Kiloparsec-scale turbulence driven by reionization may grow intergalactic magnetic fields

TL;DR

During cosmic reionization, impulsive heating creates pressure imbalances in the IGM that relax via small-scale turbulence. Using ~100 pc resolution radiation-hydrodynamics simulations, the study shows that high-resolution runs reveal pervasive turbulence with the energy spectrum following $E(k) \propto k^{-5/3}$ and eddy turnover times $\tau_{\rm eddy} \lesssim 1$ Gyr near $k \approx 1\,{\rm kpc}^{-1}$. This turbulence can power a turbulent dynamo, potentially boosting IGM magnetic fields to levels consistent with TeV blazar lower limits, with $B \approx 1.5\times10^{-9}\,{ m G}\, f_B^{1/2} \left(\frac{1+z_{\rm re}}{7}\right)^{-1/2} \left(\frac{V_{\rm dr}}{20\, {\rm km\,s^{-1}}}\right)$ for reasonable driving. However, substantial X-ray pre-heating (high $T_{\min}$) can suppress or erase turbulence, limiting magnetic-field growth and its coherence. Overall, reionization-driven, volume-filling turbulence offers a robust mechanism to generate IGM magnetic fields, with observable implications for gamma-ray halos and a path to distinguishing this origin with future TeV observations.

Abstract

The intergalactic medium (IGM) underwent intense heating that resulted in pressure disequilibrium in the wake of ionization fronts during cosmic reionization. The dynamical relaxation to restore pressure balance may have driven small-scale turbulence and, hence, the amplification of intergalactic magnetic fields. We investigate this possibility for the first time using a suite of $\approx 100$ pc resolution radiation-hydrodynamics simulations of IGM gas dynamics. We show that as the spatial resolution improves beyond that achieved with most prior studies, much of the IGM becomes turbulent unless it was pre-heated to $\gg 100~$K before reionization. In our most turbulent simulations, we find that the gas energy spectrum follows the expected $k^{-5/3}$ Kolmogorov scaling to the simulation's resolution, and the eddy turnover time of the turbulence is $< 1$ Gyr at $k \approx 1 ~$kpc$^{-1}$. Turbulence will grow magnetic fields, and we show that the fields grown by reionization-driven turbulence could explain lower limits on the strength of volume-filling B-fields from observations of TeV blazars. As reionization sweeps over the cosmos, this mechanism could create turbulence throughout the cosmic volume with a character that only depends on the amount of IGM preheating.

Figures (11)

• Figure 1: Snapshots showing the evolution of the density (top panels) and temperature (bottom panels) in our fiducial simulation. Immediately after ionization ($z = 6.99$), the gas is clumpy at sub-kpc scales, reflecting its pre-ionized cold temperature, and is nearly isothermal, reflecting the heat input from reionization. Subsequently, over-dense filaments expand, generating a medium of expansion-cooled and compression-heated gas. By $z = 6$, the gas begins to show signs of turbulence, and at $z \leq 5.5$, turbulence is observed throughout, in both the density and temperature. As relaxation slows, the turbulence dissipates, but some still persists to at least $z = 4$. The inset in the bottom right shows the physical scale.
• Figure 2: Comparison of turbulence in runs with and without X-ray pre-heating, showing our highest resolution $0.25~h^{-1}~$Mpc, $2048^3$ simulations. Left: slice through the temperature field at $z = 5$. The simulation assumes no heating before reionization such that the thermal evolution is essentially adiabatic. Right: the same, but for a run with a minimum gas temperature of $100$ K imposed at $z < 15$. We see less turbulence in this case, with it being concentrated largely around the filaments.
• Figure 3: Quantification of turbulence in our simulations. Top: The energy spectrum $E(k)$ at a time-series of redshifts, offset vertically for visualization, with redshift decreasing from bottom to top. The "bump" that moves to the left with time tracks the growing sound crossing distance since $z_{\rm re}$. At smaller scales, we find the $k^{-5/3}$ scaling characteristic of turbulence, with a fall-off at very small scales due to numerical dissipation. Bottom: the same as the top panel except without rescaling the amplitude and concentrating on $z = 5$ and different spatial resolutions (gray curves). The high-$k$ fall off shifts to the right as resolution increases, as expected if this cutoff is numerical. The scaling at smaller $k$ is close to, but slightly shallower than, the $-5/3$ Kolmogorov scaling. The blue dotted line is a $0.5$$h^{-1}$Mpc box with the fiducial resolution, and shows convergence of $E(k)$ with box size. The magenta-dashed curve shows a scenario with high X-ray pre-heating ($T_{\min} = 1000$ K), for which we do not observe the $-5/3$ scaling.
• Figure 4: Convergence of small-scale IGM turbulence with spatial resolution. Top two rows: density and temperature at $z = 6.95$ for $N_{\rm RT} = 64^3$, $128^3$, $256^3$, $512^3$, $1024^3$ (our fiducial resolution), and $2048^3$ (flash ionized). The amount of small-scale structure in the density and temperature fields just after ionization noticeably increases from left to right, and it is not well-converged until our fiducial resolution. Bottom two rows: the same, but at $z = 5$ when IGM turbulence has become significant in our fiducial simulations. The lowest resolution at which turbulent structures are clearly seen is $N_{\rm RT} = 512^3$, and the turbulent structure is not converged even at $N_{\rm gas} = 2048^3$. For relevant IGM parameters, turbulent eddies are expected to be present two orders of magnitude below this spatial resolution.
• Figure 5: Comparison of the temperature slice at $z = 5$ in Figure \ref{['fig:time_series_visualization']} at our fiducial resolution of $\Delta x = 244$$h^{-1}$pc, and the same slice in a flash-ionized box with $\Delta x = 122$$h^{-1}$pc. The top panels show the same temperature snapshots as in the lower right of Figure \ref{['fig:convergence_visualization']}, and the bottom panels show a $50$$h^{-1}$kpc zoom-in. Turbulent features are much more prominent in the higher-resolution run and are anticipated to continue down to $\sim 1~$pc.