Generation of large-scale magnetic fields due to fluctuating α\alpha in shearing systems

We explore the growth of large-scale magnetic fields in a shear flow, due to helicity fluctuations with a finite correlation time, through a study of the Kraichnan-Moffatt model of zero-mean stochastic fluctuations of the $\alpha$ parameter of dynamo theory. We derive a linear integro-differential equation for the evolution of large-scale magnetic field, using the first-order smoothing approximation and the Galilean invariance of the $\alpha$-statistics. This enables construction of a model that is non-perturbative in the shearing rate $S$ and the $\alpha$-correlation time $\tau_\alpha$. After a brief review of the salient features of the exactly solvable white-noise limit, we consider the case of small but non-zero $\tau_\alpha$. When the large-scale magnetic field varies slowly, the evolution is governed by a partial differential equation. We present modal solutions and conditions for the exponential growth rate of the large-scale magnetic field, whose drivers are the Kraichnan diffusivity, Moffatt drift, Shear and a non-zero correlation time. Of particular interest is dynamo action when the $\alpha$-fluctuations are weak; i.e. when the Kraichnan diffusivity is positive. We show that in the absence of Moffatt drift, shear does not give rise to growing solutions. But shear and Moffatt drift acting together can drive large scale dynamo action with growth rate $\gamma \propto |S|$.Comment: 19 pages, 4 figures, Accepted in Journal of Plasma Physic

Mean field dynamo action in shearing flows. II: fluctuating kinetic helicity with zero mean

Here we explore the role of temporal fluctuations in kinetic helicity on the generation of large-scale magnetic fields in presence of a background linear shear flow. Key techniques involved here are same as in our earlier work \citep[][hereafter paper~I]{JS20}, where we have used the renovating flow based model with shearing waves. Both, the velocity and the helicity fields, are treated as stochastic variables with finite correlation times, $\tau$ and $\tau_h$, respectively. Growing solutions are obtained when $\tau_h > \tau$, even when this time-scale separation, characterised by $m=\tau_h/\tau$, remains below the threshold for causing the turbulent diffusion to turn negative. In regimes when turbulent diffusion remains positive, and $\tau$ is on the order of eddy turnover time $T$, the axisymmetric modes display non-monotonic behaviour with shear rate $S$: both, the growth rate $\gamma$ and the wavenumber $k_\ast$ corresponding to the fastest growing mode, first increase, reach a maximum and then decrease with $|S|$, with $k_\ast$ being always smaller than eddy-wavenumber, thus boosting growth of magnetic fields at large length scales. The cycle period $P_{\rm cyc}$ of growing dynamo wave is inversely proportional to $|S|$ at small shear, exactly as in the fixed kinetic helicity case of paper~I. This dependence becomes shallower at larger shear. Interestingly enough, various curves corresponding to different choices of $m$ collapse on top of each other in a plot of $m P_{\rm cyc}$ with $|S|$.Comment: 14 pages, 10 figures, Submitted to MNRA

ADIABATIC BLACK HOLE GROWTH IN SERSIC MODELS OF ELLIPTICAL GALAXIES

We have examined the effect of slow growth of a central black hole on spherical galaxies that obey Sersic or R-1/m surface-brightness profiles. During such growth the actions of each stellar orbit are conserved, which allows us to compute the final distribution function (DF) if we assume that the initial DF is isotropic. We find that black hole growth leads to a central cusp or ``excess light,'' in which the surface brightness varies with radius as R-1.3 (with a weak dependence on Sersic index m), the line-of-sight velocity dispersion varies as R-1/2, and the velocity anisotropy is beta similar or equal to -0.24 to -0.28 depending on m. The excess stellar mass in the cusp scales approximately linearly with the black hole mass, and is typically 0.5-0.85 times the black hole mass. This process may strongly influence the structure of nuclear star clusters in spheroidal galaxies if they contain black holes