We perform numerical experiments to study the shear dynamo problem where we look for the growth of large-scale magnetic field due to non-helical stirring at small scales in a background linear shear flow, in previously unexplored parameter regimes. We demonstrate the large-scale dynamo action in the limit when the fluid Reynolds number (Re) is below unity whereas the magnetic Reynolds number (Rm) is above unity; the exponential growth rate scales linearly with shear, which is consistent with earlier numerical works. The limit of low Re is particularly interesting, as seeing the dynamo action in this limit would provide enough motivation for further theoretical investigations, which may focus the attention to this analytically more tractable limit of Re < 1 as compared to more formidable limit of Re > 1. We also perform simulations in the regimes when, (i) both (Re, Rm) < 1; (ii) Re > 1 & Rm < 1, and compute all components of the turbulent transport coefficients (α ij and η ij ) using the test-field method. A reasonably good agreement is seen between our results and the results of earlier analytical works (Sridhar & Singh 2010;Singh & Sridhar 2011) in the similar parameter regimes.

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 $\unicode[STIX]{x1D6FC}$ parameter of dynamo theory. We derive a linear integro-differential equation for the evolution of the large-scale magnetic field, using the first-order smoothing approximation and the Galilean invariance of the $\unicode[STIX]{x1D6FC}$-statistics. This enables construction of a model that is non-perturbative in the shearing rate $S$ and the $\unicode[STIX]{x1D6FC}$-correlation time $\unicode[STIX]{x1D70F}_{\unicode[STIX]{x1D6FC}}$. After a brief review of the salient features of the exactly solvable white-noise limit, we consider the case of small but non-zero $\unicode[STIX]{x1D70F}_{\unicode[STIX]{x1D6FC}}$. 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 $\unicode[STIX]{x1D6FC}$-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 $\unicode[STIX]{x1D6FE}\propto |S|$.

We study mean field dynamo action in a background linear shear flow by employing pulsed renewing flows with fixed kinetic helicity and non-zero correlation time (τ). We use plane shearing waves in terms of time-dependent exact solutions to the Navier–Stokes equation as derived by Singh & Sridhar (2017). This allows us to self-consistently include the anisotropic effects of shear on the stochastic flow. We determine the average response tensor governing the evolution of mean magnetic field, and study the properties of its eigenvalues that yield the growth rate (γ) and the cycle period (Pcyc) of the mean magnetic field. Both, γ and the wavenumber corresponding to the fastest growing axisymmetric mode vary non-monotonically with shear rate S when τ is comparable to the eddy turnover time T, in which case, we also find quenching of dynamo when shear becomes too strong. When $\tau /T\sim {\cal O}(1)$, the cycle period (Pcyc) of growing dynamo wave scales with shear as Pcyc ∝ |S|−1 at small shear, and it becomes nearly independent of shear as shear becomes too strong. This asymptotic behaviour at weak and strong shear has implications for magnetic activity cycles of stars in recent observations. Our study thus essentially generalizes the standard αΩ (or α2Ω) dynamo as also the α effect is affected by shear and the modelled random flow has a finite memory.

We have examined the effect of slow growth of a central black hole on spherical galaxies that obey Sérsic 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 if we assume that the initial distribution function 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 Sérsic index m), the line-of-sight velocity dispersion varies as R −1/2 , and the velocity anisotropy is β −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 if they contain black holes. Fig. 1.-Surface-brightness profile of the dwarf galaxy NGC 4459, an excess-light elliptical. The curve shows the bestfitting Sérsic profile, with index m = 3.17 (Kormendy et al. 2009). Reproduced by permission of the AAS.serve their adiabatic invariants or actions. If the galaxy began with a Sérsic surface-brightness profile, this process will naturally produce excess light relative to the Sérsic profile near the center of the galaxy, and the corresponding excess stellar mass will be simply related to the mass of the BH and the properties of the initial Sérsic profile. The main goal of the paper is to work out these relations and to compare the predictions of this simple model to the observations.Pioneering studies of this process were carried out by Peebles (1972) andYoung (1980). These studies assumed that the galaxies were spherical, as do we, but in contrast they assumed that the stellar distribution function (DF) near the center of the galaxy was Maxwellian before the formation of the BH. They found that as the BH grew the stellar DF developed a cusp in which the density varied as ρ ∼ r −3/2 , corresponding to a surface brightness I(R) ∼ R −1/2 . However, a Sérsic profile does not have a Maxwellian DF, and the properties of the cusp formed by