Abstract:Small-scale dynamo action is often held responsible for the generation of quiet Sun magnetic fields. We aim to determine the excitation conditions and saturation level of small-scale dynamos in nonrotating turbulent convection at low magnetic Prandtl numbers. We use high-resolution direct numerical simulations of weakly stratified turbulent convection. We find that the critical magnetic Reynolds number for dynamo excitation increases as the magnetic Prandtl number is decreased, which might suggest that small-s… Show more
“…Schekochihin et al. 2007; Käpylä, Käpylä & Brandenburg 2018). Figure 1.Estimated values of the critical magnetic Reynolds number and the critical Rayleigh number for the onset of dynamo action.…”
Section: Resultsmentioning
confidence: 99%
“…(2012) and Käpylä et al. (2018) showed that dynamo action can be excited at a smaller value of with the use of a larger aspect ratio. Käpylä et al.…”
Section: Resultsmentioning
confidence: 99%
“…Käpylä et al. (2018) found that, when , an aspect ratio is needed for the growth rate to saturate. In all of our simulations (including those cases with ), an aspect ratio of at least is used for the determination of ; thus the simulation domain should be sufficiently large to avoid the issue arising from the use of small values of .…”
“…Schekochihin et al. 2007; Käpylä, Käpylä & Brandenburg 2018). Figure 1.Estimated values of the critical magnetic Reynolds number and the critical Rayleigh number for the onset of dynamo action.…”
Section: Resultsmentioning
confidence: 99%
“…(2012) and Käpylä et al. (2018) showed that dynamo action can be excited at a smaller value of with the use of a larger aspect ratio. Käpylä et al.…”
Section: Resultsmentioning
confidence: 99%
“…Käpylä et al. (2018) found that, when , an aspect ratio is needed for the growth rate to saturate. In all of our simulations (including those cases with ), an aspect ratio of at least is used for the determination of ; thus the simulation domain should be sufficiently large to avoid the issue arising from the use of small values of .…”
“…Iskakov et al (2007) found supercritical solutions near PrM ≈ 0.1 when using hyperviscosity in their simulations, which does however affect the strength of the spectral bottleneck, as will be discussed in a moment. Even the re-cent convection simulations of Käpylä et al (2018) at a resolution of 1024 3 meshpoints found only decaying magnetic fields at PrM = 0.1.…”
Small-scale dynamos are expected to operate in all astrophysical fluids that are turbulent and electrically conducting, for example the interstellar medium, stellar interiors, and accretion disks, where they may also be affected by or competing with large-scale dynamos. However, the possibility of small-scale dynamos being excited at small and intermediate ratios of viscosity to magnetic diffusivity (the magnetic Prandtl number) has been debated, and the possibility of them depending on the large-scale forcing wavenumber has been raised. Here we show, using four values of the forcing wavenumber, that the small-scale dynamo does not depend on the scale-separation between the size of the simulation domain and the integral scale of the turbulence, i.e., the forcing scale. Moreover, the spectral bottleneck in turbulence, which has been implied as being responsible for raising the excitation conditions of small-scale dynamos, is found to be invariant under changing the forcing wavenumber. However, when forcing at the lowest few wavenumbers, the effective forcing wavenumber that enters in the definition of the magnetic Reynolds number is found to be about twice the minimum wavenumber of the domain. Our work is relevant to future studies of small-scale dynamos, of which several applications are being discussed.
“…This explained by the higher magnetic Prandtl number (Pm = 2) in comparison to the present study (Pm = 0.5). This also explains why a small-scale dynamo is excited in run 2a of Dobler et al (2006) with Re M = 93, while it is absent in the current run MHD0 with an almost identical magnetic Reynolds number (Re M = 95) (see e.g., Schekochihin et al 2007;Käpylä et al 2018).…”
Section: Appendix A: Comparison To Dobler Et Al (2006)mentioning
Context. Main-sequence late-type stars with masses of less than 0.35 M⊙ are fully convective.
Aims. The goal is to study convection, differential rotation, and dynamos as functions of rotation in fully convective stars.
Methods. Three-dimensional hydrodynamic and magnetohydrodynamic numerical simulations with a star-in-a-box model, in which a spherical star is immersed inside of a Cartesian cube, are used. The model corresponds to a 0.2 M⊙ main-sequence M5 dwarf. A range of rotation periods (Prot) between 4.3 and 430 d is explored.
Results. The slowly rotating model with Prot = 430 days produces anti-solar differential rotation with a slow equator and fast poles, along with predominantly axisymmetric quasi-steady large-scale magnetic fields. For intermediate rotation (Prot = 144 and 43 days) the differential rotation is solar-like (fast equator, slow poles), and the large-scale magnetic fields are mostly axisymmetric and either quasi-stationary or cyclic. The latter occurs in a similar parameter regime as in other numerical studies in spherical shells, and the cycle period is similar to observed cycles in fully convective stars with rotation periods of roughly 100 days. In the rapid rotation regime the differential rotation is weak and the large-scale magnetic fields are increasingly non-axisymmetric with a dominating m = 1 mode. This large-scale non-axisymmetric field also exhibits azimuthal dynamo waves.
Conclusions. The results of the star-in-a-box models agree with simulations of partially convective late-type stars in spherical shells in that the transitions in differential rotation and dynamo regimes occur at similar rotational regimes in terms of the Coriolis (inverse Rossby) number. This similarity between partially and fully convective stars suggests that the processes generating differential rotation and large-scale magnetism are insensitive to the geometry of the star.
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