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  • 1.
    Brandenburg, Axel
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC). Carnegie Mellon University, USA; Ilia State University, Georgia.
    Zhou, Hongzhe
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Shanghai Jiao Tong University, People’s Republic of China.
    Sharma, Ramkishor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Batchelor, Saffman, and Kazantsev spectra in galactic small-scale dynamos2023In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 518, no 3, p. 3312-3325Article in journal (Refereed)
    Abstract [en]

    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, suggestive of the build-up of long-range correlations. At large magnetic Prandtl numbers, elongated structures are seen in synthetic synchrotron emission maps showing the parity-even E polarization. We also observe a significant excess in the E polarization over the parity-odd 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, which is believed to be associated with larger scales. The E and B polarizations may be highly non-Gaussian and skewed in the kinematic regime of the dynamo. For dust emission, however, the polarized emission is always nearly Gaussian, and the excess in the E polarization is much weaker. 

  • 2.
    Zhou, Hongzhe
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Shanghai Jiao Tong University, People’s Republic of China.
    Blackman, Eric G.
    Helical dynamo growth and saturation at modest versus extreme magnetic Reynolds numbers2024In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 109, no 1, article id 015206Article in journal (Refereed)
    Abstract [en]

    Understanding magnetic field growth in astrophysical objects is a persistent challenge. In stars and galaxies, turbulent flows with net kinetic helicity are believed to be responsible for driving large-scale magnetic fields. However, numerical simulations have demonstrated that such helical dynamos in closed volumes saturate at lower magnetic field strengths when increasing the magnetic Reynolds number Rm. This would imply that helical large-scale dynamos cannot be efficient in astrophysical bodies without the help of helicity outflows such as stellar winds. But do these implications actually apply for very large Rm? Here we tackle the long-standing question of how much helical large-scale dynamo growth occurs independent of Rm in a closed volume. We analyze data from numerical simulations with a new method that tracks resistive versus nonresistive drivers of helical field growth. We identify a presaturation regime when the large-scale field grows at a rate independent of Rm, but to an Rm-dependent magnitude. The latter Rm dependence is due to a dominant resistive contribution, but whose fractional contribution to the large-scale magnetic energy decreases with increasing Rm. We argue that the resistive contribution would become negligible at large Rm and an Rm-independent dynamical contribution would dominate if the current helicity spectrum in the inertial range is steeper than k0. As such helicity spectra are plausible, this renews optimism for the relevance of closed dynamos. Our work pinpoints how modest Rm simulations can cause misapprehension of the Rm→∞ behavior.

  • 3.
    Zhou, Hongzhe
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Rochester, USA.
    Blackman, Eric G.
    Influence of inhomogeneous stochasticity on the falsifiability of mean-field theories and examples from accretion disc modelling2021In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 507, no 2, p. 2735-2743Article in journal (Refereed)
    Abstract [en]

    Despite spatial and temporal fluctuations in turbulent astrophysical systems, mean-field theories can be used to describe their secular evolution. However, observations taken over time scales much shorter than dynamical time scales capture a system in a single state of its turbulence ensemble. Comparing with mean-field theory can falsify the latter only if the theory is additionally supplied with a quantified precision. The central limit theorem provides appropriate estimates to the precision only when fluctuations contribute linearly to an observable and with constant coherent scales. Here, we introduce an error propagation formula that relaxes both limitations, allowing for non-linear functional forms of observables and inhomogeneous coherent scales and amplitudes of fluctuations. The method is exemplified in the context of accretion disc theories, where inhomogeneous fluctuations in the surface temperature are propagated to the disc emission spectrum - the latter being a non-linear and non-local function of the former. The derived precision depends non-monotonically on emission frequency. Using the same method, we investigate how binned spectral fluctuations in telescope data change with the spectral resolving power. We discuss the broader implications for falsifiability of a mean-field theory.

  • 4.
    Zhou, Hongzhe
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Blackman, Eric G.
    On the shear-current effect: toward understanding why theories and simulations have mutually and separately conflicted2021In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 507, no 4, p. 5732-5746Article in journal (Refereed)
    Abstract [en]

    The shear-current effect (SCE) of mean-field dynamo theory refers to the combination of a shear flow and a turbulent coefficient β21 with a favourable negative sign for exponential mean-field growth, rather than positive for diffusion. There have been long-standing disagreements among theoretical calculations and comparisons of theory with numerical experiments as to the sign of kinetic (⁠βu21⁠) and magnetic (⁠βb21⁠) contributions. To resolve these discrepancies, we combine an analytical approach with simulations, and show that unlike βb21⁠, the kinetic SCE βu21 has a strong dependence on the kinetic energy spectral index and can transit from positive to negative values at O(10) Reynolds numbers if the spectrum is not too steep. Conversely, βb21 is always negative regardless of the spectral index and Reynolds numbers. For very steep energy spectra, the positive βu21 can dominate even at energy equipartition urms ≃ brms, resulting in a positive total β21 even though βb21<0⁠. Our findings bridge the gap between the seemingly contradictory results from the second-order-correlation approximation versus the spectral-τ closure, for which opposite signs for βu21 have been reported, with the same sign for βb21<0⁠. The results also offer an explanation for the simulations that find βu21>0 and an inconclusive overall sign of β21 for O(10) Reynolds numbers. The transient behaviour of βu21 is demonstrated using the kinematic test-field method. We compute dynamo growth rates for cases with or without rotation, and discuss opportunities for further work.

  • 5.
    Zhou, Hongzhe
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Shanghai Jiao Tong University, PR China.
    Sharma, Ramkishor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC). Carnegie Mellon University, USA; Ilia State University, Georgia.
    Scaling of the Hosking integral in decaying magnetically dominated turbulence2022In: Journal of Plasma Physics, ISSN 0022-3778, E-ISSN 1469-7807, Vol. 88, no 6, article id 905880602Article in journal (Refereed)
    Abstract [en]

    The Saffman helicity invariant of Hosking & Schekochihin (Phys. Rev. X, vol. 11, issue 4, 2021, 041005), which we here call the Hosking integral, has emerged as an important quantity that may govern the decay properties of magnetically dominated non-helical turbulence. Using a range of different computational methods, we confirm that this quantity is indeed gauge invariant and nearly perfectly conserved in the limit of large Lundquist numbers. For direct numerical simulations with ordinary viscosity and magnetic diffusivity operators, we find that the solution develops in a nearly self-similar fashion. In a diagram quantifying the instantaneous decay coefficients of magnetic energy and integral scale, we find that the solution evolves along a line that is indeed suggestive of the governing role of the Hosking integral. The solution settles near a line in this diagram that is expected for a self-similar evolution of the magnetic energy spectrum. The solution will settle in a slightly different position when the magnetic diffusivity decreases with time, which would be compatible with the decay being governed by the reconnection time scale rather than the Alfven time.

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