Fundamental scales in the kinematic phase of the turbulent dynamo

Abstract

The turbulent dynamo is a powerful mechanism that converts turbulent kinetic energy to magnetic energy. A key question regarding the magnetic field amplification by turbulence, is, on what scale, kp, do magnetic fields become most concentrated? There has been some disagreement about whether kp is controlled by the viscous scale, kν (where turbulent kinetic energy dissipates), or the resistive scale, kη (where magnetic fields dissipate). Here we use direct numerical simulations of magnetohydrodynamic turbulence to measure characteristic scales in the kinematic phase of the turbulent dynamo. We run 104-simulations with hydrodynamic Reynolds numbers of 10 ≤ Re ≤ 3600, and magnetic Reynolds numbers of 270 ≤ Rm ≤ 4000, to explore the dependence of kp on kν and kη. Using physically motivated models for the kinetic and magnetic energy spectra, we measure kν, kη and kp, making sure that the obtained scales are numerically converged. We determine the overall dissipation scale relations $k_\nu = (0.025^{+0.005}_{-0.006})\, k_\text{turb}\, \mbox{Re}^{3/4}$ and $k_\eta = (0.88^{+0.21}_{-0.23})\, k_\nu \, \mbox{Pm}^{1/2}$, where kturb is the turbulence driving wavenumber and Pm = Rm/Re is the magnetic Prandtl number. We demonstrate that the principle dependence of kp is on kη. For plasmas where Re ≳ 100, we find that $k_p= (1.2_{-0.2}^{+0.2})\, k_\eta$, with the proportionality constant related to the power-law ‘Kazantsev’ exponent of the magnetic power spectrum. Throughout this study, we find a dichotomy in the fundamental properties of the dynamo where Re > 100, compared to Re < 100. We report a minimum critical hydrodynamic Reynolds number, Recrit = 100 for bonafide turbulent dynamo action.

Multiphase turbulence in galactic haloes: effect of the driving

“…We do not explicitly include viscosity in our model, instead, the viscosity is due to numerical dissipation (see Benzi et al 2008;Federrath et al 2011, for a discussion). The numerical viscous scale in our simulations is expected to be around 0.6 kpc, roughly at 15Δ𝑥 (where Δ𝑥 is the numerical cell size), which we obtain from fitting the power spectrum model in Kriel et al (2022) to our velocity power spectrum. For the hot ICM, we compare the numerical viscosity with the Spitzer viscosity values from Spitzer (1962) and find it to be suppressed by a factor of ∼ 600.…”

“…They also find that turbulent gas motions are predominantly solenoidal, although the driving is mainly compressive (through inner and merger shocks), similar to our results in section 3.6. Seta & Federrath (2022) study the effect of the driving parameter on the turbulent dynamo in the two-phase ISM. Similar to our study, they find 𝐹 baro to generate seeds of enstrophy in their compressive driving run at initial times.…”

“…Turbulence kinetic energy can be converted into magnetic energy (Federrath 2016;Di Gennaro et al 2021), increase the coupling between hot and cold phases and also affect the slopes of the VSF 2 (Mohapatra et al 2022a). Magnetic fields can also affect the growth rate of enstrophy, as seen in studies by Porter et al (2015) and Seta & Federrath (2022). On sub-kpc scales, the ICM is expected to be weakly collisional.…”

“…These larger density fluctuations in the hot-phase gas could also affect the relation between X-ray surface brightness fluctuations and turbulent velocities, which is used to indirectly measure turbulent gas velocities in several nearby galaxy clusters (Zhuravleva et al 2014a(Zhuravleva et al ,b, 2018. The steep slopes of the velocity structure functions of H𝛼 filaments in nearby galaxy clusters studied in Li et al (2020) could also be affected by the nature of turbulence forcing. Hence it is important to study the effects of different types of turbulence forcing in the context of the CGM, IGrM and ICM.…”

Dissipative magnetic structures and scales in small-scale dynamos

“…The question of characteristic length scales in a small-scale dynamo continued attracting attention and has been investigated in more detail by Cho & Ryu (2009) with applications to the intergalactic medium. More recently, Kriel et al (2022) confirmed the Pr −1/2 M scaling for 1 ≤ Pr M ≤ 260 also for the kinematic phase of the dynamo. The small-scale properties of interstellar turbulence can be assessed through interstellar scintillation measurements of pulsars (Cordes et al 1985;Rickett 1990;Armstrong et al 1995;Bhat et al 2004;Scalo & Elmegreen 2004).…”