lesssim$ TeV/$c^2$. This bound on $q/m$, obtained from Milky Way parameters, is rough and not based on any precise empirical test. However this bound is extremely strong and should motivate further work to better model the interaction of charged dark matter with ordered and disordered magnetic fields in galaxies and clusters of galaxies; to develop precise tests for the presence of charged dark matter based on better estimates of angular momentum exchange; and also to better understand how charged dark matter might modify the growth of magnetic fields, and the formation and interaction histories of galaxies, galaxy groups, and clusters.

Figures

Figures reproduced from arXiv: 1908.05275 by the authors.

**Figure 1.** FIG. 1. Schematic cartoon representing the ISM disk model presented in this paper. Here the central ISM disk is modeled ~ [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

**Figure 2.** FIG. 2. Timeline of events relevant for qDM induced spin-down. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** FIG. 3. Shown are our expectation for limits on charged dark matter (qDM) parameters from [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: FIG. 4. Constraints on ISM spin down assuming that qDM constitutes all of the halo DM [PITH_FULL_IMAGE:figures/full_fig_p017_4.png]

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Reference graph

Works this paper leans on

87 extracted references · 49 canonical work pages · cited by 2 Pith papers

[1]

Our particle model assumption is

Assumptions We now begin a more formal derivation of the rate of ISM spin-down. Our particle model assumption is
[2]

and since we are working in the ballistic limit we are assuming

There is only one qDM particle species of mass m with equal numbers of charges ±q which makes up a mass fractionfqdm≤ 1 of all the dark matter and only interacts with Standard Model particles through gravitational and electromagnetic forces. and since we are working in the ballistic limit we are assuming
[3]

We expand to 2nd order in ∆z/RL (2nd Born approximation) to obtain the leading-order contribution to ISM spin- down and obtain our spin-down bound

the typical Larmor radius of qDM passing through the disk is much greater than the disk thickness ( RL∼ mcσ/qB ≫ ∆z), so qDM particle trajectories are only slightly perturbed by ⃗B (the Born approximation). We expand to 2nd order in ∆z/RL (2nd Born approximation) to obtain the leading-order contribution to ISM spin- down and obtain our spin-down bound. To...
[4]

non-relativistic dynamics,
[5]

the MHD approximation,
[6]

magnetic plasma waves move slowly compared to typical qDM velocities (see [17] which reviews ISM plasma dynamics); and some are more dubious and might be made diﬀerently

the magnetic ﬁelds are quasi-static, i.e. magnetic plasma waves move slowly compared to typical qDM velocities (see [17] which reviews ISM plasma dynamics); and some are more dubious and might be made diﬀerently
[7]

the disk ISM and magnetic ﬁelds are formed and stable before the eﬀects of qDM interactions become important
[8]

the magnetic ﬁelds are concentrated near the disk (∆ z≪R)

work page

Show all 87 references

[9]

To derive a numerical bound on q/m we also assume

the gravitational deﬂection of qDM orbits is negligible during a passage through the ISM. To derive a numerical bound on q/m we also assume
[10]

the dark matter halo is rotating much more slowly than the ISM,
[11]

the ISM and embedded ordered magnetic ﬁelds orbit the galaxy center in nearly circular trajectories,
[12]

current local values of ISM and DM properties are representative of their values over cosmic time,
[13]

the local magnetic ﬁeld pattern can be adequately modeled with planar symmetry,
[14]

various assumptions on how to interpret data probing the local magnetic ﬁeld The timeline of assumed events is given in Fig 2. It is interesting to explore whether qDM interactions with magnetic ﬁelds would actually modify galaxy formation and/or the growth of magnetic ﬁelds a...
[15]

Lorentz Force in Quasi-static MHD Approximation The fundamental interaction we consider is the usual electromagnetic Lorentz force ⃗F =±q ( ⃗E + 1 c⃗ v× ⃗B ) , (6) whereq is the charge of a qDM particle passing through the ISM disk with velocity ⃗ v. Assuming the magnetic ﬁeld...
[16]

We assume that initially f+ = f− = f0, but f will evolve away from this as the qDM particles travel through the magnetic ﬁeld

Maxwell-Vlasov Equation While in what follows we work with the microscopic description of single particle trajectories, this treatment is equivalent to a more macroscopic (non-relativistic) Maxwell-Vlasov equation which, with our MHD approximation, is ∂ ∂t f± +⃗ v· ∂ ∂⃗ xf± =±...
[17]

For slight deﬂections, the time it takes to traverse the ISM of thickness ∆ z is∼ ∆z/v wherev &V is the particle’s speed

Born Approximations We wish to compute the spin-down eﬀect in the so-called ballistic limit in which particle trajectories are only slightly deﬂected from theirq = 0 paths by ⃗B as they traverse the ISM assuming that the gravitational deﬂections are negligible over this short∼...
[18]

For notational simplicity we suppress the⃗ x0 dependence in most formulae as we are considering only a small region of the disk

Momentum Transfer in the 1st Born Approximation To lowest, zeroth, order the trajectories are unperturbed by ⃗B and given by ⃗ x(0) ± (t) =⃗ x0 +⃗ v(t−t0) , ˙⃗ x(0) ± =⃗ v , (12) where ⃗ vis the initial (unperturbed) velocity while, t0 and ⃗ x0 give the time and position where...
[19]

Second Born Approximation Since Pharaoh took the ﬁrst Born, we rely on the second Born to avenge this injustice, which is the approximation ⃗ x(1) ± (τ) =⃗ x0 +⃗ vτ±δ⃗ x(τ) , ˙⃗ x(1) ± (τ) =⃗ v±δ ˙⃗ x(τ), (16) so using Eq. (11), the leading order momentum transfer is now ∆⃗ p(...
[20]

Four Particle Average of Momentum Transfer To simplify our main result further, we average the momentum transfer overtwo pairs of particles (4 particles total) moving in opposite directions,±⃗ vbut intersecting the central plane at the same location ⃗ x0 as depicted schematica...
[21]

Momentum Transfer from a Distribution of Particles The rate of momentum per unit area transferred between a distribution of qDM passing through a small patch of a galactic disk ISM is given by integrating the momentum transferred per particle multiplied by the rate of qDM part...
[22]

Spin Down and other Disk Disruptions Here we work in the galaxy rest frame and assume the ISM follows nearly circular orbits around galactic centers. Deﬁne the spin-down rate for a small patch of the ISM disk as the inverse of the fractional rate of loss of ISM angular momentu...
[23]

voltages

Planar Magnetic Fields If we assume that ⃗B only varies slowly in directions parallel to the plane of the disk, meaning over length scales much larger than the disk thickness, then one may approximate the magnetic ﬁeld as having planar symmetry: ⃗B(⃗ x,z)→ ⃗B(z) since most qDM...
[24]

One expects the vz→ 0 trajectories to already be co-rotating with the ISM and ∆ ⃗ p→ 0 so the assumption that the distribution is not signiﬁcantly modiﬁed is in error

Momentum Transfer Saturation The vz → 0 limit of the 2nd Born approximation is not accurate because the path length of low inclination orbits particles is so long that their deﬂection becomes large invalidating the approximation and overestimating the 11 momentum transfer. One...
[25]

(44) where σ is the 1-D velocity dispersion

Maxwellian Velocity Distribution For simplicity, we adopt a Maxwellian velocity distribution in the galaxy frame f0(⃗ v) = ρqdm (2π)3/2mσ3 e− |⃗ v|2 2σ2 . (44) where σ is the 1-D velocity dispersion. Thus we are assuming the qDM halo is not rotating. This is a symmetric distri...
[26]

We fully expect τsd to ﬂuctuate within a galaxy and over the history of a galaxy

Mean Spin Down Rate We have computed a local spin-down rate in terms ofτsd(⃗ x0,t ). We fully expect τsd to ﬂuctuate within a galaxy and over the history of a galaxy. In the ﬂat rotation curve and rapid cooling regime the radius of the ISM will decrease according to Eq. (38), ...
[27]

A rough estimate of when spin-up can occur is when Rρ qdm≤ Σism

qDM Spin Up The caveat is that iffqdm is too small then the inertia of the qDM is not suﬃcient to signiﬁcantly spin-down the ISM; rather the qDM will be spun-up to co-rotate with the ISM without signiﬁcantly aﬀecting the ISM. A rough estimate of when spin-up can occur is when ...
[28]

Here we suppose that these evolutionary eﬀects can be modeled as if the current conﬁguration has been constant over an interval of duration Tism

Spin Down Limits on Charged Dark Matter While it is fully expected that the magnetic ﬁeld (Φ(ˆz)) will increase over time as the a galactic dynamo grows the ﬁeld, the ﬁeld direction, ˆV· ˆΦ, will vary, and the amount of ISM gas (Σ ism) will decrease over time as gas is turned ...
[29]

Global Galactic Parameters As mentioned previously, we will ﬁrst apply qDM limits on spin-down by looking at the Galactic disk in the region of the solar neighborhood; not because it is the optimal location from which to derive the tightest constraints, but rather because we h...
[30]

brown dwarfs and atomic hydrogen

Inventory of the Disk Contents The inventory of gas and stars is also uncertain since the disk extends to quite a large distance above and below us, and much of this mass is diﬃcult to detect and localize at large distance, e.g. brown dwarfs and atomic hydrogen. Diﬀerent metho...
[31]

In this case, the pitch angle, ψ, is the angle between the spiral arms and the circular orbits

Local Magnetic Field A simple picture of magnetic ﬁelds in spiral galaxies is that ⃗B lies in the plane of the galaxy along the spiral arms. In this case, the pitch angle, ψ, is the angle between the spiral arms and the circular orbits. If the spiral arms are wound tightly, th...
[32]

Measured RM maps are signiﬁcantly more complicated than a dipole pattern

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freeze-in

Local Limits on qDM We have motivated the local values ρdm = 0.008M⊙/pc3, Σism = 17.2M⊙/pc2, σ = 270 km/sec, Φeﬀ = 1018 Volt, ψ = 15◦ and Tism = 5 Gyr. Substituting these values into Eq. (49) we ﬁnd the spin-down timescale to be ¯τsd≈ 0.6 Gyr fqdm (1 + 0.2 lnfqdm) (mc 2 GeV 10...
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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

Our particle model assumption is

Assumptions We now begin a more formal derivation of the rate of ISM spin-down. Our particle model assumption is

[2] [2]

and since we are working in the ballistic limit we are assuming

There is only one qDM particle species of mass m with equal numbers of charges ±q which makes up a mass fractionfqdm≤ 1 of all the dark matter and only interacts with Standard Model particles through gravitational and electromagnetic forces. and since we are working in the ballistic limit we are assuming

[3] [3]

We expand to 2nd order in ∆z/RL (2nd Born approximation) to obtain the leading-order contribution to ISM spin- down and obtain our spin-down bound

the typical Larmor radius of qDM passing through the disk is much greater than the disk thickness ( RL∼ mcσ/qB ≫ ∆z), so qDM particle trajectories are only slightly perturbed by ⃗B (the Born approximation). We expand to 2nd order in ∆z/RL (2nd Born approximation) to obtain the leading-order contribution to ISM spin- down and obtain our spin-down bound. To...

[4] [4]

non-relativistic dynamics,

[5] [5]

the MHD approximation,

[6] [6]

magnetic plasma waves move slowly compared to typical qDM velocities (see [17] which reviews ISM plasma dynamics); and some are more dubious and might be made diﬀerently

the magnetic ﬁelds are quasi-static, i.e. magnetic plasma waves move slowly compared to typical qDM velocities (see [17] which reviews ISM plasma dynamics); and some are more dubious and might be made diﬀerently

[7] [7]

the disk ISM and magnetic ﬁelds are formed and stable before the eﬀects of qDM interactions become important

[8] [8]

the magnetic ﬁelds are concentrated near the disk (∆ z≪R)

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