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Nonhelical turbulence within a linear shear flow has demonstrated efficient amplification of large-scale magnetic fields in numerical simulations, but its precise mechanism remains elusive. The incoherent $\alpha$ mechanism proposes that a zero-mean fluctuating transport coefficient $\alpha$ (linked to kinetic helicity) in the shear flow is a candidate driver. Previous renovating-flow models have proposed that the correlation time of helicity fluctuations must be sufficiently extended to overcome turbulent magnetic diffusivity, yet only empirical validation of this concept has been obtained. In this study, we conduct direct numerical simulations of weakly compressible nonhelical hydrodynamic turbulence. We scrutinize the correlation times of velocity and kinetic helicity fluctuations in distinct flow configurations, including rotation, shearing, and Keplerian flows, as well as the shearing burgulence counterpart. Our findings indicate that rotation contributes to a prolonged correlation time of helicity compared to velocity, particularly notable in auto-correlations of both volume-averaged quantities and individual Fourier modes due to the formation of large-scale vortices. In contrast, moderate shear strength does not exhibit significant scale separation, with shear flows elongating vortices in the shear direction. Shearing burgulence, characterized by shorter helicity correlation times, appears less conducive to hosting the incoherent $\alpha$ effect. Notably, at modest shear rates, only Keplerian flows exhibit sufficiently coherent helicity fluctuations, in contrast to shearing flows. However, the relative strength of helicity fluctuations compared to turbulent diffusivity is significantly lower, raising doubts about the viability of the incoherent $\alpha$ effect as a potential dynamo driver in the subsonic flows examined in this study., Comment: 31 pages, 17 figures; revised based on the referees' reports

The dynamics of accreting and outgoing flows around compact objects depends crucially on the strengths and configurations of the magnetic fields therein, especially of the large-scale fields that remain coherent beyond turbulence scales. Possible origins of these large-scale magnetic fields include flux advection and disc dynamo actions. However, most numerical simulations have to adopt an initially strong large-scale field rather than allow them to be self-consistently advected or amplified, due to limited computational resources. The situation can be partially cured by using sub-grid models where dynamo actions only reachable at high resolutions are mimicked by artificial terms in low-resolution simulations. In this work, we couple thin-disc models with local shearing-box simulation results to facilitate more realistic sub-grid dynamo implementations. For helical dynamos, detailed spatial profiles of dynamo drivers inferred from local simulations are used, and the nonlinear quenching and saturation is constrained by magnetic helicity evolution. In the inner disc region, saturated fields have dipole configurations and the plasma $\beta$ reaches $\simeq 0.1$ to $100$, with correlation lengths $\simeq h$ in the vertical direction and $\simeq 10h$ in the radial direction, where $h$ is the disc scale height. The dynamo cycle period is $\simeq 40$ orbital time scale, compatible with previous global simulations. Additionally, we explore two dynamo mechanisms which do not require a net kinetic helicity and have only been studied in shearing-box setups. We show that such dynamos are possible in thin accretion discs, but produce field configurations that are incompatible with previous results. We discuss implications for future general-relativistic magnetohydrodynamics simulations., Comment: 12 pages, 13 figures. Accepted by MNRAS

Understanding large-scale magnetic field growth in astrophysical objects is a persistent challenge. We tackle the long-standing question of how much helical large-scale dynamo growth occurs independent of the magnetic Reynolds number (Rm) in a closed volume. From modest-Rm numerical simulations, we identify a pre-saturation regime when the large-scale field grows independently of Rm, but to an Rm-dependent magnitude. For plausible magnetic spectra however, the analysis predicts the magnitude to be Rm-independent and substantial as Rm$\to\infty$. This gives renewed optimism for the relevance of closed dynamos and pinpoints how modest Rm and hyper-diffusive simulations can cause misapprehension of the Rm$\to\infty$ behavior., Comment: manuscript shortened to 6 pages, 1 figure; added Supplemental Material

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., Comment: 14 pages, 25 figures, 5 tables, MNRAS, in press

The Saffman helicity invariant of Hosking and Schekochihin (2021, PRX 11, 041005), which we here call the Hosking integral, has emerged as an important quantity that may govern the decay properties of magnetically dominated nonhelical 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 Alfv\'en time., Comment: 19 pages, 7 figures, 2 tables; accepted by JPP

The shear-current effect (SCE) of mean-field dynamo theory refers to the combination of a shear flow and a turbulent coefficient $\beta_{21}$ with a favorable 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 ($\beta^u_{21}$) and magnetic ($\beta^b_{21}$) contributions. To resolve these discrepancies, we combine an analytical approach with simulations, and show that unlike $\beta^b_{21}$, the kinetic SCE $\beta^u_{21}$ has a strong dependence on the kinetic energy spectral index and can transit from positive to negative values at $\mathcal{O}(10)$ Reynolds numbers if the spectrum is not too steep. Conversely, $\beta^b_{21}$ is always negative regardless of the spectral index and Reynolds numbers. For very steep energy spectra, the positive $\beta^u_{21}$ can dominate even at energy equipartition $u_\text{rms}\simeq b_\text{rms}$, resulting in a positive total $\beta_{21}$ even though $\beta^b_{21}<0$. Our findings bridge the gap between the seemingly contradictory results from the second-order-correlation approximation (SOCA) versus the spectral-$\tau$ closure (STC), for which opposite signs for $\beta^u_{21}$ have been reported, with the same sign for $\beta^b_{21}<0$. The results also offer an explanation for the simulations that find $\beta^u_{21}>0$ and an inconclusive overall sign of $\beta_{21}$ for $\mathcal{O}(10)$ Reynolds numbers. The transient behavior of $\beta^u_{21}$ 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., Comment: 17 pages, 12 figures; accepted by MNRAS

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 nonlinear 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 nonlinear 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., Comment: 10 pages, 4 figures; accepted by MNRAS

The buildup of small-scale magnetic helicity which accompanies the oppositely signed growth on large scales is central to conventional dynamical quenching theories of mean-field dynamos. However, the conventional formalism presumes isotropic turbulence and thereby excludes part of the magnetic Lorentz back-reaction. This renders it insufficient to predict the full quenching for general anisotropic flows. To overcome this deficiency, we derive a new generalized quenching formalism that includes the full back-reacting Lorentz force, and a new "selective-damping-$\tau$" closure which conserves magnetic helicity. We apply the formalism to examples of $\bm\alpha^2$ dynamos and show its predicted quenching for different cases of turbulence---isotropic helical, anisotropic helical, and anisotropic non-helical. It predicts stronger-than-conventional quenching in general, but reduces to the conventional case in the helical isotropic limit., Comment: 16 pages, 2 figures; submitted to Journal of Plasma Physics

Transport coefficients in turbulence are comprised of correlation functions between turbulent fluctuations and efficient methods to calculate them are desirable. For example, in mean field dynamo theories used to model the growth of large scale magnetic fields of stars and galaxies, the turbulent electromotive force is commonly approximated by a series of tensor products of turbulent transport coefficients with successively higher order spatial derivatives of the mean magnetic field. One ingredient of standard models is the kinematic coefficient of the zeroth order term, namely the averaged kinetic pseudotensor $\bm{\alpha}$, that converts toroidal to poloidal fields. Here we demonstrate an efficient way to calculate this quantity for rotating stratified turbulence, whereby the pre-averaged quantity is calculated for the motion of a single plume, and the average is then taken over an ensemble of plumes of different orientations. We calculate the plume dynamics in the most convenient frame, before transforming back to the lab frame and averaging. Our concise configuration space calculation gives essentially identical results to previous lengthier approaches. The present application exemplifies what is a broadly applicable method., Comment: 6 pages; 1 figure; accepted by MNRAS Letters

Mean field electrodynamics (MFE) facilitates practical modeling of secular, large scale properties of astrophysical or laboratory systems with fluctuations.Practitioners commonly assume wide scale separation between mean and fluctuating quantities, to justify equality of ensemble and spatial or temporal averages.Often however, real systems do not exhibit such scale separation. This raises two questions: (I) what are the appropriate generalized equations of MFE in the presence of mesoscale fluctuations? (II) how precise are theoretical predictions from MFE? We address both by first deriving the equations of MFE for different types of averaging, along with mesoscale correction terms that depend on the ratio of averaging scale to variation scale of the mean. We then show that even if these terms are small, predictions of MFE can still have a significant precision error. This error has an intrinsic contribution from the dynamo input parameters and a filtering contribution from differences in the way observations and theory are projected through the measurement kernel.Minimizing the sum of these contributions can produce an optimal scale of averaging that makes the theory maximally precise.The precision error is important to quantify when comparing to observations because it quantifies the resolution of predictive power. We exemplify these principles for galactic dynamos, comment on broader implications, and identify possibilities for further work., Comment: 35 pages, 10 figures. Published in Journal of Plasma Physics; Mar. 21 2019: Typos of a sign in (3.6) and indices of $\xi$ in the paragraphs containing (B7)-(B9) corrected

Galactic dynamo models sustained by supernova (SN) driven turbulence and differential rotation have revealed that the sustenance of large scale fields requires a flux of small scale magnetic helicity to be viable. Here we generalize a minimalist analytic version of such galactic dynamos to explore some heretofore unincluded contributions from shear on the total turbulent energy and turbulent correlation time, with the helicity fluxes maintained by either winds, diffusion, or magnetic buoyancy. We construct an analytic framework for modeling the turbulent energy and correlation time as functions of SN rate and shear. We compare our prescription with previous approaches that only include rotation. The solutions depend separately on the rotation period and the eddy turnover time and not just on their ratio (the Rossby number). We consider models in which these two time scales are allowed to be independent and also a case in which they are mutually dependent on radius when a radial dependent SN rate model is invoked. For the case of a fixed rotation period (or fixed radius) we show that the influence of shear is dramatic for low Rossby numbers, reducing the correlation time of the turbulence, which in turn, strongly reduces the saturation value of the dynamo compared to the case when the shear is ignored. We also show that even in the absence of winds or diffusive fluxes, magnetic buoyancy may be able to sustain sufficient helicity fluxes to avoid quenching., Comment: 11 pages, 11 figures