Dark matter and generation of galactic magnetic fields

A new scenario for creation of galactic magnetic fields is proposed which is operative at the cosmological epoch of the galaxy formation, and which relies on unconventional properties of dark matter. Namely, it requires existence of feeble but long range interaction between the dark matter particles and electrons. In particular, millicharged dark matter particles or mirror particles with the photon kinetic mixing to the usual photon can be considered. We show that in rotating protogalaxies circular electric currents can be generated by the interactions of free electrons with dark matter particles in the halo, while the impact of such interactions on galactic protons is considerably weaker. The induced currents may be strong enough to create the observed magnetic fields on the galaxy scales with the help of moderate dynamo amplification. In addition, the angular momentum transfer from the rotating gas to dark matter component could change the dark matter profile and formation of cusps at galactic centers would be inhibited. The global motion of the ionized gas could produce sufficiently large magnetic fields also in filaments and galaxy clusters.

Suggested mechanisms of generation of large scale magnetic fields: Conventional physics. Either too weak field strength or too short coherence length or both. New physics. Generation of B in the very early universe, or at a later stage, during or around recombination, z = 1000, or close to the present day.
Creation during inflation: suppressed by conformal invariance of QED; can be broken either by conformal anomaly or by a new interaction, e.g. by RA µ A µterm, it also breaks gauge invariance. B with a large coherence length can be created, but very weak. Postinflationary early universe models all lead to too small coherence scales. E.g. phase transitions might lead to very large B but at tiny scales.
Generation of B at BBN: t > 1 sec, T < 1 MeV. Short coherence scale, l c < 1 pc. In the case of large and inhomogeneous lepton asymmetry B could be generated at such scales and by chaotic field line reconnection (like Brownian motion) might extend to galactic, but not intergalactic scales.
In all the cases huge, sometimes even unrealistic, dynamo amplification by galactic rotation is necessary. This could help to amplify galactic magnetic fields from originally weak seed fields, but not intergalactic B.
Additional problem with galactic fields: Developed magnetic fields B ∼ few µG observed in young galaxies, at z ∼ 2 -when the universe age was about 1/3 of the present age T 14 Gyr As a result, seed fields can be generated, B seed ∼ 10 −20 G, at the galactic lengthscale ∼ 10 kpc. Is it enough ?
What is B ∼ 1 µG for galactic fields ? It is in fact a dynamo saturation limit when equipartition between the magnetic and turbulent energy densities is achieved: with e-folding time τ dyn = 0.2 ÷ 0.5 Gyr Hence B seed (t 0 ) ∼ 10 −20 G at t 0 ∼ 1 Gyr is enough for B(t) ∼ µG at t = 14 Gyr But for B(t) ∼ µG at t = 4 Gyr (z 2) one needs B seed (t 0 ) > 10 −15 G !! Consider a protogalaxy rotating in the background of CMB photons. The pressure exerted by photons on electrons is by far larger than that exerted on protons, F ∝ σ ∝ α/m 2 e,p . So circular electric current, proportional to the rotational velocity, v rot , must be induced. The acceleration is even smaller, a ∝ F/m ∝ α/m 3 e,p .
Pressure force acting on electrons: where σ eγ = 8πα 2 /3m 2 e = 6.65×10 −25 cm 2 , α = e 2 = 1/137 (CGS system of units), and thus factor B F = σ eγ ρ γ /e is Note, that the conductivity does not depend on the density of charge carriers, n e , unless the latter is so small that the resistance is dominated by neutral particles.
Thus the difference between rotational velocities of e and p is ∆v e = τ ep F/2m e and the current j = en e ∆v e . Naively estimating B by the Biot-Savart law as B ∼ 4πjR where R is the galaxy radius, we find that for a typical galaxy with R ∼ 10 kpc v rot ∼ 100 km/s: B ∼ µG, very close to the observed value without any dynamo. HOWEVER THIS IS WRONG! Time to reach stationary (Biot-Savart) limit is longer than the cosmological time.
MHD equation modified by presence of external force: In the limit of high conductivity, the second term in the equation, the advection term, can lead to dynamo amplification of magnetic seed fields once the value of the latter is non-zero.
But without source term ∇× F /e MHD equation CANNOT generate non-zero magnetic seeds: if B = 0 at t = t 0 , then B = 0 FOREVER Assuming B = 0 at t = 0, we find that the source term induces: The largest value of the magnetic seed is generated around the hydrogen recombination and photon decoupling, z rec ∼ 10 3 , or t rec ∼ 5 × 10 5 yr. Earlier the plasma was strongly coupled and the relative motion of electrons and protons was negligible.
The seed field generated at this epoch with coherence length λ ∼ 1 kpc, corresponding to the present scale of a typical galaxy ∼ 1 Mpc, is where Ω λ = | ∇× v| λ 10 3 (δT /T ) 2 /λ. However such seed is still too weak. The seeds with the coherence length ∼ a few kpc and B seed > 10 −15 G are needed to fit the observations. Now: new DM particles, X, instead of CMB photons. The generated current is proportional to the cross-section of Xe-elastic scattering, σ Xe , to n X /n e , and to p X = m X v rot . Therefore, to produce stronger than CMB force on electrons, σ Xe should be large. This is possible if X have long range interaction, so σ Xe is strongly enhanced at low momentum transfer. So we consider millicharged particles with the mass from a few keV to several MeV.
How millicharged particles appear ?
BBN bounds can be relaxed if the lepton asymmetry is non-zero. If X-particles were thermally produced, their abundance would be: where g X is the number of the spin states of X-particle and g * f is the effective number of particle species in the plasma at T = T f .
If m X < m e , X-particles can annihilate only into photons with Thus Hence X's would be overproduced if < 3.4·10 −5 . Additional annihilation intoνν or dark photons could help. CMB demands Ω X h 2 < 0.005 or so If m X > m e , then XX → e + e − and:
Drag force from X-particles on electrons: where κ(z) is the dark matter overdensity in galactic halo with respect to its mean density at redshift z.
If m X < m e , then If m X > m e , then DM of X-particles and LLS formation. Light X's. Prior to recombination τ Xe < t U and X's are frozen in eγliquid. After recombination and till reionization they behave as usual WDM. After reionization τ Xe again becomes smaller than the cosmological time and thus the rotating ordinary matter in a protogalaxy would transfer a part of angular momentum to X-particles and involve it in its turbulent motion.
Estimate of field generated by light X. We use the obtained above equations but integrate till reionization, z = 6 and thus t u = 1 Gyr, R = 100 kpc and κ = 100, v rot = 10 km/sec and impose the limit Ω x h 2 = 0.007 to find: B can rise by factor 100, becoming 10 −9 G, when the protogalaxy shrinks from 100 kpc to 10 kpc, by far larger then the minimal necessary strength of the seed.
Heavier X: m X > m e , so larger charge is allowed, > 10 −4 . X-particles can make all dark matter. After reionization, electron scatterings would not force X-particles into galaxy rotation and thus the effective integration time can be larger and magnetic fields as large as 10 −12 G can be generated.