21 research outputs found
Batchelor, Saffman, and Kazantsev spectra in galactic small-scale dynamos
The magnetic fields in galaxy clusters and probably also in the interstellar
medium are believed to be generated by a small-scale dynamo. Theoretically,
during its kinematic stage, it is characterized by a Kazantsev spectrum, which
peaks at the resistive scale. It is only slightly shallower than the Saffman
spectrum that is expected for random and causally connected magnetic fields.
Causally disconnected fields have the even steeper Batchelor spectrum. Here we
show that all three spectra are present in the small-scale dynamo. During the
kinematic stage, the Batchelor spectrum occurs on scales larger than the
energy-carrying scale of the turbulence, and the Kazantsev spectrum on smaller
scales within the inertial range of the turbulence -- even for a magnetic
Prandtl number of unity. In the saturated state, the dynamo develops a Saffman
spectrum on large scales. At large magnetic Prandtl numbers, elongated
structures are seen in the parity-even E polarization, but not in the
parity-odd B polarization. We also observe a significant excess in the E
polarization over the B polarization at subresistive scales, and a deficiency
at larger scales. This finding is at odds with the observed excess in the
Galactic microwave foreground emission. The E and B polarizations become
Gaussian in the saturated state, but may be highly non-Gaussian and skewed in
the kinematic regime of the dynamo.Comment: 11 pages, 24 figures, 5 tables, submitted to MNRA
Inverse cascading for initial MHD turbulence spectra between Saffman and Batchelor
In decaying magnetohydrodynamic (MHD) turbulence with a strong magnetic
field, the spectral magnetic energy density is known to increase with time at
small wavenumbers , provided the spectrum at low is sufficiently steep.
This is inverse cascading and occurs for an initial Batchelor spectrum, where
the magnetic energy per linear wavenumber interval increases like . For an
initial Saffman spectrum that is proportional to , however, inverse
cascading has not been found in the past. We study here the case of an
intermediate spectrum, which may be relevant for magnetogenesis in the
early Universe during the electroweak epoch. This case is not well understood
in view of the standard Taylor expansion of the magnetic energy spectrum for
small . Using high resolution MHD simulations, we show that also in this
case there is inverse cascading with a strength just as expected from the
conservation of the Hosking integral, which governs the decay of an initial
Batchelor spectrum. Even for shallower spectra with spectral index
, our simulations suggest a spectral increase at small with
time proportional to . The critical spectral index of
is related to the slope of the spectral envelope in the Hosking
phenomenology. Although we cannot exclude the possibility of artifacts from the
finite size of the computational domain, our simulations with mesh
points now suggest inverse cascading even for an initial Saffman spectrum.Comment: 16 pages, 7 figures, 3 tables, submitted to J. Plasma Physic
Backreaction of axion-SU(2) dynamics during inflation
We consider the effects of backreaction on axion-SU(2) dynamics during
inflation. We use the linear evolution equations for the gauge field modes and
compute their backreaction on the background quantities numerically using the
Hartree approximation. We find a new dynamical attractor solution for the axion
field and the vacuum expectation value of the gauge field, where the latter has
an opposite sign with respect to the chromo-natural inflation solution. Our
findings are of particular interest to the phenomenology of axion-SU(2)
inflation, redefining parts of the viable parameter space. In addition, the
backreaction effects lead to characteristic oscillatory features in the
primordial gravitational wave background that are potentially detectable with
upcoming gravitational wave detectors.Comment: 24 pages, 13 figures, 2 table
Shallow relic gravitational wave spectrum with acoustic peak
We study the gravitational wave (GW) spectrum produced by acoustic waves in
the early universe, such as would be produced by a first order phase
transition, focusing on the low-frequency side of the peak. We confirm with
numerical simulations the Sound Shell model prediction of a steep rise with
wave number of to a peak whose magnitude grows at a rate
, where is the Hubble rate and the peak wave
number, set by the peak wave number of the fluid velocity power spectrum. We
also show that hitherto neglected terms give a shallower part with amplitude
in the range , which in
the limit of small rises as . This linear rise has been seen in other
modelling and also in direct numerical simulations. The relative amplitude
between the linearly rising part and the peak therefore depends on the peak
wave number of the velocity spectrum and the lifetime of the source, which in
an expanding background is bounded above by the Hubble time . For slow
phase transitions, which have the lowest peak wave number and the loudest
signals, the acoustic GW peak appears as a localized enhancement of the
spectrum, with a rise to the peak less steep than . The shape of the peak,
absent in vortical turbulence, may help to lift degeneracies in phase
transition parameter estimation at future GW observatories.Comment: 20 pages, 8 figure
Magnetohydrodynamics predicts heavy-tailed distributions of axion-photon conversion
The interconversion of axionlike particles (ALPs) and photons in magnetised
astrophysical environments provides a promising route to search for ALPs. The
strongest limits to date on light ALPs use galaxy clusters as ALP-photon
converters. However, such studies traditionally rely on simple models of the
cluster magnetic fields, with the state-of-the-art being Gaussian random fields
(GRFs). We present the first systematic study of ALP-photon conversion in more
realistic, turbulent fields from dedicated magnetohydrodynamic (MHD)
simulations, which we compare with GRF models. For GRFs, we analytically derive
the distribution of conversion ratios at fixed energy and find that it follows
an exponential law. We find that the MHD models agree with the exponential law
for typical, small-amplitude mixings but exhibit distinctly heavy tails for
rare and large mixings. We explain how non-Gaussian features, e.g.~coherent
structures and local spikes in the MHD magnetic field, are responsible for the
heavy tail. Our results suggest that limits placed on ALPs using GRFs are
robust.Comment: 18 pages, 9 figures. v2: major changes to match the published
version. Extended appendix to include details on the statistical analysi