On weak and strong magnetohydrodynamic turbulence

Recent numerical and observational studies contain conflicting reports on the spectrum of magnetohydrodynamic turbulence. In an attempt to clarify the issue we investigate anisotropic incompressible magnetohydrodynamic turbulence with a strong guide field $B_0$. We perform numerical simulations of the reduced MHD equations in a special setting that allows us to elucidate the transition between weak and strong turbulent regimes. Denote $k_{\|}$, $k_\perp$ characteristic field-parallel and field-perpendicular wavenumbers of the fluctuations, and $b_{\lambda}$ the fluctuating field at the scale $\lambda\sim 1/k_{\perp}$. We find that when the critical balance condition, $k_{\|}B_0\sim k_{\perp} b_{\lambda}$, is satisfied, the turbulence is strong, and the energy spectrum is $E(k_{\perp})\propto k^{-3/2}_{\perp}$. As the $k_{\|}$ width of the spectrum increases, the turbulence rapidly becomes weaker, and in the limit $k_{\|}B_0\gg k_{\perp} b_{\lambda}$, the spectrum approaches $E(k_{\perp})\propto k_{\perp}^{-2}$. The observed sensitivity of the spectrum to the balance of linear and nonlinear interactions may explain the conflicting numerical and observational findings where this balance condition is not well controlled.Comment: 4 pages, 2 figure

Probing gaseous halos of galaxies with radio jets

Reproduced with permission from Astronomy & Astrophysics. © 2019 ESOContext. Gaseous halos play a key role in understanding inflow, feedback, and the overall baryon budget in galaxies. Literature models predict transitions of the state of the gaseous halo between cold and hot accretion, winds, fountains, and hydrostatic halos at certain galaxy masses. Since luminosities of radio AGN are sensitive to halo densities, any significant transition would be expected to show up in the radio luminosities of large samples of galaxies. The LOw Frequency ARray (LOFAR) Two-Metre Sky Survey (LoTSS) has identified a galaxy stellar mass scale, 10 11 M ⊙, above which the radio luminosities increase disproportionately. Aims. We investigate if radio luminosities of galaxies, especially the marked rise at galaxy masses around 10 11 M ⊙, can be explained with standard assumptions regarding jet powers, scaling between black hole mass and galaxy mass, and gaseous halos. Methods. Based on observational data and theoretical constraints, we developed models for the radio luminosity of radio AGN in halos under infall, galactic wind, and hydrostatic conditions. We compared these models to LoTSS data for a large sample of galaxies in the mass range between 10 8.5 M ⊙ and 10 12 M ⊙. Results. Under the assumption that the same characteristic upper limit to jet powers known from high galaxy masses holds at all masses, we find the maximum radio luminosities for the hydrostatic gas halos to lie close to the upper envelope of the distribution of the LOFAR data. The marked rise in radio luminosity at 10 11 M ⊙ is matched in our model and is related to a significant change in halo gas density around this galaxy mass, which is a consequence of lower cooling rates at a higher virial temperature. Wind and infall models overpredict the radio luminosities for small galaxy masses and have no particular steepening of the run of the radio luminosities predicted at any galaxy mass. Conclusions. Radio AGN could have the same characteristic Eddington-scaled upper limit to jet powers in galaxies of all masses in the sample if the galaxies have hydrostatic gas halos in phases when radio AGN are active. We find no evidence of a change of the type of galaxy halo with the galaxy mass. Galactic winds and quasi-spherical cosmological inflow phases cannot frequently occur at the same time as powerful jet episodes unless the jet properties in these phases are significantly different from what we assumed in our model.Peer reviewedFinal Accepted Versio

HEDGING CLASS I MILK: THE "ACCELERATION" AND "MOVER" EFFECT

A volatile closing basis prevents class I hedgers from locking in a minimum price. The closing basis is composed of an "acceleration" and "mover" effect. The mover effect always works to the producer's advantage unlike the acceleration effect. This research discusses hedging strategies to minimize the acceleration effect.Marketing,