Turbulent dynamos in a collapsing cloud

TL;DR

The study develops a framework for magnetic-field evolution in collapsing turbulent clouds using supercomoving magnetohydrodynamics, revealing that dynamo action drives super-exponential growth of $B$ as collapse proceeds, due to increasing eddy turnover rates. By combining analytical scaling with direct numerical simulations (SSD and LSD) in a collapsing background, the authors demonstrate that the instantaneous dynamo growth rate grows with time and that the saturated field strength scales with density faster than pure flux freezing, $B\propto\rho^{5/6}$ in driven cases (vs $\rho^{2/3}$ for flux-freezing). The work extends standard dynamo theory to evolving systems and implies magnetic fields can become dynamically important much earlier in star and galaxy formation than previously thought. The methodology, based on a reformulation in supercomoving variables, applies to both collapsing and expanding environments and provides a concrete path to integrate dynamo physics into evolving astrophysical plasmas, including decaying turbulence scenarios and a range of forcing conditions.

Abstract

The amplification of magnetic fields is crucial for understanding the observed magnetization of stars and galaxies. Turbulent dynamo is the primary mechanism responsible for that but the understanding of its action in a collapsing environment is still rudimentary and relies on limited numerical experiments. We develop an analytical framework and perform numerical simulations to investigate the behavior of small-scale and large-scale dynamos in a collapsing turbulent cloud. This approach is also applicable to expanding environments and facilitates the application of standard dynamo theory to evolving systems. Using a supercomoving formulation of the magnetohydrodynamic (MHD) equations, we demonstrate that dynamo action in a collapsing background leads to a super-exponential growth of magnetic fields in time, significantly faster than the exponential growth seen in stationary turbulence. The enhancement is mainly due to the increasing eddy turnover rate during the collapse, which boosts the instantaneous growth rate of the dynamo. We also show that the scaling of final saturated magnetic field strength with density robustly exceeds the expectation from considerations of pure flux-freezing. Apart from establishing a formal framework for studying magnetic field evolution in collapsing (or expanding) turbulent plasmas, these findings suggest that during star and galaxy formation magnetic fields can become dynamically relevant much earlier than previously thought.

Figures (7)

• Figure 1: Comparison of magnetic field evolution in SSD with $\text{Re} = R_\text{m} = 415$ for different cases. Without collapse, there is exponential growth due to standard dynamo (dash-dotted). With collapse ($t_{\rm ff} = 50$) and without forcing (dotted), there is no dynamo; flux freezing competes with resistive diffusion. With both collapse and forcing the dynamo grows the magnetic field super-exponentially (dashed), which is further enhanced by the collapse (solid). The dashed curve isolates the super-exponential growth by removing the factor $1/a^2$ arising from the overall collapse.
• Figure 2: The rms supercomoving magnetic field compensated for the compression, $\tilde{B}_\text{rms}/B_0$, in the SSD, for various values of $t_{\rm ff}$ specified in the legend. The solid and dotted curves represent two choices of the scale factor at which the collapse ends, $a_*=0.5$ and 0.2, respectively, and the green circles mark the corresponding time. The inset presents the physical $B_{\rm rms}$ focusing on the nonlinear stage. The blue curves correspond to $t_{\rm ff} < t_\text{nl}$ and the others to $t_{\rm ff} \gtrsim t_\text{nl}$. The green curves represent the dynamo in a stationary background ($a=1$).
• Figure 3: The dependence of the saturated rms strength of the physical magnetic field on $a_*$ for $t_{\rm ff} = 50$. The error bars show the $5 \sigma$ deviation. The dashed lines show the scaling of Eq. \ref{['eq:kcoldynamo4']}.
• Figure 4: As Fig. \ref{['fig:compare_ssd']} but for the LSD with $\text{Re} = 180$ and $R_\text{m} = 18$.
• Figure 5: As Fig. \ref{['fig:collapse_ssd5']} but for the LSD.